arXiv:1001.0043v2  [astro-ph.EP]  13 Jan 2010Strong Constraints to the Putative Planet Candidate around VB 10 using
Doppler spectroscopy1
Guillem Anglada-Escud´ e
Department of Terrestrial Magnetism, Carnegie Institution o f Washington
5241 Broad Branch Road, NW, Washington, DC 20015 USA
anglada@dtm.ciw.edu
Evgenya Shkolnik
Department of Terrestrial Magnetism, Carnegie Institution o f Washington
5241 Broad Branch Road, NW, Washington, DC 20015 USA
shkolnik@dtm.ciw.edu
Alycia J. Weinberger
Department of Terrestrial Magnetism, Carnegie Institution o f Washington
5241 Broad Branch Road, NW, Washington, DC 20015 USA
weinberger@dtm.ciw.edu
Ian B. Thompson
The Observatories of the Carnegie Institution of Washington
813 Santa Barbara Street, Pasadena, CA 91101 USA
ian@obs.carnegiescience.edu
David J. Osip
Las Campanas Observatory, Carnegie Institution of Washington
Colina El Pino Casilla 601, La Serena, Chile
dosip@lco.cl
John H. Debes
Goddard Space Flight Center, NASA Postdoctoral Program
8463 Greenbelt Rd, Greenbelt, MD 20770, USA
john.H.debes@nasa.gov
ABSTRACT– 2 –
We present new radial velocity measurements of the ultra-co ol dwarf VB 10,
which was recently announced to host a giant planet detected with astrometry. The
new observations were obtained using optical spectrograph s(MIKE/Magellan and ES-
PaDOnS/CHFT) and cover a 63% of the reported period of 270 day s. We apply Least-
squares periodograms to identify the most signiﬁcant signa ls and evaluate their corre-
spondingFalse Alarm Probabilities. We show that this metho d is the proper generaliza-
tion to astrometric data because (1) it mitigates the coupli ng of the orbital parameters
with the parallax and proper motion, and (2) it permits a dire ct generalization to
include non-linear Keplerian parameters in a combined ﬁt to astrometry and radial ve-
locity data. In fact, our analysis of the astrometry alone un covers the reported 270 d
period and an even stronger signal at ∼50 days. We estimate the uncertainties in the
parameters using a Markov Chain Monte Carlo approach. The no minal precision of the
new Doppler measurements is about 150 s−1while their standard deviation is 250 ms−1.
However, the best ﬁt solutions still have RMS of 200 ms−1indicating that the excess
in variability is due to uncontrolled systematic errors rat her than the candidate com-
panions detected in the astrometry. Although the new data al one cannot rule-out the
presence of a candidate, when combined with published radia l velocity measurements,
the False Alarm Probabilities of the best solutions grow to u nacceptable levels strongly
suggesting that the observed astrometric wobble is not due t o an unseen companion.
Subject headings: astrometry, methods: statistical, stars: individual (VB 1 0), tech-
niques: radial velocities
1. Introduction
Pravdo & Shaklan (2009) recently announced the discovery of an astrometric companion to
VB 10, an ultra-cool dwarf with a mass of ≈0.08 M ⊙. From a Keplerian ﬁt to the motion, they
determined a mass of 6 M Jand a period of 270 d. Thus VB 10 became the lowest mass star
known to harbor a planetary companion. The mass ratio betwee n VB 10 and its companion, ∼13,
also is intriguing. A similar mass ratio for a Solar-type sta r would make the companion a brown
dwarf, but brown dwarfs as small separation companions to st ars are quite rare. VB 10 is itself the
secondary in a wide binary with V1428 Aql, a M2.5 star (van Bie sbroeck 1961). At a distance of
1Based on observations collected with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory,
Chile, at the W. M. Keck Observatory and the Canada-France-H awaii Telescope (CFHT). The Keck Observatory is
operated as a scientiﬁc partnership between the California Institute of Technology, the University of California, and
NASA, and was made possible by the generous ﬁnancial support of the W. M. Keck Foundation. CFHT is operated
by the National Research Council of Canada, the Institut Nat ional des Sciences de l’Univers of the Centre National
de la Recherche Scientique of France, and the University of H awaii.– 3 –
5.8 pc from the Sun, the 74′′separation of this proper motion binary corresponds to a pro jected
separation of 430 AU.
