Datasets:

ashishkgpian

/

adspapers_5_10

like 0

2013A&A...549A..94V

https://arxiv.org/pdf/1211.4367.pdf

<document> <section_header_level_1><location><page_1><loc_8><loc_82><loc_94><loc_87></location>Atmospheric constraints for the CO 2 partial pressure on terrestrial planets near the outer edge of the habitable zone</section_header_level_1> <text><location><page_1><loc_19><loc_80><loc_82><loc_81></location>P. von Paris 1 , 2 , 3 , J.L. Grenfell 4 , P. Hedelt 1 , 2 /star , H. Rauer 3 , 4 , F. Selsis 1 , 2 , and B. Stracke 3</text> <unordered_list> <list_item><location><page_1><loc_11><loc_77><loc_49><loc_78></location>1 Univ. Bordeaux, LAB, UMR 5804, F-33270, Floirac, France</list_item> <list_item><location><page_1><loc_11><loc_76><loc_43><loc_77></location>2 CNRS, LAB, UMR 5804, F-33270, Floirac, France</list_item> <list_item><location><page_1><loc_11><loc_75><loc_87><loc_76></location>3 Institut fur Planetenforschung, Deutsches Zentrum fur Luft- und Raumfahrt (DLR), Rutherfordstr. 2, 12489 Berlin, Germany</list_item> <list_item><location><page_1><loc_11><loc_73><loc_87><loc_74></location>4 Zentrum fur Astronomie und Astrophysik (ZAA), TechnischeUniversitat Berlin, Hardenbergstr. 36, 10623 Berlin, Germany</list_item> </unordered_list> <text><location><page_1><loc_11><loc_71><loc_36><loc_72></location>Preprint online version: October 15, 2018</text> <section_header_level_1><location><page_1><loc_47><loc_69><loc_55><loc_70></location>ABSTRACT</section_header_level_1> <text><location><page_1><loc_11><loc_64><loc_91><loc_67></location>Context. In recent years, several potentially habitable, probably terrestrial exoplanets and exoplanet candidates have been discovered. The amount of CO2 in their atmosphere is of great importance for surface conditions and habitability. In the absence of detailed information on the geochemistry of the planet, this amount could be considered as a free parameter.</text> <text><location><page_1><loc_11><loc_59><loc_91><loc_64></location>Aims. Up to now, CO2 partial pressures for terrestrial planets have been obtained assuming an available volatile reservoir and outgassing scenarios. This study aims at calculating the allowed maximum CO2 pressure at the surface of terrestrial exoplanets orbiting near the outer boundary of the habitable zone by coupling the radiative e ff ects of the CO2 and its condensation at the surface. These constraints might limit the permitted amount of atmospheric CO2, independent of the planetary reservoir.</text> <text><location><page_1><loc_11><loc_56><loc_91><loc_59></location>Methods. A1Dradiative-convective cloud-free atmospheric model was used to calculate surface conditions for hypothetical terrestrial exoplanets. CO2 partial pressures are fixed according to surface temperature and vapor pressure curve. Considered scenarios cover a wide range of parameters, such as gravity, central star type and orbital distance, atmospheric N2 content and surface albedo.</text> <text><location><page_1><loc_11><loc_49><loc_91><loc_56></location>Results. Results show that for planets in the habitable zone around K-, G-, and F-type stars the allowed CO2 pressure is limited by the vapor pressure curve and not by the planetary reservoir. The maximum CO2 pressure lies below the CO2 vapor pressure at the critical point of p crit = 73.8 bar. For M-type stars, due to the stellar spectrum being shifted to the near-IR, CO2 pressures above p crit are possible for almost all scenarios considered across the habitable zone. This implies that determining CO2 partial pressures for terrestrial planets by using only geological models is probably too simplified and might over-estimate atmospheric CO2 towards the outer edge of the habitable zone.</text> <text><location><page_1><loc_11><loc_47><loc_61><loc_48></location>Key words. Planets and satellites: atmospheres, Planets and satellites: composition</text> <section_header_level_1><location><page_1><loc_7><loc_43><loc_19><loc_44></location>1. Introduction</section_header_level_1> <text><location><page_1><loc_7><loc_30><loc_50><loc_42></location>Given the di ffi culties and challenges of detecting sub-surface life on Earth, any life to be first discovered beyond our own solar system will most likely be restricted to the planetary surface and atmosphere. This is the basis of the concept of the habitable zone (HZ, e.g., Dole 1964, Hart 1978, Kasting et al. 1993). The HZ is defined as the region around a star where a rocky planet with a suitable atmosphere can host liquid water on its surface, a condition motivated by the fact that all life as we know it requires liquid water.</text> <text><location><page_1><loc_7><loc_14><loc_50><loc_30></location>Several studies have implied that small, potentially rocky planets are common (e.g., Howard et al. 2010, Wittenmyer et al. 2011, Borucki et al. 2011, Mayor et al. 2011, Cassan et al. 2012, Gaidos et al. 2012). Hence, it is not unreasonable to assume that planets in the HZ of their central stars may also be relatively common. Indeed, some potentially habitable (candidate) super-Earths in or very close to the HZ of their central star have already been discovered (Udry et al. 2007, Mayor et al. 2009, Borucki et al. 2011, Pepe et al. 2011, Bonfils et al. 2011, Anglada-Escud'e et al. 2012, Delfosse et al. 2012, Borucki et al. 2012). Also, Neptune- or Jupiter-like planets have been discovered in the HZ (e.g., Lovis et al. 2006, Fischer et al. 2008,</text> <text><location><page_1><loc_52><loc_41><loc_95><loc_44></location>Haghighipour et al. 2010, Tinney et al. 2011) which raises the possibility of habitable satellites around these planets.</text> <text><location><page_1><loc_52><loc_36><loc_95><loc_41></location>A simple criterion for the potential habitability of a planet, which is immediately accessible from the discovery data, is its equilibrium temperature, T eq. The equilibrium temperature is calculated by</text> <formula><location><page_1><loc_52><loc_32><loc_95><loc_35></location>T eq = ( (1 -A ) F 4 σ ) 0 . 25 (1)</formula> <text><location><page_1><loc_52><loc_17><loc_95><loc_30></location>where A is the planetary albedo, F the stellar flux at the orbital distance of the planet and σ the Stefan-Boltzmann constant. As was discussed by, e.g., Selsis et al. (2007) and Kaltenegger & Sasselov (2011), a habitable planet should have T eq /lessorsimilar 270K to avoid a runaway heating of the surface and corresponding loss of the complete surface water reservoir. For low values of T eq near the outer edge of the HZ (e.g., model calculations for GL 581 d suggest T eq ∼ 190K, von Paris et al. 2010), a massive greenhouse e ff ect must be provided by the atmosphere to obtain habitable surface conditions.</text> <text><location><page_1><loc_52><loc_10><loc_95><loc_17></location>H2O is the most obvious candidate of radiatively active gases which could provide the necessary greenhouse warming. It provides the bulk of the greenhouse e ff ect on Earth. Furthermore, H2O is by definition present on the surface of a habitable planet. The H2O partial pressure in an atmosphere of a potentially habitable planet is controlled by evaporation (or sublimation) from</text> <text><location><page_2><loc_7><loc_88><loc_50><loc_93></location>the surface reservoir, taking into account the water vapor pressure curve. Besides H2O, CO2 is usually considered the most important greenhouse gas for the determination of the outer boundary of the HZ (e.g., Kasting et al. 1993).</text> <text><location><page_2><loc_7><loc_65><loc_50><loc_88></location>On Earth, CO2 is controlled by processes such as volcanic outgassing or rock weathering. To estimate CO2 partial pressures for terrestrial exoplanets, up to now only geological models were used (e.g., Elkins-Tanton & Seager 2008, Kite et al. 2009, Kite et al. 2011, Edson et al. 2012, Abbot et al. 2012). Furthermore, the volatile content of habitable zone planets is expected to be highly variable due to orbital migration (e.g., Raymond et al. 2004). For instance, planets originating from the outer planetary system and made of a large fraction of cometary material can migrate to habitable orbital distances, resulting in the so-called ocean-planets (L'eger et al. 2004). Planetary CO2 reservoirs of the order of thousands of bars are certainly plausible, when considering typical solar system values for the composition of the cometary material. It is possible that the silicate carbonate cycle, which regulates the level of atmospheric CO2 on Earth, does not operate on ocean planets in the absence of continents. Such large reservoirs of CO2 are therefore a concern for habitability if totally outgassed into a CO2-rich envelope.</text> <text><location><page_2><loc_7><loc_58><loc_50><loc_64></location>Fig. 1 shows the phase diagram of CO2. The critical point lies at T crit = 303K and p crit = 73.8 bar. At a given surface temperature below T crit, the vapor pressure curve actually limits the amount of CO2 which can be outgassed into the atmosphere, independent of the planetary reservoir.</text> <figure> <location><page_2><loc_9><loc_35><loc_46><loc_55></location> <caption>Fig. 1. CO2 phase diagram.</caption> </figure> <text><location><page_2><loc_7><loc_14><loc_50><loc_29></location>It is the aim of this study to quantify this maximum CO2 partial pressure for a range of possible planetary scenarios near the outer edge of the HZ, based on the phase diagram in Fig. 1. In order to put constraints on atmospheric CO2, the interplay between CO2 greenhouse e ff ect, surface temperature and CO2 partial pressure must be taken into account. Therefore, this work will use an atmospheric model which consistently calculates temperature profiles and surface conditions. It will be investigated how di ff erent parameters such as planetary gravity, orbital distance and central star type, N2 pressure and surface albedo influence the behavior of the maximum CO2 partial pressure.</text> <text><location><page_2><loc_7><loc_10><loc_50><loc_13></location>The paper is organized as follows: Sect. 2 presents the model and scenarios, Sect. 3 the results and Sect. 4 a discussion. We conclude with Sect. 5.</text> <section_header_level_1><location><page_2><loc_52><loc_92><loc_61><loc_93></location>2. Methods</section_header_level_1> <section_header_level_1><location><page_2><loc_52><loc_90><loc_69><loc_91></location>2.1. Atmosphericmodel</section_header_level_1> <text><location><page_2><loc_52><loc_85><loc_95><loc_89></location>We used a cloud-free, one-dimensional radiative-convective model to determine the globally averaged atmospheric temperature-pressure profile.</text> <text><location><page_2><loc_52><loc_76><loc_95><loc_85></location>The original model was first described by Kasting et al. (1984a) and Kasting et al. (1984b). Further developments were introduced by e.g. Kasting (1988), Kasting (1991), Kasting et al. (1993) Mischna et al. (2000), Pavlov et al. (2000) and Segura et al. (2003). The model version used in this work is taken from von Paris et al. (2008) and von Paris et al. (2010) where more details on the model are given.</text> <text><location><page_2><loc_52><loc_68><loc_95><loc_76></location>The model atmospheres are assumed to be composed of N2, H2O, and CO2. Temperature profiles are obtained on 52 model layers, approximately spaced equidistantly in log (pressure). The pressure grid is determined from the surface pressure p surf (variable, see below) up to a pressure of 6.6 × 10 -5 bar (fixed) at the model lid.</text> <text><location><page_2><loc_52><loc_47><loc_95><loc_68></location>The model calculates the temperature profile by solving the radiative transfer equation. The radiative fluxes are calculated separately for the stellar (mostly visible) and the planetary (mostly IR) flux. The stellar part of the radiative transfer uses gaseous opacities from Pavlov et al. (2000) and Rayleigh scattering formulations from von Paris et al. (2010). Gaseous opacities in the IR are based on Hitemp data (Rothman et al. 1995) and continuum absorption adapted from Clough et al. (1989) and Kasting et al. (1984a). The purpose of the 1D model used here is to calculate an arbitrary range of temperature-pressure scenarios ranging from the outer to the inner boundary of the HZ. Therefore, we used Hitemp in order to have reliable results for wet, hot atmospheres. The choice of the specific opacity database (e.g., Hitran 2008, Hitran 2004, etc.) for gaseous absorption is not critical for the results presented below, i.e. relatively dry, cold scenarios.</text> <text><location><page_2><loc_52><loc_42><loc_95><loc_47></location>If the calculated radiative lapse rate is sub-adiabatic, the model performs convective adjustment, assuming a wet adiabatic lapse rate. This wet adiabatic lapse rate is determined considering either CO2 or H2O as condensing species.</text> <text><location><page_2><loc_52><loc_36><loc_95><loc_42></location>The treatment of CO2 condensation for the calculation of the adiabatic lapse rate follows von Paris et al. (2010). We assume that CO2 condensation occurs when the atmosphere is supersaturated with respect to CO2, as described by the super saturation ratio S s:</text> <formula><location><page_2><loc_52><loc_32><loc_95><loc_35></location>p CO2 p vap , CO2 = S s = 1 . 34 (2)</formula> <text><location><page_2><loc_52><loc_21><loc_95><loc_32></location>where p CO2 is the partial CO2 pressure and p vap , CO2 the saturation vapor pressure of CO2. The chosen value of S s is motivated by measurements reported in Glandorf et al. (2002). Condensation of an atmospheric constituent can occur when S s is closer to unity than the value chosen here. Note that other studies (e.g., Kasting 1991 or Kasting et al. 1993) assumed S s = 1 which represents the thermodynamic lower limit where condensation could occur.</text> <text><location><page_2><loc_52><loc_10><loc_95><loc_21></location>The water profile in the model is calculated based on the relative humidity distribution of Manabe & Wetherald (1967). Above the cold trap, the water profile is set to an isoprofile taken from the cold trap value. Despite the fact that CO2 is allowed to condense, the major atmospheric constituents N2 and CO2 are isoprofiles throughout the entire atmosphere, i.e. are assumed to be well-mixed. The impact of fixing the CO2 mixing ratio at the saturation value on the atmospheric energy budget is expected to be rather small, hence would not change our results</text> <text><location><page_3><loc_7><loc_85><loc_50><loc_93></location>by much. A more consistent treatment of CO2 condensation (including an altitude-dependent CO2 profile) would involve vertical mass transport and an atmospheric pressure grid which is not in hydrostatic equilibrium in the region of CO2 condensation. Introducing this into our atmospheric model is beyond the scope of the current work.