An astrometric planetary companion candidate to the M9 Dwarf TVLM 513-46546
Salvador Curiel, Gisela N. Ortiz-León, Amy J. Mioduszewski, Rosa M. Torres
DDraft version August 5, 2020
Typeset using L A TEX twocolumn style in AASTeX62
An astrometric planetary companion candidate to the M9 Dwarf TVLM 513 − Salvador Curiel, Gisela N. Ortiz-Le´on, Amy J. Mioduszewski, and Rosa M. Torres Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico (UNAM), Apdo Postal 70-264, M´exico, D.F., M´exico. Max Planck Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, D-53121 Bonn, Germany National Radio Astronomy Observatory, Domenici Science Operations Center, 1003 Lopezville Road, Socorro, NM 87801, USA Centro Universitario de Tonal´a, Universidad de Guadalajara, Avenida Nuevo Perif´erico No. 555, Ejido San Jos´e Tatepozco, C.P.48525, Tonal´a, Jalisco, M´exico (Received 2020 May 6; Accepted 2020 June 17)
Submitted to AJABSTRACTAstrometric observations of the M9 dwarf TVLM 513–46546 taken with the VLBA reveal an astro-metric signature consistent with a period of 221 ± p = 0.35 − M J , a circular orbit ( e (cid:39) − − ◦ . The detected companion, TVLM 513 b , is one of the few giant-mass plan-ets found associated to UCDs. The presence of a Saturn-like planet on a circular orbit, 0.3 AU froma 0.06 − M (cid:12) star, represents a challenge to planet formation theory. This is the first astrometricdetection of a planet at radio wavelengths. Keywords: astrometry − circumstellar matter − planetary systems − stars: coronae − stars: individual(TVLM 513 − − stars: X-rays: stars INTRODUCTIONThe search for extrasolar planets is one of the mostvibrant fields in modern astrophysics. Thanks to theadvent of new instrumentation and data analysis meth-ods, many exoplanets have been discovered and char-acterized in recent years. Currently, one of the maintargets for exoplanet searches are main-sequence low-mass stars, known as M dwarfs, since they are the mostnumerous stars in the Galaxy and are known to host alarge number of small planets (e.g., Chabrier & Baraffe2000; Bonfils et al. 2013; Dressing & Charbonneau 2013;Gillon et al. 2017). However, the occurrence of giant-mass planets around M dwarfs is low compared to theiroccurrence around Sun-like stars (e.g., Endl et al. 2006;Cumming et al. 2008; Bonfils et al. 2013), which isconsistent with core-accretion models that predict fewJovian-mass planets orbiting M dwarfs (e.g., Laughlinet al. 2004; Adam et al. 2005; Ida & Lin 2005; Kennedy& Kenyon 2008).
Corresponding author: Salvador [email protected]
Ultracool Dwarfs (UCDs) are at the lower mass endof the M dwarf stellar class. The occurrence of gi-ant planets around UCDs is an important observa-tional constraint for planet formation theories. For in-stance, the core-accretion theory predicts that giant-mass planet formation scales with the central star mass;therefore, giant-mass planet formation is expected to below around M dwarfs and, especially, around UCDs (e.g.,Laughlin et al. 2004; Kennedy & Kenyon 2008). Giantplanets around UCDs can also be formed via disk in-stability if their disks are suitably unstable (e.g., Boss2006).In recent years, UCDs have been found to host Earth-and Mars-mass planets (e.g., Kubas et al. 2012; Muir-head et al. 2012; Gillon et al. 2017). Radial velocity(RV) measurements of this kind of star have been usedto search for giant planets on compact orbits, excludinga large population of giant-mass planets on very tightorbits < a r X i v : . [ a s t r o - ph . E P ] A ug Curiel et al.
In the near future, Gaia’s astrometric observationshave the potential to detect many (probably thousands)exoplanets and brown dwarfs associated with solar-typeand low-mass stars (e.g., Casertano et al. 2008; Sozzettiet al. 2014; Perryman et al. 2014). Very long baselineinterferometry (VLBI) astrometric observations can alsoreveal sub stellar companions (brown dwarfs and giant-mass planets) around pre-main-sequence stars and M-dwarf stars. This technique has already yielded massupper limits of a few planetary companion candidates(Bower et al. 2009, 2011). Observations carried outin the optical wavelength range with 10 m class tele-scopes allow similar astrometric searches, but they re-quire conversion of relative to absolute astrometry (e.g.,Sahlmann et al. 2016).Astrometric planet searches consist of measuring thepositional shift (or reflex motion) of the star aroundthe center of mass of the orbit due to the gravitationalpull of a companion. This technique allows the discov-ery and characterization of extrasolar planets, providedthat the astrometric accuracy is much smaller than theamplitude of the reflex motion. For instance, a reflexmotion of 1 mas will be produced by a 5 Jupiter-massplanet on a three-year orbit around a Sun-like star at 10pc (Sozzetti 2005; Sahlmann 2012). Several astrometricplanet searches have been conducted toward UCDs, butthey have not yet found new exoplanets (e.g., Pravdo& Shaklan 1996; Boss et al. 2009; Forbrich et al. 2013).However, these searches have been crucial primarily be-cause they have enabled the determination of precisetrigonometric distances, which are important to deter-mine the luminosity, mass, and ages of UCDs. Theseproperties are central to understanding the physics ofthese objects (e.g., Dahn et al. 2002; Andrei et al. 2011;Dupuy & Liu 2012; Dupuy & Kraus 2013; Smart et al.2013; Sahlmann et al. 2014).At present, low-mass brown dwarfs (several tens ofJupiter masses) have been found orbiting a few UCDsand TTauri stars (e.g., Sahlmann et al. 2013; Curiel etal. 2019). Until now, only a few UCDs have been studiedwith VLBI (TVLM 513 − − ± ∼
400 Myr and a mass between 0.06 and 0.08 M (cid:12) (Mart´ın et al. 1994; Reid et al. 2002; Hallinan etal. 2008), while membership in the young/old disk kine-matic category of Leggett (1992) is suggested by a lowspace velocity (Leggett et al. 1998). This estimated massplaces TVLM 513 just at the brown dwarf boundary(Hallinan et al. 2006). Forbrich et al. (2013) investi-gated the possibility that the residuals of their parallaxfit could be associated with the reflex motion of the Mdwarf due to an unseen companion. In their analysis,they considered only circular orbits on the plane of thesky. However, even when the residuals are significantlylarger than the astrometric precision, their analysis sug-gested that the VLBI astrometry, in principle, excludesthe presence of unseen companions with masses higherthan ∼ J at orbital periods of ∼
10 days or ∼ J at periods ∼