Such low-mass stars have not been the target of intensive pre cision radial velocity (PRV)
monitoring because they have low visual ﬂuxes and high stell ar activity. For example, the dedicated
HARPS M-dwarf planet search observes stars2only brighter than V=14 and of moderate to low
activity levels (Bonﬁls et al. 2007). VB 10 has V mag = 17.3 and is known to be a ﬂare star
(Berger et al. 2008). PRV and lensing planet searches have so far found only 13 stars under 0.5
M⊙hosting 18 planets, and of these, more than half have masses b elow 0.1 M J.
Despite the challenges, searches for planetary companions to low mass stars are of continuing
interest. Low-mass stars appear less likely to have lower ma ss stellar companions and less likely to
harbor planets than Solar-mass stars (Cumming et al. 2008). When they do have companions, they
tend to be stars of nearly equal mass to the primary (Burgasse r et al. 2007). The mass function of
planets orbiting M dwarfs, and how it diﬀers from the planet ma ss function for higher-mass stars,
provides a constraint on the planet formation mechanism(s) in general. Disks suﬃciently massive
to form Jupiter-mass planets appear to be rare around brown d warfs, whose disks generally look
like lower mass versions of T Tauri disks (Scholz et al. 2006) . High mass companions would have
to form via a binary-like fragmentation mechanism (e.g. Fon t-Ribera et al. 2009). Thus how a 6
MJplanet could form around an ∼80 MJstar and how common such high-mass ratio companions
remain important questions (Boss et al. 2009).
The reported planet’s astrometric orbit predicts a radial v elocity (RV) amplitude of at least 1
km s−1for a circular orbit and up to several km s−1for an eccentric orbit. This magnitude signal is
detectable with ordinary RV measurements without requirin g the adoption of precision techniques
such as an iodine cell or simultaneous thorium reference.
Although several RV measurements of VB 10 exist in the litera ture before 2009, it is diﬃcult
to combine the historical RVs (see list in Table 4 of Pravdo & S haklan (2009)), as each observation
used diﬀerent calibration techniques and/or RV standards th at introduce zero-point oﬀsets and the
typical uncertainties are also large ( ∼1.5 km s−1). The most precise measurements in the literature
were recently published by Zapatero Osorio et al. (2009) (he reafter Z09), but provide only a “hint
of variability.” These data did little to constrain the orbi tal parameters of the planet beyond what
the astrometry had already done (Anglada-Escud´ e et al. 200 9).
Here, we present a more precise set of RV observations over 17 5 days (or 65% of the reported
orbital period). We also present general techniques for joi nt ﬁtting of astrometric and RV data and
show how they can be used to constrain the orbit of the candida te planet.
2http://www.eso.org/sci/observing/proposals/77/gto/h arps/3.txt– 4 –
2. New Data
We acquired spectra at 7 epochs in 2009 with the MIKE spectrog raph at the Magellan Clay
telescope at Las CampanasObservatory(Chile). We usedthe0 .35′′andthe0.5′′slits whichproduce
a spectral resolution of ≈45,000 and 35,000, respectively, across the 4900 – 10000 ˚A range of the
red chip. The seeing was in the range from 0 .5 to 1.1′′. These data were reduced using the facility
pipeline (Kelson 2003).
We also have in hand a single spectrum of VB 10 taken in 2006 usi ng the HIRES (Vogt et al.
1994)) on the Keck I 10-m telescope. We used the 0.861′′slit to obtain a spectral resolution of
λ/∆λ≈58,000 at λ∼7000˚A. We used the GG475 order-blocking ﬁlter and the red cross-di sperser
to maximize throughput in the red orders.