</text> <section_header_level_1><location><page_3><loc_7><loc_82><loc_22><loc_83></location>2.2. Modelprocedure</section_header_level_1> <text><location><page_3><loc_7><loc_72><loc_50><loc_81></location>The simulations started with a CO2 partial pressure of 73.8 bar, corresponding to the pressure at the critical point, p crit, and an isothermal temperature profile of 320 K, i.e. higher than the critical temperature of 303 K. The choice of the initial temperature profile is not critical for the final outcome of the simulations. We did not allow for CO2 partial pressures higher than 73.8 bar, even though higher pressures are certainly possible (e.g., Venus).</text> <text><location><page_3><loc_7><loc_69><loc_50><loc_72></location>The surface pressure in model iteration step t + 1 is recalculated based on the surface temperature T surf as</text> <formula><location><page_3><loc_7><loc_67><loc_50><loc_68></location>p surf( T surf) = p N2 + p H2O( T surf) + p CO2( T surf) (3)</formula> <text><location><page_3><loc_7><loc_63><loc_50><loc_66></location>where p N2 is the fixed background pressure of N2. The water vapor pressure is obtained from</text> <formula><location><page_3><loc_7><loc_59><loc_50><loc_62></location>p H2O( T surf) = min ( pvap , H2O(Tsurf) , pocean ) (4)</formula> <text><location><page_3><loc_7><loc_54><loc_50><loc_59></location>with p vap , H2O( T surf) the water vapor saturation pressure at surface temperature and p ocean the ocean reservoir assumed (here, 1 Earth ocean, i.e. 270 bar). The CO2 partial pressure is accordingly calculated as</text> <formula><location><page_3><loc_7><loc_50><loc_50><loc_53></location>p CO2( T surf) = min ( pvap , CO2(Tsurf) , pCO 2 ) (5)</formula> <text><location><page_3><loc_7><loc_41><loc_50><loc_50></location>Note that this corresponds to assuming a super-saturation ratio of S s = 1 at the surface, in contrast to S s = 1.34 used for the atmospheric CO2 adiabatic lapse rate (see eq. 2). This is motivated by the fact that atmospheric condensation generally requires S s > 1 (i.e., the presence of condensation nuclei). At the surface, however, atmosphere and reservoir are in equilibrium, hence the partial pressure follows the vapor pressure curve.</text> <text><location><page_3><loc_10><loc_40><loc_38><loc_41></location>The mixing ratio of N2 is then adjusted via</text> <formula><location><page_3><loc_7><loc_36><loc_50><loc_39></location>CN 2 , t + 1 = CN 2 , t · p surf , t p surf , t + 1 (6)</formula> <text><location><page_3><loc_7><loc_32><loc_50><loc_35></location>where CN 2 , t + 1, CN 2 , t are the N2 concentrations and p surf , t + 1, p surf , t the surface pressures at iteration steps ( t + 1) and t .</text> <text><location><page_3><loc_7><loc_30><loc_50><loc_32></location>Based on the new value for the surface pressure p surf , the pressure grid on the 52 model levels is then re-calculated.</text> <text><location><page_3><loc_7><loc_27><loc_50><loc_30></location>Fig. 2 shows a flow chart of the model to illustrate the model procedure.</text> <text><location><page_3><loc_7><loc_23><loc_50><loc_27></location>The CO2 saturation vapor pressure p vap , CO2 is taken from Ambrose (1956). It is divided into two temperature regimes. For T > 216 . 6 K (gas over liquid):</text> <formula><location><page_3><loc_7><loc_12><loc_50><loc_21></location>d ln( p vap , CO2) d ln( T ) = 2 . 303 · T · (7) ( 867 . 2124 T 2 + 18 . 65612 · 10 -3 -2 · 72 . 4882 · 10 -6 · T + 3 · 93 · 10 -9 T 2 )</formula> <text><location><page_3><loc_10><loc_10><loc_32><loc_11></location>For T ≤ 216 . 6 K (gas over solid):</text> <figure> <location><page_3><loc_59><loc_79><loc_95><loc_93></location> <caption>Fig. 2. Flow chart of the model.</caption> </figure> <formula><location><page_3><loc_52><loc_66><loc_95><loc_72></location>d ln( p vap , CO2) d ln( T ) = 2 . 303 · T · (8) ( 1284 . 07 ( T -4 . 718) 2 + 1 . 256 · 10 -4 )</formula> <text><location><page_3><loc_52><loc_57><loc_95><loc_65></location>If surface temperatures remain above 303 K throughout the entire simulation, the maximum CO2 partial pressure is assumed to lie above the critical pressure. However, if surface temperatures converge to values below 303 K, the corresponding CO2 partial pressure is taken as the maximum possible CO2 pressure for the particular planetary scenario.</text> <section_header_level_1><location><page_3><loc_52><loc_54><loc_70><loc_55></location>2.3. Parametervariations</section_header_level_1> <text><location><page_3><loc_52><loc_47><loc_95><loc_53></location>We varied five important model parameters: The planetary gravity, related to its mass and radius, the type of the central star and the energy input from the star, related to orbital distance, as well as model surface albedo and N2 partial pressure. Table 1 summarizes the varied parameters.</text> <unordered_list> <list_item><location><page_3><loc_53><loc_39><loc_95><loc_45></location>-We assumed three di ff erent values for planetary gravity (1x, 2x and 3x Earth's gravity) which roughly corresponds to planetary masses of 1, 5 and 11 Earth masses, respectively, according to mass-radius relationships for rocky planets (e.g., Sotin et al. 2007).</list_item> <list_item><location><page_3><loc_53><loc_25><loc_95><loc_39></location>-We used spectra of AD Leo, /epsilon1 Eri, the Sun and σ Boo as examples for M-, K-, G- and F-type stars, respectively. The same sample of stars has been used for numerous studies regarding the influence of stellar type on atmospheric conditions (e.g., Segura et al. 2003, Segura et al. 2005, Grenfell et al. 2007a, Grenfell et al. 2007b, Kitzmann et al. 2010). Stellar e ff ective temperatures increased from M- to F-type stars, from about 3,400 K to 6,700 K, respectively. A more detailed description of the stellar spectra as well as data sources and references can be found in Kitzmann et al. (2010).</list_item> <list_item><location><page_3><loc_53><loc_22><loc_95><loc_24></location>-The incoming stellar insolation SI at the top of the model atmospheres is calculated from</list_item> </unordered_list> <formula><location><page_3><loc_54><loc_20><loc_95><loc_21></location>SI = S · S 0 (9)</formula> <text><location><page_3><loc_54><loc_10><loc_95><loc_19></location>where S 0 is the flux currently received by modern Earth (i.e., S 0 = 1366Wm -2 ) and S is a constant factor related to orbital distance (e.g., for Earth, S = 1). In this study, S was varied from S = 0.2 to S = 0.5. Corresponding orbital distances ranged from 0.21-0.34AU, 0.85-1.35AU, 1.41-2.23AU and 2.67-4.22AU for the M-, K-, G- and F-type stars, respectively (based on Kitzmann et al. 2010). The range of stellar</text> <table> <location><page_4><loc_21><loc_85><loc_81><loc_91></location> <caption>Table 1. Parameter (range) for the runs performed</caption> </table> <text><location><page_4><loc_10><loc_75><loc_50><loc_82></location>insolation considered here roughly covers the outer limit of the HZ for the stellar types used in this work (e.g., GL 581 d with S = 0.29 and early Mars with S = 0.32, are both potentially habitable) as well as orbits slightly closer to or slightly farther away from the central star.</text> <unordered_list> <list_item><location><page_4><loc_8><loc_60><loc_50><loc_75></location>-The above runs (nominal runs in Table 1) were performed with the N2 partial pressure fixed at 1 bar. Increasing the amount of N2 (at fixed values of CO2 partial pressures) leads to two competing e ff ects, a cooling e ff ect (related to enhanced Rayleigh scattering), and a warming e ff ect (due to pressure broadening of absorption lines and continuum absorption). Several studies have shown that increasing N2 partial pressures might indeed help to obtain habitable surface conditions in atmospheric simulations (e.g., Goldblatt et al. 2009, von Paris et al. 2010). Hence, we varied the N2 partial pressure from 0.1 to 10 bar, for the 1 g runs (N2 study in Table 1).</list_item> <list_item><location><page_4><loc_8><loc_39><loc_50><loc_59></location>-For all the model scenarios described above, the measured mean surface albedo of the Earth ( A surf = 0.13, taken from Rossow & Schi ff er 1999) is used. However, the surface albedo has an important impact on the calculated surface temperature (e.g., von Paris et al. 2008, Rosing et al. 2010, Wordsworth et al. 2010b). Our model calculations do not take into account the possible increase of surface albedo due to condensing and freezing CO2 during the iterations. In this regard, our calculated CO2 partial pressures are likely to be upper limits. Measurements and modeling of the albedo of CO2 snow by Warren et al. (1990) suggest that the albedo of CO2 snow and ice might be significantly higher than 0.13. Therefore, we performed additional calculations ( AS study in Table 1) with a surface albedo of A surf = 0.4 for the 1 g scenarios, at stellar insolations corresponding to S = 0.2 and S = 0.4 and a N2 partial pressure of 1 bar, respectively.</list_item> </unordered_list> <section_header_level_1><location><page_4><loc_7><loc_35><loc_15><loc_36></location>3. Results</section_header_level_1> <text><location><page_4><loc_7><loc_16><loc_50><loc_34></location>Fig. 3 shows the maximum partial pressures of CO2 as a function of stellar insolation (hence, orbital distance, see Eq. 9) for the nominal runs of Table 1. Additionally shown as triple dot-dashed line in Fig. 3 is the CO2 partial pressure when using an equilibrium temperature assuming zero albedo (i.e., the maximum equilibrium temperature, T eq , max, see eq. 1). This shows that detailed atmospheric modeling (taking into account the greenhouse effect) is indeed needed to obtain consistent constraints on the CO2 partial pressure. Also indicated in Fig. 3 (by the horizontal plain line) is the boundary between liquid and solid phase of surface CO2, i.e. the triple point pressure of 5.1 bar (see the phase diagram, Fig. 1). For maximum CO2 pressures below 5.1 bar, the atmosphere is in equilibrium with CO2 ice, above 5.1 bar, the formation of (shallow) CO2 oceans is suggested.</text> <text><location><page_4><loc_7><loc_10><loc_50><loc_16></location>Fig. 4 shows sample temperatures profile of the simulations, i.e. a 1 g planet at S = 0.35, with a N2 pressure of 1 bar and AS = 0.13. As can be clearly seen, the K- and M-star planets retain their initial CO2 inventory of 73.8 bar (since at the surface, the atmosphere is not saturated with respect to CO2), whereas</text> <text><location><page_4><loc_52><loc_62><loc_95><loc_82></location>for the F- and G-star planets, CO2 partial pressures are below the critical pressure, at 10.9 and 23.2 bar, respectively. The upper stratosphere is sensitive to absorption of stellar radiation in the near-IR bands of CO2 and H2O, resulting in about 30 K increase for an M-star planet compared to the F-star planet. Additionally shown in Fig. 4 are the CO2 vapor pressure curve ( S s = 1, dashed line, eq. 5) which intersects the temperature profile (for the F star and the G star) at the surface. Furthermore, Fig. 4 shows the CO2 condensation curve from eq. 2 ( S s = 1.34) indicating the CO2 convective regime. It is clearly seen that the atmospheres of the F-star and the G-star planet are dominated by a CO2 convective regime, followed by a very shallow near-surface H2O convective regime. In contrast, the K- and M-star planets show a relatively extensive lower troposphere dominated by H2O condensation.</text> <figure> <location><page_4><loc_55><loc_39><loc_92><loc_60></location> <caption>Fig. 4. Temperature profile for 1 g planets at S = 0.35.</caption> </figure> <section_header_level_1><location><page_4><loc_52><loc_30><loc_69><loc_31></location>3.1. Effectofstellartype</section_header_level_1> <text><location><page_4><loc_52><loc_10><loc_95><loc_29></location>From Fig. 3, it is clear that with increasing stellar e ff ective temperature (changing stellar type from M to F), the maximum partial pressure of CO2 decreases. Also, the minimum stellar insolation S min for which maximum CO2 pressures above p crit are possible depends sensitively on the stellar type ( S min = 0.25 for the M-star planets and S min ≥ 0.5 for the F-star planets). This is due to the distribution of the stellar energy received by the model planets. With increasing stellar e ff ective temperature, the stellar spectrum is shifted towards lower (bluer) wavelengths, as illustrated by Fig. 5. Broadly, the stellar spectrum can be separated into three regimes, 1) a Rayleigh scattering regime, 2) an absorption regime and 3) a 'window' in between. The Rayleigh scattering regime is here defined as the spectral range where the Rayleigh cross section remains larger than 10 -2 of the maximum value ( λ /lessorsimilar 0.75 µ m).</text> <figure> <location><page_5><loc_12><loc_51><loc_91><loc_91></location> </figure> <text><location><page_5><loc_43><loc_51><loc_44><loc_52></location>0</text> <text><location><page_5><loc_78><loc_51><loc_79><loc_52></location>0</text> <figure> <location><page_5><loc_11><loc_20><loc_46><loc_40></location> <caption>Fig. 3. Maximum CO2 partial pressure as a function of gravity and stellar insolation (as defined by Eq. 9). The critical pressure p crit is indicated by the dot-dashed horizontal line. The triple-dot dashed line indicates the highest CO2 pressure calculated for the maximum equilibrium temperature ( A = 0, eq. 1).Fig. 5. Cumulative energy of di ff erent central stars. Regimes are indicated by vertical lines.</caption> </figure> <text><location><page_5><loc_7><loc_10><loc_50><loc_12></location>The absorption regime starts at about 1.5 µ m where the first strong water and CO2 absorption bands occur. At the high CO2</text> <text><location><page_5><loc_52><loc_27><loc_95><loc_41></location>partial pressures considered in this work, both the Rayleigh scattering regime and the absorption regime are almost entirely optically thick to incoming stellar radiation (i.e., no radiation reaching the surface). In the Rayleigh scattering regime, radiation is reflected back to space (high spectral albedo), whereas in the absorption regime, the radiation is deposited in the upper to middle atmosphere (very low spectral albedo), as illustrated in Fig. 6 for a 2 and 20 bar CO2 atmosphere. Depending on spectral type, the actual percentage of stellar radiation contained in the 'window' changes quite considerably, as illustrated in Fig. 5 (around 50% for the M star, only 30% for the F star).</text> <text><location><page_5><loc_52><loc_19><loc_95><loc_26></location>Therefore, the planetary albedo becomes larger for increasing stellar e ff ective temperature (M to F) because of the increasingly important contribution of Rayleigh scattering, and thus surface temperatures and corresponding CO2 partial pressures are lower.