710 days (Forbrich et al. 2013). Gawro´nskiet al. (2017) also excluded the possibility of compan-ions more massive than Jupiter in orbits with periodslonger than ∼ OBSERVATIONSWe use the VLBA to conduct new observations ofTVLM 513 over a time interval of 1.5 yr starting in2018 June. A total of 18 epochs were observed as partof projects BC236, BC244, and BC255 (see Table 1 fordetails). The observations were taken at a frequencyof 8.4 GHz in dual polarization mode with 256 MHz or512 MHz (last two epochs) of total bandwidth in eachpolarization. The observations consisted of alternatescans on the target and the phase-reference calibrator,J1455+2131, with an on-source time of ∼ ∼
50 minutes to im-prove the phase calibration. In addition, two geodetic-like blocks of ∼
30 minutes each were included at thebeginning and the end of the observing sessions. Thesescans are used to estimate and remove phase offsets in-troduced by tropospheric and clock errors.To complement our analysis, we also include in thispaper archival VLBA data from project BF100, whichused the same phase calibrator and observed in a totalof nine epochs (see also Table 1) from 2010 March to2011 August. These data were taken at a frequencyof 8.4 GHz with 64 MHz of total bandwidth in dualpolarization mode.We use AIPS (Greisen 2003) to reduce our new and thearchival data following standard procedures for phase-referencing observations (e.g., Ortiz-Le´on et al. 2017;Curiel et al. 2019). Particular care was taken when cal-ibrating the archival data since they used an old posi-tion for the phase calibrator during correlation. Then,before deriving any calibration, we correct the positionof the phase calibrator to the new position as measuredin our new data. Offsets of − − µ as and two weightings schemes, purenatural (robust parameter = 5) and partial uniform (ro-bust = 0). Detections of TVLM 513 were achieved inall 18 new epochs, and six epochs of the old projectBF100. Our images have, on average, rms noise levels of ∼ µ Jy beam − for natural weighting, i.e. three timesbetter than previous VLBA observations (Forbrich etal. 2013), as a result of increased bandwidth and largerintegration time. Source positions and positional uncer-tainties for pure natural and partial uniform weightingwere first obtained by fitting a Gaussian model to thesource brightness distribution. This was done using theAIPS task JMFIT. In addition, we measured the posi-tion of the pixel with maximum flux density using thetask MAXFIT. Table 1 gives the measured positionswith MAXFIT for partial uniform weighting. To esti-mate the errors in positions, we use the equation for theexpected theoretical astrometric uncertainty given by σ (cid:39) θ res / N , (1)where θ res is the resolution of the interferometer, andS/N the signal-to-noise ratio (Thompson et al. 2017).Then we quadratically added half of the pixel size to thisuncertainty. For each epoch, the resolution was taken asthe geometric mean of the major and minor size of the telescope beam. The S/N is directly provided by JM-FIT. Figure 1 shows the intensity map obtained on 2018October 12 with partial uniform weighting. Also shownare the positions as measured with JMFIT and MAX-FIT. We see that the JMFIT position does not coincidewith the position of the pixel with maximum flux. Thisis because the procedure used to obtain the centroid isaffected by the asymmetry of the emission. Here JMFITis also sensitive to the box selected to define the region inthe image to be fitted. The MAXFIT positions are notaffected by source asymmetries, therefore, they providea better estimation of the star position. FITTING OF THE ASTROMETRIC DATA3.1.
Least-squares Periodogram
We use a periodogram code to search for astrometricsignatures that indicate the possible presence of one ormore companions to the main source. The periodogramof the astrometric data is obtained using a modifiedversion of the classic least-squares periodogram methoddescribed by Curiel et al. (2019). The new version ofthe code, which we call a recursive least-squares peri-odogram with a circular orbit (RLSCP), takes into ac-count the possibility of fitting the Keplerian orbits ofseveral companions (see also, e.g., Anglada-Escud´e &Tuomi. 2012). This recursive periodogram consists offitting all the parameters of the already detected signalstogether with the signal of a new companion, which isunder investigation. We start assuming circular orbits,but we can include a fixed eccentricity for the signalsalready found. When no previous planets have been de-tected, the initial periodogram is obtained by comparingthe least-squares fits of the basic model (proper motionsand parallax only) and a one-companion model (propermotions, parallax, and Keplerian orbit of a single com-panion). When a signal has already been detected, therecursive periodogram compares the least-squares fits ofa one- and two-companion model (proper motions, par-allax, and Keplerian orbits of two companions), and soon.The weighted least-squares solution is obtained by fit-ting all of the free parameters in the model for a givenperiod. The sum of the weighted residuals divided byN obs is the so-called χ statistic, where N obs is the num-ber of data points. Then, each χ P of a given model with k P − free parameters can be compared to the χ of thenull hypothesis with k − free parameters by computingthe power, z , as (e.g., Anglada-Escud´e & Tuomi. 2012;Curiel et al. 2019): z ( P ) = ( χ k − χ P ) / ( N k +1 − N k ) χ P / ( N obs − N k +1 ) , (2) Curiel et al. where χ k is the χ statistic for the model with k planets(the null hypothesis), χ P is the χ statistic for the modelincluding one more planet with an orbital period P , N k is the number of free parameters in the model with k planets, and N k +1 is the number of free parameters inthe model including one more candidate in a circularorbit with an orbital period P . In this model, a large z is interpreted as a very significant solution. The valuesof z follow a Fisher F -distribution with N k +1 − N k and N obs − N k +1 degrees of freedom (Scargle 1982; Cumming2004). Even if only noise is present, a periodogram willcontain several peaks (see Scargle 1982, as an example)whose existence has to be considered in obtaining theprobability that a peak in the periodogram has a powerhigher than z ( P ) by chance, which is the so-called false-alarm probability (FAP),FAP = 1 − (1 − Prob[z > z(P)]) O , (3)where O is the number of independent frequencies. Inthe case of uneven sampling, O can be quite large andis roughly the number of periodogram peaks one couldexpect from a data set with only Gaussian noise and thesame cadence as the real observations. We adopt therecipe O ∼ ∆ T /P min given in Cumming (2004, Section2.2), where ∆ T is the time span of the observations and P min is the minimum period searched. For instance,assuming that ∆ T = 560 days and P min = 20 days, theastrometric data is expected to have O ∼
28 peaks.3.2.