To increase the phase coverage, an additional spectrum was o btained using the ESPaDOnS on
the CFHT 3.6-m telescope. ESPaDOnS is ﬁber fed from the Casse grain to Coud´ e focus where the
ﬁber image is projected onto a Bowen-Walraven slicer at the s pectrograph entrance. ESPaDOnS’
‘star+sky’ mode records the full spectrum over 40 grating or ders covering 3700 to 10400 ˚A at
a spectral resolution of λ/∆λ≈68,000. The data were reduced using Libre Esprit described in
Donati et al. (1997, 2007).
Each stellar exposure is bias-subtracted and ﬂat-ﬁelded fo r pixel-to-pixel sensitivity variations.
After optimal extraction, the 1-D spectra are wavelength ca librated with a thorium-argon arc. To
correct for instrumental drifts, we used the telluric molec ular oxygen A band (from 7620 – 7660
˚A) which aligns the MIKE spectra to 40 m s−1, after which we corrected for the heliocentric
velocity. Consistency tests with the bluer Oxygen band show s comparable values but with larger
measurement error.
The ﬁnal spectra are of moderate S/N reaching ≈25 per pixel at 8000 ˚A. Each night, spectra
were also taken of a M-dwarf RV standard, namely GJ 699 (Barna rd’s star; SpT = M4V) and/or
GJ 908 (SpT = M1V).
To measure VB 10’s RV, we cross-correlated each of 9 orders be tween 7000 and 9000 ˚A (ex-
cluding those with strong telluric absorption) where VB 10 e mits most of its optical light, with the
spectrumofGJ699 and/orGJ908taken onthesamenight usingI RAF’s1fxcorroutine(Fitzpatrick
1993). Both GJ 699 and GJ 908 have been monitored for planets f or years and none has been found
within the RV stability level of 0.1 km s−1. Here we use the systemic RVs published by a planet-
search team (Nidever et al. 2002): RV(GJ 699) = –110.506 km s−1and RV(GJ 908) = –71.147
km s−1. The zero-point of the absolute RVs is uncertain at the 0.4 km s−1level. We measured
the RVs from the gaussian peak ﬁtted to the cross-correlatio n function (CCF) of each order and
adopt the average RV of all orders with a mean standard deviat ion of the individual measurements
of 0.150 km s−1. The average of all our measurements is 36.02 km s−1with a standard deviation
1IRAF (Image Reduction and Analysis Facility), http://iraf .noao.edu/– 5 –
of 0.25 km s−1. An observing log with the measured RVs and uncertainties fo r VB 10 is shown in
Table 1.
3. Data Analysis: Combining Astrometry and Radial Velocities
In this section, we reanalyze the original astrometric data to calculate the likelihood of astro-
metrically allowed solutions, and then combine the astrome try and RV data sets in a consistent
framework to quantify how the new RV measurements constrain the possibleorbits of the candidate
signals observed in the astrometry of VB 10b.
3.1. Least-squares periodograms
The most popular method to look for periodicities in data is t he so-called Lomb-Scargle
periodogram. A version adapted to deal with astrometric two -dimensional data developed by
Catanzarite et al. (2006) (Joint Lomb Scargle periodogram) was implemented in the discovery pa-
per of VB 10b (Pravdo & Shaklan 2009). Any method based on the L omb-Scargle periodogram
performs optimally only under an important implicit assump tion: all other signals (e.g. linear
trend, an average oﬀset, etc.) can be subtracted from the data without aﬀecting the signiﬁcance of
the signal under investigation. This assumption does not ho ld for astrometry because the proper
motion and the parallax are also a signiﬁcant part of the sign al and they typically correlate with
the periodic motion of a planet (see Black & Scargle 1982).
