LISA Pathfinder (LPF; Antonucci et al. 2011), a European Space Agency (ESA) mission that operated near the first Sun–Earth Lagrange point (L1) from 2016 January through 2017 July, is in an ideal orbit to make such measurements. However, LPF flew no instrumentation dedicated to micrometeoroid or dust detection. LPF’s primary objective was to demonstrate technologies for a future space-based observatory of millihertz-band gravitational waves. The key achievement of LPF was placing two gold-platinum cubes known as “test masses” into a freefall so pure that it was characterized by accelerations at the femto-g level (e.g., Armano et al. 2016, 2018b), the level required to detect the minute disturbances caused by passing gravitational waves. In order to reach this level of performance, the test masses were released into cavities inside the spacecraft and a control system was employed to keep the spacecraft centered on the test masses. This control system was designed to counteract disturbances on the spacecraft, including those caused by impacts from micrometeoroids. Shortly before LPF’s launch, it was realized that data from the control system, if properly calibrated, could be used to detect and characterize these impacts and infer information about the impacting particles (e.g., Thorpe et al. 2016). While such impact events have been reported by other spacecraft, LPF’s unique instrumentation makes it sensitive to much smaller and much more numerous impacts and allows the impact geometry to be more fully constrained. Early results from the first few months of LPF operations suggested that such events could indeed be identified and were roughly consistent with the pre-launch predictions of their effect on the control system (e.g., Thorpe et al. 2017). In this paper we present results from the first systematic search for micrometeoroid impacts in the LPF data set. Our data set consists of 4348 hr of data in both the nominal LPF configuration and the “Disturbance Reduction System” (DRS) configuration, in which a NASA-supplied controller and thruster system took over control of the spacecraft (Anderson et al. 2018). Our data set corresponds to the times when LPF was operating in a “quiet” mode, without any intentional signal injections or other disturbances. During this period, we have identified 54 impact candidates using our detection pipeline and manual vetoing. We have characterized the properties of this data set and compared it to several theoretical models for the underlying dust population.


Since Colgate & White (1966) proposed that neutrinos play a crucial role in reviving the stalled shock in core-collapse supernovae (CCSNe), numerical models have incorporated neutrino transport in some form, with varying degrees of sophistication. The neutrino transport problem in CCSNe poses one of the most computationally challenging problems to date. The extreme range in densities within the supernova results in optically thick regions in which neutrinos are diffusive, and optically thin regions in which neutrinos are decoupled from the fluid and can stream freely. The so-called gain region behind the stalled shock, which the success of the explosion hinges upon, lies within the semitransparent region between the two regimes, where an accurate treatment of the neutrino distribution function is important (for modern reviews of the topic, see Mezzacappa 2005; Janka 2012; Burrows 2013). The most accurate treatment of neutrino transport calls for the solution of the full Boltzmann equation (Mihalas & Mihalas 1984),
(1)$$\begin{eqnarray*}
\frac{\partial f}{\partial t} + \boldsymbol {u} \cdot \nabla f = \mathcal {C}(f),
\end{eqnarray*}$$(shown here the Newtonian form for clarity) which describes the neutrino momentum distribution f at every point in space (Fig. 1). Evolving through time, this results in a 7D problem. The left-hand side of the equation is the advection equation, which couples together the spatial dimensions. The right-hand side contains the collision integral, which accounts for interactions between neutrinos and matter, and couple together the momentum space dimensions. Interaction rates are sensitive to the neutrino energy, necessitating an energy-dependent treatment. Additionally, there are three flavors of neutrinos (electron, muon, and tauon) and respective antineutrinos for a total of six species. Due to the different interaction rates of each species, their transport behaviour is considerably different, thus the core-collapse problem also calls for a flavour-dependent treatment. In general, even flavour can evolve via neutrino oscillations, a purely quantum mechanical effect (Wolfenstein 1978; Mikheyev & Smirnov 1985).


We have carried out analyses of X-ray and optical photometric data of an MCV Paloma. Using the X-ray data from XMM-Newton, we derive 10 significant periods in Paloma, including two fundamental periods of 156 ± 1 minutes and 130 ± 1 minutes. However, using our optical data, we derive seven significant periods in which

 and

 are consistent with ∼1.5σ level to that derived from X-ray data. The peaks corresponding to the frequencies Ω, ω,

, and

 are well matched with those derived by Schwarz et al. (2007). The orbital modulation in the X-ray light curves is generally explained by the absorption of X-rays emitted near the WD surface by material fixed in the orbital frame, but a strong signal at the orbital period in the X-ray power spectra of Paloma indicates that an explicit orbital modulation is most likely due to the attenuation introduced by the impact site of the accretion stream with the accretion disk or magnetosphere. On the other hand, X-ray modulation at the spin period can arise due to the self-occultation of emission regions by the WD or due to photoelectric absorption and electron scattering in the accretion curtain (Norton et al. 1996). The occurrence of the spin peak indicates that the symmetry of the two pole caps is broken and the amount of asymmetry depends on whether the signal corresponding to the rotation of the asymmetrically placed pole is strong or weak, i.e., the degree of asymmetry is proportional to the power of the spin peak (Wynn & King 1992). Along with the spin frequency, the presence of significant peaks in the X-ray power spectrum at ω − Ω, Ω,

,

,

,

,

,

, and

 also predict that Paloma is an asymmetric system in which both the emission poles are not diametrically opposite and have slightly different emission properties (see Norton et al. 1996). Furthermore, the presence of significant power at spin, beat and

 frequencies suggest that Paloma is a disk-less accreting system (see Wynn & King 1992; Norton et al. 1996). Additionally, an increase in power of the beat or

 components accompanied by the decrease in power at the spin component as the X-ray energy increases is a characteristic of the disk-less accretion. This is clearly visible in the X-ray power density spectra of Paloma, which is further attributed to the absorption of low-energy photons by the accretion column itself. Other than the orbital, spin, and beat periods, photometric observations of Paloma show peaks at frequencies

 and

. Such similar positive and negative sideband frequencies corresponding to the spin and orbital periods are also observed from photometric observations in nearly synchronous IP V697 Sco (Warner & Woudt 2002), suggesting that Paloma may have a close resemblance to V697 Sco.


Top left: the revised, CO(J = 1 → 0)-based Mgas from VLASPECS confirm that z = 2–3 galaxies detected in the ASPECS survey (green circles; tentative detections are marked with a plus sign) closely follow the “star formation law” (i.e., Mgas–SFR relation) at high redshift. CO-detected main-sequence galaxies at similar redshifts from the PHIBBS1/2 surveys (typically based on CO J = 3 → 2, but using a metallicity-dependent conversion factor; Tacconi et al. 2018) and local galaxies from the xCOLD GASS CO(J = 1 → 0) survey (Saintonge et al. 2017) are shown for comparison. Bottom left: same as the top left panel, but plotting the depletion time tdep against Mgas. All samples cover a similar range in tdep, but the average tdep for the (higher Mgas) high-z samples appear lower. Top right: the r31 brightness temperature ratio of VLASPECS galaxies (green circles) is similar to that of strongly lensed z ∼ 3 Lyman-break galaxies (red triangles; Riechers et al. 2010), z > 2 main-sequence galaxies from the PHIBSS survey (gray crosses; Bolatto et al. 2015), and z > 2 dusty star-forming galaxies (DSFGs; blue squares; compilation from Sharon et al. 2016; including data from Danielson et al. 2011; Ivison et al. 2011; Riechers et al. 2011a, 2011b, 2013; Thomson et al. 2012; Fu et al. 2013; Sharon et al. 2013, 2015; other DSFGs shown as light gray squares are from Nayyeri et al. 2017; Dannerbauer et al. 2019; Harrington et al. 2019; Leung et al. 2019; Sharon et al. 2019) and clustered DSFGs (dark gray squares; Bussmann et al. 2015; Gómez-Guijarro et al. 2019), but ∼2 times higher on average than BzK-selected main-sequence galaxies at z ∼ 1.5 (magenta crosses; Daddi et al. 2015). Nearby galaxy samples from the xCOLD GASS survey (Lamperti et al. 2020) and two studies of infrared-luminous galaxies (Yao et al. 2003; Papadopoulos et al. 2012) are shown for comparison. Dashed lines and shaded regions indicate mean/median values and spread for high-z samples with >2 galaxies or clusters, with the same color coding as the symbols. Dashed–dotted lines indicate mean values for the low-z samples. Bottom right: same as the top right panel, but shown as binned histograms in r31 (excluding upper limits) and across the full redshift range, and only including samples for which mean/median values are indicated in the top right panels.


Two additional interesting sources for a comparison are the radio galaxies M 87 (z = 0.0044) and 3C 84 (also called NGC 1275, z = 0.0176). Both sources have a viewing angle similar to NGC 3894: 15°  θ   25° (Mertens et al. 2016) and θ   18° (Giovannini et al. 2018), respectively. The velocities of the jet components are about 0.2c in 3C 84 (Suzuki et al. 2012) and in the inner part of M 87 (Mertens et al. 2016), similar to what we find for NGC 3894. The three sources have a comparable photon index (Γ ∼ 2.1). Although it is less distant and more extended (∼100 kpc), M 87 shows a γ-ray luminosity of 6−7 × 1041 erg s−1, similar to NGC 3894. Different is the case of 3C 84, which has two-sided compact (parsec scale) jets and a distance similar to NGC 3894, but it presents a γ-ray luminosity more than 200 times higher (2 × 1044 erg s−1). Unlike NGC 3894, for which no observations with Cherenkov telescopes have been performed, M 87 and 3C 84 are also detected at very high energy (VHE, E > 100 GeV; Aharonian et al. 2006; Aleksić et al. 2012). In particular, at VHE, M 87 displayed strong variability on timescales as short as one day, but no unique signature of the region responsible for the VHE flares has been identified (Abramowski et al. 2012). Despite the long-term monitoring of M 87 during 2012−2015 in a low-activity state, the production site of γ-rays remains unclear (MAGIC Collaboration 2020). However, the correlation observed between the radio and X-ray activities is a strong indication that most often the emitting region is close to the core in this source. In the case of 3C 84, several works on radio, X-ray, and γ-ray variability suggest that short-term and long-term variability may be produced in different regions of the source. In particular, short-term variability seems related to the injection of fresh particles that are accelerated in a shock in the core region, whereas long-term variability is more likely connected with the jet structure (e.g., Fukazawa et al. 2016; Hodgson et al. 2018). Similarly to M 87 and 3C 84, long-term radio and X-ray monitoring of NGC 3894 may provide important information about the origin of the γ-ray emission.