Least-squares and AGA Fitting Algorithms
Here we use the least-squares algorithm and the asex-ual genetic algorithm (AGA) presented by Curiel et al.(2019). In short, we use the source barycentric two-dimensional position described as a function of time( α ( t ), δ ( t )), accounting for the (secular) effects of propermotions ( µ α and µ δ ), the (periodic) effect of the paral-lax Π, and the (Keplerian) gravitational perturbationinduced on the host star by one or more companions,such as low-mass stars, substellar companions, or plan-ets (mutual interactions between companions are nottaken into account). Given a discrete set of N obs datapoints ( α ( i ), δ ( i )) with associated measurement errors σ i , one seeks for the best possible model (in other words,the closest fit) for these data using a specific form ofthe fitting function, ( α ( t ), δ ( t )). This function has,in general, several adjustable parameters, whose valuesare obtained by minimizing a ”merit function,” whichmeasures the agreement between the data ( α ( i ), δ ( i ))and the model function ( α ( t ), δ ( t )). The maximum-likelihood estimate of the model parameters ( c i , ..., c k )is obtained by minimizing the χ function (e.g., Cant´oet al. 2009; Curiel et al. 2019): χ min = (cid:80) Ni =1 (cid:16) α i − α ( t i ; c ,...,c k ) σ i (cid:17) + (cid:80) Ni =1 (cid:16) δ i − δ ( t i ; c ,...,c k ) σ i (cid:17) , (4)where each data point ( α i , δ i ) has a measurement errorthat is independently random and distributed as a nor-mal distribution about the ”true” model with standarddeviation σ i . RESULTS AND DISCUSSIONThe new VLBA astrometric observations of theM9 dwarf TVLM 513 cover a time span of about 558days, with an observational cadence that varies duringall the time observed. Including previous VLBA obser-vations of this source, the time span of the observationsincreases to about 3574 days. However, the observationswere carried out in two time blocks, one of about 1 yrand the other of about 1.5 yr, separated by about 7 yr(see Table 1). The time span and cadence of the newand the combined data are adequate to fit the propermotions and the parallax of this source, as well as tosearch for substellar companions with orbital periodsbetween a few days and more than 1 yr. Below, we usethe recursive least-squares periodogram (see sec. 3.1),and the least-squares and the AGA algorithms presentedby Curiel et al. (2019) to fit the astrometric data of thissource.The observation taken on 2018 November 5 was car-ried out under bad weather conditions. Six stations ex-perienced precipitation or high winds during a signifi-cant part of the experiment, and Maunakea experiencedtechnical issues. As a result, the quality of the image andthe astrometry was affected. We found that this epochshows high residuals of the parallax fit in comparisonwith that seen in the rest of the observations that weretaken under better weather conditions. Therefore, wedo not include this epoch in our analysis. Hence, weuse a total of 23 epochs in the analysis we present here.For the astrometric fits that we present here, we haveused the astrometric position of the source obtained withpartial uniform weighting using the task MAXFIT anderrors from equation 1 (see sec. 2 for more details).4.1.