We use instead a Least-squares periodogram. The weighted Le ast-squares solution is obtained
by ﬁtting all the free parameters in the model for a given peri od. The sum of the weighted residuals
divided by Nis the so-called χ2statistic. Then, each χ2
Pof a given model with kPparameters, can
be compared to the χ2
0of the null hypothesis with k0free parameters by computing the power, z,
as
z(P) =(χ2
0−χ2
P)/(kP−k0)
χ2
P/(Nobs−kP)(1)
where a large zis interpreted as a very signiﬁcant solution. The values of zfollow a Fisher F-
distribution with kP−k0andNobs−kPdegrees of freedom (Scargle 1982; Cumming 2004). Even
if only noise is present, a periodogram will contain several peaks (see Scargle 1982, as an example)
whoseexistencehavetobeconsideredinobtainingtheproba bilityofaspuriousdetection. Assuming
Gaussian noise, the probability that a peak in the periodogr am has a power higher than z(P) by
chance is the so-called False Alarm Probability (FAP) :
FAP = 1 −(1−Prob[z > z(P)])M(2)
whereMis the number of independent frequencies. In the case of unev en sampling, Mcan be quite
large and is roughly the number of periodogram peaks one coul d expect from a data set with only– 6 –
Gaussian noise and thesame cadence as thereal observations . We adopt the recipe M≈2∆T/Pmin
given in Cumming (2004, Sec 2.2), where ∆ Tis the time-span of the observations and Pminis the
minimum period searched. One still has to select Pminarbitrarily. Assuming a Pmin= 20 days, the
astrometric data alone has M∼300, and the combination of astrometry and RVs has M∼360.
In our particular problem, the null hypothesis is the basic k inematic model with k0= 6 param-
eters: 2 coordinates, 2 proper motions, parallax and system ic RV. As a ﬁrst approach, our simplest
non-null hypothesis considers circular orbits, astrometr ic data only and one RV measurement. For
a given period, the number of free parameters is then kP= 10: the 6 kinematic ones plus the four
Thiele Innes elements A,B,FandG(e.g. Wright & Howard 2009). Since the model is linear in all
10 parameters, the power can be eﬃciently computed for many p eriods between 20 days and 4000
days to obtain a familiar representation of the periodogram that we call a Circular Least-squares
Periodogram (CLP). The CLP of the astrometric data, shown at top in Figure 1, displays two
obvious peaks: the reported one at 270 days (Pravdo & Shaklan 2009) and a more signiﬁcant one
at 49.9 days, both with high power and very low FAPs.
To ﬁnd the full Keplerian solution for both periods and estim ate their FAPs, we perform a
Least-squares periodogram sampling a grid of ﬁxed eccentri city-period (eP) pairs and ﬁtting all
other parameters. For each eP pair kPis 11: the null-hypothesis ( X0,Y0,µX,µY,πandv0)
plus all the other Keplerian elements: Mass of the planet, Ω, ω,i, and the Mean anomaly at the
initial epoch M0(see Wright & Howard 2009, for a recent review). We analyze bo thastrometry
onlyandastrometry+RVs . Theχ2of the best ﬁt solution is then used to obtain each FAP as
previously described. Figure 1 shows the resulting color-c oded FAPs for each eccentricity–period
pair (eP-map).
3.1.1. Astrometry only
A value of M= 300 has been used to obtain the FAP, and our result at 270 d qua litatively
agrees with Pravdo & Shaklan (2009), however the more signiﬁ cant period is at ∼50 d. For both
periods, there are regions with FAP <1% spanning all possible eccentricities (second row in Fig-
ure 1). The best ﬁts and their χ2per degree of freedom (¯ χ2) are summarized in Table 2. The
obtained results for the 270 d period are in agreement with th ose reported in the discovery paper
by Pravdo & Shaklan (2009). The best ﬁt solution for the 50 d pe riod has mass ∼15 MJ, which
would be a very low mass brown dwarf. It is important to point o ut that the best ﬁt inclination is
close to 90 (edge on) for both solutions. The uncertainties o n the orbital parameters are quantiﬁed
in Sec 3.2.– 7 –
3.1.2. Astrometry+RVs
We now ﬁt jointly for the best orbital solution to the astrome try and RVs. Our campaign
covered about 65% of the 270 d orbit. The standard deviation o f all our RVs measurements is
250 m s−1(null hypothesis) which is larger than the individual uncer tainties in Table 4. When we
cross-correlate our standards, we measure a similar RMS of 2 00 m s−1, which indicates that the
diﬀerence is due to an uncontrolled or unmeasured systematic . The RMS of the RVs for the best
ﬁt solution is 200 m s−1, which is not statistically diﬀerent from the RMS of the null h ypothesis.