There are some existing studies applying machine learning to transient studies. For example, the spectral types of the SNe can be classified based on their light-curve data (Möller et al. 2016; Muthukrishna et al. 2019a; Takahashi et al. 2020; Villar et al. 2020), and transients can be identified from the astronomical survey images (Goldstein et al. 2015; Mahabal et al. 2019; Gómez et al. 2020). The light curves of SNe Ia can be well modeled by functional principal component analysis (FPCA; He et al. 2018), where it was shown remarkably that a set of FPCA eigenvectors that are independent of the photometric filters can be derived from the observed light curves of SNe Ia. There are a few studies of the application of deep learning neural networks to the spectral data of SNe. For example, Muthukrishna et al. (2019b) used a convolutional neural network (CNN) for automated SN type classification based on SN spectra. Several other works (Chen et al. 2020; Vogl et al. 2020; Kerzendorf et al. 2021) applied a Gaussian process, principal component analysis (PCA), and deep learning neural networks to radiative transfer models of SNe. Sasdelli et al. (2016) used unsupervised learning algorithms to investigate the subtypes of SNe Ia. Stahl et al. (2020) developed neural networks to predict the photometric properties of SNe Ia (phase and Δm
15) based on spectroscopic data. Saunders et al. (2018) used PCA to find low dimensional representations of the spectral sequences of 140 well-observed SNe Ia. Chen et al. (2020), in particular, built an artificial intelligence assisted inversion (AIAI) of radiative transfer models and used that to link the observed SN spectra with theoretical models. The AIAI is able to retrieve the elemental abundances and density and temperature profiles from observed SN spectra. The AIAI approach has the potential for quantitatively coupling complex theoretical models with the ever-increasing amount of high-quality observational data.


The strength of emission features scales not only with the mass-loss rate but also with the volume-filling factor (fv), terminal velocity, and radius of the star which are compressed into one parameter to reduce the effort when computing model grids. There are two ways to spectroscopically quantify mass-loss rates of hot massive stars using scaling relations. Stars with optically thin winds (OB stars), the wind strength parameter Q is usually applied (Puls et al. 1996; Sabín-Sanjulián et al. 2014, 2017; Holgado et al. 2018), where Q is proportional to the integrated optical depth over the resonance zone:
(1)$$\begin{eqnarray*}
Q=\frac{\dot{M}\, [\mathrm{ M}_{\odot }\mathrm{yr}^{-1}]/\sqrt{f_{\rm v}}}{(R\, [R_{\odot }] \upsilon _{\infty }\, [\mathrm{km\,s^{-1}}])^{3/2}},
\end{eqnarray*}$$and fV has been set to unity (see Section 4.3). For optically thick conditions, there is an additional dependence on $\upsilon _{\infty }$ (e.g. Puls et al. 1996). The transformed radius (Schmutz, Hamann & Wessolowski 1989; Gräfener, Koesterke & Hamann 2002; Hamann & Gräfener 2004) or the equivalent approach of the transformed mass-loss rate ($\dot{M}_{\rm t}$, Bestenlehner et al. 2014) is usually used for optically thick winds (WR stars), where the line equivalent width is preserved:
(2)$$\begin{eqnarray*}
\log (\dot{M}) &=& \log (\dot{M}_{\rm t}) + 0.5\log (f_{\rm v}) + \log \left(\frac{\upsilon _{\infty }}{1000\, \mathrm{km\, s}^{-1}} \right) \nonumber \\
&&+ \,0.75\log \left(\frac{L}{10^6L_{\odot }} \right).
\end{eqnarray*}$$Both scaling relations are equivalent except for the exponent of the $\upsilon _{\infty }$ dependence, $\dot{M} \varpropto\upsilon _{\infty }^{3/2}$ (wind strength Q), and $\dot{M} \varpropto\upsilon _{\infty }$ (transformed mass-loss rate $\dot{M}_{\mathrm{t}}$). In our study, we compared both scaling relations and find that optically thin winds are preferably scaled with the wind strength parameter while optically thick winds are better scaled with the transformed mass-loss rate. If $\upsilon _{\infty }$ in the model has a reasonable value, the differences between both scaling relations are small. However, if the line is in emission and the terminal velocity of the synthetic spectrum is too high, the line centre is fitted well with the Q scaling relation, but the synthetic spectrum shows extended wings. This overestimates the actual mass-loss rate. By fitting Balmer lines in absorption, a degeneracy between log g and $\dot{M}$ can occur using the $\dot{M}_{\mathrm{t}}$ scaling relation. We used the $\dot{M}_{\mathrm{t}}$ scaling relation for R136a1, a2, a3, a5, b, and H36 and Q for the remaining O stars in our sample.


Steady and smooth decline: Since falling from the peak of the 2012b event, SN 2009ip has only continued to fade and is now the faintest it has ever been in the optical. Immediately after the 2012 event (around day 200), it was declining somewhat slower than the rate of 56Co decay for a 56Ni mass of 0.04 $\, {\rm M}_{\odot }$ (shown by the dashed grey line in Fig. 2). During that time, its light curve and spectral properties were consistent with those of late-time SNe IIn, and it had an underlying broad-line spectrum similar to that of SN 1987A (Graham et al. 2014; Smith et al. 2014). Up to about day 1000 it continued to fade smoothly at a slower rate around 0.003 mag d−1, and spectroscopically it continued to resemble late-time interaction in SNe IIn (Fox et al. 2015; Smith et al. 2016b; Graham et al. 2017). Our new HST photometry shows that from about day 1000 to day 3000, SN 2009ip has continued to fade smoothly and steadily in the optical, at an even slower rate. While the HST cadence is obviously sparse at these late times, the filters with more than two observations (F555W and F814W) show no significant deviation from a steady decline; there is no evidence of any rebrightening or irregularity in the fading rate. From 2015 to 2021, the decline rates in the various optical filters are 0.00051 ± 0.00001 mag d−1 in F555W, 0.00068 ± 0.00002 mag d−1 in F606W, 0.00092 ± 0.00001 mag d−1 in F657N, and 0.00050 ± 0.00001 mag d−1 in F814W. (The UV is an exception, as discussed below.) While this decline is much slower than radioactive decay, such slow decline rates are not at all unusual for SNe IIn with late-time CSM interaction. SNe IIn span a wide diversity of late-time decay rates, ranging from some SNe IIn that have essentially flat light curves for many years, like SN 2005ip (Smith et al. 2009, 2017; Stritzinger et al. 2012; Fox et al. 2020), down to those that have only weak CSM interaction and faster decline rates that are difficult to distinguish from radioactive decay or light echoes. Some SNe IIn even rebrighten at late times, like SN 2006jd (Stritzinger et al. 2012). In any case, it seems as if SN 2009ip is levelling off and approaching a constant V absolute magnitude of −7.5 or so. In all three broad continuum filters, the object is now fainter than the progenitor, and the light curve has not exhibited any additional eruptive variability since the 2012b event.


Let us first define some terminology before describing our results. “Outflow” means the flow with a positive radial velocity vr, including both “turbulent outflow” and “real outflow.” In the former case, the test particle will first move outward but will eventually return after moving outward for some distance. In the latter case, the test particle continues to flow outward and eventually escapes the outer boundary of the simulation domain. “Real outflow” consists of two components, i.e., jet and wind. The jet region is defined as the region occupied by the time-averaged magnetic field lines connected to the ergosphere (described by

r

erg

≡

r

g

+

1
−

a

2

cos

2

θ

r

g

;

 Visser 2007) of the black hole. We note that this definition coincides with other notions of the jet based on velocity and magnetization, as seen even in early two-dimensional simulations (McKinney & Gammie 2004). Moreover, turbulence tends not to have a strong effect on these field lines, so that in both individual snapshots and a time-averaged sense, the field lines connecting to the ergosphere coincide with β  2 and σ > 1 (McKinney et al. 2012, see Figures 3 and 6). Thus, the jet region is bounded by the magnetic field line whose foot point is rooted at the black hole ergosphere with θ = 90°, i.e., the boundary between the black hole ergosphere and the accretion flow (refer to the red lines in Figure 5). In this case, all magnetic field lines in the jet region are anchored to the black hole ergosphere and thus can extract the spin energy of the black hole via the Blandford & Znajek mechanism (Blandford & Znajek 1977; hereafter BZ77) to power the jet (“BZ-jet”). Real outflows outside of this boundary are powered by the rotation energy of the accretion flow, and we call them wind. Note that our definition of wind adopted here is different from that adopted in some literature, where they require that the Bernoulli parameter of wind must satisfy Be > 0. We do not add this requirement because we find that for a nonsteady accretion flow, Be is not constant along the trajectories but usually increases outward, at least to the radius within which turbulence is well developed (Yuan et al. 2015). We find that even though Be is negative at a small radius, it can become positive when it propagates outward.


The H i mass fraction of every gas particle in the baryonic runs is calculated based on the particle’s temperature and density and the cosmic UV background radiation flux while including a prescription for self-shielding of H2 and dust shielding in both H i and H2 (Christensen et al. 2012). This allows for the straightforward calculation of the total H i mass of each simulated galaxy. We create mock H i data cubes only for the 42 halos that contain

. Specifically, we create mock data cubes that mimic ALFALFA observations (Haynes et al. 2011). After specifying a viewing angle (see below), our code considers the line-of-sight velocity of each gas particle. The velocity of each particle is tracked in the simulation by solving Newton’s equations of motion, but any turbulent velocity of the gas is not taken into account. Velocity dispersions in dwarf galaxies can be on the order of the rotational velocity, ∼10–15 km s−1 (e.g., Stanimirović et al. 2004; Tamburro et al. 2009; Oh et al. 2015). Dispersions are thought to be driven at least partially by thermal velocities or supernovae (Tamburro et al. 2009; Stilp et al. 2013a, 2013b). In our simulations, supernovae inject thermal energy, and the thermal state of the H i gas needs to be considered in the mock H i linewidth for a realistic comparison to observations. To account for the thermal velocity, the H i mass of each gas particle is assumed to be distributed along the line-of-sight in a Gaussian distribution with a standard deviation given by the thermal velocity dispersion,

, where T is the temperature of the gas particle. After this thermal broadening is calculated, a mock H i data cube can be generated by specifying the spatial and velocity resolution. For all of our galaxies, we adopt a spatial resolution of 54 pixels across 2Rvir. In practice, this corresponds to a range of ∼1 kpc resolution in our lowest-mass galaxies up to ∼9 kpc resolution in our most massive galaxies. However, the spatial resolution plays no role in our study, since measurements of the VF are based on spatially unresolved H i data. For the velocity resolution, we match the ALFALFA specification of 11.2 km s−1 (two-channel boxcar-smoothed).