Single-source Astrometry
First, we used both the least-squares and the AGAalgorithms (Curiel et al. 2019) to fit the proper motionsand parallax to the 17 new VLBA astrometric observa-tions without taking into account any possible compan-ion (single-source solution). Then, we fitted all of theVLBA astrometric data, including six previous VLBAdetections of this source, obtained by Forbrich et al.(2013) (see Table 1). The results of a single-source so-lution are shown in Table 2 and Figure 2. We find thatthe fitted parameters (proper motions and parallax) arevery similar in both cases. However, the residuals arelarge and show a temporal trend that suggests the pres-ence of at least one companion with a possible orbitalperiod of a few hundred days (see Figure 2).We also fitted the astrometric data with accelerationterms, which take into account an astrometric signaturedue to a possible companion with a large orbital period.We find that the fits do not improve substantially whenincluding acceleration terms (see Table 3). The fittedacceleration terms are small in the case of the combinedVLBA data ( a α = − ± − and a δ = 0.0332 ± − ) and somewhat larger us-ing only the new VLBA data, but they are consistentwith zero within the errors. In this case the accelera-tion terms are a α = − ± a δ = 0.41 ± − , which suggests that this source might have acompanion with an orbital period larger than about 1.5yr (the time span of the new astrometric VLBA data)and smaller than 9.8 yr (the time span of the combinedastrometric VLBA data).In what follows, we obtain the astrometric fit of thedata without taking into account possible accelerationterms. 4.2. Single-companion Astrometry
The RLSCP of the new astrometric VLBA data (seeFigure 3) does not show a narrow prominent peak. How-ever, it shows a somewhat (cid:48)(cid:48) broad signal (cid:48)(cid:48) with an orbitalperiod between 200 and 300 days. The periodogram alsoshows that this broad signal is part of a large plateau-likestructure that extends beyond the orbital periods con-sidered in the plot (1000 days). This plateau has a dropin the periodogram power around 297 days, suggestingthat there may be two broad signals in the periodogram,one at about 241 days and the other one with an orbitalperiod larger than the time span of the new VLBA ob-servations (about 1.5 yr). The main broad signal is notwell constrained but seems to have a relatively weakpeak at about 241 days. The FAP of this main peakis 1.43%, suggesting that this signal is real and that itcould be due to a companion.The RLSCP of the combined (old and new) VLBAdata also shows a broad signal between 200 and 300days, nearly coinciding with the broad signal observedin the periodogram of the new data. In this case, theperiodogram appears somewhat noisier, especially at or-bital periods larger than 100 days. The main peak of thecombined data is located at 220 days and has an FAPof 5.39%, which, although it is somewhat above the 1% limit usually used to consider a signal as possibly real,also suggests that the signal is real and due to the pres-ence of a companion.To further investigate the possibility that the peakthat appears in the periodograms is real, we computedthe recursive periodogram of the two data sets includingthe signal of this possible companion (two-companionsolution). We now fit simultaneously the parametersof the already detected signal together with the signalunder investigation (a second possible companion). Toobtain an improved global solution (with two possiblecandidates), we include in the fitting the orbital periodof the first companion using, as an initial guess, the or-bital period of the peak in the initial periodogram. TheRLSCP algorithm includes the possibility that the or-bital period of the first companion adjusts during thesimultaneous fit of both possible companions. The re-sultant periodogram is shown in Figure 3. The newperiodograms show that the signal of the initial candi-date disappears, leaving some residual noise. In addi-tion, the new periodograms show no significant signals,indicating that there is only one significant signal in theperiodogram. The new periodogram of the combineddata shows two very narrow and relatively strong sig-nals between 3 and 5 days that do not appear in theperiodogram of the new VLBA data. These signals aremost likely spurious signals or artifacts. The new peri-odograms also show a slow rising signal close to the endof the plot. This suggest that there may be a secondcompanion that, if real, produces a small astrometricsignal and that its orbital period is larger than the timespan of the new VLBA data ( >
558 days). Further ob-servations will be needed to confirm this putative secondcompanion.We then used both the least-squares and the AGAalgorithms to fit the astrometric observations of thissource, including a possible single companion (singlecompanion solution). First we used both methods tofit the new VLBA astrometric observations to obtainproper motions and parallax, taking into account a sin-gle companion. Table 4 summarizes the best fit and the χ red per degree of freedom ( χ red = χ / ( N data − N par − N data = 2 × N points and N par is the number offitted parameters). The fits of the parallax, proper mo-tions, and orbital motions of the candidate are presentedin Figure 4. The fit of the astrometric data clearly im-proves when including a companion, as seen by the χ red .The χ red is now about a factor of 2 smaller, comparedwith the single-source solution. Tables 2 and 4 andFigures 2 and 4 show that the residuals of the single-companion solution (RMS ∼ Curiel et al. (RMS ∼ ∼ < µas ). Theastrometric signal in the source due to the companionis 0.17 ± σ . Althoughthe astrometric signal is small with a relatively largeerror, the same signal appears when we analyze bothdatasets using three different algorithms (periodogram,least-squares, and AGA). This indicates that this astro-metric signal is real.Table 4 summarizes the best fit of the new VLBA as-trometric data, including a companion. The orbit ofthe companion has an orbital period P ∼
241 days, aposition angle of the line of nodes Ω ∼ ◦ , and an in-clination angle i ∼ ◦ , which indicates that the orbit ofthe companion is prograde ( i < ◦ ). However, the largeerror in the inclination angle ( ∼ ◦ ) suggests that theorbit could also be retrograde ( i > ◦ ). In addition, theastrometric fit of the data indicates that the eccentricityof the orbit is not well constrained; thus, we use a fixedeccentricity, e = 0. The orbital period obtained with theastrometric fit is consistent with that obtained with theperiodogram. The orbit of the companion is relativelywell fitted; however, the errors of the orbital parametersare large. This is consistent with the relatively broad sig-nal observed in the periodogram (see Figure 3). Furtherobservations are needed to better constrain the orbitalparameters of this companion. With this astrometricfit, we cannot estimate the dynamical mass of the sys-tem; thus to estimate the mass of the companion, weuse the lower and upper limits of the best estimatedmass for this source M ∗ = 0 . − . M (cid:12) (Mart´ın et al.1994; Reid et al. 2002; Hallinan et al. 2008) as a fixedmass. Table 4 summarizes the estimated parameters ofthe companion, hereafter TVLM 513 b . We find that themass of the companion is between 0.00036 ( M ∗ = 0 . M (cid:12) ) and 0.00044 M (cid:12) ( M ∗ = 0 . M (cid:12) ), which is consis-tent with a planetary companion with a mass between0.38 and 0.46 M J . The semimajor axis of the orbit ofthis planetary companion is between 0.295 and 0.325 au.We also fitted the combined VLBA data, including theKeplerian fit of a single companion (single-companionsolution). Table 4 summarizes the best fit and the χ red per degree of freedom. The fit of the combined dataalso improves when including a companion. The residu-als of the single-companion solution (RMS ∼ ∼ χ red is smaller by a factor of 1.7 compared to the single-source solution. The orbital fit to the combined datais in general similar to that obtained in the case of the fit of the new VLBA astrometric data (see Table 4 andFigures 4). The orbital parameters and their estimatederrors are similar, with relatively small differences fromthose obtained using only the new VLBA data (see Ta-ble 4). The estimated mass and the semimajor axis ofthe orbit of the companion are also similar to those ob-tained with the new VLBA data. These results furthersupport the detection of a planetary companion.These results indicate that the best fit of the orbit ofthe companion is obtained with the new VLBA data.This is not surprising because these observations are ingeneral deeper and with smaller error bars than previousVLBA observations. However, it is important to pointout that the astrometric signal appears in both the newVLBA data and the combined data. Furthermore, thesame astrometric signal is found using the two differentalgorithms (least-squares and AGA) that we have usedhere, which is also consistent with the astrometric signalfound in the least-squares periodogram. Figures 4 sug-gests a reasonably good astrometric fit. However, theresiduals, although small (RMS ∼ ∼ ∼ Distance to TVLM 513
Table 4 shows that the estimated parallax to TVLM 513does not change substantially when fitting only the newVLBA data or combining the new data with the previ-ous VLBA data. Taking into account that the differentfits give slightly different values for the parallax, wehave calculated the weighted average of the estimatedparallax as follows: < Π > = (cid:80) Ni π i /σ i (cid:80) Ni /σ i , (5)and the uncertainty is: σ ( < Π > ) = (cid:118)(cid:117)(cid:117)(cid:116) (cid:80) Ni (1 /σ i )( π i − < Π > ) (cid:80) Ni /σ i , (6)where π i and σ i are the estimated parallax of each fitand its uncertainty, respectively.We obtain that the weighted parallax is of 93.368 ± d = 10 . ± . ± Proper Motions
Table 4 also shows that the estimated proper motionsof TVLM 513 do not change substantially when fittingthe new VLBA data and the combined data. The fitof the combined VLBA data gives slightly better es-timates for the proper motions because they cover alarger time span. We obtain that the weighted aver-age proper motions are µ α = − . ± .