This is another indication that our measurements contain sy stematic errors at the level of 100 −200
m/s. Despite of that, we use the nominal errors in the Least-s quares solution as the best estimates
for the individual uncertainties we can provide. In Figure 2 , we show the best solutions to both
signals including all the data.
For the 270 d period, our RV non detection cannot exclude a small region of orbital solutions
arounde∼0.8 with a FAP between 1%–5% – see Figure 1, third row right panel . We now add
the RVs measurements by Z09 and solve for a joint solution. A z ero-point oﬀset between datasets
is added as an additional free parameter. The combined RV mea surements force the eccentricity
to large values which apparently still provides a reasonabl e ﬁt to the astrometry (see top panels in
Figure 2). However, the FAPs are now all higher than 10% (Figu re 1, bottom right panel), which
indicates that the signal can be barely distinguished from t he noise ﬂuctuations. The “hint” of
detection in Z09 based on one discrepant value at 3 .1−σout of ﬁve can be due to random errors
with a non negligible probability.
For the 50 d period, there are still several orbits that provi de a decent ﬁt to the combined
astrometry and the new RV data with a FAP lower than 1%. These o ccupy a small space around
the best joint solution, with e= 0.90 (see Figure 1, 3rd row, left panel) and an inclination clos e
to 0. Large eccentricity causes the duration of fast RV varia tion to be very short (and diﬃcult to
catch); an inclination close to 0 tends to suppress any RVs si gnal. Such inclination is in apparent
contradiction with the one obtained using the astrometry al one (∼90 deg). The reason is the
following: while the new ﬁt to the astrometry forced by the RV s is much worse than the one
obtained from the astrometry alone, such a solution still re presents an improvement compared to
the null hypothesis. Adding Z09 data to the ﬁt increases the F AP of the most likely solution to 2%,
an eccentricity of 0 .91 and the inclination close to 0 (see Table 2). This suggests that the signal at
50 d is also spurious, even though it has slightly better chan ces of survival than the one at 270 d.
3.2.A Posteriori Probability Distributions
We adapt the method developed by Ford (2005, 2006) to assess u ncertainties in orbit determi-
nations by obtaining the a posteriori probability distribution for the parameters using a Markov
Chain with a Gibbs sampler strategy. Our problem is identica l to the one described by Ford (2005),
where now the χ2contains both RV and astrometric observations and the model has a few more– 8 –
free parameters. Several properly adjusted MCMC with 106steps have been computed obtaining
compatible results. The step sizes of the Gibbs sampler are i nitialized with the formal errors from
the best ﬁt Least-squares solution, and adjusted to obtain a transition probability between 10%
and 20%. The ﬁrst 105steps of each chain are rejected. The ﬁnal distributions mat ch very well the
areas of low FAPs in the eP-maps (see Figure 3 as an example) gi ving further proof that the chains
have converged to the equilibrium distributions. The MCMC c ontains 13 free parameters – the 11
from the Least-squares periodogram plus eccentricity and p eriod. When the RVs measurements
from Z09 are included, and additional oﬀset parameter is incl uded.
Table 2 presents the standard deviations obtained via the MC MC for both the 50 d and 270 d
periods using astrometry alone and astrometry + all RV data. As an example, we show the two
dimensional density of states in period-eccentricity spac e in Figure 3 (left) obtained in both cases
aroundthe 270 d signal. Themarginalized distributionsfor ein theform of histograms are shownin
Figure 3 (right). For the astrometry-alone case, the distri bution of eis almost uniform. It becomes
strongly peaked towards high eccentricities when all the RV data are included. Since the best ﬁt
solution at 270 d is poor (¯ χ2= 1.76), the corresponding χ2minimum is not very deep which is
reﬂected in a signiﬁcant increase in the derived uncertaint ies (See Table 2). The same happens to
the signal at 50 d with the exception of the inclination that h as a small uncertainty (4 deg) close
to 0. Even though this solution has a low FAP, the inclination has to be coincidentally very small
to suppress any RV signal and very diﬀerent from using astrome try only (94 deg), rasing serious
doubts of its reality.