</text> <section_header_level_1><location><page_5><loc_52><loc_15><loc_73><loc_16></location>3.2. Effectofplanetarygravity</section_header_level_1> <text><location><page_5><loc_52><loc_10><loc_95><loc_13></location>The most noticeable e ff ect when changing the planetary gravity g is the e ff ect on atmospheric column density C . At constant pressure p , C and g are related linearly via C ∼ pg -1 . Hence, an</text> <figure> <location><page_6><loc_10><loc_72><loc_46><loc_92></location> <caption>Fig. 6. Spectral albedo for a 2 and a 20 bar CO2 atmosphere with surface temperature 288 K (corresponding to 17 mbar of H2O), 1bar of N2 and AS = 0.13. 1 g and 3 g planets indicated in black and red, respectively. Window regime is indicated by vertical lines.</caption> </figure> <text><location><page_6><loc_7><loc_58><loc_50><loc_60></location>increase in gravity leads to a corresponding decrease of atmospheric column density.</text> <text><location><page_6><loc_7><loc_41><loc_50><loc_58></location>This leads to three important e ff ects. Firstly, such a decrease in atmospheric column density leads to decreased Rayleigh scattering, hence a lower planetary albedo (see Fig. 6), hence favors surface warming. Furthermore, less atmospheric column density leads to less near-IR absorption of stellar radiation, hence higher albedo (again, see Fig. 6), hence surface warming (more starlight reaches the surface) and stratospheric cooling. On the other hand, a decreased atmospheric column density leads to less greenhouse e ff ect (GHE), hence surface cooling. The net result on surface temperature when combining these three e ff ects (either cooling or warming) depends on the amount of CO2 and the stellar type which determines the planetary albedo and stellar energy distribution (see Figs. 5 and 6).</text> <figure> <location><page_6><loc_10><loc_18><loc_46><loc_37></location> <caption>Fig. 7. E ff ect of varying planetary gravity on the calculated maximum CO2 pressures. Ratio between calculated CO2 pressures at 1 g and 3 g . (Super-)critical pressures which have a ratio of unity at higher values of S not shown.</caption> </figure> <text><location><page_6><loc_52><loc_71><loc_95><loc_93></location>Fig. 7 shows the ratio between calculated CO2 pressures at 1 g and 3 g . At low stellar insolation, hence low CO2 pressures (see Fig. 3), increasing gravity leads to cooler surface temperatures, and consequently lower CO2 partial pressures (i.e., a ratio higher than 1 for all stars except the F star in Fig. 7). This indicates that the impact of the reduced GHE is dominating, in agreement with other studies of optically rather thin planetary atmospheres (e.g., Rauer et al. 2011). In contrast, at higher stellar insolation (and correspondingly higher CO2 pressures), increasing gravity leads to warmer surface temperatures, hence higher CO2 partial pressures (i.e., a ratio lower than 1 in Fig. 7), implying that the decrease of the GHE is compensated by the decrease in planetary albedo. The influence of the stellar type is clearly seen in Fig. 7. For the M-star planet, with very little radiation in the Rayleigh regime (see Fig. 5), the e ff ect of increasing gravity is much higher than for the F-star planet, for which Rayleigh scattering is very important.</text> <section_header_level_1><location><page_6><loc_52><loc_67><loc_74><loc_68></location>3.3. Implicationsforhabitability</section_header_level_1> <text><location><page_6><loc_52><loc_60><loc_95><loc_65></location>As can be inferred from Fig. 3, our calculations imply that relatively massive CO2 atmospheres of the order of several bars are possible for almost all scenarios, even for planets orbiting far from their central star (stellar insolation S /greaterorsimilar 0.25).</text> <text><location><page_6><loc_52><loc_40><loc_95><loc_58></location>At the triple point temperature of water, i.e. 273 K, which permits its liquid phase, the CO2 vapor pressure is about 34 bar (see Fig. 1). Hence, Fig. 3 implies that liquid surface water can be achieved for stellar insolation S 34bar as low as S 34bar = 0.25 for the M-type star and S 34bar = 0.4 for the F-type star, providing a su ffi ciently large source of CO2 is available for outgassing on the planet. This is, however, not the outer edge of the HZ, since surface temperature is not necessarily a monotonic function of CO2 partial pressure (known as the maximum greenhouse effect, e.g., Kasting et al. 1993). The CO2 pressures corresponding to the maximum surface temperatures are therefore expected to be somewhat lower than the maximum CO2 pressures in Fig. 3. Hence, the outer edge of the HZ is most likely located at lower stellar insolation (i.e., farther away from the star), than S 34bar.</text> <section_header_level_1><location><page_6><loc_52><loc_36><loc_69><loc_37></location>3.4. N 2 partialpressure</section_header_level_1> <text><location><page_6><loc_52><loc_25><loc_95><loc_34></location>The results of the N2 study (Sect. 2.3 and Table 1) are shown in Fig. 8. As expected, for the high CO2 partial pressures found for higher stellar insolation, the e ff ect of varying N2 is negligible, given that CO2 is a much more e ffi cient Rayleigh scatterer than N2. However, for lower stellar insolation, and consequently lower CO2 partial pressures, the e ff ect of N2 becomes discernible.</text> <text><location><page_6><loc_52><loc_10><loc_95><loc_24></location>At these lower stellar insolation, the warming e ff ect of adding N2 to the atmosphere is clearly dominating, since the calculated maximum CO2 pressures increase with increasing N2 partial pressure. The e ff ect is rather pronounced (almost a factor of 4 when increasing pN 2 from 0.1 to 10 bar) for the M star since Rayleigh scattering does not contribute greatly to the overall energy budget for these cases (most of the stellar radiation is emitted at wavelengths where Rayleigh scattering is negligible, see Fig. 5). For the F-star simulations, maximum CO2 pressures increase only by about 30%, i.e. warming and cooling e ff ects approximately cancel out.</text> <figure> <location><page_7><loc_8><loc_72><loc_48><loc_92></location> <caption>Fig. 8. E ff ect of varying N2 partial pressure pN 2 on the calculated maximum CO2 pressures. (Super-)critical pressures which have a ratio of unity at higher values of S not shown.</caption> </figure> <section_header_level_1><location><page_7><loc_7><loc_62><loc_21><loc_63></location>3.5. Surfacealbedo</section_header_level_1> <text><location><page_7><loc_7><loc_50><loc_50><loc_61></location>The results of the surface albedo study (Sect. 2.3 and Table 1) are presented in Fig. 9 which shows the decrease in calculated maximum CO2 pressure when increasing the surface albedo. At S = 0.2, the decrease of CO2 pressure is rather large, reaching about a factor of 20 for the M-type star. For a planet orbiting around an F-star, calculations imply maximum CO2 pressures of the order of 0.1 bar, so rather a teneous atmosphere. At S = 0.4, the e ff ect of increasing surface albedo is smaller than at S = 0.2, but still reaches about a factor of 2-3 for the F-type star.</text> <figure> <location><page_7><loc_8><loc_18><loc_49><loc_47></location> <caption>Fig. 9. E ff ect of varying surface albedo on the calculated maximum CO2 pressures. (Super-)critical pressures at S = 0.4 for the M and K star not shown (indicated by horizontal line at pCO 2 = 73.8 bar).</caption> </figure> <text><location><page_7><loc_52><loc_78><loc_95><loc_93></location>Fig. 9 shows that, at S = 0.2, the M-star planet is much more sensitive to a change in surface albedo (a reduction of a factor of about 20 in CO2 pressure) than the F-star planet (a factor of 8), as seen by the steeper slope of the M-star line. The sensitivity is generally increasing for increasing stellar e ff ective temperature (type from M to F). This is due to the larger amount of stellar energy emitted in the window regime (see Sect. 3.1 and Fig. 5). Hence, the response to an increase in surface albedo, which a ff ects principally the window, is more pronounced for the Mstar planet and for lower stellar insolation (and correspondingly lower CO2 partial pressures). For example, at S = 0.4, the reduction for the F-star planet is decreased to about a factor of 2.</text> <text><location><page_7><loc_52><loc_63><loc_95><loc_77></location>In order to investigate the combined e ff ect of, e.g., an increase in N2 partial pressure and an increase in surface albedo, we performed some additional test runs with both parameters changed. For the M star case, for example, the e ff ect of N2 was nearly unaltered even at high surface albedo. At S = 0.2, an increase in surface albedo reduced the maximum CO2 pressure from 8.2 to roughly 0.4 bar (see Fig. 9) whereas an increase of N2 partial pressure increased the maximum CO2 from 8.2 to 16.3 bar (see Fig. 8). At high surface albedo and high N2 pressure, the maximum CO2 pressure obtained was 14.3 bar, i.e. nearly as high as for the simulations at low surface albedo.</text> <section_header_level_1><location><page_7><loc_52><loc_60><loc_63><loc_61></location>4. Discussion</section_header_level_1> <section_header_level_1><location><page_7><loc_52><loc_57><loc_68><loc_59></location>4.1. H 2 O-CO 2 oceans</section_header_level_1> <text><location><page_7><loc_52><loc_45><loc_95><loc_57></location>As has been shown above (Fig. 3), for planets orbiting within the HZ of K-G-F stars there is a region of liquid surface CO2 combined with surface temperatures above 273 K, i.e. liquid surface H2O. This means that it is possible to form H2OCO2 oceans. Then, the question of planetary habitability would depend strongly on the pH of the liquid, even though extremophiles on Earth could support quite low pH values (e.g., Rothschild & Mancinelli 2001). A detailed investigation of this interesting issue is however beyond the scope of this work.</text> <section_header_level_1><location><page_7><loc_52><loc_42><loc_80><loc_43></location>4.2. Implicationsofmodelassumptions</section_header_level_1> <text><location><page_7><loc_52><loc_29><loc_95><loc_41></location>The 1D atmospheric model used in this work is based on relatively few, simple assumptions. Most of these assumptions are physically justified, i.e. the assumption of adiabatic temperature gradients in the troposphere or radiative transfer as the main energy transport mechanism in the upper atmosphere. However, some of them (presence of clouds, greenhouse gases, water profile, etc.) are model-specific, hence need to be discussed further with respect to their possible influence on the results presented above.</text> <text><location><page_7><loc_52><loc_15><loc_95><loc_29></location>The model is a cloud-free code, hence the potential impact of CO2 clouds on the climate is neglected. It was shown by several authors that this potential impact could be quite large (e.g., Forget & Pierrehumbert 1997, Mischna et al. 2000, Colaprete & Toon 2003, Wordsworth et al. 2010b, Wordsworth et al. 2011). However, this e ff ect depends sensitively on cloud opacity, cloud coverage and cloud altitude. In addition, the e ff ect of clouds is also probably very dependent on stellar type (see, e.g., Kitzmann et al. 2010 investigating the e ff ect of stellar type for H2O clouds). Investigating this is therefore a subject of further studies.</text> <text><location><page_7><loc_52><loc_10><loc_95><loc_15></location>Furthermore, the model atmospheres considered in this work contained only the greenhouse gases CO2 and water. This choice may be restrictive when applied to our own solar system, since other species, such as O3, SO2, CH4, and N2O, have been con-</text> <text><location><page_8><loc_7><loc_81><loc_50><loc_93></location>sidered in models of the early Earth or early Mars climate (e.g., Yung et al. 1997, Buick 2007, Haqq-Misra et al. 2008). But given that the concentration of these gases depend on very specific planetary scenarios (e.g., outgassing history, biospheric evolution, etc.), assuming them in the context of exoplanets (without any geological or other constraints) is rather arbitrary. However, the impact on stratospheric temperatures through the absorption of UV (e.g., O3 and SO2) or near-IR (e.g., CH4) stellar radiation is potentially important.</text> <text><location><page_8><loc_7><loc_57><loc_50><loc_81></location>Radiative transfer in dense, CO2-dominated atmospheres presents many challenges (e.g., collision-induced absorption, sub-Lorentzian behavior of line wings, etc.). The parametrization of the collision-induced absorption (CIA) used in this study is taken from Kasting et al. (1984b). A recent study (Wordsworth et al. 2010a) presented a revised parametrization, showing that the calculation presented by Kasting et al. (1984b) most likely over-estimates the opacity. In order to estimate the impact of the CIA uncertainties on our results, we performed a sensitivity study with a reduced (by roughly a factor of 2) CIA. The conclusions however did not change qualitatively. At S = 0.2, calculated CO2 maximum pressures around K-, G- and F-stars decreased by less than 50%, for the M-star the maximum CO2 pressure decreased from 8.2 to 3.0 bar. At S = 0.35, results changed less than 20% except for the K-star planet, where a maximum CO2 pressure of 47.3bar was calculated, instead of 73.8 bar (i.e., the critical pressure of CO2, see Fig. 3). Therefore, our calculations (using Kasting et al. 1984b) are likely to be overestimates of the maximum CO2 partial pressures.</text> <text><location><page_8><loc_7><loc_36><loc_50><loc_57></location>The model uses a super-saturation of S s = 1.34 to determine the CO2 convective regime (see eq. 2). The choice of S s has been shown to be very important for early Mars climate simulations, e.g. Pollack et al. (1987) (using S s = ∞ ) find significantly higher surface temperatures ( > 30K) than Kasting (1991) (using S s = 1). The assumed S s = 1.34 is based on Glandorf et al. (2002), a value observed for specific conditions (e.g., dust loading available for nucleation) which could be di ff erent on exoplanets (as low as S s = 1, but also possibly significantly higher). In this sense, the calculated maximum CO2 pressures are not necessarily upper limits. To further investigate this, we performed some sensitivity simulations with S s = 1. As expected, calculated maximum CO2 pressures were lower, of the same order of magnitude as for the CIA study mentioned above. However, the main conclusions obtained in this work (i.e., the existence of maximum CO2 pressures far below the critical pressure) were not a ff ected.