In this work, we present well-calibrated optical photometric (−0.2 to +413 d), polarimetric (−2 to +31 d) and optical (−5 to +391 d), NIR (−5 to +22 d) spectroscopic studies of SN 2012au, based on data obtained using many observational facilities around the globe. Analysis based on our photometric observations suggests that SN 2012au appears to be one of the most luminous SNe Ib (MB, peak = −18.06 ± 0.12 mag), though fainter than the threshold limit of SLSNe I (M$_\mathrm{ g}\, \lt -$19.8 mag; Quimby et al. 2018). The MR, peak (∼ –18.67 ± 0.11 mag) of SN 2012au is brighter than the average values of SNe Ib and Ic, but closer to those reported for SNe Ic-BL (Drout et al. 2011). Similarly, the peak bolometric luminosity of SN 2012au (∼ [6.56 ± 0.70] × 1042 erg s−1) is higher than the mean peak luminosities of SNe Ib and Ic, but still lower than those of SNe Ic-BL (Lyman et al. 2016). Using the early bolometric light curve of SN 2012au, the estimated values of Mej, Ek, MNi, and T0 are ∼5.1 ± 0.7 M⊙, ∼ (4.8 ± 0.6) × 1051 erg, ∼0.27−0.30 M⊙, and ∼66.0 ± 9.4 d, respectively. These physical parameters of SN 2012au are close to those inferred for SN 2009jf (a bright SN Ib: Sahu et al. 2011) and – on average – larger than for classical SNe Ib/c but smaller than for some SNe Ic-BL. SN 2012au manifests larger Mej and MNi in comparison with most of the SNe IIb, Ib, and Ic, which may be the prime reason behind the luminous peak of SN 2012au, as seen in the case of SLSNe I (Nicholl et al. 2015). On the other hand, light-curve decline rates of SN 2012au (at phases ≥+40 d) in all the optical bands are shallower than typically observed in the case of SNe Ib and slow-decaying SLSNe I, and theoretically predicated for 56Co $\rightarrow \, ^{56}$fe decay. As SN 2012au exhibits comparatively larger Mej, a larger optical depth resulting in a larger diffusion time-scale (for the trapped energy to cross the outer envelope) could broaden the light curve. Therefore, high trapping of gamma-rays at late phases or higher opacity of massive ejecta are among the plausible interpretations for the modest luminosity decline rate of SN 2012au in comparison with other SNe Ib (Clocchiatti & Wheeler 1997). However, smoothly distributed circumstellar media up to a larger radius could be another possibility behind the late-time shallower decay rate for SN 2012au, but an absence of the CSMI in the late-time spectra ruled out this scenario (Milisavljevic et al. 2018). The late-time bolometric light curve of SN 2012au is better constrained by $L~\varpropto\, t^{-2}$, a conventional magnetic dipole equation. Hence for SN 2012au the shallower decay of the late-time light curve might be a potential indicator of a central engine powering source that is accelerating the inner ejecta.


Let ui be the evolved quantity at the coordinate position xi. Then, THC_M1 approximates the derivative of the flux f(u) at the location xi as
(31)$$\begin{eqnarray}
\partial _x f (u) \simeq \frac{F_{i - 1 / 2} - F_{i + 1 / 2}}{\Delta x},
\end{eqnarray}$$where Fi − 1/2 and Fi + 1/2 are numerical fluxes defined at $x_i \mp \frac{\Delta x}{2}$, respectively. The fluxes are constructed as linear combination of a non-diffusive second order flux $F^{\operatorname{HO}}$ and a diffusive first order correction $F^{\operatorname{LO}}$:
(32)$$\begin{eqnarray}
F_{i + 1 / 2} = F_{i + 1 / 2}^{\operatorname{HO}} - A_{i + 1 / 2} \varphi _{i + 1 / 2} \left(F_{i + 1 / 2}^{\operatorname{HO}} - F_{i + 1 / 2}^{\operatorname{LO}}\right) .
\end{eqnarray}$$The term φi + 1/2 is the so-called flux limiter (LeVeque 1992), while Ai + 1/2 is a coefficient introduced to switch off the diffusive correction at high optical depth (more below). The role of the flux limiter is to introduce numerical dissipation in the presence of unresolved features in the solution u and ensure the non-linear stability of the scheme. In particular, if Ai + 1/2φi + 1/2 = 0 the second-order flux is used, while if Ai + 1/2φi + 1/2 = 1, then the low order flux is used. A standard second order non-diffusive flux is used for $F^{\operatorname{HO}}$, while the Lax–Friedrichs flux is used for $F^{\operatorname{LO}}$:
(33)$$\begin{eqnarray}
F^{\operatorname{HO}}_{i + 1 / 2} = \frac{f (u_i) + f (u_{i + 1})}{2},
\end{eqnarray}$$(34)$$\begin{eqnarray}
F^{\operatorname{LO}}_{i + 1 / 2} = \frac{1}{2} [f (u_i) + f (u_{i + 1})] - \frac{c_{i + 1 / 2}}{2} [u_{i + 1} - u_i] .
\end{eqnarray}$$The characteristic speed in the Lax–Friedrichs flux ci is taken to be the maximum value of the speed of light between the right and left cells
(35)$$\begin{eqnarray}
c_{i + 1 / 2} = \max _{a \in \lbrace i, i + 1 \rbrace } \left\lbrace \left| \alpha _a \sqrt{\gamma _a^{x x}} \pm \beta _a^x \right| \right\rbrace .
\end{eqnarray}$$We remark that it is known that the M1 system can, in some circumstances, lead to acausal (faster than light) propagation of neutrinos in GR (Shibata et al. 2011). For this reason, one might argue that a better choice of the characteristic velocity for the Lax–Friedrichs formula would have been given by the eigenvalue of the Jacobian of $\boldsymbol{F}$. These values are known analytically (Shibata et al. 2011), however in our preliminary tests we found that the use of the full eigenvalues resulted did not improve on the stability or accuracy of the M1 solver.


To distinguish the emission from AGNs and star formation we use the fact that star-forming galaxies (SFGs) are known to exhibit radio–IR correlation across a wide range of luminosities and redshifts (see Condon 1992; Appleton et al. 2004; Basu et al. 2015). The correlation between 1.4 GHz luminosity and IR luminosity (monochromatic IR luminosity as well as bolometric IR luminosity between 8.0 and 1000 $\mu$m) in SFGs is attributed to the fact that both radio and IR emission are closely related to star formation (Ivison et al. 2010). AGNs with predominant radio emission from jet deviate from radio–IR correlation by showing radio-excess (Morić et al. 2010; Del Moro et al. 2013). Therefore, we examine if our NLS1s show radio-excess in the radio–IR correlation. We note that radio–IR correlation can be represented as the ratio of IR flux to 1.4 GHz radio flux density i.e. q=log(SIR/$S_{\rm 1.4 \, GHz}$) (see Appleton et al. 2004). For our radio-detected NLS1s we estimate q$_{\rm 22\, {\mu }m}$=log($S_{\rm 22 {\mu }m}$/$S_{\rm 1.4 \, GHz}$), where IR flux at 22 $\mu$m is taken from Wide-field Infrared Survey Explorer (WISE),2 and 1.4 GHz flux density is taken from FIRST whenever available, otherwise from NVSS. WISE is an all sky survey carried out at four MIR photometric bands namely W1 [3.6 $\mu$m], W2 [4.6 $\mu$m], W3 [12 $\mu$m], and W4 [22 $\mu$m], with 5σ sensitivity of 0.08, 0.11, 1.0, and 6.0 mJy, and angular resolution of 6.1, 6.4, 6.5, and 12.0, respectively (Wright et al. 2010). Using the most recent version of WISE source catalogue (AllWISE3 data release) we obtain MIR counterparts for 481, 480, 440, and 354 of our 498 radio-detected NLS1s with SNR ≥ 5.0 in W1, W2, W3, and W4 bands, respectively. The WISE counterparts of our radio-detected NLS1s are searched within a circle of 2.0 arcsec radius centred at SDSS optical positions. q$_{\rm 22 {\mu }m}$ is estimated using k-corrected fluxes, where IR spectral index is derived using W3 and W4 band fluxes, and radio spectral index is derived using 1.4 GHz and 150 MHz flux densities, whenever available, otherwise an average radio spectral index of −0.7 is considered.


Efforts have been made to model the signals caused by different sources of stellar variability within the RV time series (e.g., Tuomi et al. 2013; Rajpaul et al. 2015; Davis et al. 2017; Simola et al. 2019). Several solutions have been successfully proposed in order to deal with stellar oscillations and granulation phenomena, such as: calculating stellar evolution sequences (e.g., Christensen-Dalsgaard et al. 1995); fitting a two-level structure tracking (TST) algorithm based on a two-level representation of granulation (Del Moro 2004); using daytime spectra of the Sun in order to measure the solar oscillations (e.g., Kjeldsen et al. 2008; Lefebvre et al. 2008); and characterizing the statistical properties of magnetic activity cycles focusing on HARPS observations (e.g., Pepe et al. 2011; Dumusque et al. 2011b). However, properly modeling the other sources of stellar activity remains extremely challenging (e.g., Nava et al. 2019). In the present work, we deal with the cross correlation function (CCF) that is derived from the stellar spectrum (e.g., Hatzes 1996; Hatzes & Cochran 2000; Fiorenzano et al. 2005). As it is well known, the CCF barycenter estimates the RV of the star. The asymmetry and the full width at half maximum (FWHM) of the CCF give a strong indication for stellar activity, meaning that variations in RV are caused by active regions rather than by an exoplanet (e.g., Hatzes 1996; Queloz et al. 2001; Boisse et al. 2011; Figueira et al. 2013; Simola et al. 2019). Several solutions have been successfully proposed for mitigating stellar activity perturbations when working with RV measurements, including: decorrelating RV data against activity indicators such as log ${{R'}_{{\rm{HK}}}}$R′HK (e.g., Wilson 1968; Noyes et al. 1984) or Hα (e.g., Robertson et al. 2014); modeling stellar activity by fitting Gaussian processes (GPs, Rasmussen & Williams 2005; Haywood et al. 2014; Rajpaul et al. 2015); or moving averages (e.g., Tuomi et al. 2013) to the RV data. A common statistic employed for identifying changes in the shape of the CCF is the bisector span (e.g., Hatzes 1996; Queloz et al. 2001).


The clearest examples of host–AGN interaction are arguably found in nearby brightest cluster galaxies. The AGN in these systems have been shown to deposit vast amounts of energy into the surrounding intracluster medium via heating and (mega-parsec scale) jets both observationally and by means of modelling (e.g. Binney 2004; Scannapieco, Silk & Bouwens 2005; Gitti, Brighenti & McNamara 2012, for a review; English, Hardcastle & Krause 2016), which maintain the hot-gas reservoirs in these systems, prevent cooling flows, and thus suppress star formation (e.g. Binney & Tabor 1995; Li et al. 2015). In lower density environments (where the majority of galaxies live), the empirical picture is much less clear. Direct observational evidence for AGN feedback on galactic scales in such environments remains sparse. More specifically, while outflows have been observationally detected in a number of instances around AGN in various gas phases, most of these detections have been made in ultra-luminous infrared galaxies or some of the closest quasar–host galaxies (e.g. Rupke, Veilleux & Sanders 2005b; Nyland et al. 2013; Harrison et al. 2014), with only a few examples where the AGN have been shown to couple with kpc-scale outflows that are capable of impacting star-formation on galactic scales (for a review Cicone et al. 2014; Harrison 2017). Thus, it is still unclear to what extent the general AGN population could drive kpc-scale galactic outflows capable of possibly limiting or quenching star-formation in the local Universe. Indeed, recent observational work has cast doubt on the ability of AGN to directly regulate star formation in the nearby Universe. For example, Schawinski et al. (2014) found that black hole accretion occurs preferentially in quenched galaxies that experienced a rapid decay of their star-formation rates. Based on stellar population analysis, such a time delay between the peak of star formation and the onset of AGN activity has been reported to be of at least several dynamical time-scales (e.g. Kaviraj et al. 2015; Shabala et al. 2017, for radio and e.g. Schawinski et al. 2007; Kaviraj 2009; Wild, Heckman & Charlot 2010 for optical). AGN may therefore not play a significant direct role in regulating their associated star formation episodes as they would not couple directly to the cold-gas reservoir (see, e.g. the models of Kaviraj et al. 2011). Using observations for cold-gas outflows, this has been directly confirmed for radio AGN, which are found to couple mainly to residual gas in galaxies where the gas reservoir is already significantly depleted (e.g. Sarzi et al. 2016). A fuller understanding of the role of AGN in regulating star formation demands a direct study of whether outflows of neutral material (which are ultimately responsible for quenching star formation) are more likely launched in AGN hosts. Most importantly, a quantitative statement about the putative role of AGN in influencing the evolution of their host galaxy requires a study that employs a complete sample of such AGN in the local Universe. Performing such an analysis is the purpose of this paper.