4. Discussion and Conclusions
The non-detection of a signiﬁcant RV variation in our data se t already discards most orbital
conﬁgurations allowed by the astrometry. When combined wit h Z09 RVs measurements, there are
no remaining solutions with a FAP lower than 10% around the 27 0 d period, so the presence of
a planet candidate at that period is not supported by the obse rvations. For the 50 d period, the
constraints arealso strongandbecome almost deﬁnitive whe ntheZ09data is included. Even highly
eccentric solutions have a relatively large FAP ( >2%). We ﬁnd that particular combinations of
eccentricity, inclination and ωcan ﬁt an almost ﬂat RV curve indicating that the analytic met hods
applied to estimate FAPs for high eccentricities tend to giv e over optimistic results and that this
issue should be studied in more detail.
We have developed and implemented useful tools for detailed analysis of combined astrometric
and RV data: Circular Least-squares periodogram as the prop er generalization of the classic Lomb-
Scargle periodogram to deal with astrometric data, eP-maps to visualize the most likely period–
eccentricity combinations and a Bayesian characterizatio n of the parameter uncertainties based on
a MCMC approach.
VB 10 is also part of the Carnegie Astrometric Planet Search p rogram (Boss et al. 2009). RV– 9 –
measurements with precision techniques in the near-infrar ed (Bean et al. 2009) may provide the
required accuracy to put even stronger limits to the existen ce of VB10b or ﬁnd other planets in the
system. VB 10 will certainly be observed by the space astrome try mission Gaia (Perryman et al.
2001), which would be capable of ﬁnding a planet with a period of 270 d and as small as 0 .2 MJ.
REFERENCES
Anglada-Escud´ e, G., Boss, A. P., & Weinberger, A. J. 2009, i n ASP Conf. Ser., Vol. in press,
Pathways Towards Habitable Planets, ed. V. Coud´ e du Forest o, D. M. Gelino & I. Ribas
(San Francisco, CA: ASP)
Bean, J. L., Seifahrt, A., Hartman, H., Nilsson, H., Wiedema nn, G., Reiners, A., Dreizler, S., &
Henry, T. J. 2009, in ASPConf. Ser., Vol. in press, Pathways T owards Habitable Planets, ed.
V. Coud´ e du Foresto, D. M. Gelino & I. Ribas (San Francisco, C A: ASP), arXiv:0911.3148
Berger, E. et al. 2008, ApJ, 676, 1307
Black, D. C. & Scargle, J. D. 1982, ApJ, 263, 854
Bonﬁls, X. et al. 2007, A&A, 474, 293
Boss, A. P. et al. 2009, PASP, 121, 1218
Burgasser, A. J., Reid, I. N., Siegler, N., Close, L., Allen, P., Lowrance, P., & Gizis, J. 2007, in
Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Kei l (Tucson, AZ: Univ. of AZ
Press), 427
Catanzarite, J., Shao, M., Tanner, A., Unwin, S., & Yu, J. 200 6, PASP, 118, 1319
Cumming, A. 2004, MNRAS, 354, 1165