</text> <text><location><page_8><loc_7><loc_19><loc_50><loc_36></location>The relative humidity profile used in this work (Manabe & Wetherald 1967) has been derived from observations of modern Earth. It has been used in many 1D simulations of terrestrial exoplanets, both Earth-like (e.g., Segura et al. 2003, Grenfell et al. 2007a) and not (e.g., von Paris et al. 2010, Wordsworth et al. 2010b). Since the humidity profile is anything but trivial to model in 1D simulations, some authors chose to fix relative humidity at an isoprofile (e.g., Kasting 1991). However, given the large amounts of CO2 in the model atmospheres (73.8 bar at 303 K), the impact of water (42 mbar at 303 K) on atmospheric structure (via near-IR absorption) and surface conditions (via the GHE) is somewhat negligible. Therefore, the choice of the relative humidity profile is probably not important.</text> <section_header_level_1><location><page_8><loc_7><loc_16><loc_26><loc_17></location>4.3. Synchronousrotation</section_header_level_1> <text><location><page_8><loc_7><loc_10><loc_50><loc_15></location>For planets orbiting very close to their star, tidal locking of the planetary rotation with the orbital period is very likely. The time scale t lock of tidal locking is very sensitive to orbital distance ( t lock ∼ a 6 , a orbital distance, see e.g. Grießmeier et al.</text> <text><location><page_8><loc_52><loc_75><loc_95><loc_93></location>2005). Hence, tidal locking is mainly an issue for the habitability of planets orbiting around M stars due to the closeness of the HZ to the star. It has been argued that for planets with a perpetual nightside, the atmosphere could collapse since the nightside forms a cold trap for the volatiles, which, in the context of this work, could present an alternative way of obtaining maximum CO2 pressures. However, as has been shown by numerous modeling studies (e.g., Joshi et al. 1997, Joshi 2003, Wordsworth et al. 2011, Kite et al. 2011), moderately dense atmospheres containing hundreds of millibars or more of CO2 are su ffi cient to avoid atmospheric collapse by means of atmospheric circulation. Hence, the M-star simulations presented in this work are not thought to be subject to atmospheric collapse induced by synchronous rotation.</text> <section_header_level_1><location><page_8><loc_52><loc_72><loc_64><loc_73></location>5. Conclusions</section_header_level_1> <text><location><page_8><loc_52><loc_62><loc_95><loc_71></location>We have presented a detailed parameter study to constrain the maximum CO2 partial pressure possible for terrestrial exoplanets, using a 1D cloud-free atmospheric model. Parameters investigated included the central star type, the orbital distance and the planetary gravity. Furthermore, we investigated the influence of N2 partial pressure and the surface albedo on the maximum CO2 partial pressure.</text> <text><location><page_8><loc_52><loc_45><loc_95><loc_61></location>Results imply that super-critical atmospheres (i.e., p CO2 ≥ p crit = 73.8 bar) are possible for planets around M stars for stellar insolation corresponding to S crit = 0.25 or higher. For increasingly bluer stars (i.e., higher e ff ective temperatures), this super-critical stellar insolation increases (e.g., S crit > 0.5 for an F-type star). For lower stellar insolation, the calculations presented here imply that there is indeed a maximum CO2 partial pressure, even if the planets are orbiting well within the habitable zone. Nevertheless, massive CO2 atmospheres of the order of bars are still possible for most scenarios. For planets orbiting very far from an F-type central star (e.g., S = 0.2 in this work), CO2 partial pressures could be constrained to be less than 1 bar.</text> <text><location><page_8><loc_52><loc_33><loc_95><loc_45></location>The e ff ect of planetary gravity is twofold. For low stellar insolation and corresponding cold surface temperatures, increasing planetary gravity leads to a decrease of maximum CO2 partial pressure due to less atmospheric greenhouse e ff ect. At higher stellar insolation, an increase of planetary gravity increases the calculated maximum CO2 partial pressure because of less Rayleigh scattering. For F-star planets, the e ff ect is up to a factor of 2, depending on stellar insolation, whereas for an M-star planet, a factor of about 4 has been calculated.</text> <text><location><page_8><loc_52><loc_21><loc_95><loc_33></location>Increasing the N2 partial pressure leads to warmer surface temperatures for all cases, hence corresponding maximum CO2 pressures are higher. The e ff ect reaches up to a factor of 3 for planets around an M star, upon increasing the N2 partial pressure from 0.1 to 10 bar. The surface albedo has an important e ff ect on the values of the maximum CO2 partial pressure. A higher surface albedo leads to cooler surface temperatures, hence less CO2 in the atmosphere. Decreases of about a factor of 20 have been shown when increasing the surface albedo from 0.13 to 0.4.</text> <text><location><page_8><loc_52><loc_10><loc_95><loc_21></location>The presence of CO2 and H2O clouds could alter these results because of their potentially large impact on the planetary energy balance. However, our (clear-sky) results show in a robust way that the composition and the evolution of planetary atmospheres strongly depend on orbital and planetary parameters. Although a consistent model for the determination of CO2 partial pressures must take processes such as sequestration or outgassing into account, our results show that there is a fundamental thermodynamic limit to the amount of CO2 in terrestrial</text> <text><location><page_9><loc_7><loc_88><loc_50><loc_93></location>atmospheres, independent of the planetary reservoir. Hence, a more detailed coupling between interior, surface and atmosphere models should be used to accurately predict atmospheric composition of terrestrial planets.</text> <text><location><page_9><loc_7><loc_82><loc_50><loc_87></location>Acknowledgements. P.v.P., P.H. and F. Selsis acknowledge support from the European Research Council (Starting Grant 209622: E3ARTHs). This research has been partly supported by the Helmholtz Association through the research alliance 'Planetary Evolution and Life'. We thank M. Godolt and D. Kitzmann for valuable discussions and comments regarding this manuscript.</text> <section_header_level_1><location><page_9><loc_7><loc_79><loc_16><loc_80></location>References</section_header_level_1> <text><location><page_9><loc_7><loc_76><loc_47><loc_78></location>Abbot, D. S., Cowan, N. B., & Ciesla, F. J. 2012, accepted in Astrophys. J. Ambrose, D. 1956, Trans. Faraday Society, 52, 772</text> <text><location><page_9><loc_7><loc_75><loc_50><loc_76></location>Anglada-Escud'e, G., Arriagada, P., Vogt, S. S., et al. 2012, Astrophys. J. Letters,</text> <text><location><page_9><loc_9><loc_74><loc_14><loc_74></location>751, L16</text> <text><location><page_9><loc_7><loc_69><loc_50><loc_73></location>Bonfils, X., Delfosse, X., Udry, S., et al. 2011, submitted to Astron. Astrophys. Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, Astrophys. J., 736, 19 Borucki, W. J., Koch, D. G., Batalha, N., et al. 2012, Astrophys. J., 745, 120 Buick, R. 2007, Geobiology, 5, 97</text> <unordered_list> <list_item><location><page_9><loc_7><loc_68><loc_43><loc_69></location>Cassan, A., Kubas, D., Beaulieu, J.-P., et al. 2012, Nature, 481, 167</list_item> </unordered_list> <text><location><page_9><loc_7><loc_67><loc_43><loc_68></location>Clough, S., Kneizys, F., & Davies, R. 1989, Atm. Research, 23, 229</text> <unordered_list> <list_item><location><page_9><loc_7><loc_66><loc_39><loc_67></location>Colaprete, A. & Toon, O. B. 2003, J. Geophys. Res., 108, 6</list_item> <list_item><location><page_9><loc_7><loc_64><loc_50><loc_66></location>Delfosse, X., Bonfils, X., Forveille, T., et al. 2012, submitted to Astron. Astrophys.</list_item> <list_item><location><page_9><loc_7><loc_62><loc_50><loc_64></location>Dole, S. H. 1964, Habitable planets for man (New York, Blaisdell Pub. Co. [1964] [1st ed.].)</list_item> <list_item><location><page_9><loc_7><loc_60><loc_50><loc_62></location>Edson, A. R., Kasting, J. F., Pollard, D., Lee, S., & Bannon, P. R. 2012, Astrobiology, 12, 562</list_item> </unordered_list> <text><location><page_9><loc_7><loc_59><loc_42><loc_60></location>Elkins-Tanton, L. T. & Seager, S. 2008, Astrophys. J., 685, 1237</text> <unordered_list> <list_item><location><page_9><loc_7><loc_57><loc_49><loc_58></location>Fischer, D. A., Marcy, G. W., Butler, R. P., et al. 2008, Astrophys. J., 675, 790 Forget, F. & Pierrehumbert, R. T. 1997, Science, 278, 1273</list_item> <list_item><location><page_9><loc_7><loc_54><loc_50><loc_56></location>Gaidos, E., Fischer, D. A., Mann, A. W., & L'epine, S. 2012, Astrophys. J., 746, 36</list_item> <list_item><location><page_9><loc_7><loc_52><loc_50><loc_54></location>Glandorf, D. L., Colaprete, A., Tolbert, M. A., & Toon, O. B. 2002, Icarus, 160, 66</list_item> <list_item><location><page_9><loc_7><loc_50><loc_50><loc_52></location>Goldblatt, C., Claire, M. W., Lenton, T. M., et al. 2009, Nature Geoscience, 2, 891</list_item> <list_item><location><page_9><loc_7><loc_47><loc_50><loc_50></location>Grenfell, J. L., Grießmeier, J.-M., Patzer, B., et al. 2007a, Astrobiology, 7, 208 Grenfell, J. L., Stracke, B., von Paris, P., et al. 2007b, Planet. Space Science, 55, 661</list_item> <list_item><location><page_9><loc_7><loc_45><loc_50><loc_47></location>Grießmeier, J.-M., Stadelmann, A., Motschmann, U., et al. 2005, Astrobiology, 5, 587</list_item> <list_item><location><page_9><loc_7><loc_42><loc_50><loc_45></location>Haghighipour, N., Vogt, S. S., Butler, R. P., et al. 2010, Astrophys. J., 715, 271 Haqq-Misra, J., Domagal-Goldman, S., Kasting, P., & Kasting, J. F. 2008, Astrobiology, 8, 1127</list_item> </unordered_list> <text><location><page_9><loc_7><loc_41><loc_24><loc_41></location>Hart, M. H. 1978, Icarus, 33, 23</text> <text><location><page_9><loc_7><loc_38><loc_48><loc_40></location>Howard, A. W., Marcy, G. W., Johnson, J. A., et al. 2010, Science, 330, 653 Joshi, M. 2003, Astrobiology, 3, 415</text> <unordered_list> <list_item><location><page_9><loc_7><loc_37><loc_45><loc_38></location>Joshi, M. M., Haberle, R. M., & Reynolds, R. T. 1997, Icarus, 129, 450</list_item> </unordered_list> <text><location><page_9><loc_7><loc_36><loc_44><loc_37></location>Kaltenegger, L. & Sasselov, D. 2011, Astrophys. J. Letters, 736, L25</text> <text><location><page_9><loc_7><loc_35><loc_26><loc_36></location>Kasting, J. F. 1988, Icarus, 74, 472</text> <text><location><page_9><loc_7><loc_34><loc_24><loc_35></location>Kasting, J. F. 1991, Icarus, 94, 1</text> <unordered_list> <list_item><location><page_9><loc_7><loc_33><loc_45><loc_34></location>Kasting, J. F., Pollack, J. B., & Ackerman, T. P. 1984a, Icarus, 57, 335</list_item> </unordered_list> <text><location><page_9><loc_7><loc_32><loc_49><loc_33></location>Kasting, J. F., Pollack, J. B., & Crisp, D. 1984b, J. Atmospheric Chem., 1, 403</text> <text><location><page_9><loc_7><loc_31><loc_46><loc_32></location>Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108</text> <text><location><page_9><loc_7><loc_30><loc_42><loc_31></location>Kite, E. S., Gaidos, E., & Manga, M. 2011, Astrophys. J., 743, 41</text> <text><location><page_9><loc_7><loc_29><loc_44><loc_30></location>Kite, E. S., Manga, M., & Gaidos, E. 2009, Astrophys. J., 700, 1732</text> <unordered_list> <list_item><location><page_9><loc_7><loc_27><loc_50><loc_29></location>Kitzmann, D., Patzer, A. B. C., von Paris, P., et al. 2010, Astron. Astrophys., 511, A66</list_item> </unordered_list> <text><location><page_9><loc_7><loc_19><loc_50><loc_27></location>L'eger, A., Selsis, F., Sotin, C., et al. 2004, Icarus, 169, 499 Lovis, C., Mayor, M., Pepe, F., et al. 2006, Nature, 441, 305 Manabe, S. & Wetherald, R. T. 1967, J. Atmosph. Sciences, 24, 241 Mayor, M., Bonfils, X., Forveille, T., et al. 2009, Astron. Astrophys., 507, 487 Mayor, M., Marmier, M., Lovis, C., et al. 2011, submitted to Astron. Astrophys. Mischna, M. A., Kasting, J. F., Pavlov, A., & Freedman, R. 2000, Icarus, 145, 546</text> <unordered_list> <list_item><location><page_9><loc_7><loc_17><loc_50><loc_19></location>Pavlov, A. A., Kasting, J. F., Brown, L. L., Rages, K. A., & Freedman, R. 2000, J. Geophys. Res., 105, 11981</list_item> <list_item><location><page_9><loc_7><loc_14><loc_50><loc_17></location>Pepe, F., Lovis, C., S'egransan, D., et al. 2011, Astron. Astrophys., 534, A58 Pollack, J. B., Kasting, J. F., Richardson, S. M., & Poliako ff , K. 1987, Icarus, 71, 203</list_item> <list_item><location><page_9><loc_7><loc_10><loc_50><loc_14></location>Rauer, H., Gebauer, S., von Paris, P., et al. 2011, Astron. Astrophys., 529, A8 Raymond, S. N., Quinn, T., & Lunine, J. I. 2004, Icarus, 168, 1 Rosing, M. T., Bird, D. K., Sleep, N. H., & Bjerrum, C. J. 2010, Nature, 464, 744</list_item> </unordered_list> <text><location><page_9><loc_52><loc_92><loc_93><loc_93></location>Rossow, W. B. & Schi ff er, R. A. 1999, Bull. Americ. Meteor. Soc., 80, 2261</text> <text><location><page_9><loc_52><loc_91><loc_95><loc_92></location>Rothman, L. S., Wattson, R. B., Gamache, R., Schroeder, J. W., & McCann,</text> <unordered_list> <list_item><location><page_9><loc_54><loc_88><loc_95><loc_91></location>A. 1995, in Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, Vol. 2471, Proc. SPIE Vol. 2471, p. 105-111, Atmospheric Propagation and Remote Sensing IV, J. Christopher Dainty; Ed.,</list_item> </unordered_list> <text><location><page_9><loc_52><loc_66><loc_95><loc_87></location>ed. J. C. Dainty, 105-111 Rothschild, L. J. & Mancinelli, R. L. 2001, Nature, 409, 1092 Segura, A., Kasting, J. F., Meadows, V., et al. 2005, Astrobiology, 5, 706 Segura, A., Krelove, K., Kasting, J. F., et al. 2003, Astrobiology, 3, 689 Selsis, F., Kasting, J. F., Levrard, B., et al. 2007, Astron. Astrophys., 476, 1373 Sotin, C., Grasset, O., & Mocquet, A. 2007, Icarus, 191, 337 Tinney, C. G., Wittenmyer, R. A., Butler, R. P., et al. 2011, Astrophys. J., 732, 31 Udry, S., Bonfils, X., Delfosse, X., et al. 2007, Astron. Astrophys., 469, L43 von Paris, P., Gebauer, S., Godolt, M., et al. 2010, Astron. Astrophys., 522, A23 von Paris, P., Rauer, H., Grenfell, J. L., et al. 2008, Planet. Space Science, 56, 1244 Warren, S. G., Wiscombe, W. J., & Firestone, J. F. 1990, J. Geophys. Res., 95, 14717 Wittenmyer, R. A., Tinney, C. G., Butler, R. P., et al. 2011, Astrophys. J., 738, 81 Wordsworth, R., Forget, F., & Eymet, V. 2010a, Icarus, 210, 992 Wordsworth, R., Forget, F., Selsis, F., et al. 2010b, Astron. Astrophys., 522, A22 Wordsworth, R. D., Forget, F., Selsis, F., et al. 2011, Astrophys. J. Letters, 733, L48</text> <unordered_list> <list_item><location><page_9><loc_52><loc_65><loc_85><loc_66></location>Yung, Y. L., Nair, H., & Gerstell, M. F. 1997, Icarus, 130, 222</list_item> </unordered_list> </document>