011 mas yr − and µ δ = − . ± .
010 mas yr − .4.5. Expected RV
The solution that we obtain for the single-companionastrometry can be used to estimate an expected inducedRV of the star due to the gravitational pull of the com-panion as follows (e.g., Cant´o et al. 2009; Curiel et al.2019): K = (cid:18) πGT (cid:19) / m p sin ( i )( M ∗ + m p ) / √ − e (7) where G is the gravitational constant, and T , M ∗ , m p ,and e are the orbital period, the star and companionmasses, and the eccentricity of the orbit of the compan-ion. Using the solutions of the astrometric fit given inTable 4, we obtain that the maximum RV of TVLM 513induced by TVLM 513 b is K ∼ −
81 m s − (for thecombined and the new VLBA data, respectively). ThisRV could, in principle, be observed with high spectralresolution spectrographs. Future short- and long-termhigh-resolution spectroscopic observations of TVLM 513may be able to detect the RV signal that we find thatTVLM 513 b induces on TVLM 513. Furthermore, thesekinds of observations may also be able to confirm the pu-tative second companion suggested by the periodogram.4.6. Flux variability of the source
The radio continuum flux density of TVLM 513 isclearly variable in time. Figure 5 shows that the fluxdensity of this source has short-term, and probably long-term, variability. The time scale of the short-term vari-ability is of a few days, where the flux changes by abouta factor of 2 or so. This flux variability is observed withboth the VLBA observations obtained at 8.4 GHz andthe European VLBI Network (EVN) observations ob-tained at 5 GHz obtained by Gawro´nski et al. (2017).This source is well known to be variable on a time scaleof ∼ ∼ F lux = f + f m e − ( t − t σ . (8)This function fits a single gaussian function plus a fluxbase to all of the VLBA epochs. Here f is a constantflux density (in mJy), f m is the maximum increment inthe flux density (in mJy) during the outburst, t is thetime of the maximum flux of the source during the out-burst (in days from the first observed epoch), and σ isthe FWHM (in days) of the gaussian function. In this Curiel et al. fit, the single outburst observed about 10 yr ago is fittedwith a single gaussian function. The fit of the observedflux density data gives f = 0.14 mJy, f m = 0.71 mJy, t = 23.21 days, and σ = 9.60 days. This fit suggests thatthe source had a maximum flux outburst of about 0.85mJy centered at the epoch JD = 2,455,297.139, whichis very close to the third observed epoch (BF100C; seeTable 1), and that the outburst had an FWHM of 9.60days and lasted for about 70 days. For the fit, we haveonly used the observations obtained with the VLBA be-cause they were obtained at 8.4 GHz, while the EVNobservations were obtained at 5 GHz. In Figure 5 weplot the observed flux densities, the fit that we obtain,and the residuals of the fit. The residuals of the fit showthat the previous VLBA observations can be well fittedwith a single gaussian function with an amplitude ofabout 0.71 mJy and an FWHM of about 9.60 days, andthat the new VLBA observations do not show a similaroutburst. The fit also shows that the source is gener-ally weak, having a mean flux density around 0.14 mJywith a small flux fluctuation of about 0.1 mJy in shortperiods of time, probably of a few days, or even shorter.The source may also have strong outbursts, such as theone observed about 10 yr ago that lasted for about 70days (see Figure 5). The large temporal gap of about 7yr in the VLBA data precludes the possibility of findingwhether these outbursts may be periodic or not. Ourrecent VLBA observations, which were obtained in atime span of about 560 days, do not show any strongoutbursts, suggesting that if the source undergoes pe-riodic outbursts, they are probably at intervals longerthan this time scale. Thus, we find that the sourceseems to undergo flux fluctuations with at least threedifferent time spans: a) a short-period variation with atime span of about 1.96 hr, observed with the VLA andcorrelating with the rotation period of this UCD; b) anintermediate-period variation with a time span of a fewdays (not well established), observed with the VLBA;and c) a possible longer-period variation, observed withthe VLBA as a single outburst about 10 yr ago. Futureobservations will tell whether the source undergoes pe-riodic outbursts, as that observed about 10 yr ago, andwhat their origin may be.4.7. First exoplanet found with radio astrometry
There is only one exoplanet that has been foundusing astrometry (HD 176051 b; Muterspaugh et al.2010). It was found using optical differential astrom-etry. This planetary companion is associated with arelatively nearby (14.99 ± M (cid:12) ), and has an estimated mass of 1.5 ± M J , assuming that it is associated with the low mass star. The mass of the planetary companion is expectedto be higher if it is associated to the higher-mass star.The best fit of the astrometric data of the M9 dwarfTVLM 513 indicates that this UCD has at least onesubstellar companion, TVLM 513 b . Furthermore, theestimated weighted average mass and semi-major axisof TVLM 513 b are 0.347 ± M J , and 0.2789 ± M (cid:12) ), or 0.418 ± M J , and0.3072 ± M (cid:12) ). The estimatedweighted average period and inclination angle of the or-bit are 221 ± ± ◦ , respectively. Theestimated mass is consistent with this planetary com-panion being a Saturn-mass planet (0.30 M J ). Figure 6shows all the confirmed planets that have been found upto now