There are still several sources of systematics we do not consider in this paper. For instance, whether the use of a different mass distribution models for these lenses could significantly affect the final result. Therefore, we performed a sensitivity analysis and repeated the above calculation using the extend power law (EPL) lens model, in which the luminosity density profile [v(r) ∼ r−δ] is different from the total mass (luminous plus dark matter) density profile ρ(r) ∼ r−α. Such lens model has found widespread astrophysical applications in the literature (Cao et al. 2016a; Xia et al. 2017; Qi et al. 2019), considering the anisotropic distribution of stellar velocity dispersion β (Koopmans 2005; Cao et al. 2017b; Chen et al. 2019). With the EPL lens parameters (α, β, δ) modelled by Gaussian distributions α = 2.00 ± 0.08, δ = 2.40 ± 0.11, and β = 0.18 ± 0.13 (Gerhard et al. 2001; Bolton, Rappaport & Burles 2006; Graur et al. 2014; Schwab, Bolton & Rappaport 2010), the scatter plot of the deviation Tzs in EPL model is shown in Fig. 4. Our results provide the deviation Tzs = 0.974 ± 0.017 [corresponding to c(zs) = 2.922(± 0.051) × 105 km s−1], and the median value Med(Tzs) = 0.983 with the median absolute deviation MAD(Tzs) = 0.259 for the full lens sample. Therefore, our results show that the assumed lens model has a slight impact on the SOL constraint, which highlights the importance of auxiliary data (such as more high quality integral field unit) in improving constraints on the density profile of gravitational lenses. More detailed models of mass distribution, such as Navarro–Frenk–White density profile (suitable for dark matter distribution; Navarro, Frenk & White 1997), Sersic-like profile (suitable for stellar light distribution) (Sérsic 1968), pseudo-isothermal elliptical mass distribution, could also be considered in this context (Kassiola & Kovner 1993). However, strong lensing observables we used are determined by the total mass inside the Einstein radius. Hence, they are not so sensitive to the details of the very central distribution like cusps (besides the extremal cases). Moreover, the Einstein rings of the lenses we used corresponded to less than 10 kpc hence the NFW profile of the dark halo would not likely be manifested.


In this paper, we report on spectroscopic CH3CN, CH3OH (methanol), and dust continuum observations with the Atacama Large Millimeter/submillimeter Array (ALMA) at 349 GHz with an angular resolution of 0′′.1. We exploit the CH3CN (19K–18K) K-ladder, with excitation energies ranging from 168 K (for K = 0) to 881 K (for K = 10), to probe, at different radii, the physical conditions in the accretion disk of an early-type young star. We targeted the star-forming region G023.01−00.41, at a trigonometric distance of 4.59

$^{+0.38}_{-0.33}$

−0.33

+0.38

 kpc from the Sun (Brunthaler et al. 2009), where we recently revealed the accretion disk around a young star of 104.6 L⊙, corresponding to a ZAMS star of 20 M⊙ (Sanna et al. 2019, their Fig. 1); the disk was imaged by means of spectroscopic ALMA observations of both CH3CN and CH3OH lines at 0′′.2 resolution inthe 230 GHz band. The disk extends up to radii of 3000 au from the central star where it warps above the midplane; here, we resolve the outer disk regions in two apparent spirals projected onto the plane of the sky. We showed that molecular gas is falling in and slowly rotating with sub-Keplerian velocities down to radii of 500 au from the central star, where we measured a mass infall rate of 6 × 10−4 M⊙ yr−1 (Sanna et al. 2019, their Fig. 5). The disk and star system drives a radio continuum jet and a molecular outflow aligned along a position angle of 57°, measured east of north (Sanna et al. 2016, their Fig. 2); their projected axis is oriented perpendicular to the disk midplane whose inclination with respect to the line-of-sight was estimated to be less than 30° (namely, the disk is seen approximately edge-on; Sanna et al. 2014, 2019). Previously, we also measured the average gas conditions over the same extent of the whole disk, by means of Submillimeter Array (SMA) observations of the CH3CN (12K–11K) emission, and we estimated a kinetic temperature of 195 K and CH3CN column density of 5.1 × 1016 cm−2 (Sanna et al. 2014, their Fig. 2 and Table 4).


The initialization of solar flares remains an unsolved problem. Early ideas on how the initialization might occur were described by Norman & Smith (1978). They argued that flare process cannot start in the entire flare volume at one instant, and proposed that the flare onset was localized in a small part of an active region, from which the energy release extends as dissipation spreading process throughout the flare volume. Two types of agents that may lead to this kind of a dissipation process were addressed: electron beams and shock waves. These agents can trigger flares at large distances from their initial locations, causing sympathetic (simultaneous) flares or leading to a sequential flare energy release in one active region (Liu et al. 2009; Zuccarello et al. 2009). These triggering processes were numerically studied by Karlický & Jungwirth (1989) and Odstrčil & Karlický (1997). Karlický & Jungwirth (1989) assumed that electron beams, penetrating into the current sheet in the magnetic reconnection region, generate Langmuir waves. Then, using the particle-in-cell model, the authors studied the effects of these electrostatic waves on the plasma system. Sufficiently strong Langmuir waves were found to be able to generate ion-sound waves through the three-wave decay process (Bárta & Karlický 2000). These ion-sound waves increase electrical resistivity in the current sheet system, which results in the onset of the energy dissipation. Thus, the electron beams are able to cause magnetic reconnection. Odstrčil & Karlický (1997) studied the mechanism for the flare trigger by shock waves. They used a 2D magnetohydrodynamic model with the MHD shock wave propagating towards the current sheet. A portion of the shock wave passed through the sheet, and the rest was reflected. Nothing occurred at the very beginning of the wave-current sheet interaction. However, after some time, specific plasma flows around the current sheet were formed, which led to the start of magnetic reconnection. This shows that for reconnection to be triggered, the enhanced electrical resistivity as well as the plasma flows are important.


Given their very large column densities, the most obscured sources can effectively be detected in the X-rays at rest-frame energies

 because their primary continuum is strongly suppressed at softer energies. This can be currently done: (i) locally (

) by targeting bright sources (e.g.,

; Baumgartner et al. 2013) Seyfert-type (

 ) with hard X-ray (

 keV) surveys, such as those performed by Swift/BAT and INTEGRAL (Krivonos et al. 2007; Ajello et al. 2008); and (ii) at high redshifts (

) with the most sensitive Chandra/XMM-Newton observations of the deep/medium survey fields (e.g., Civano et al. 2016; Luo et al. 2017). Through either spectral or hardness ratio analysis, they allow one to quantify and characterize the obscured Compton-thin (

) AGN population and further shed light on the known decreasing trend between the numerical relevance of this population compared to all AGN (absorbed fraction) and the source luminosity (Lawrence & Elvis 1982; Gilli et al. 2007; Burlon et al. 2011; Buchner et al. 2015) and its redshift evolution (La Franca et al. 2005; Ballantyne et al. 2006; Treister & Urry 2006; Aird et al. 2015a; Buchner et al. 2015; Liu et al. 2017). They also allow exploration of the importance of the CT population, although with different constraining power and different non-negligible degrees of bias—especially at the highest column densities and lowest luminosities (e.g., Burlon et al. 2011; Brightman et al. 2014; Buchner et al. 2015; Lanzuisi et al. 2015; Ricci et al. 2015). Indeed, the large diversity in the spectral shapes, as well as poorly explored observational parameters in low counting regimes26

26
I.e., at the highest column densities or at the high/low-energy spectral boundaries where the instruments are less sensitive.
 such as the high energy cut-off and the reflection strength at high energies (Treister et al. 2009; Ballantyne et al. 2011, hereafter BA11), the scattered fractions at low energies (Brightman & Ueda 2012; Lanzuisi et al. 2015), or physical parameters such as the Eddington ratio (Draper & Ballantyne 2010), may further introduce uncertainty or biases, enlarging the possible range of the fraction of CT sources to an order of magnitude (Akylas et al. 2012) or even significantly reducing their importance (Gandhi et al. 2007). Indeed, given the paucity of CT sources effectively contributing to the CXB missing flux, the most recent population-synthesis models have tried to explain the CXB missing component as mainly a pronounced reflection contribution from less obscured sources with a reduced contribution by CT AGN (Treister et al. 2009; Ballantyne et al. 2011; Akylas et al. 2012).


At present, few very wide binaries are known where a planetary system was discovered around one of the stellar components. The star HD 20782 is the binary companion of HD 20781, with a projected separation of ~9000 AU, and it hosts a Jupiter-mass planet on a very eccentric orbit at ~1.4 AU (Jones et al. 2006)2. The very high eccentricity reported in the literature (e = 0.97) could be the result of significant perturbations experienced by the planet during the evolution of the system and might be due to the stellar companion. In this binary system, where both the components can be well analysed separately, a comparative study of the physical properties of the pair could help explain the nature of the planetary system. To investigate any existing link between the planet formation mechanisms and the chemical composition of the host stars, Mack et al. (2014) performed a detailed elemental abundance analysis of the atmospheres of HD 20781/82, by considering that both stars host planets. This kind of study, when at least one component hosts a close-in giant planet, could result in the evidence of chemical imprints left in the parent star suggesting the ingestion of material from the circumstellar disk (and possibly also from planets) driven by the dynamical evolution of the planet orbit. When a star with a close-in giant planet is found to be enriched with elements of high condensation temperature, as suggested by Schuler et al. (2011b), this can be related to the inward migration of the planet from the outer regions of the circumstellar disk, where it formed, to the present position closer to the star (Ida & Lin 2008; Raymond et al. 2011). Mack et al. (2014) found quite significant positive trends for both stars with the condensation temperature among the elemental abundances, and suggested that the host stars accreted rocky bodies with mass between 10 and 20 M⊕ initially formed inside the location of the detected planets. Searches for abundance anomalies possibly caused by the ingestion of planetary material by the central star were also conducted by (Desidera et al. 2004, 2007; and references therein) for a sample of wide binaries. These authors found that the amount of iron accreted by the companion that is nominally richer in metal (in binaries with components having Teff> 5500 K) is comparable to the estimates of the rocky material accreted by the Sun during its main-sequence lifetime, and therefore concluded that the metal enrichment due to the ingestion of material of planetary origin is not a common event.