2013A&A...550A..39B

https://arxiv.org/pdf/1212.6494.pdf

<document> <section_header_level_1><location><page_1><loc_10><loc_82><loc_92><loc_87></location>High energy emission from the nebula around the Black Widow binary system containing millisecond pulsar B1957+20</section_header_level_1> <text><location><page_1><loc_41><loc_80><loc_61><loc_81></location>W. Bednarek 1 &J. Sitarek 2</text> <text><location><page_1><loc_11><loc_75><loc_53><loc_78></location>1 2 IFAE, Edifici Cn., Campus UAB, E-08193 Bellaterra, Spain e-mail: bednar@astro.phys.uni.lodz.pl; jsitarek@ifae.es</text> <text><location><page_1><loc_11><loc_77><loc_68><loc_78></location>Department of Astrophysics, University of Ł´od´z, ul. Pomo rska 149 / 153, 90-236 Ł´od´z, Poland</text> <text><location><page_1><loc_11><loc_72><loc_23><loc_73></location>Received ; accepted</text> <section_header_level_1><location><page_1><loc_47><loc_70><loc_55><loc_71></location>ABSTRACT</section_header_level_1> <text><location><page_1><loc_11><loc_65><loc_91><loc_69></location>Context. The features of pulsed γ -ray emission from classical and millisecond pulsars indicate that the high energy radiation processes in their inner magnetospheres occur in a similar way. In the last decade several TeV γ -ray nebulae have been discovered around classical pulsars. The above facts suggest that γ -rays should be produced also in the surroundings of millisecond pulsars.</text> <text><location><page_1><loc_11><loc_61><loc_91><loc_65></location>Aims. We discuss a model for the bow shock nebula around the well known Black Widow binary system containing the millisecond pulsar B1957 + 20. This model predicts the existence of a synchrotron X-ray and inverse Compton γ -ray nebula around this system. Wewant to find out whether γ -ray emission from the nebula around B1957 + 20 could be detected by the future and present Cherenkov telescopes.</text> <text><location><page_1><loc_11><loc_56><loc_91><loc_60></location>Methods. Using the Monte Carlo method we followed the propagation of relativistic electrons in the vicinity of the pulsar. We calculated the very high energy radiation produced by them in the synchrotron process and the inverse Compton scattering of the Microwave Background Radiation and of the infrared radiation from the galactic disk. We also computed the X-ray emission produced by the electrons in the synchrotron process.</text> <text><location><page_1><loc_11><loc_50><loc_91><loc_56></location>Results. Weshow that the hard X-ray tail emission observed from the vicinity of B1957 + 20 can be explained by our model. Moreover, we predict that the TeV γ -ray emission produced by the electrons in the inverse Compton process should be detectable by the future Cherenkov Telescope Array and possibly by the long term observations with the present Cherenkov arrays such as MAGIC and VERITAS. The γ -ray emission from B1957 + 20 is expected to be extended, inhomogeneous, and shifted from the present location of the binary system by a distance comparable to the radius of the nebula.</text> <text><location><page_1><loc_11><loc_48><loc_81><loc_49></location>Key words. pulsars: general - stars: binaries: close - radiation mechanisms: non-thermal - gamma-rays: general</text> <section_header_level_1><location><page_1><loc_7><loc_44><loc_19><loc_45></location>1. Introduction</section_header_level_1> <text><location><page_1><loc_7><loc_18><loc_50><loc_42></location>PSR B1957 + 20 was the first millisecond pulsar (MSP) discovered within the binary system belonging to the class of Black Widows (Fruchter et al. 1988). This pulsar has a very small mass companion ( ∼ 0 . 022 M /circledot , van Paradijs et al. 1988) which evaporates under the irradiation from the pulsar magnetosphere. The pulsar has the period of 1.607 ms, the surface magnetic field of ∼ 10 8 G, and the rotational energy loss rate of 7 . 5 × 10 34 erg s -1 . The distance to the binary system is estimated on 2.5 kpc (from the model for Galactic electron density) consistent with the recently established lower limit ∼ 2 kpc (van Kerkwijk et al. 2011). The binary system is compact with the orbital radius of 1 . 5 × 10 11 cm. The companion star has the radius ∼ 10 10 cmand the surface temperature which varies between 2900 K for the unilluminated side to 8300 K for the illuminated side (Fruchter et al. 1995, Reynolds et al. 2007). Therefore, stellar radiation is not expected to create a very strong target for relativistic particles within the binary system. At present, the companion star loses mass at a rather low rate estimated on 10 -10 M /circledot yr -1 (Takata et al. (2012).</text> <text><location><page_1><loc_7><loc_10><loc_50><loc_19></location>The importance of the high energy processes in the vicinity of PSR B1957 + 20 has become clear with the discovery of an H α emission nebula (Kulkarni & Hester 1988). This emission is expected to be produced in shocks formed in the interaction of the pulsar wind with the interstellar medium. A clear bow shock has been detected which apex is located at the distance of ∼ 0 . 02 pc from the pulsar. The bow shock appears due to the motion of</text> <text><location><page_1><loc_52><loc_28><loc_95><loc_45></location>the binary system with the velocity 220 km s -1 through the interstellar medium (Arzoumanian et al. 1994). The X-ray emission has been also reported from the direction of the binary system in the observations of Chandra (Stappers et al. 2003, Huang & Becker 2007, Huang et al. 2012). This emission comes from the interior of the bow shock creating a tail behind the moving binary system. The length of the tail is ∼ 10 18 cm (Huang et al. 2012). The X-ray emission is well described by a single power law spectrum with the index in the range 2 . 3 -2 . 6 depending on the absorption model. The extended X-ray feature has been interpreted as emission from energetic electrons which radiate on the crossing time scale of this region by the pulsar moving with velocity of 220 km s -1 (Cheng et al. 2006).</text> <text><location><page_1><loc_52><loc_10><loc_95><loc_28></location>The Black Widow binary system containing B1957 + 20 was claimed in the past to be a GeV-TeV γ -ray source (Brink et al. 1990). But this early report was not confirmed in the analysis of the EGRET data (Buccheri et al. 1996). In fact, such high energy emission has been suspected already since the discovery of Black Widow pulsars as a result of either the acceleration of particles within the binary system or in the the shock waves of the pulsar wind (e.g. Arons & Tavani 1993, Cheng et al. 2006, Takata et al. 2012). Recently, a pulsed GeV emission from the pulsar B1957 + 20 has been discovered by Fermi (Guillemot et al. 2012). The pulsed spectrum is flat above 0.1 GeV (spectral index close to 2) and extends up to ∼ 4 GeV. The phasogram (light curve folded with the period of the pulsar) shows two well separated peaks. Such structure is also common in the case of classi-</text> <figure> <location><page_2><loc_7><loc_65><loc_52><loc_92></location> <caption>Fig. 1. Schematic representation of the bow shock nebula around binary system containing the millisecond pulsar B1957 + 20. The bow shock is created due to the motion of the binary system through the interstellar space with the velocity of ∼ 220 km s -1 . Relativistic electrons with the Lorentz factors γ e are accelerated by the pulsar itself or by the shocks due to the pulsar wind interactions. The electrons are collimated by the bow shock in the direction opposite to the motion of the binary system. These electrons comptonize the Microwave Background Radiation (MBR) and the infrared radiation (INF) from the galactic disk. As a result γ -ray photons are produced (tagged as E γ ) at the region behind the pulsar.</caption> </figure> <text><location><page_2><loc_7><loc_33><loc_50><loc_46></location>pulsars. Therefore, it is expected that the radiation processes in the inner magnetosphere of the millisecond pulsar B1957 + 20 are similar to those occurring in the case of classical pulsars. This strongly indicate that also processes of acceleration of particles in the pulsar wind are expected to occur similarly. Very recently, Wu et al. (2012) reports detection of orbital modulation of the γ -ray emission at energies above ∼ 2.7 GeV from the Black Widow pulsar PSR B1957 + 20. This emission is expected to be produced by electrons from the pulsar wind which comptonize stellar radiation.</text> <text><location><page_2><loc_7><loc_22><loc_50><loc_32></location>We investigate the radiation processes in the supposed pulsar wind nebula around the binary system containing PSR B1957 + 20. The synchrotron X-ray and inverse Compton (IC) γ -ray emission is calculated from such nebula for the range of likely parameters. Based on the comparison of the calculated synchrotron spectrum with the observed X-ray emission we conclude on the detectability of the TeV γ -ray emission from the bow shock nebula surrounding PSR B1957 + 20.</text> <section_header_level_1><location><page_2><loc_7><loc_17><loc_50><loc_20></location>2. The nebula around binary system downstream of the bow shock</section_header_level_1> <text><location><page_2><loc_7><loc_10><loc_50><loc_16></location>Since the proprieties of high energy γ -ray emission from the millisecond pulsars and classical radio pulsars are surprisingly similar (see the first pulsar catalogue, Abdo et al. 2010), it seems clear that the processes occurring in their inner magnetospheres are these same. Therefore, millisecond pulsars should</text> <text><location><page_2><loc_52><loc_53><loc_95><loc_93></location>also produce relativistic pulsar winds with the parameters similar to those observed around classical pulsars. However, nebulae around MSPs are expected to have a very complicated structure (and also other proprieties) since many MSPs form compact binary systems which additionally move in the interstellar space with large velocities. In fact, this is the case of the binary system PSR B1957 + 20. The pulsar wind around B1957 + 20 is expected to interact with the induced wind of the low mass companion star within a small solid angle, of the order of ∼ 0.01 sr, corresponding to eclipse time of the pulsar radio emission by the wind of the companion star (Fruchter et al. 1988). Therefore, most of the pulsar wind is expected to escape una ff ected from the binary system. Due to the fast velocity of the binary system, the pulsar wind has to interact with the interstellar medium creating a bow shock. Such bow shock has been detected in H α emission in the case of B1957 + 20. The distance of the apex of the bow shock to the pulsar is estimated on ∼ 0 . 02 pc (Kulkarni & Hester 1988). This bow shock confines the pulsar wind at least in the direction of pulsar's motion. Relativistic electrons in the wind can di ff use mainly in the direction opposite to the pulsar's motion. Cheng et al. (2006) have proposed that the synchrotron radiation from such ultrarelativistic electrons is responsible for the observed X-ray tail extending along the axis of the bow shock in the direction opposite to the pulsar velocity. We intend to perform calculations of the Inverse Compton (IC) γ -ray emission from such relativistic electrons applying general scenario proposed by Cheng et al. (2006). These authors argue that e ffi cient synchrotron emission by electrons can occur on the dynamical time scale of the pulsar crossing the length of the tail estimated on ∼ 10 18 cm (Huang et al. 2012). This dynamical time scale is equal to,</text> <formula><location><page_2><loc_52><loc_50><loc_95><loc_52></location>τ dyn = R / v bin ≈ 1 . 5 × 10 11 R 1 s , (1)</formula> <text><location><page_2><loc_52><loc_29><loc_95><loc_50></location>where the velocity of the binary system is v bin = 220 km s -1 and the length of the tail is R = 1 R 1 pc. Applying the observed length of the synchrotron emission, we can estimate the optical depth for electrons on the IC scattering of the Microwave Background Radiation (MBR) in the Thomson regime (true for electrons with energies below ∼ 100 TeV) on, τ = c τ dyn n MBR σ T ≈ 0 . 35, where c is the velocity of light, σ T is the Thomson cross section, and n MBR is the photon density of the Microwave Background Radiation. Note however that electrons cool only partially in the region of observed X-ray emission. Many of them escape from this region but continue to interact with the MBR and other soft photon field, producing high energy γ -rays. Therefore, we expect the appearance of the γ -ray nebula in the vicinity of the Black Widow binary pulsar. This nebula should be shifted in respect to the observed location of the binary system in the direction opposite to the pulsar's motion.</text> <text><location><page_2><loc_52><loc_27><loc_95><loc_29></location>On the other hand, the energy loss time scale of electrons on the IC scattering in the Thomson regime is,</text> <formula><location><page_2><loc_52><loc_25><loc_95><loc_26></location>τ T IC = m e c 2 γ e / (4 cU rad σ T γ 2 e / 3) s , (2)</formula> <text><location><page_2><loc_52><loc_10><loc_95><loc_24></location>where U rad is the energy density of the soft radiation field equal to 0 . 3 eV cm -3 for the Microwave Background Radiation (MBR) and to ∼ 1 . 5 eV cm -3 for the infrared radiation with characteristic energies ∼ 0 . 01 eV, produced in the galactic disk (e.g. see the values calculated in Hui et al. (2011) based on the GALPROP code developed by Strong & Moskalenko 1998), and m e is the rest mass of an electron. For these energy densities we obtain the energy loss time scales of the order of τ T IC ∼ 6 . 3 × 10 19 /γ e s for the MBR and ∼ 1 . 3 × 10 19 /γ e s for the infrared radiation, where γ e is the Lorentz factor of the electrons. In order to cool the electrons e ffi ciently on the IC process during the dynamical time of</text> <text><location><page_3><loc_7><loc_79><loc_50><loc_93></location>the moving pulsar, the emission region should have the diameter of the order of R ≈ 8 . 5 × 10 7 /γ e pc. For example, in the region of 10 pc, electrons with energies larger than ∼ 4 TeV (but below ∼ 100 TeV since the electrons have to interact in the Thomson regime) should be able to produce e ffi ciently γ -rays in the IC process by scattering infrared photons from the galactic disk. Note that, the region of the γ -ray production in the IC process should be clearly shifted from the pulsar position in the direction of the observed tail X-ray emission. This region should be also inhomogeneous with higher energy γ -rays produced closer to the pulsar.