Cumming, A., Butler, R. P., Marcy, G. W., Vogt, S. S., Wright, J. T., & Fischer, D. A. 2008,
PASP, 120, 531
Donati, J.-F., Jardine, M. M., Gregory, S. G., Petit, P., Bou vier, J., Dougados, C., M´ enard, F.,
Cameron, A. C., Harries, T. J., Jeﬀers, S. V., & Paletou, F. 200 7, MNRAS, 380, 1297
Donati, J.-F., Semel, M., Carter, B. D., Rees, D. E., & Collie r Cameron, A. 1997, MNRAS, 291,
658
Fitzpatrick, M. J. 1993, in ASP Conf. Ser., Vol. 52, Astronom ical Data Analysis Software and
Systems II, ed. R. J. Hanisch, R. J. V. Brissenden, & J. Barnes , 472
Font-Ribera, A., Miralda Escud´ e, J., & Ribas, I. 2009, ApJ, 694, 183
Ford, E. B. 2005, AJ, 129, 1706– 10 –
Ford, E. B. 2006, ApJ, 642, 505
Ford, E. B., Kozinsky, B., & Rasio, F. A. 2000, ApJ, 535, 385
Kelson, D. D. 2003, PASP, 115, 688
Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & V ogt, S. S. 2002, ApJS, 141, 503
Perryman, M. A. C. et al. 2001, A&A, 369, 339
Pravdo, S. H. & Shaklan, S. B. 2009, ApJ, 700, 623
Scargle, J. D. 1982, ApJ, 263, 835
Scholz, A., Jayawardhana, R., , & Wood, K. 2006, ApJ, 645, 149 8
Tamuz, O. et al. 2008, A&A, 480, L33
van Biesbroeck, G. 1961, AJ, 66, 528
Vogt, S. S. et al. 1994, in SPIE Conf. Ser., Vol. 2198, Instrum entation in Astronomy VIII, ed. D. L.
Crawford & E. R. Craine, 362
Wright, J. T. & Howard, A. W. 2009, ApJS, 182, 205
Zapatero-Osorio, M. R., Mart´ ın, E. L., del Burgo, C., Deshp ande, R., Rodler, F., & Montgomery,
M. M. 2009, A&A, 505, L5
This preprint was prepared with the AAS L ATEX macros v5.2.– 11 –
Table 1. Log of RVs
Telescope UT Date HJD Slit Width RV (w/ GJ 699)aRV (w/ GJ 908)a
+Instrument –2450000′′km s−1km s−1
Keck I + HIRES 2006 Aug 12 3959.57 0.86 – 35.59 ±0.15
Clay+MIKE 2009 Jun 06 4988.74 0.35 36.23 ±0.13 35.99 ±0.15
Clay+MIKE 2009 Jun 07 4989.82 0.50 36.22 ±0.13 36.09 ±0.20
Clay+MIKE 2009 Jun 08 4990.75 0.50 36.15 ±0.12 36.10 ±0.22
Clay+MIKE 2009 Jun 30 5012.72 0.35 35.72 ±0.11 –
Clay+MIKE 2009 Jul 25 5037.66 0.50 35.96 ±0.11 36.03 ±0.11
Clay+MIKE 2009 Sep 04 5078.58 0.50 35.96 ±0.09 36.37 ±0.24
Clay+MIKE 2009 Oct 15 5119.54 0.50 36.30 ±0.14 36.41 ±0.13
Clay+MIKE 2009 Oct 26 5130.51 0.50 36.41 ±0.16 36.27 ±0.18
CFHT+ESPaDOnS 2009 Nov 29 5164.69 –b– 35.74 ±0.20
aUncertainties are the standard deviation of the 9 orders of t he cross correlation and do not include the 40
m s−1systematic uncertainty from the telluric wavelength corre ction. Absolute radial velocity determination
has an uncertainty of 0 .4 km/s but it is not relevant for orbital ﬁtting purposes.
bESPaDOnS is a ﬁber fed spectrograph with an eﬀective resolut ion of R ∼68000 in the wavelength range
of interest
Table 2. Best ﬁtting valuesa. Uncertainties obtained from a MCMC with 106steps.