Measurements of star-planet alignments are essential to improving our understanding of exoplanet formation and evolution, especially for planets that migrated close to their star. Disk-driven migration is expected to conserve the initial alignment between the angular momentums of the protoplanetary disk and of the planetary orbits (e.g., Winn & Fabrycky 2015). A variety of formation and migration pathways can, however, lead to misalignments between the spins of a star and of its planets’ orbits, namely: a primordial tilt of the star or the protoplanetary disk (e.g., Lai et al. 2011; Bate et al. 2010; Fielding et al. 2015); a tidal torque on the protoplanetary disk from a neighboring star (e.g., Lai 2014; Batygin 2012; Zanazzi & Lai 2018); a tidal torque on the inner planetary system from an outer companion (e.g., Huber et al. 2013); and scattering or secular interactions between the inner planets and an outer planetary or stellar companion (e.g., Wu & Murray 2003; Chatterjee et al. 2008; Fabrycky & Tremaine 2007; Teyssandier et al. 2013). In this context, determining the orbital architecture of multi-planet systems is of great relevance as the mutual inclinations between theplanets, and with the star, can help distinguish among various formation and migration scenarios. Early measurements revealed coplanar orbits that are well aligned with the stellar equator in multi-planet systems (e.g. Figueira et al. 2012; Hirano et al. 2012; Sanchis-Ojeda et al. 2012; Albrecht et al. 2013; Chaplin et al. 2013; Van Eylen et al. 2014), standing in contrast to the broad distribution of misalignments observed for hot Jupiters (e.g., Naoz et al. 2012; Albrecht et al. 2012; Davies et al. 2014) and suggesting that their orbital planes still trace a primordial alignment with the protoplanetary disk. Interestingly, spin-orbit measurements in young systems (100 Myr) have shown prograde and aligned orbits (Palle et al. 2020; Zhou et al. 2020; Mann et al. 2020). Other studies have unveiled substantial misalignments in multi-planet systems (Huber et al. 2013; Walkowicz & Basri 2013; Hirano et al. 2014; Hjorth et al. 2021; Zhang et al. 2021), hinting at more complex formation processes (e.g., Spalding & Batygin 2014; Spalding & Millholland 2020) or dynamical histories (e.g. Gratia & Fabrycky 2017).


Each 7-tile observation with Swift-XRT covers ∼ 0.8 deg2, with typical exposures of 1–2 ks per tile. In such exposure times, our detection limit is 6–10 × 10−13 erg cm−2 s−1(corresponding to 90 per cent completeness; see Evans et al. 2014, fig. 14). This is significantly more sensitive than the RASS, which covers 92 per cent of the sky down to 0.1 ct s−1 in the PSPC6 (Voges et al. 1999), which corresponds to 2.8 × 10−12 erg cm−2 s−1 in the 0.3–10 keV band covered by XRT (assuming the canonical AGN spectrum described above). For absorbed sources (i.e. with little flux in the ROSAT bandpass), the increase in sensitivity of Swift-XRT over ROSAT is even greater. The XSS provides hard-band coverage, being sensitive to ∼ 3 × 10−12 erg cm−2 s−1 in the 2–10 keV band (Warwick et al. 2012), however it only covers ∼ 2/3 of the sky. Because of the sensitivity of the XRT compared to these catalogues, and the low spatial coverage of deeper catalogues like 1CSC (Evans et al. 2010),7 3XMMi-DR4 (Watson et al., in preparation) and 1SXPS (Evans et al. 2014), we expect to discover uncatalogued X-ray sources that are serendipitously present in the IceCube error region. We therefore need to be able to identify the true X-ray counterpart to the neutrino trigger from among the unrelated objects detected in the field of view. The first step is to remove any sources which are already known X-ray emitters (and are not in outburst at the time of the Swift observations). We searched the X-ray Master catalogue8 for any catalogued X-ray object with a position agreeing with our XRT position at the 3σ level (including any systematic errors on the catalogued positions). For all observations after 2012 October9 we also searched for matches in the 1SXPS catalogue. The sources with catalogue matches are indicated in Table 2, and details of the matches are given in Table 4. In all cases where a match was found, the XRT flux was consistent with (at the 2σ level) or occasionally slightly lower than the catalogued flux, therefore these sources were all rejected as possible counterparts.


While these large monitoring campaigns are important for establishing the distribution of accretion variability events, their low angular resolution precludes a detailed investigation of how the envelope structure may influence the response to accretion luminosity variations. Modeling of the envelope response predicts that higher-resolution observations may be more sensitive to accretion rate changes, as the change in brightness of the outer envelope is likely to be dominated by heating from the interstellar radiation field (ISRF; Johnstone et al. 2013). The details of the envelope structure, including the likely presence of outflow cavities and dust sublimation fronts, may also impact the observed response (Baek et al. 2020; hereafter, B20). High-resolution monitoring of embedded protostars with millimeter wavelength facilities should thus be able to probe the envelope structure, in addition to identifying variability behavior. In this paper, we thus analyze observations from the Atacama Large Millimeter/submillimeter Array (ALMA) and the Submillimeter Array (SMA) of variable protostars in Serpens Main, monitored by the JCMT Transient Survey. Particular emphasis is placed on EC 53 (V371 Ser), which exhibits ∼18 month periodic accretion bursts, the most recent of which was observed at high cadence with the SMA and JCMT. We interpret the light curves from our monitoring programs using a simple toy model of the propagation of accretion bursts through the envelope, which we also use to further explore how the properties of the envelope and observational setup affect the burst response. The remainder of this paper is organized as follows. In Section 2, we describe our variable protostar targets and the ALMA, SMA, and JCMT observations, while in Section 3, we provide the details of our data reduction and present light curves of our targets. In Section 4, we develop a toy model to interpret the SMA and JCMT observations of EC 53, and this is followed in Section 5 by a further exploration with the toy model of the observation of generic accretion bursts. We then discuss our results and observational/modeling caveats in Section 6, and finish with a brief summary of our major conclusions in Section 7.


Figure 6 shows the merger rate density computed with Eq. (9) for each of the data introduced in Sect. 4.2 and for the two z >  4 ALPINE bins. For the sake of simplicity, in this case we report only the data points obtained by adopting the Kitzbichler & White (2008) prescription for the merger timescale. When using the TMM(z) redshift evolution from Jiang et al. (2014) and Snyder et al. (2017), we obtain similar trends but shifted to higher merger rate densities. The error bar on each point is computed by propagating the merger fraction and number density uncertainties on Eq. (9). At 1 ≲ z ≲ 5, Duncan et al. (2019) found that the volume-averaged merger rate is quite constant. On the other hand, from our data we find a slight decrease both at z   1 and at z >  4. At these early epochs, this difference could be caused by the poor constraints on the GSMFs adopted by Duncan et al. (2019) which result in large uncertainties on their data, making it impossible to draw robust conclusions at z ∼ 5. Nevertheless, our derived merger rate densities are in agreement, within the uncertainties, with other results derived in the literature. For example, Mundy et al. (2017) studied the evolution of the merger rate density up to z ∼ 3.5 for a large sample of log(M*/M⊙)> 10 galaxies. They found that, for close pairs with projected separations 5   rp   20 kpc, the ΓMM(z) evolution is better described by a power-law of the form Γ0(1 + z)γ, with

Γ
0

=
1
.

64

−
0.41

+
0.58

×

10

−
4

$ \Gamma_0 = 1.64^{+0.58}_{-0.41} \times 10^{-4} $

 and

γ
=

0.48

−
1.15

+
1.00

$ \gamma = {0.48}^{+1.00}_{-1.15} $

. We report their results, along with the uncertainties, in Fig. 6 and extrapolate them to the redshifts explored by ALPINE. As evident, our data points are comparable with the results by Mundy et al. (2017). If we also fit our merger rate densities (derived assuming the Kitzbichler & White (2008) merger timescale) with a power-law function we obtain Γ0 = (2.40 ± 0.63) × 10−4 and γ = −0.16 ± 0.23, that are consistent with the above outcomes. The power-law fit on the data computed with the timescales by Jiang et al. (2014) is in agreement with the Mundy et al. (2017) findings, as well. If we instead consider the results obtained with the Snyder et al. (2017) timescale, we find a rapid increase of the merger rate density with redshift, which departs from the upper envelope of Mundy et al. (2017) already at z ≳ 1.


During this first gravity assist manoeuvre of Venus, the Solar Orbiter RPW instrument also detected dust impacts inside the planet’s induced magnetosphere (Fig. 10). In the absence of dedicated dust detectors, the electric antenna measurements provide the only opportunity to monitor dust particles in the space plasma environment. This method has been widely applied since the 1980s allowing to estimate the mass and size distribution of the impacting dust particles from the observed characteristics of the electric field signal (Gurnett et al. 1997; Meyer-Vernet 2001; Ye et al. 2014, 2018). One of the main mechanisms believed to convert the particle’s kinetic energy of the dust into an electrical signal is the impact ionization process which generates clouds of electrons and ions around the spacecraft body (Gurnett et al. 1983; Aubier et al. 1983; Meyer-Vernet 1985). Because of the very large relative velocity between the spacecraft and the particles, when a dust particle hits the spacecraft, it instantly vaporizes, forming a hot ionized gas with free electrons and positive or negative ions that expand away from the impact site (Drapatz & Michel 1974). These charged particles are hence attracted to, or repulsed from, the spacecraft surface depending on its electric potential relative to the surrounding ambient plasma. This induces an abrupt changes in the spacecraft potential which is then observed in the voltage data (e.g., escaping electrons generate a positive spacecraft signal). Recently, Mann et al. (2019) reviewed our current knowledge on dust antenna measurements, modeling works, and their prospect to inner heliospheric missions. Since TDS is designed to capture waveforms snapshots, it is well adapted to resolve voltage spikes associated with dust impacts. Thereby, Zaslavsky et al. (2021) provided a first analysis of dust measurements recorded by TDS, along Solar Orbiter’s orbit, with promising results on the impact rate and dust grains radial velocities.


The Orion Bar is probably the best studied PDR in our Galaxy. It is located between the Orion Molecular Cloud 1 and the H ii region excited by the Trapezium cluster, and is exposed to an FUV field a few 104 times the mean interstellar radiation field. Owing to its proximity (417 pc, Menten et al. 2007) and nearly edge-on orientation, the Bar provides an ideal laboratory for testing PDR models (e.g., Jansen et al. 1995; Gorti & Hollenbach 2002; Andree-Labsch et al. 2017) and a primary target for observational studies of physical and chemical structures of PDRs (e.g., Tielens et al. 1993; Walmsley et al. 2000; van der Wiel et al. 2009; Arab et al. 2012; Peng et al. 2012; Goicoechea et al. 2016; Nagy et al. 2017). Observations of various molecular spectral lines have shown that the emissions could be better interpreted with an inhomogeneous density structure containing an extended and relatively low density (

 cm−3) medium and a compact and high-density (

 cm−3) component (e.g., Hogerheijde et al. 1995; Young Owl et al. 2000; Leurini et al. 2006, 2010; Goicoechea et al. 2016). However, due to the scarcity of high-resolution observations capable of spatially resolving the density structure, the nature of the high-density clumps or condensations is still not well understood. Lis & Schilke (2003) mapped the Bar in H13CN (1–0) with the Plateau de Bure Interferometer (PdBI) at an angular resolution of about 5″, and detected 10 dense clumps. They proposed that the H13CN clumps are in virial equilibrium and may be collapsing to form stars. Goicoechea et al. (2016) performed Atacama Large Millimeter/submillimeter Array HCO+ (4–3) observations of the Bar and detected over-dense substructures close to the cloud edge, and found that the substructures have masses much lower than the mass needed to make them gravitationally unstable. These two interferometric observations both target molecular spectral lines. A high-resolution map of the dust continuum emission of the Bar, which is highly desirable in constraining the mass and density of the dense condensations, is still lacking. Here we report our Submillimeter Array (SMA) observations of the dust continuum and molecular spectral line observations of the Bar.