</text> <text><location><page_3><loc_7><loc_59><loc_50><loc_79></location>In the above estimates we neglected the energy density of stellar photons, in respect to the MBR and infrared radiation at the region of the acceleration of electrons (the shock in the pulsar wind). In fact, the energy density of stellar photons depends on the distance from the star as U /star ≈ 4 . 5 × 10 -5 / D 2 18 eV cm -3 , where the distance from the star is D = 10 18 D 18 cm. It is assumed that the companion star in the binary system PSR 1957 + 20 has the radius 10 10 cm and most of its surface has temperature close to ∼ 3000 K (Fruchter et al. 1995). For these parameters, the electron energy losses are dominated by scattering of the infrared photons for distances above ∼ 5 × 10 15 cm. Note also that the scattering of the optical photons from the star occurs in the Klein-Nishina regime for electrons with energies above ∼ 100 GeV. Therefore, the e ff ects of scattering stellar radiation by the TeV electrons can be safely neglected.</text> <text><location><page_3><loc_7><loc_30><loc_50><loc_59></location>The region of the γ -ray production can be also a ff ected by the di ff usion of the electrons in the pulsar wind downstream of the pulsar wind shock. We estimate the di ff usion distance of the electrons, as a function of their energy, and compare it with the time scale corresponding to the dynamical motion of the pulsar. For the Bohm di ff usion approximation, the di ff usion distance is R dif = √ 2 D dif t , where D dif = cR L / 3 is the di ff usion coe ffi cient, R L is the Larmor radius of electrons, B is the magnetic field strength in the considered region, and t is the di ff usion time. If B is fixed on 1 µ G, then D dif ≈ 1 . 5 × 10 19 γ e cm 2 s -1 and R dif ≈ 5 . 5 × 10 9 √ γ e t cm. The spread of the emission region due to the di ff usion process is smaller than that one due to the motion of the pulsar, i.e. R dif < R dyn = v pul t , for the following condition t > 6 . 2 × 10 4 γ e s. We compare this condition with the energy loss time scale on the IC process in the Thomson regime (see Eq. 2 and estimates below). It is found that electrons with energies below ∼ 7 TeV lose energy on production of γ -rays when the ballistic motion of the binary system determines the morphology of the γ -ray source. We conclude that depending on the electron energy, the dimension of the γ -ray source is determined either by the motion of the Black Widow binary system through the interstellar medium or by the di ff usion process of the electrons.</text> <section_header_level_1><location><page_3><loc_7><loc_27><loc_35><loc_28></location>3. Relativistic electrons in nebula</section_header_level_1> <text><location><page_3><loc_7><loc_22><loc_50><loc_26></location>We estimate the magnetic field strength around the pulsar, above its light cylinder radius, by extrapolating it from the pulsar surface. The magnetic field strength is then given by,</text> <formula><location><page_3><loc_7><loc_19><loc_50><loc_21></location>B ( R ) ≈ 4 . 4 × 10 -6 σ 1 / 2 B 8 / ( P 2 ms R 18) G , (3)</formula> <text><location><page_3><loc_7><loc_9><loc_50><loc_19></location>where R = 10 18 R 18 cm is the distance from the pulsar, B NS = 10 8 B 8 G is the magnetic field strength on the neutron star surface, P = 10 -3 P ms s is the period of the millisecond pulsar, and σ is the magnetization parameter of the pulsar wind. σ has been estimated in the case of the Crab Nebula on 0.003 (de Jager & Harding 1992) and in the case of the Vela Nebula on ∼ 0.1 (Sefako & de Jager 2003). σ is expected to be in the range</text> <text><location><page_3><loc_52><loc_80><loc_95><loc_93></location>0 . 001 -0 . 01 in the modeling of the Crab Nebula presented by Kennel & Coroniti (1984). The magnetic field given by Eq. 3, is expected to be enhanced at the shock region in the pulsar wind by a factor of ∼ 3. Downstream of the shock, electrons are isotropized and start to radiate e ffi ciently synchrotron radiation. Therefore, the magnetic field in the region downstream of the shock is an important factor which determines the di ff usion of the relativistic electrons and production of the synchrotron radiation. The maximum energies to which the electrons can be accelerated in the pulsar shock region can be estimated from,</text> <formula><location><page_3><loc_52><loc_77><loc_95><loc_79></location>E max = cR sh B ( R sh) ≈ 4 × 10 6 σ 1 / 2 B 8 / P 2 ms GeV . (4)</formula> <text><location><page_3><loc_52><loc_72><loc_95><loc_77></location>Note that this simple formula gives the energies of electrons present in the Crab Nebula comparable to those expected from the modelling of its multi-TeV γ -ray spectrum (e.g. de Jager & Harding 1992).</text> <text><location><page_3><loc_52><loc_65><loc_95><loc_72></location>As noted above, Chandra has detected the tail behind the pulsar B1957 + 20 in the energy range 0.3-8 keV (Huang et al. 2012). If this emission is due to the synchrotron process from the relativistic electrons, then the Lorentz factors of the electrons can be estimated from,</text> <formula><location><page_3><loc_52><loc_63><loc_95><loc_65></location>ε = m e c 2 ( B / B cr) γ 2 e , (5)</formula> <text><location><page_3><loc_52><loc_41><loc_95><loc_62></location>where ε = 8 keV is the energy of synchrotron photons, B and B cr = 4 . 4 × 10 13 G are the magnetic field in the emission region and the critical magnetic field strength. The inspection of the above equations allows us to conclude that the production of the synchrotron photons with ∼ 10 keV energies is possible provided that the Lorentz factors of electrons are at least γ e = 2 . 2 × 10 8 P ms R 1 / 2 18 / ( σ 1 / 4 B 1 / 2 8 ), obtained by substitution of Eq. 3 into Eq. (5). Electrons are accelerated to such energies provided that the magnetic field is strong enough, i.e. the shock in the pulsar wind appears close to the pulsar. For the parameters of PSR B1957 + 20, the distance of the shock has to be below R 18 ≈ 3 . 4 × 10 3 σ 3 / 2 , which equals to R sh ≈ 10 17 -10 20 cm for σ in the range 0 . 001 -0 . 1. This condition is consistent with the observations of the PWNe around classical pulsars. For example, in the case of the Crab Nebula the shock is located at the distance of ∼ 3 × 10 17 cm (Kennel & Coroniti 1984).</text> <text><location><page_3><loc_52><loc_30><loc_95><loc_41></location>It is not clear at present in what process electrons reach such large energies. This might be reconnection of the magnetic field or the shock acceleration mechanism. In the second case, the limit on the maximum energies of the electrons have to be consistent with the limit due to the presence of the synchrotron energy losses already during the acceleration process. The maximum energies of the electrons, due to the saturation by the synchrotron energy losses, can be derived from the comparison of the electron acceleration time scale,</text> <formula><location><page_3><loc_52><loc_27><loc_95><loc_29></location>τ acc ≈ 1 E e / ( χ -1 B ) s , (6)</formula> <text><location><page_3><loc_52><loc_26><loc_81><loc_27></location>with the synchrotron energy loss time scale,</text> <formula><location><page_3><loc_52><loc_23><loc_95><loc_25></location>τ syn = E e / ˙ E syn ≈ 370 / ( B 2 E ) s , (7)</formula> <text><location><page_3><loc_52><loc_17><loc_95><loc_23></location>where ˙ E syn = (4 / 3) cU B σ T E 2 e / m 2 e ≈ 0 . 0027 B 2 E 2 TeV / s, the acceleration e ffi ciency is parametrised by the factor χ = 10 -1 χ -1, and E e is the electron energy in TeV. Energies of the electrons can not be larger than,</text> <formula><location><page_3><loc_52><loc_13><loc_95><loc_16></location>E max syn ≈ 2 × 10 4 ( χ -1 B ) 1 / 2 GeV ≈ 5 × 10 6 P ms R 1 / 2 18 σ 1 / 4 B 1 / 2 8 GeV , (8)</formula> <text><location><page_3><loc_52><loc_10><loc_95><loc_12></location>For the pulsar with the parameters of PSR B1957 + 20, E max is lower than E syn max for the location of the shock at R 18 > 0 . 05 σ 3 / 2 ,</text> <text><location><page_4><loc_7><loc_85><loc_50><loc_93></location>which corresponds to R sh > 1 . 6 × 10 15 cmfor σ = 0 . 1. Therefore, we conclude that for the expected localizations of the shock in the nebula around the pulsar B1957 + 20 (above ∼ 10 15 cm), the synchrotron energy losses can not limit the acceleration process of the electrons below the maximum possible energies given by Eq. 4.</text> <section_header_level_1><location><page_4><loc_7><loc_82><loc_39><loc_83></location>4. Production of high energy radiation</section_header_level_1> <text><location><page_4><loc_7><loc_46><loc_50><loc_81></location>We calculate the γ -ray spectra produced by relativistic electrons in the IC scattering of the MBR and the infrared radiation from the galactic disk. These electrons also produce synchrotron emission which can extend up X-ray energy range. It is commonly expected that electrons accelerated at the pulsar wind shock obtain the power law spectrum. We assume that this spectrum has a lower energy cut-o ff at energies corresponding to the Lorentz factor of the pulsar wind, i.e γ w is equal to a few times 10 6 . In our calculations we fix this value on 3 TeV, in agreement with the modelling of the PWNe (Kennel & Coroniti 1984) and recent calculations of the spectra of the electrons leaving the inner magnetospheres of the millisecond pulsars in the frame of the pair starved polar cap model (e.g. Zajczyk et al. 2010). The electrons take a significant part of the energy lost by the millisecond pulsar, which is of the order of ∼ 10%. The spectrum of the electrons extends up to the maximum energy described in Sect. 3. These electrons are accelerated close to the pulsar wind shock and di ff use to the outer region creating a tail trailing behind the pulsar. In this calculations we take the energy density of the infrared galactic disk emission equal to 1 . 5 eV cm -3 . It is assumed that the magnetic field is enhanced by a factor of 3 in the pulsar wind shock and at larger distances continue to drop according to Eq. 3 up to the minimum value B min. This minimum magnetic field strength can be even below the magnetic field strength in the interstellar space (of the order of ∼ 2-6 µ G), since the volume of the pulsar wind nebula is not penetrated by the interstellar medium.</text> <text><location><page_4><loc_7><loc_17><loc_50><loc_46></location>We assume that electrons are injected at the distance of the shock from the pulsar, R sh. They slowly di ff use outward according to the Bohm di ff usion model in a decreasing magnetic field. During the di ff usion process, the electrons interact with the background radiation producing GeV-TeV γ -rays in the IC process. We apply the Monte Carlo method in order to determine the energy of the γ -ray photons and the distance from the pulsar at which they are produced. For this purpose we modify the numerical code developed for the interaction and di ff usion of electrons (Bednarek & Sitarek 2007). This code allows us not only to calculate the spectrum of γ -rays produced by electrons but also determine their production sites around the pulsar, i.e. allowing us to study the morphology of the γ -ray source. Since the electrons are immersed in a relatively strong magnetic field, especially close to the pulsar wind shock, we also include in the simulations their synchrotron energy losses during the di ff usion process. We calculate the X-ray spectra produced by these electrons in the synchrotron process. In order to obtain reasonable precision of the IC γ -ray spectra, we simulate the propagation of 1 . 5 × 10 4 electrons per decade of the spectrum. The spectra are obtained within di ff erent regions around the pulsar defined by the radius R Neb.</text> <text><location><page_4><loc_7><loc_10><loc_50><loc_17></location>We investigate the dependence of the X-ray and γ -ray spectra on di ff erent parameters which determine the acceleration of the electrons (i.e. the magnetization parameter of the pulsar wind σ , the spectral index of the electrons' spectrum α ', the radius of the pulsar wind shock R sh; and the minimum value of the magnetic field in the nebula B min). As shown in Fig. 2, the TeV γ -ray</text> <text><location><page_4><loc_52><loc_71><loc_95><loc_93></location>spectra produced by the electrons in the IC process only weakly depend on the range of the considered parameters. On the other hand, the synchrotron X-ray emission depends on these parameters much stronger (intensity, shape, energy range). The strong dependence of the synchrotron emission is due to the strong dependence of the magnetic field in the vicinity of the pulsar on the assumed parameters of the model. On the other hand, relatively weak dependence of the IC emission is due to the homogeneity of the background radiation field (MBR and infrared galactic background) which is up-scattered by the relativistic electrons. Weconclude that the TeV γ -ray fluxes expected in this model depend rather weakly on the details of the electron spectrum (in the considered range of parameters). However, their intensity is obviously determined by the energy conversion e ffi ciency from the pulsar to the relativistic particles. In contrast, the spectra of the synchrotron radiation in the X-ray range much stronger depend on the spectrum of the electrons and the propagation model.