for which the planetary mass has been estimated(either m p or m p × sin ( i )). We include TVLM 513 b inthis figure. This figure shows that TVLM 513 b is locatedin a region in the M ∗ − m p and M ∗ − a p phase spacewhere very few planets have been found. TVLM 513is one of the lowest-mass stars with known Jovian-massplanetary companions.The estimated weighted average astrometric signal ofTVLM 513 is 0.145 ± (cid:48)(cid:48) jitter (cid:48)(cid:48) added to the truesource position due to stellar activity. It is estimatedthat M9 UCD have stellar radius of ∼ (cid:12) (e.g.,Chabrier etal. 2000; Dahn et al. 2002; Hallinan et al.2006). Thus, assuming that the radio emission is origi-nated within ∼ b .As we have mentioned before, in recent years, it hasbeen found that giant-mass planets, such as the one wehave found orbiting TVLM 513, have a very low occur-rence around UCDs, which is consistent with predictionsof planetary formation theories. The core-accretion the-ory predicts that the formation of giant-mass planetsscales with the mass of the central star; thus, it is ex-pected that very few Jovian-mass planets are formedaround UCDs (e.g., Laughlin et al. 2004; Kennedy &Kenyon 2008). The core-accretion theory indicates thatthese planets would be formed in orbits far from thestar, at several au. On the other hand, it is expectedthat disk instability may also be able to form giant-massplanets around UCDs (e.g., Boss 2006). In this case, theorbit of the planet is expected to be relatively closer tothe star, from a few to several au. The semimajor axisof the orbit of TVLM 513 b , a ∼ b was formed by the same colli-sional accumulation process that led to the formation ofthe terrestrial planets in our solar system. Alternatively,TVLM 513 b may have formed with a wider orbit, at sev-eral au from the star, and then migrated inward to itscurrent orbit. However, it is not clear what would stopthe migration of the planet at 0.3 au. Further theoreti-cal models will be required to understand the formationof giant-mass planets, such as the one we find associatedwith the M9 UCD TVLM 513.Finally, to our knowledge, this is the second exoplanetfound using astrometry and the first exoplanet foundusing absolute astrometry. In addition, this is also thefirst exoplanet found using radio astrometric observa-tions. This result suggests that radio observations withthe VLBA can be used to search for giant-mass planetsaround very low mass stars, such as M dwarfs, and inparticular around UCDs. CONCLUSIONSThe multi-epoch VLBA observations of the M9 dwarfTVLM 513 that we present here allow us to carry outa precise analysis of the spatial wobbling of this sourcedue to its parallax and its proper motions, as well as tosearch for possible companions. The precise astromet-ric observations obtained with the VLBA were crucial tocarry out this kind of study. We find that the determina-tion of the distance to this source improves significantly.Here we present different ways to analyze the VLBAastrometric observations of the M9 dwarf TVLM 513.We have used two different algorithms (a least-squaresalgorithm and a genetic algorithm) to fit the astrometricmulti-epoch data obtained with the VLBA. First, weonly fit the parallax and proper motions of the host star.The residuals of this fit are large compared with the noise of the observed data and the expected precision ofthe multi-epoch VLBA observations.We have searched for possible companions using a re-cursive least-squares periodogram, finding a companioncandidate in the periodogram. We also find that the as-trometric fit improves substantially when including theorbit of a companion in the fit. We find that the pa-rameters of the orbit are consistent with a planetarycompanion of 0.347 ± M J , with an orbital periodof 221 ± ± M (cid:12) ), or 0.418 ± M J , withan orbital period of 221 ± ± M (cid:12) ). The estimated or-bital motions of TVLM 513 b are consistent with being aSaturn-like planet in a compact, probably circular orbitand with a large inclination angle ( ∼ ◦ ). This is thesecond exoplanet found with the astrometry techniqueand the first exoplanet found using absolute astrometry.It is also the first exoplanet that has been found withradio astrometric observations.We thank the reviewer for his/her valuable com-ments that helped to improve this paper. S.C. acknowl-edges support from UNAM and CONACyT, M´exico.This work was supported by UNAM-PAPIIT IN103318.G.N.O.-L. acknowledges support from the von Hum-boldt Stiftung. The Long Baseline Observatory is a fa-cility of the National Science Foundation operated undera cooperative agreement by Associated Universities, Inc.The National Radio Astronomy Observatory is a facil-ity of the National Science Foundation operated under acooperative agreement by Associated Universities, Inc.ORCID iDsSalvador Curiel https:/orcid.org/0000-0003-4576-0436Gisela N. Ortiz-Le´on https:/orcid.org/0000-0002-2863-676XRosa M. Torres https:/orcid.org/0000-0002-7179-6427REFERENCES Adams, F. C., Bodenheimer, P., & Laughlin, G. 2005,Astron. Nachr., 326, 913Andrei, A. H., Smart, R. L., Penna, J. L., et al. 2011, AJ,141, 54Anglada-Escud´e, G., & Tuomi, M. 2012, A&A, 548, A58Berger, E. 2002, ApJ, 572, 503 Berger, E., Gizis, J. E., Giampapa, M. S., et al. 2008, ApJ,673, 1080Blake, C. H., Charbonneau, D., & White, R. J. 2010, ApJ,723, 684Bonfils, X., Delfosse, X., Udry, S., et al. 2013, A&A, 549,A109Boss, A. P. 2006, ApJ, 643, 501 Curiel et al.