The majority of GPS pulsars are characterized by high dispersion measure (DM > 200 pc cm−3), which may very well be a coincidence of the specialized environments that harbour them. The conventional flux measurement techniques which rely on estimating the baseline level of the pulse profile may be affected by interstellar scattering which results in smearing of the pulse across the entire period. In some cases, when the pulse broadening time is a significant fraction of the pulse period (30 per cent or more) one can see a relatively sharp pulse, but at the same time the extended scattering tail may obscure the real baseline level, which leads to an underestimation of the pulsar flux. For pulsars with DMs in 200–300 pc cm−3 range this usually happens between 300 and 600 MHz (Lewandowski et al. 2013, 2015a). This leads to a somewhat pseudo-correlation between high DM and GPS pulsars (Kijak et al. 2007, 2011b) where serious underestimation of the flux at lower frequencies for high DM pulsars may give rise to an inverted spectra. The interferometric imaging technique provide a more robust measurement of the pulsar flux owing to the baseline lying at zero level thereby reducing errors made during the baseline subtraction. Dembska et al. (2015b), D15 hereafter, used the imaging technique to measure the flux of six high DM pulsars at 610 MHz to explore their suspected GPS nature. Their studies revealed that in four of the six cases the measured flux was underestimated due to scattering effects and the corrected flux followed a normal power-law spectra. In pulsar B1823−13 they confirmed the presence of GPS characteristics. However, the case of PSR B1800−21 defied expectations as the interferometric flux measurements turned out to be significantly lower than the earlier measurements using conventional methods. This gave rise to various questions regarding the spectral nature of this pulsar. There was also a possibility of the two measurement techniques being incompatible and errors during the measurement processes.


The HH 212 region in Orion (at 450 pc) can be considered an ideal laboratory to investigate the interplay of infall, outflow, and rotation in the earliest evolutionary phases of the star forming process. HH 212 is a low-mass Class 0 source driving a symmetric and bipolar jet extensively observed in typical molecular tracers such as H2, SiO, and CO (e.g. Zinnecker et al. 1998). High-spatial resolution observations (down to \hbox{${\simeq}0\farcs3{-}0\farcs4$}≃ 0 .̋ 3−0 .̋ 4) performed with the SubMillimeter Array (SMA; Lee et al. 2006, 2007a, 2008), the IRAM Plateau de Bure (PdB) interferometer (Codella et al. 2007; Cabrit et al. 2007, 2012), and the Atacama Large Millimeter Array (ALMA; see Lee et al. 2014; Codella et al. 2014a) reveal the inner ± 1″−2″ = 450−900 AU collimated jet (width ≃100 AU) close to the protostar. HH 212 is also associated with a flattened rotating envelope in the equator perpendicular to the jet axis observed firstly with the NRAO Very Large Array (VLA) in NH3 emission by Wiseman et al. (2001) on 6000 AU scales. More recent SMA and ALMA observations in the CO isotopologues and HCO+ on ~2000, 800 AU scales indicates that the flattened envelope is rotating and infalling onto the central source, and can therefore be identified as a pseudo-disk according to magnetised core collapse models (Lee et al. 2006, 2014). In addition, a compact (≤120 AU), optically thick dust peak is observed by Codella et al. (2007), Lee et al. (2006, 2014) and attributed to an edge-on disk rather than the inner envelope. This seems to be confirmed by HCO+ and C17O emission showing signatures of a compact disk of radius ~90 AU Keplerian rotating around a source of ≃0.2−0.3 M⊙ (Lee et al. 2014; Codella et al. 2014a). Keplerian rotating disks had previously only been observed towards other three Class 0 objects: IRAS 4A2 (Choi et al. 2010), L1527 (Tobin et al. 2012; Sakai et al. 2014), and VLA1623A (Murillo et al. 2013), but HH 212 can be considered as the only object clearly revealing both a disk and a fast collimated jet, calling for further observations aimed to characterise its inner regions.


Figure 3 shows rough upper limits of the 56Ni yields from NDAFs with outflows (blue shaded region) and CCSNe (the red and green shaded regions shows the conditions of [Mg/Fe] = 0 and [O/Fe] = 0 and explosion energies in the range of 1–100 or 150 B) as functions of the progenitor-star mass. The black lines denote the medians of these regions. The CCSN data are adopted from Umeda & Nomoto (2008), because it is believed that the abundances of the most metal-poor halo stars satisfy the conditions [Mg/Fe] ≥ 0 and [O/Fe] ≥ 0, according to observations. That means for [Mg/Fe]  0 or [O/Fe]  0, the 56Ni yields should be less than those shown in Figure 3 (Umeda & Nomoto 2008). It should be mentioned that the shaded regions in Figure 3 just reflect the rough upper limits of the 56Ni yields; or rather, the ability of CCSNe and NDAFs to synthesize 56Ni, because we set the terms for the fall-free approximation of the density profile, p ≥ 0.3, for the NDAF outflows, and [Mg/Fe] = 0 and [O/Fe] = 0 for the CCSNe. More importantly, contrary to energetic CCSNe requiring a high explosion energy, the BH-mass growth (i.e., fallback accretion) favors the condition of a low explosion energy. In other words, there is energy and matter competition between CCSN explosions and BH fallback accretion. Hence, Figure 3 indicates that the upper limits of the total 56Ni yields should depend weakly upon the explosion energy. Hypernova models can increase 56Ni yields by ten times or more relative to normal CCSNe (e.g., Nomoto et al. 2004), and have been included to investigate the galactic evolution of SN rates (e.g., De Donder & Vanbeveren 2003). In such energetic explosions, fallback accretion is generally inefficient. As well as the hypernova models (e.g., Kobayashi et al. 2020), we consider that nucleosynthesis in the NDAF outflows in the centers of faint or failed CCSNe is another plausible way to explain observations of the metal abundance in our neighborhood and the chemical evolution of galaxies. Moreover, Kobayashi et al. (2020) estimated that the proportion of failed SNe was perhaps as large as 50% early in the history of the Galaxy, which might support the consequence of the NDAF outflows on nucleosynthesis.


In the present study, the Parker (1965) cosmic-ray TPE is solved stochastically, modifying the model presented by Engelbrecht & Burger (2015b). This equation, neglecting possible sources of CRs such as the Jovian magnetosphere, is given by
1

where p and r denote particle momentum and position,

 is the omnidirectional cosmic-ray distribution function, such that the cosmic-ray differential intensity is

 (see, e.g., Moraal 2013), and

 and K denote, respectively, the solar wind velocity and heliospheric diffusion tensor. Various processes modulating an initial, boundary CR differential intensity jB are described by this TPE, including CR drift due to gradients and curvatures of the heliospheric magnetic field and along the heliospheric current sheet, diffusion (both described by the first term on the right-hand side of Equation (1)), the outward convection of cosmic rays by the solar wind (second term on the right-hand side of Equation (1)), and adiabatic cooling (third term on the right-hand side of Equation (1)). Equation (1) can be written in terms of a set of equivalent Itō SDEs (see, e.g., Strauss & Effenberger 2017, and references therein) given by
2

with subscripts

 referring to heliocentric spherical polar coordinates

 and CR kinetic energy E, xi(t) are Itō processes (see, e.g., Gardiner 2004), and dWi satisfy a Weiner process, such that (Strauss & Effenberger 2017)
3

where η (t) represents a pseudo-random, Gaussian distributed number between zero and one. Pseudo-random numbers are here generated using the Mersenne Twister algorithm developed by Matsumoto & Nishimura (1998). Equation (2) is solved in the time-backward manner using the Euler–Maruyama approximation (Maruyama 1955). Therefore, the evolution of a sufficiently large number of pseudo-particles N at a particular energy/rigidity, and at a pre-specified point in phase-space and time

 (e.g., at Earth), are followed to their exit positions, times, and energies at a pre-specified boundary

. Then the CR intensity at the initial point can be calculated using (Strauss & Effenberger 2017)
4

using the assumed boundary CR intensity. Note that N = 10,000 is used throughout this study. The tensor B and vector A are related to the CR transport coefficients, and are given by, e.g., Pei et al. (2010) and Engelbrecht & Burger (2015b), such that, for a fully 3D HMF,
5

where κ denotes one of the elements of the diffusion tensor K in Equation (1) in heliocentric spherical coordinates. The present study employs the diffusion tensor transformation proposed by Burger et al. (2008) to convert the diffusion tensor in HMF-aligned coordinates K′, given by
6

where parallel and perpendicular subscripts denote diffusion coefficients parallel and perpendicular to the assumed HMF, and κA the drift coefficient (see, e.g., Forman et al. 1974), to a diffusion tensor in spherical coordinates. Note that elements of the above tensor are related to the mean free paths (MFPs) discussed below by κ = vλ/3, with v the particle speed. The vector A is given by (Engelbrecht & Burger 2015b)
7

with Eo the CR rest-mass energy. Note that the signs of AE, as well as of the solar wind and drift speeds Vsw and Vd, are chosen so as to render explicitly the time-backward nature of the approach taken to solving Equation (2), and thus Equation (1), in this study.


To calculate the dissipation we must study the properties of the wave launching region near the radiative/convective interface in these stars. In stars with convective cores, we focus on the interface of the convective envelope rather than the core, since this is found to give the maximum dissipation in the mass range we consider. In the vicinity of a radiative/convective interface at r = rc in a stellar model, we fit the buoyancy frequency profile with the linear fit3(40)$$\begin{eqnarray}
N^2(r) = \left(\frac{r}{r_c}-1\right) \left.\frac{\mathrm{d}N^2}{\mathrm{d}\ln r}\right|_{r=r_c}.
\end{eqnarray}$$The dynamical tide in the vicinity of r ∼ rc can then be shown to satisfy Airy’s differential equation (Goodman & Dickson 1998), and the energy flux in gravity waves can be calculated. We will omit the details of this calculation, since they have been reported elsewhere (e.g. Goodman & Dickson 1998; Barker 2011), and just quote the resulting tidal quality factor due to gravity waves, which is determined from
(41)$$\begin{eqnarray}
\frac{1}{Q^{\prime }_{\mathrm{IGW}}} = \frac{2\left[\Gamma \left(\frac{1}{3}\right)\right]^2}{3^{\frac{1}{3}}(2l+1) (l(l+1))^{\frac{4}{3}}}\frac{R}{GM^2} \mathcal {G} |\omega |^{\frac{8}{3}}.
\end{eqnarray}$$The quantities that depend on the radiative/convective interface region in a particular stellar model are encapsulated in the quantity
(42)$$\begin{eqnarray}
\mathcal {G} = \sigma _c^2 \rho _c r_c^5 \left|\frac{\mathrm{d}N^2}{\mathrm{d}\ln r}\right|_{r=r_c}^{-\frac{1}{3}},
\end{eqnarray}$$which takes the value $\mathcal {G}_\odot \approx 2\times 10^{47}\,\mathrm{kg}\,\mathrm{m}^2\,\mathrm{s}^{2/3}$ for the current Sun (in which σc = −1.18). In this expression, ρc = ρ(rc), and the parameter
(43)$$\begin{eqnarray}
\sigma _c=\frac{\omega _{\mathrm{ dyn}}^2}{A}\left.\frac{\partial \xi _{d,r}}{\partial r}\right|_{r=r_c},
\end{eqnarray}$$where the derivative of the dynamical tide radial displacement ξd, r is determined by integrating the linear differential equation given in equation (3) in Goodman & Dickson (1998). Note that σc (and $Q^{\prime }_\mathrm{IGW}$, for that matter) is defined such that it depends on the properties of the star but not on A.