</text> <text><location><page_4><loc_52><loc_26><loc_95><loc_71></location>We also investigate the γ -ray production in di ff erent volume around the Black Widow binary system B1957 + 20. The IC γ -ray and the synchrotron X-ray spectra are calculated assuming that this emission is produced within the region with the radius equal to 1.5 pc, 2.5 pc, 5 pc, 10 pc, and 15 pc (see Fig. 3). These dimensions correspond roughly to the angular size of the γ -ray source on the sky equal to 2, 3.4, 7, 14, and 20 arc min for the distance of the source equal to 2.5 kpc. The electrons expand into such a region due to their di ff usion in the nebula. Moreover, the TeV γ -ray source is also expected to be shifted from the present location of the Black Widow binary due to its motion and / or limitted in specific directions by the di ff usion of the electrons confined by the presence of the bow shock. In the case of a source with the radius above ∼ 5 pc, the TeV γ -ray source should appear extended for the telescope array such as MAGIC. Our calculations show that most of the TeV γ -ray emission (i.e. within a factor of two) is already produced within a region with the radius of 5 pc. The shapes of the spectra, produced in specific parts of the γ -ray source, are quite similar since the background radiation field (MBR and infrared), scattered by the relativistic electrons, fills this region homogeneously. Moreover the cooling process of the electrons is not very e ffi cient. The electrons do not usually interact frequently but in a specific interaction lose significant amount of their energy when producing TeV γ -rays. Due to the ine ffi cient cooling, the parts of the spectra at low energies (in the GeV range), produced in the Thomson regime, are very similar. On the other hand, the synchrotron X-ray emission does not depend on the considered radius of the source at energies above a few keV. This can be understood since the hard synchrotron radiation is mainly produced close to the pulsar wind shock within the region with the extend of ∼ 2 pc. There is however an important contribution from the outer nebula to the part of the synchrotron spectrum at lower energies (below a few keV) since these electrons can still produce keV photons in the assumed minimum magnetic field.</text> <section_header_level_1><location><page_4><loc_52><loc_22><loc_90><loc_23></location>5. Comparison with observations of B1957+20</section_header_level_1> <text><location><page_4><loc_52><loc_10><loc_95><loc_21></location>Finally, we compare the example calculations performed in terms of this modelling with the available observations of the Black Widow binary system B1957 + 20. The X-ray emission, extending along the direction of the motion of the binary, has been detected by Chandra (Stappers et al. 2003, Huang et al. 2012). The X-ray synchrotron emission expected in our model has to be consistent with this observed spectral features. Recently, the pulsed GeV γ -ray emission has been also reported from B1957 + 20 (Guillemot et al. 2012). The IC γ -ray emission, pro-</text> <figure> <location><page_5><loc_7><loc_50><loc_94><loc_92></location> <caption>Fig. 2. Gamma-ray (IC) and X-ray (synchrotron) spectra (Spectral Energy Distribution - SED) produced in the nebula around the Black Widow binary system containing the millisecond pulsar B1957 + 20 for di ff erent model parameters. The spectra are produced by relativistic electrons which scatter the MBR and the infrared photons from the galactic disk. The maximum energies of the electrons are given by Eq. 4 and the minimum energies are equal to E w = 3 TeV. (a) Dependence of SED on the magnetization parameter σ = 0 . 1 (dashed), 0.01 (dotted), and 0.001 (solid) for the pulsar wind shock radius R sh = 10 16 cm, the power law spectrum of the electrons with spectral index α = 2 . 5 and the minimum magnetic field strength B min = 0 . 5 µ G. (b) Dependence of SED on the radius of the pulsar wind shock R sh = 10 15 cm (dotted), 10 16 cm (solid), and 10 17 cm (dashed), for σ = 0 . 01, α = 2 . 5, and B min = 0 . 5 µ G. (c) Dependence of SED on the spectral index of the electrons α = 2 . 1 (dashed), 2.5 (solid), and 3 (dotted) for R sh = 10 16 cm, σ = 0 . 01 and B min = 0 . 5 µ G. (d) Dependence of SED on the minimum value of the magnetic field B min = 0 . 5 µ G (dotted), 1 µ G (solid), and 2 µ G (dashed) for R sh = 10 16 cm, σ = 0 . 01, and α = 2 . 5. It is assumed that the relativistic electrons take 10% of the rotational energy lost by the pulsar. The 100 hrs di ff erential sensitivity of the MAGIC stereo system (thin dotted, Aleksic et al. 2012) and the 100 hrs CTA sensitivity (Actis et al. 2011) are also marked.</caption> </figure> <text><location><page_5><loc_7><loc_28><loc_50><loc_32></location>ced in the nebula by relativistic electrons, has to be below this pulsed emission. There are not available any positive detections or the upper limits on the TeV γ -ray emission from this source.</text> <text><location><page_5><loc_7><loc_10><loc_50><loc_27></location>We have chosen intermediate parameters of the nebula from the range considered in Sect. 4. The IC and the synchrotron spectra are confronted with the available observations of the binary system containing B1957 + 20 in Fig. 4. We have got good consistency with the level and shape of the X-ray spectrum from the nebula. Note that the X-ray observations put strong constraints on the parameters of the considered model. The emission extending up to ∼ 10 keV requires the presence of electrons with energies at least ∼ 4 . 7 × 10 5 B -1 / 2 µ G GeV(see Eq. 5). On the other hand, the observed X-ray flux constrains the number of the relativistic electrons (which we fix on 10% of the pulsar energy loss rate) and the synchrotron energy loss rate which depends on ∝ B 2 E 2 e . Therefore, it is not so easy to model the observed X-ray spectrum</text> <text><location><page_5><loc_52><loc_10><loc_95><loc_32></location>correctly since the change of the parameters have strong e ff ect on the energies and intensity of the emitted synchrotron radiation (see calculations in Fig. 2). We conclude that observed X-ray extended emission put strong constraints on the parameters of the considered model. Having obtained consistency with the observed synchrotron spectrum, we calculate the IC γ -ray spectrum for the same parameters (see the caption of Fig. 4). These spectra are confronted then with the sensitivities of the Cherenkov telescopes. We show the level of the IC emission expected from the region with the radius of ∼ 5 pc, which is shifted from the present location of the binary system by about the same distance in the direction opposite to the movement of the binary due to the motion of the binary system. Therefore, we conclude that the TeV γ -ray source should be extended for the Cherenkov telescopes. The IC γ -ray spectrum is clearly above the 100 hr sensitivity of the future Cherenkov telescope Array (CTA). It is also on the 100 hr sensitivity limit of the MAGIC Cherenkov telescopes.</text> <figure> <location><page_6><loc_7><loc_71><loc_49><loc_92></location> <caption>Fig. 3. SED of the γ -ray spectrum from the IC process and the synchrotron X-ray emission produced by relativistic electrons in the nebula around the Black Widow binary system B1957 + 20, integrated over a region with the radius: R Neb = 1 . 5 (dot-dotdashed curve) pc, 2.5 pc (dotted), 5 pc (dashed), 10 pc (solid), and 15 pc (dot-dashed). The other parameters of the model are: σ = 0 . 01, the pulsar wind shock radius R sh = 10 16 cm, the power law spectrum of the electrons with the spectral index α = 2 . 1 between E w = 3 TeV and E max (given by Eq. 4), and the minimum magnetic field strength B min = 0 . 5 µ G. The γ -ray spectra are produced by relativistic electrons which scatter the MBR and the infrared photons from the galactic disk.</caption> </figure> <text><location><page_6><loc_7><loc_44><loc_50><loc_52></location>We conclude that even with the present Cherenkov telescopes (MAGIC, VERITAS) the bow shock nebula around the Black Widow millisecond pulsar B1957 + 20 might be detected. Note however that as the source is expected to be extended, the sensitivity of the present Cherenkov telescopes might become worse than the point source sensitivity shown in Figs. 2-4.</text> <section_header_level_1><location><page_6><loc_7><loc_40><loc_19><loc_42></location>6. Conclusion</section_header_level_1> <text><location><page_6><loc_7><loc_10><loc_50><loc_39></location>Assuming that the millisecond pulsars are able to accelerate electrons to relativistic energies in their vicinity, similarly as observed in the case of nebulae around classical pulsars, we calculate the synchrotron and the IC high energy emission from their nebulae. In fact, the existence of an extended synchrotron nebula has been recently confirmed in the Chandra observations in the case of the Black Widow binary system containing millisecond pulsar B1957 + 20. Therefore, as an example, we consider the bow shock nebula around this object. Note that in contrast to the nebulae around classical pulsars, the soft radiation field in the nebula around B1957 + 20 is not dominated by the synchrotron radiation but by the MBR and infrared radiation from the galactic disk. We have investigated the features of the X-ray and γ -ray spectra for likely range of parameters which determine the nebula, assuming that the propagation of electrons is determined by the di ff usion process and / or the dynamical movement of the binary system. We conclude that the observed extended X-ray emission from the bow shock nebula can be explained by the synchrotron radiation of electrons provided that the energy conversion e ffi ciency from the pulsar to the relativistic electrons is of the order of 10%. The TeV γ -ray emission, produced by the same electrons in the IC scattering process, is expected to be detectable by the future CTA instrument. The predicted emission</text> <figure> <location><page_6><loc_52><loc_71><loc_93><loc_92></location> <caption>Fig. 4. The observations of the Black Widow binary containing millisecond pulsar B1957 + 20: the X-ray tail emission detected by Chandra (Huang et al. 2012) and the pulsed, phase averaged γ -ray emission discovered by Fermi (Guillemot et al. 2012) are compared with the calculations of the IC and the synchrotron emission by relativistic electrons in the nebula around this system. The γ -ray spectra are produced by the electrons which scatter both the MBR and the infrared photons from the galactic disk. The electrons have a power law spectrum with the index of -2 . 1 between E w = 3 TeV and E max = 160 TeV, given by Eq. 4 (thick dashed curves). The other parameters of the model are: the magnetization parameter σ = 0 . 01, the location of the shock R sh = 10 16 cm, the minimum magnetic field strength B min = 0 . 5 µ G, the confinement region of the electrons has the radius of R Neb = 5 pc. The 100 hrs di ff erential sensitivity of the MAGIC stereo system is marked by the thin dotted curve (Aleksic et al. 2012) and 100 hrs CTA sensitivity is marked by the thin dot-dashed curve (Actis et al. 2011).</caption> </figure> <text><location><page_6><loc_52><loc_32><loc_95><loc_42></location>is also on the level of the 100 hr sensitivity limit of the MAGIC telescopes. However, since the nebula is expected to be extended, due to rather slow cooling process of electrons, the detectability of the TeV γ -ray emission from the nebula around B1957 + 20 may be di ffi cult. Note also that due to the motion of the binary system the TeV γ -ray nebula should be shifted in respect to the direction towards the binary system by the distance comparable to the extend of the source (see also Cheng et al. 2006).</text> <text><location><page_6><loc_52><loc_10><loc_95><loc_32></location>Other bow shock nebulae around energetic pulsars should also emit synchrotron and IC high energy emission from their surrounding. However their detectability will strongly depend on the distance to the nebula. It can not be too large since the expected flux will be below detectability of the Cherenkov telescopes. But it should not be too close since the TeV γ -ray nebula will have very large dimensions on the sky which again will make problematic its detectability with the Cherenkov telescopes. For example, the bow shock nebula around nearby Geminga pulsar (at the distance 169 pc) may not be detected by the present Cherenkov telescopes. Due to its small distance, the angular size of the TeV nebula expected in terms of discussed above model, should be of the order of a few degrees, i.e more in accordance with the recent report on the presence of the extended ∼ 20 TeV γ -ray source with diameter (2 . 8 ± 0 . 8) 0 , towards the Geminga pulsar by the MILAGRO observatory (Abdo et al. 2009). However, such nebulae might be detected by the</text> <text><location><page_7><loc_7><loc_91><loc_50><loc_93></location>planned CTA which field of view can be as large as 8-9 degrees (Actis et al. 2011).</text> <text><location><page_7><loc_7><loc_85><loc_50><loc_89></location>Acknowledgements. We would like to thank the Editor Steven N. Shore and the Referee for useful comments. This work is supported by the grants from the Polish MNiSzW through the NCN No. 2011 / 01 / B / ST9 / 00411 and UMO2011 / 01 / M / ST9 / 01891.</text> <section_header_level_1><location><page_7><loc_7><loc_82><loc_16><loc_83></location>References</section_header_level_1> <text><location><page_7><loc_7><loc_52><loc_39><loc_81></location>Abdo, A.A. et al. 2009 ApJ 700, L127 Abdo, A.A. et al. 2010 ApJS 187, 460 Actis, M. et al.. 2011 Exp.Astron. 32, 193 Aleksic, J. et al. 2012 APh 35, 435 Arons, J., Tavani, M. 1993 ApJ 403, 249 Arzoumanian, Z. et al. 1994 ApJ 426, L85 Bednarek, W., Sitarek, J. 2007 MNRAS 377, 920 Brink, C. et al. 1990 ApJ 364, L37 Buccheri, R. et al. 1996 A&AS 115, 305 Cheng, K.S., Taam, R.E., Wang, W. 2006 ApJ 641, 427 de Jager, O.C., Harding, A.K. 1992 ApJ 396, 161 Fruchter, A.S. et al. 1988 Nature 333, 237 Fruchter, A.S. et al. 1996 ApJ 443, 21 Guillemot, L. et al. 2012 ApJ 744, 33 Huang, H.H., Becker, W. 2007 A&A 463, L5 Huang, R.H.H. et al. 2012 ApJ, in press (arXiv:1209.5871) Hui, C.Y. et al. 2011 ApJ 726, 100 Kennel, C.F., Coroniti, F.V. 1984 ApJ 283, 694 Kulkarni, S.R., Hester, J.J. 1988 Nature, 335, 801 Reynolds, M.T. et al. 2007 MNRAS 379, 1117 Sefako, R.R., de Jager, O.C. 2003 ApJ 593, 1013 Stappers, B.W. et al. 2003 Science 299, 1372 Strong, A.W., Moskalenko, I.V. 1998 ApJ 509, 212 Takata, J., Cheng, K.S., Taam, R.E. 2012 ApJ 745, 100 van Kerkwijk, M.H. et al. 2011 ApJ 728, 95 van paradijs, J. et al. 1988 Nature 334, 684 Wu, E.M.H. et al. 2012 ApJ, in press (arXiv:1210.7209)</text> <text><location><page_7><loc_7><loc_48><loc_50><loc_52></location>Zajczyk, A. et al. 2010, in Proc. High Time Resolution Astrophysics -The Era of Extremely Large Telescopes Agios Nikolaos (Crete Greece), Procceedings of Science published on line: http: // pos.sissa.it / cgi-bin / reader / conf.cgi?confid = 108, id.52</text> </document>