Boss, A. P., Weinberger, A. J., Anglada-Escud´e, G., et al.2009, PASP, 121, 1218Bower, G. C., Bolatto, A., Ford, E. B., & Kalas, P. 2009,ApJ, 701, 1922Bower, G. C., Bolatto, A., Ford, E. B., et al. 2011, ApJ,740, 32Cant´o, J., Curiel, S, & Mart´ınez-G´omez, E. 2009, A&A,501, 1259Casertano, S., Lattanzi, M. G., Sozzetti, A., et al. 2008,A&A, 482, 699Chabrier, G. & Baraffe, I. 2000, ARA&A, 38, 337Chabrier, G., Baraffe, I., Allard, F. & Hauschildt, P. 2000,ApJ, 542, 464Close, L. M., Siegler, N., Freed, M., & Biller, B. 2003, ApJ,587, 407Cumming, A. 2004, MNRAS, 354, 1165Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008,PASP, 120, 531Curiel, S., Ortiz-Le´on, G. N., Mioduszewski, A.J., & Torres,R. M. 2019, ApJ, 884, 13Dahn, C. C., Harris, H. C., Vrba, F. J., et al. 2002, AJ, 124,1170Dressing, C. D. & Charbonneau, D. 2013, ApJ, 767, 95Dupuy, T. J., & Kraus, A. L. 2013, Sci, 341, 1492Dupuy, T. J., & Liu, M. C. 2012, ApJS, 201, 19Dupuy, T. J., Forbrich, J, Rizzuto, A. et al. 2016, ApJ, 827,23Endl, M., Cochran, W. D., K¨urster, M., Paulson, D. B., etal. 2006, ApJ, 649, 436Forbrich, J., Berger, E., & Reid, M. J. 2013, ApJ, 777, 70Forbrich, J., Dupuy, T. J., Reid, M. J., et al. 2016, ApJ,827, 22Gawro´nski, M. P., Go´zdziewski, K., & Katarzy´nski, K.2017, MNRAS, 466, 4211Gillon, M., Triaud, A. H. M. J., Demory, B. O. et al. 2017,Natur, 542, 456Greisen, 2003, in Information Handling in Astronomy:Historical Vistas, Vol. 285, ed. A. Heck (New York:Springer), 109Hallinan, G., Antonova, A., Doyle, J. G.. et al. 2006, ApJ,653, 690Hallinan, G., Brouke, S., Lane, C. et al. 2007, ApJ, 663, L25Hallinan, G., Antonova, A., Doyle, J. G.. et al. 2008, ApJ,684, 644Ida, S., & Lin, D. N. C. 2005, ApJ, 626, 1045Kennedy, G. M., & Kenyon, S. J. 2008, ApJ, 673, 502Kubas, D., Beaulieu, J. P., Bennett, D. P. 2012, A&A, 540,A78 Laughlin, G., Bodenheimer, P., & Adams, F. C. 2004,ApJL, 612, L73Leggett, S. K. 1992, ApJS, 82, 351Leggett, S. K., Allard, F., & Hauschildt, P. H. 1998, ApJ,509, 836Mart´ın, E. L., Rebolo, R. & Magazz´u 1994, ApJ, 436, 262Muirhead, P. S., Johnson, J. A., Apps, K., et al. 2012, ApJ,747, 144Muterspaugh, M. W., Lane, B. F., Kulkarni, S. R., et al.2010, AJ, 140, 1657Ortiz-Le´on, G. N., Loinard, L., Kounkel, M. A., et al. 2017,ApJ, 834, 1410Osten, R. A., Hawley, S. L., Bastian, T. S., & Reid, I. N.2006, ApJ, 637, 518Perryman, M., Hartman, J., Bakos, G. ´A., & Lindegren, L.2014, ApJ, 797, 14Pravdo, S. H., & Shaklan, S. B. 1996, ApJ, 465, 264Reid, I. N., Cruz, K. L., Kirkpatrick, J. D., et al. 2008, AJ,136, 1290Reid, I. N., Kirkpatrick, J. D., Liebert, J., et al. 2002, AJ,124, 519Rodler, F., Deshpande, R., Zapatero-Osorio, M.R., et al.2012, A&A, 538, A141Sahlmann, J. 2012, Ph.D. Thesis, Observatoire de Gen`eve,Universit´e de Gen`eveSahlmann, J., Lazorenko, P. F., S´egransan, D., et al. 2013,A&A, 556, A133Sahlmann, J., Lazorenko, P. F., S´egransan, D. et al. 2014,A&A, 565, A20Sahlmann, J., Lazorenko, P. F., S´egransan, D., et al. 2016,A&A, 595, A77Scargle, J. D. 1982, ApJ, 263, 835Schneider, J., Dedieu, C., Le Sidaner, P., Savalle, R., &Zolotukhin, I.. 2011, A&A, 532, A79Smart, R. L., Tinney, C. G., Bucciarelli, B., et al. 2013,MNRAS, 433, 2054Sozzetti, A. 2005, PASP, 117, 1021Sozzetti, A., Giacobbe, P., Lattanzi, M. G., et al. 2014,MNRAS, 437, 497.Stumpf, M. B., Brandner, W., Joergens, V. et al. 2010,ApJ, 724, 1-11Thompson, A. Richard, Moran, James M., & Swenson,George W., Jr. 2017, Interferometry and Synthesis inRadio Astronomy, 3rd EditionWest, A. A., Morgan, D. P., Bochanski, J. J., et al. 2011,AJ, 141, 97White, S. M., Lim, J. & Kundu, M. R. 1994, ApJ, 422, 293 Table 1.