The selected YSOs (Class I and Class II ) are mostly concentrated in the whole ring around H ii region Sh2-104. The high density of the YSOs located in the ring show that these YSOs are physically associated with Sh2-104. The dynamical age of Sh2-104 can be used to decide whether these YSOs are triggered by the H ii region. Using a simple model described by Dyson & Williams (1980) and assuming a H ii region expanding in a homogeneous medium, we estimate the dynamical age of the H ii region as
12

where

 is the radius of the Strömgren sphere given by

 =

, where

 is the ionizing luminosity,

 is the initial number density of the ambient medium around the H ii region, and

 cm3 s−1 is the hydrogen recombination coefficient to all levels above the ground level. For the ionized medium we adopt a sound velocity of

 km s−1. Moreover, we adopt the radius (37) of the ring as that of H ii region Sh2-104, which is obtained from Figure 11. Taking the distance of ∼4 kpc to Sh2-104 (Deharveng et al. 2003), the H ii region radius is 4.4 pc. As a rough estimate,

 can be determined by distributing the total molecular mass over a sphere (e.g., Zavagno et al. 2007; Cichowolski et al. 2009; Paron et al. 2009; Anderson et al. 2015; Duronea et al. 2015). The mass of the ring is

. Using this mass, we only consider the number of atoms that can be ionized, so this would imply that

 cm−3. H ii region Sh2-104 is excited by an O6V center star (Crampton et al. 1978; Lahulla 1985). For an O6V star, the ionizing luminosity (

) is

 s−1 (Martins et al. 2005). Inoue (2001) suggested that only half of the Lyman continuum photons from the central source in a Galactic H ii region ionize neutral hydrogen; the remainder are absorbed by dust grains within the ionized region. Finally, we obtain the ionizing luminosity of

 s−1. Hence, we derived a dynamical age of

 yr for the H ii region Sh2-104. Additionally, from the

 color–magnitude diagram for the selected YSOs, we derive that the majority of the YSOs have masses in the range 1.8–6.0

, and an age range of 0.15–1.0 Myr. Comparing the dynamical age of H ii region Sh2-104 with that of the YSOs shown on the ring, we conclude that these YSOs are likely to be triggered by H ii region Sh2-104. This also means that the CC or RDI processes induce the formation of these YSOs. Deharveng et al. (2003) suggested that H ii region Sh2-104 is a typical candidate for triggering star formation by the CC process.


The dominant paradigms for jet production are outlined in the works of Blandford & Znajek (1977; BZ model) and Blandford & Payne (1982; BP model). In both of the models, the large-scale ordered magnetic fields threading the accretion flow or spinning black hole are required. It is suggested that the large-scale magnetic fields may diffuse outward rapidly if the half-thickness of the accretion disk H is significantly less than the radius r (Lubow et al. 1994; Heyvaerts et al. 1996; Guan & Gammie 2009). Then, the jet discussed in our paper should be produced in a geometrically thick disk (Maccarone et al. 2003; Sikora et al. 2007; Coriat et al. 2011; Russell et al. 2011), such as the ADAF or the slim disk (Abramowicz et al. 1988). Our work focuses on the jet produced in the ADAF, for which the accretion rate is relatively low. The jet power (

) in the BP and BZ models is associated with the strength of the large-scale ordered poloidal magnetic field

. In the BP model, the jet power can be described as (e.g., Livio et al. 1999; Cao 2002; Li & Cao 2012)
3

where

 is the angular velocity of the disk,

 is the torque applied on the disk, and

 is introduced to describe the contribution of different radius to the jet power. In the BP model, the energy of the jet is mainly from the inner region of the disk. Then, μ should be larger than or equal to 0, i.e.,
4

The strength of the large-scale poloidal magnetic field remains uncertain, but is believed to be associated with the accreting process (e.g., Moderski & Sikora 1996; Ghosh & Abramowicz 1997; Livio et al. 1999; Meier 2001; Nemmen et al. 2007). In addition, the strength of the small-scale magnetic field (

) in the magnetohydrodynamic turbulence of the disk is usually used to estimate the strength of

, i.e.,

 in the ADAF (Livio et al. 1999; Meier 2001; Wu & Cao 2008). In the accretion flow,

 may be radius dependent. In order to model this behavior, we adopt (Livio et al. 1999; Meier 2001; Wu & Cao 2008; Li & Cao 2012)
5

where

 is the stress in the magnetohydrodynamic accretion flow. If the parameter s in Equation (5) is larger than 0,

 in the outer region will suppress the magnetorotational instability (Velikhov 1959; Chandrasekhar 1960; Balbus & Hawley 1991, 1998), which is responsible for the angular momentum transport. Then, s should be larger than or equal to 0, i.e.,
6

Based on the above discussion, Equation (3) becomes
7

where

 and

 are taken and ζ is a constant. In the BZ model, the variability of jet power, which is induced by the fluctuations of the magnetic field in the vicinity of black hole, does not present a significant difference to Equation (7). Then, we use Equation (7) to describe the jet power. This equation reveals that the power of the jet depends linearly on the accretion rate in the ADAF, which has been used in a number of works (e.g., Meier 2001; Nemmen et al. 2007; Martínez-Sansigre & Rawlings 2011). Equation (7) is similar to Equation (1) but with

 and

. It was discussed previously that the variabilities based on Equation (2) (or Equation (7)) with varying γ (

) do not show significant difference. Then, the variability of jet power based on Equation (7) would follow that of the accretion rate or LX except for the amplitude of the variability, which has been found in the observation of GX 339–4 (Casella et al. 2010). This fact implies that Equation (7) is applicable to describing the jet power. In our work, we take

 (please see the discussion in Section 3.2). In this situation, we take

, which corresponds to the case in which 10% of the gravitational energy released in the accretion process enters the jet.


We carried out a detailed 2D modeling of the galaxy using GALFIT (Peng et al. 2002). In that, we model the central bright component using a Sérsic profile (Sersic 1968) while the extended faint stellar envelope was modeled with an exponential profile. The best-fit models and residuals are displayed in Figure 6. The details of our GALFIT modeling is presented in Appendix C Based on the two-component modeling of the SDSS i-band image of the galaxy, we arrive at an insight revealing the nature of the galaxy’s light distribution. The best-fit model of the extended host galaxy reveals a faint, lopsided, LSB exponential profile that is presumably due to an old stellar host. The presence of an exponential profile as found in many BCDs (e.g., Papaderos et al. 2002; Lian et al. 2015), as well as in SHOC 579, is not convincing enough for a thin stellar disk; possibilities of a triaxial stellar system cannot be ignored. The central surface brightness of the disk is μ
0 = 22 mag arcsec−2 (e.g., Brown et al. 2001; Schombert et al. 2001; Adami et al. 2006; Pahwa & Saha 2018) with a scale length of R

d
 = 1.54 kpc. Note that the disk is relatively smaller in size and the scale length is similar to that of dwarf LSB galaxies (Schombert et al. 1995; Papaderos et al. 1996b; Schombert et al. 2001; Gil de Paz & Madore 2005). The Sérsic profile for the inner component has a Sérsic index of n = 1.48 and an effective radius of 217 pc. Because our GALFIT modeling is performed using the SDSS i-band image, it hence does not contain strong nebular emission lines (e.g., Hα line) for the given redshift of the galaxy. Nevertheless, the contributions from the nebular continuum cannot be ruled out. In fact, the contribution from the nebular continuum has especially been found to be significant in the SDSS i-band image (e.g., Izotov et al. 2011). Therefore, an exponential light distribution indicating a stellar-disk-like structure around the blueberry source may be a generic property of an extended nebular halo, similar to that seen in several luminous BCDs (e.g., Papaderos et al. 2002).


In Figure 4, the peak values of LZ for the subsamples in different cuts of

, obtained from Sample B, are larger (∼2000 kpc km s−1) than those expected for a distribution dominated by TD stars (∼1600 kpc kms−1, assuming the Sun’s position at R = 8.5 kpc). Sample B is selected in a range of metallicity and α-elements abundance (−0.9  [Fe/H]  − 0.6 and +0.1  [α/Fe]  +0.2) that excludes the majority of thin-disk stars (see, for example, Figure 4 in Hayden et al. (2015) and Figure 2 in Cheng et al. (2012)). In this range of abundances, however, the outer thin-disk stars have been identified, −0.7  [Fe/H]  −0.2, and 0.0  [α/Fe]  +0.2 (Lee et al. 2011b; Bovy et al. 2012b). The total number of stars in Sample B is 415, while the number of likely outer thin-disk stars, selected according to the above criteria, is 77. This means that Sample B has a contamination from “likely” outer thin-disk stars on the order of ∼18%. This would explain the large values of LZ obtained for the TD. To investigate further, we explored the trend of the mean rotational velocity,

, for Sample B (−0.9  [Fe/H]  −0.6; +0.1  [α/Fe]  +0.2) as a function of metallicity. It is known that thin-disk stars show a negative rotational velocity gradient (

) as the metallicity increases, while TD stars exhibit a positive or zero velocity gradient (Lee et al. 2011b). Figure 7 shows the mean Galactocentric rotational velocity, as a function of the metallicity, for Sample B, in two different intervals of vertical distance,

 (black), and

 (red). Visual inspection of this figure reveals that the mean rotational velocity has a zero or slightly positive gradient as the metallicity increases. Therefore, it is unlikely that Sample B has significant contamination from outer thin-disk stars. We conclude that in the range of abundances where Sample B is selected, the majority of the stars belong to the TD, while other works claim that in such an interval of metallicity and α-abundance, the outer thin-disk stars are still present (Lee et al. 2011b; Bovy et al. 2012b). It remains unclear the reason why these TD stars possess such large rotational velocities, requiring further investigation.


In the previous section, we found no clusters and set the upper limit on the number of observed clusters. In this section, we consider that the clusters are originated from supernovae, and evaluate the detectable range. We use the number of neutrinos emitted from core-collapse supernovae (ccSNe) and failed ccSNe, which result in black hole formations, derived from the Nakazato model (Nakazato et al. 2013). This model provides 20 s supernova neutrino data and is parameterized by an initial mass M
init, metallicity Z, and shock revival time t
revive. The electron antineutrino flux arriving at Earth,

Fe¯Earth(r)

, is written as (Dighe & Smirnov 2000)
1

Fe¯Earth(r,E,t)=14πr2p¯d2Ne¯0dEdt+1−p¯d2Nx0dEdt,

where r is the distance from the Earth to a supernova,

d2Ne¯0/dEdt

 is the number of emitted electron antineutrinos per MeV per second, d
2
N

x0/dEdt is that of the antineutrinos

νμ¯

,

ντ¯

 and

p¯

 is the survival probability, which is 0.665 (normal mass ordering) or 0.0216 (inverted mass ordering) with

sin2θ12=0.320

 and

sin2θ13=0.0216

 (de Salas et al. 2018). We multiply

Fe¯Earth(r,E,t)

 by the cross section of the IBD σ
IBD(E) (Strumia & Vissani 2003), selection efficiency ϵ
eff(E), livetime ratio η
 livetime, and number of target protons in KamLAND

target

, then integrate with the time of 20 s and the neutrino energy of 1.8–111 MeV. The expected number of observed supernova events N
KL(r) at KamLAND as a function of r is estimated from
2

NKL(r)=ηlivetimetarget×∫dtdEFe¯Earth(r,E,t)σIBD(E)ϵeff(E).