2013A&A...550A..48V

https://arxiv.org/pdf/1212.3793.pdf

"<document>\n<section_header_level_1><location><page_1><loc_21><loc_85><loc_81><loc_86></location>Mo(...TRUNCATED)

2013A&A...550A.123P

https://arxiv.org/pdf/1301.5240.pdf

"<document>\n<section_header_level_1><location><page_1><loc_8><loc_82><loc_94><loc_87></location>On (...TRUNCATED)

2013A&A...551A..13C

https://arxiv.org/pdf/1302.6074.pdf

"<document>\n<section_header_level_1><location><page_1><loc_8><loc_85><loc_92><loc_87></location>Str(...TRUNCATED)

2013A&A...551A..41R

https://arxiv.org/pdf/1301.0812.pdf

"<document>\n<section_header_level_1><location><page_1><loc_7><loc_82><loc_95><loc_87></location>The(...TRUNCATED)

2013A&A...551A..65S

https://arxiv.org/pdf/1301.3629.pdf

"<document>\n<section_header_level_1><location><page_1><loc_16><loc_85><loc_84><loc_87></location>Bo(...TRUNCATED)

2013A&A...552A.109F

https://arxiv.org/pdf/1303.3136.pdf

"<document>\n<section_header_level_1><location><page_1><loc_7><loc_80><loc_93><loc_87></location>A c(...TRUNCATED)

2013A&A...553A.113J

https://arxiv.org/pdf/1305.2129.pdf

"<document>\n<section_header_level_1><location><page_1><loc_14><loc_85><loc_88><loc_87></location>Es(...TRUNCATED)

2013A&A...553A.124R

https://arxiv.org/pdf/1304.3459.pdf

"<document>\n<section_header_level_1><location><page_1><loc_16><loc_82><loc_86><loc_87></location>Un(...TRUNCATED)