Observed Epochs and Measured VLBA Positions
Project Date Start UT Stop UT Julian Date α (J2000) σ α δ (J2000) σ δ rms ( µ Jy) Flux Density ( µ Jy)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)BF100A 2010 Mar 18 07:57:38 12:51:46 2,455,273.9338 15 01 8.15964647 0.00000853 22 50 1.4994274 0.0001280 49 310 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Curiel et al.
Table 2.
Single-source Astrometry Fits a Parameter VLBA new VLBA combinedParameters FittedEpochs 17 23 µ α (mas yr − ) − ± − ± µ δ (mas yr − ) − ± − ± ± ± D (pc) 10.7009 ± ± α (mas) b δ (mas) b χ , χ red a The parameters presented here were obtained with AGA.Very similar results were obtained with the least-squaresfitting method. The second column contains theastrometric fit of the new VLBA data. The third columncorresponds to the astrometric fit of the combined VLBAdata. b The rms dispersion of the residual.
Table 3.
Single-source Astrometry Fits a Parameter VLBA new VLBA combinedParameters FittedEpochs 17 23 µ α (mas yr − ) − ± − ± µ δ (mas yr − ) − ± − ± a α (mas yr − ) − ± − ± a δ (mas yr − ) 0.41 ± ± ± ± D (pc) 10.7058 ± ± α (mas) b δ (mas) b χ , χ red a The parameters presented here were obtained with AGA.Very similar results were obtained with the least-squaresfitting method. The astrometric fit includes accelerationterms. The second column contains the astrometric fit ofthe new VLBA data. The third column corresponds to theastrometric fit of the combined VLBA data. b The rms dispersion of the residual. Table 4.
Single-companion Astrometry Fits a Parameter VLBA new VLBA combinedParameters FittedEpochs 17 23 µ α (mas yr − ) − ± − ± µ δ (mas yr − ) − ± − ± ± ± P (days) 241 ±
20 220 ± T (days) 2,458,263 ±
21 2,457,631 ± e b ω (deg) b ±
35 139 ± a (mas) 0.17 ± ± i (deg) 88 ±
36 71 ± D (pc) 10.7151 ± ± m ( M (cid:12) ) c m ( M (cid:12) ) 0.00044 ± ± ± ± m ( M J ) 0.46 ± ± ± ± a ( au ) 0.0018 ± ± ± ± a ( au ) 0.325 ± ± ± ± α (mas) d δ (mas) d χ , χ red a The parameters presented here were obtained with AGA. Very similar results were obtained withthe least-squares fitting method. The astrometric fit includes the orbital motions of a companion.The second column contains the astrometric fit of the new VLBA data. The third columncorresponds to the astrometric fit of the combined VLBA data. b Fixed eccentricity. c Fixed mass of the star. d The rms dispersion of the residual. Curiel et al. h m . s . s . s . s RA (J2000) +22 ◦ . . . . . . D e c ( J ) Figure 1.
The intensity map of TVLM 513 taken on 2018 October 12 is shown here as an example. The contours are 4, 5,and 6 × σ , where σ = 19 µJy beam − is the rms noise level. The plus signs mark the fitted peak positions obtained with themaximum-fit algorithm MAXFIT (cyan) and with a Gaussian brightness distribution obtained with JMFIT (magenta). Figure 2.
Parallax fit to the VLBA data. The left panels show the fit for the VLBA new data and the right panels show the fitof the combined VLBA data. The upper panels show the observed data and the astrometric fit obtained when fitting only theproper motions and the parallax of TVLM 513. The lower panels show the residuals in R.A. and decl. as a function of time.The residuals show a clear temporal trend that suggests that they could be due to at least one companion. Curiel et al.
Figure 3. Left:
RLSCP periodogram obtained by fixing the eccentricity e = 0. The upper panel shows the periodogramobtained with the new astrometric VLBA data. The lower panel corresponds to the fit obtained with the combined VLBA data.The horizontal lines indicate the limits of the false alarm probabilities FAP = 1% and 0.1%. Right: same as the left panels,but in this case the plot shows the RLSCP periodogram obtained by including two possible astrometric signals: the detectedastrometric signal that appears in the initial periodogram (left panels) and the signal of a possible second companion. Theseperiodograms do not show clear evidence of a second companion. However, the periodograms show a very weak temporal trendat orbital periods larger than 300 days, which may suggest the presence of a second companion. The two very narrow peaksbetween 3 and 5 days are most likely spurious signals or artifacts. Figure 4.
Single-companion astrometric fit of TVLM 513 using only the new (left) and the combined (right) VLBA data.The upper two panels show the parallax fit of the source after subtracting proper motions and the astrometric signal of thecompanion. The middle panels show the astrometric fit of the companion after removing parallax and proper motions. Thelower panels show the residuals of the astrometric fit. Curiel et al.
Figure 5.
Radio flux density of TVLM 513 as a function of time. This figure includes all of the VLBI observations obtainedwith the VLBA (blue and green) and EVN (magenta). The VLBA observations were obtained at a frequency of 8.4 GHz, whilethe EVN observations were obtained at a frequency of 5 GHz. The flux density of the source presents short-term temporal fluxdensity variations and seems to have a general tendency to decrease as function of time. The solid line corresponds to the fit ofthe data obtained with the VLBA. The lower panel shows the residuals of the fit, showing that the outburst observed about 10yr ago is well fitted with a single gaussian function. − − − − Planetary Mass [M J ] − − − M a ss o f ho s t s t a r [ M (cid:12) ] Radial VelocityTransitImagingMicrolensingAstrometryThis work − − − Semi major axis [au] − − − M a ss o f ho s t s t a r [ M (cid:12) ] Radial VelocityTransitImagingMicrolensingAstrometryThis work
Figure 6.
Distribution of the planetary mass and the semimajor axis of the planetary orbit vs. the mass of the host starof known exoplanets and candidates as listed at exoplanet.eu (Schneider et al. 2011). The five main detection methods aremarked by different colors. The two black stars indicate the position of TVLM 513 bb