Actually, observed events in KamLAND follow a Poisson distribution with mean N
KL. To reproduce the time distribution of supernova neutrinos in KamLAND, we make the probability density function (PDF) of them. We carry out MC simulation based on the above Poisson distribution and PDF, then search for a neutrino cluster that requires two DC events within a 10 s window. N
KL yields 10–30 events for a ccSN within 10 s in case of r = 25 kpc. Here, the number of accidentally contaminated DC events in the supernova neutrino burst is negligibly small (10−5 events) within the distance we expect N
KL > 1. These calculations provide detection probabilities as a function of distance as shown in Figure 3. We use all available parameter combinations in this estimation, thus blue and red bands include model and neutrino mass ordering uncertainties. KamLAND has a 95% probability to the supernova neutrino burst detection with the distance for r ≤ 40–59 kpc and r ≤ 65–81 kpc for the ccSN and failed ccSN, respectively. In either case, our Galaxy (r ≲ 25 kpc) is covered with a ≥99% detection probability. Consequently, this result gives an upper limit on the supernova rate within our Galaxy, which includes ccSN rate and failed ccSN rate,

RSNgal0.15yr−1

 (90% CL) assuming that the SN rate on the Large Magellanic Cloud and Small Magellanic Cloud are much smaller than the Galactic SN rate (Tammann et al. 1994).


In the standard ΛCDM paradigm, most of the mass in the universe resides in structures known as dark matter halos. These provide the gravitational well within which cold gas collapses, forms stars, and, at a larger scale, forms progenitors of the galaxies we observe today (e.g., White & Rees 1978; Fall & Efstathiou 1980; Blumenthal et al. 1984; Frenk & White 2012; Wechsler & Tinker 2018). The dark matter halo itself forms from the gravitational collapse of initial perturbations in the density field at the very early universe (e.g., van Albada 1960, 1961; Peebles 1970; White 1976). The emergence of the hierarchical model of structure formation (Press & Schechter 1974; Gott et al. 1975; White & Rees 1978) supported by cosmological hydrodynamical simulations and semianalytical models suggests a bottom-up scenario, in which massive halos formed from a sequence of mergers (so-called merger trees) and mass accretion, as opposed to initial rapid collapse models (e.g., White & Frenk 1991; Navarro & Benz 1991; Katz et al. 1992; Kauffmann et al. 1993; Lacey & Cole 1993; Somerville & Primack 1999). Discovery of very massive galaxies at high redshifts (

), which constitute most of the luminous baryonic component inside the dark matter halos, however, suggests a rapid buildup of the bulk of their stellar mass at z > 2, with intense star formation activity at early times. Submillimeter observations further confirm the starburst populations with star formation rates (SFRs) exceeding hundreds of solar masses per year (e.g., Blain et al. 2002; Capak et al. 2008; Marchesini et al. 2010; Smolčić et al. 2015). There have been many recent spectroscopic confirmations of such sources at high-redshift galaxies experiencing suppressed star formation activity (e.g., Belli et al. 2014, 2017b, 2017a, 2019; Whitaker et al. 2014; Newman et al. 2015; Glazebrook et al. 2017; Newman et al. 2018; Schreiber et al. 2018; Forrest et al. 2020; Tanaka et al. 2019; Valentino et al. 2020). To use these systems to constrain galaxy formation and evolution scenarios and study feedback and quenching mechanisms at early times requires a robust photometric selection of these objects followed by deep spectroscopic observations.


We calculate the expected radio fluxes following the prescriptions of Piran, Nakar & Rosswog (2013). We consider an expanding spherical, non-relativistic ejecta that collects mass from the uniform circum-merger medium with particle density n as it moves outwards with velocity v ≡ βc, where c is the speed of light. The velocity of the ejecta decreases as it collects more mass. The relation between ejecta velocity and radius (R) can be calculated by assuming that kinetic energy is conserved (see equation 14 of Piran et al. 2013):
(2)
\begin{eqnarray*}
M(R)(\beta c)^2 \approx E(\ge \beta),
\end{eqnarray*}
where M is the collected mass at radius R from the merger, and E(≥β) is the kinetic energy of the part of the ejecta that was launched with velocities faster than βc. In our case, this means that initially only the component with 0.3c velocity affects the evolution of the ejecta front and hence the radio flux until it slows down to 0.1c where the slower component can catch up. With R and β known functions of time, we can calculate the emitted radio flux as (see equations 4 and 6 and table 2 in Piran et al. 2013)
(3)
\begin{eqnarray*}
F(t)\approx 4\, \mbox{mJy}\, R_{17}^3 n_{-1}^{15/8} \beta ^{19/4} d_{200}^{-2}\left(\frac{\nu }{6\, \mbox{GHz}}\right)^{-3/4},
\end{eqnarray*}
where $R_{17}\equiv (R/10^{17}\, \mbox{cm})$, $n_{-1}\equiv (n/0.1\, \mbox{cm}^{-3})$, and $d_{200}\equiv (d/200\, \mbox{Mpc})$. We assume that the observational frequency νobs = 6 GHz is greater than both the typical synchrotron frequency of electrons in the forward shock driven by the ejecta (νm), and the synchrotron self-absorption frequency (νa; see e.g. Piran et al. 2013). We further assume that electrons and the magnetic field carry $\epsilon _{\rm e}\approx \epsilon _{\rm m}\sim 10{{\ \rm per\ cent}}$ of the total internal energy of the shocked gas, and that the power-law index of the distribution of the accelerated electrons’ Lorentz factors is p = 2.5.


The equation of state is
14

where

,

,

, and

 are the gas pressure from nucleons, the radiation pressure of photons, the degeneracy pressure of electrons, and the radiation pressure of neutrinos, respectively. k, T,

, a, and h are the Boltzmann constant, temperature of the disk, proton mass, radiation constant, and Planck constant, respectively. The equation can be applied anywhere on the disk to describe the pressure, but we also need an equation to completely give the vertical distributions of the density, temperature, and pressure. For simplicity, we assume the polytropic relation, i.e.,

, in the vertical direction, with K as a constant (e.g., Lee et al. 2005; Liu et al. 2008, 2010a, 2012a, 2013). Here we also assume the electron fraction

 is 0.5 (e.g., Di Matteo et al. 2002; Gu et al. 2006; Liu et al. 2014), because its influences are very limited on the structure and neutrino luminosity of the disk, unless we care about the types of neutrinos emitted from the disk (e.g., Liu et al. 2013).

 is the mass fraction of free nucleons, and its expression is obtained by taking

 as (e.g., Kohri et al. 2005)
15

where

 and

.

 is the energy density of neutrinos, which can be expressed as (e.g., Lee et al. 2005; Liu et al. 2012a)
16

where

 is the total optical depth for neutrinos,

 and

 are the absorption and scattering optical depth for neutrinos, and the subscript i  runs for the three species of neutrinos

,

, and

, which can be defined as (Di Matteo et al. 2002; Lee et al. 2005; Liu et al. 2012a)
17

18

where

 is the summation of the cooling rates per unit volume due to the neutrino reactions for different neutrinos, especially the Urca processes and electron–positron pair annihilation (e.g., Di Matteo et al. 2002; Liu et al. 2007). The neutrino scattering processes include scattering by free protons, free neutrons, α-particles, and electrons (e.g., Di Matteo et al. 2002).


AstroSat data enabled us to derive the X-ray spectrum in the 0.8–70 keV energy band as shown in Figure 7. The spectrum was fitted reasonably well using two models. The first model was defined as an absorbed Fermi–Dirac cutoff model along with a blackbody, an Fe emission line, and three Gaussian absorption lines introduced to model cyclotron scattering features and its two higher harmonics as observed in the spectrum. The CompTT model was used as the second model in combination with an Fe emission line and three Gaussian absorptions lines as defined in the first model. The CompTT model is generally used for neutron-star-based low-mass X-ray binaries such as Z-type and atoll sources with a relatively lower magnetic field (

 G) of the neutron star (Ferinelli et al. 2008). However, the model could also successfully define the spectrum of some of the pulsars in Be binaries, for example, Cep X-4 (Jaiswal & Naik 2015), 4U 1907+09 (Varun et al. 2019), and GRO J2058+42 (Molkov et al. 2019). The parameters derived from the two models are tabulated in Table 2. The first model estimated a blackbody temperature of 0.83 ± 0.04 keV and detected the presence of a cyclotron resonance scattering feature and its harmonics. The Comptonization model, on the other hand, enabled us to determine the input photon Wien temperature of 0.52 ± 0.02 keV, the plasma temperature of 8.22 ± 0.10 keV, and the plasma optical depth of 5.21 ± 0.12 for the phase-averaged spectra. The Wien temperature, per the CompTT model, originates far from the neutron star surface and closer to the inner accretion disk i.e., at the outer transition layer; hence, the Wien temperature is always found to be relatively lower than the neutron star blackbody temperature as it originates closer to the inner transition layer, i.e., near the surface of the neutron star (Ferinelli et al. 2008). For the CompTT model, bulk Comptonization occurs in the innermost part of the transition layer region, while thermal Comptonization is dominant in the outer transition layer and presumably within some extended region located above the accretion disk. Similar deviations were also observed in the case of Cep X-4 fitted with the CompTT model and a blackbody combined with the FDCUT model (Table 1 of Jaiswal & Naik 2015). However, the centroid energy of the cyclotron absorption features and its detected harmonics are found to be consistent within errors for the two models (Table 2).


A clear transition in the spectra is observed at scales

 with a change in the spectral indices of all fields. In particular, the spectrum of the perpendicular magnetic fluctuations steepens at

 following a power law with a spectral index

 for another decade. The location of the break does not show any significant dependence on the number of particles, the spatial resolution, and the resistivity adopted, provided that a sufficient number of grid points allows us to cover approximatively a decade at sub-proton scales, i.e., that the scale at which resistive dissipation acts is sufficiently separated from the region of the break. The parallel component of the magnetic field, together with the density, follows a similar but slightly shallower slope with a spectral index of

 in very good agreement with observations (Chen et al. 2012, 2013b) and other simulations (Howes et al. 2011; Passot et al. 2014). As a result, magnetic fluctuations tend to become isotropic at small scales, resulting in an increase of the magnetic compressibility, as observed in the solar wind (Podesta & TenBarge 2012; Salem et al. 2012; Kiyani et al. 2013). The spectrum of the perpendicular velocity fluctuations quickly drops above

 without any clear power-law trend. The observation of a spectral index of

 has been ascribed to the effect of the electron Landau damping by previous studies (Howes et al. 2011; Passot et al. 2014); however, this cannot be the case in our simulations, where the electron kinetics is not taken into account. Alternatively, the presence of coherent structures, such as current sheets, can produce a steepening of the energy spectra (e.g., Wan et al. 2012; Karimabadi et al. 2013). The increase of intermittency at small scales, observed in our simulations, seems to confirm this path toward the dissipation. We have to note, however, that a

 power law for the magnetic energy and the density spectra (not far from the 2.8 found here) has been also interpreted as related to the dimensionality (1D or 2D) of the magnetic and the density intermittent structures, without invoking dissipation (Boldyrev & Perez 2012; Meyrand & Galtier 2013).