Parameter Astrometry 50 d Astrometry 270 d Astro+ all RV 50 d A stro+ all RV 270 d
X0(mas) -16.6 ±1.6 -14.1d±3.2 -21.15±2.3 -17.9 ±4.7
Y0(mas) -408.0 ±1.9 -406.1d±3.5 409.52±2.8 -410.5 ±5.51
µR.A.(mas/yr) -588.98 ±0.25 -589.08 ±0.25 -588.66±0.29 -589.21 ±0.26
µDec(mas/yr) -1360.95 ±0.25 -1361.08 ±0.24 -1361.02 ±0.25 -1361.36 ±0.20
π(mas) 168.3 ±1.51 169.5 ±1.4 169.95±1.37 169.24 ±1.30
v0(km/s) 35.2 ±1.4 35.4d±1.050 36.06±0.11 36.05 ±0.08
voﬀset(km/s) - - 1.5±0.42 1.5 ±0.36
P(days) 49.7 ±0.5 272.1 ±4.1 49.84±0.11 278.5 ±2.7
Mass(MJ) 17.5 ±4.4 7.1 ±2.7 13.7±6.4 5.0 ±2.9
e 0.22c±0.30 0.48c±0.31 0.91±0.13 0.90 ±0.16
i(deg) 93 ±5 90 ±15 4±5 110c±50
Ω(deg) 40 ±20 220 ±25 13c±100 40c±66
ω(deg) 20 ±40 30c±80 122c±60 17c±90
M0(deg) 270 ±0 170c±108 340c±70 156c±80
a(AU)d0.12 0.36 0.12 0.36
¯χ2
02.28 2.28 2.75 2.75
¯χ20.87 0.93 1.62 1.76
aThe mass of VB 10 is assumed to be 0 .078 M ⊙according to Pravdo & Shaklan (2009)
bLarge uncertainty due to correlation with the eccentricity
cUnconstrained or poorly constrained
dDerived quantity using Kepler equations– 12 –
Fig. 1.— Top panel. Circular Least-squares periodogramshowingthe two most si gniﬁcant periods
with their corresponding False Alarm Probabilities (FAP). Second row. FAPs obtained for a grid
of Eccentricity–Period pairs around the 50 d (left) and the 2 70 d (right) when only astrometry is
considered. Third row. FAPs obtained when our new RV are included to the ﬁt. Bottom row.
Final FAPs obtained when all published RV data are combined i n a joint ﬁt.– 13 –
0 0.2 0.4 0.6 0.8 1
Phase-4-20246810R.A.(mas)
0 0.2 0.4 0.6 0.8 1-4-20246810
0 0.2 0.4 0.6 0.8 1
Phase-4-20246810 Dec (mas)
0 0.2 0.4 0.6 0.8 1-4-20246810
0 0.2 0.4 0.6 0.8 1
Phase-4-20246810R.A.(mas)
0 0.2 0.4 0.6 0.8 1-4-20246810
0 0.2 0.4 0.6 0.8 1
Phase-4-20246810 Dec (mas)
0 0.2 0.4 0.6 0.8 1-4-20246810
0 0.2 0.4 0.6 0.8 1
Phase32333435363738RV (km/s)
0 0.2 0.4 0.6 0.8 132333435363738
0 0.2 0.4 0.6 0.8 1
Phase32333435363738
MIKE
HIRES
CFHT
NIRSPEC Z09P = 49.84 days P = 278.5 days
Fig. 2.— The best ﬁt (lowest χ2) joint solutions to the Pravdo & Shaklan (2009) astrometry a nd
used RVs for the two signals. Top panels contain the astromet ric oﬀsets after the removal of the
corresponding parallax and the proper motion. The lower pan els contain all RVs used. Each RV
point represents the weighted average of the values obtaine d using both reference stars if available.
The best ﬁt oﬀset has been applied to Z09 data (Green triangles ). Phase 0 corresponds to the ﬁrst
astrometric epoch at JD 2451438 .64 and the corresponding folding periods are given on the top .
Fig. 3.— Left: Steps in period-eccentricity space of a Marko v Chain of 106elements applied to the
astrometry only (black) and to the astrometry+all RV data (b rown). The distribution resembles
the FAP contours on the eP-maps around 270 days indicating th at the chain has successfully
converged to the equilibrium distribution. Right: Histogr am reproducing the marginalized density
distributions in efor the astrometry only and astrometry+RV around the 270 d so lution.