A decade of radial-velocity monitoring of Vega and new limits on the presence of planets
Spencer A. Hurt, Samuel N. Quinn, David W. Latham, Andrew Vanderburg, Gilbert A. Esquerdo, Michael L. Calkins, Perry Berlind, Ruth Angus, Christian A. Latham, George Zhou
DD RAFT VERSION J ANUARY
25, 2021Typeset using L A TEX twocolumn style in AASTeX63
A decade of radial-velocity monitoring of Vega and new limits on the presence of planets S PENCER
A. H
URT , S AMUEL
N. Q
UINN , D AVID
W. L
ATHAM , A NDREW V ANDERBURG , G ILBERT
A. E
SQUERDO , M ICHAEL
L. C
ALKINS , P ERRY B ERLIND , R UTH A NGUS ,
4, 5 C HRISTIAN
A. L
ATHAM , AND G EORGE Z HOU ∗ Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA Department of Astronomy, University of Wisconsin -Madison, 475 North Charter Street, Madison, WI 53706, USA Department of Astrophysics, American Museum of Natural History, 200 Central Park West, Manhattan, NY, USA Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, Manhattan, NY, USA
ABSTRACTWe present an analysis of 1524 spectra of Vega spanning 10 years, in which we search for periodic radialvelocity variations. A signal with a periodicity of 0.676 days and a semi-amplitude of ∼
10 m s − is consistentwith the rotation period measured over much shorter time spans by previous spectroscopic and spectropolari-metric studies, confirming the presence of surface features on this A0 star. The timescale of evolution of thesefeatures can provide insight into the mechanism that sustains the weak magnetic fields in normal A type stars.Modeling the radial velocities with a Gaussian process using a quasi-periodic kernel suggests that the charac-teristic spot evolution timescale is ∼
180 days, though we cannot exclude the possibility that it is much longer.Such long timescales may indicate the presence of failed fossil magnetic fields on Vega.
TESS data reveal Vega’sphotometric rotational modulation for the first time, with a total amplitude of only 10 ppm, and a comparison ofthe spectroscopic and photometric amplitudes suggest the surface features may be dominated by bright plagesrather than dark spots. For the shortest orbital periods, transit and radial velocity injection recovery tests ex-clude the presence of transiting planets larger than 2 R ⊕ and most non-transiting giant planets. At long periods,we combine our radial velocities with direct imaging from the literature to produce detection limits for Veganplanets and brown dwarfs out to distances of 15 au. Finally, we detect a candidate radial velocity signal with aperiod of 2.43 days and a semi-amplitude of 6 m s − . If caused by an orbiting companion, its minimum masswould be ∼ M ⊕ ; because of Vega’s pole-on orientation, this would correspond to a Jovian planet if the orbitis aligned with the stellar spin. We discuss the prospects for confirmation of this candidate planet. INTRODUCTIONThe search for exoplanets has traditionally focused on low-mass (FGKM) stars, as intermediate mass stars pose sev-eral observational challenges. For example, their larger sizeand mass translate to smaller transit and radial velocity sig-nals for a given planet size, and rapid rotation and reducedradial velocity information content prevent precise Dopplerspectroscopy (e.g., Beatty & Gaudi 2015). However, carefultarget selection and expanded observational techniques havehelped to overcome these difficulties and have led to new op-portunities for planet characterization. When A-type starsleave the main sequence, they cool and spin down, providingRV surveys a means to explore planet populations around in-termediate mass stars. Observations of post-main sequence
Corresponding author: Spencer [email protected] ∗ NASA Hubble Fellow stars show that ‘retired A stars’ are more likely than Sun-likestars to host massive planets (Johnson et al. 2010a,b; Ghezziet al. 2018). However, these analyses suggest a low occur-rence rate of planets on close-in orbits. Data from NASA’sTransiting Exoplanet Survey Satellite (
TESS ; Ricker et al.2015), reveal that the same is true of A-type main sequencestars: the occurrence rate of hot Jupiters orbiting A stars islow, and not dissimilar to that of hot Jupiters orbiting solar-type stars (Zhou et al. 2019).A-type stars are often over-represented in wide-field tran-sit surveys due to their intrinsic brightness, so despite thechallenges of detecting and characterizing hot Jupiters orbit-ing A stars, many have now been discovered. While A-typestars are often rapidly rotating and this poses problems formass measurements, it can facilitate characterization some-times not possible for other stars. Stellar obliquity, for exam-ple, can be measured from spectroscopic transit observationsor transits across a gravity darkened stellar surface. For hotJupiter hosts above the Kraft break (Kraft 1967), spin-orbit a r X i v : . [ a s t r o - ph . E P ] J a n H URT ET AL .misalignment is often observed (such that stellar obliquitiesappear to be consistent with an isotropic distribution; Winnet al. 2010; Schlaufman 2010; Albrecht et al. 2012), and Astars appear to be no exception (e.g., Collier Cameron et al.2010; Zhou et al. 2016, 2019; Ahlers et al. 2020a,b). It isunclear if this is due to primordial misalignment or orbitalmigration and whether this stellar obliquity extends to smallplanets or long period planets.Due to their intrinsic brightness, A stars are good targetsfor imaging surveys, for which the brightness of the stars isamong the primary concerns. A stars are also intrinsicallyyoung (since their main-sequence lifetimes are short), whichenhances the likelihood of detecting debris disks before theydisperse or self-luminous planets and brown dwarfs beforethey cool. Vega is a 0 th magnitude A0V star (see Table 1for additional stellar parameters) and the anchor of the Vegamagnitude system. Given its brightness and its special his-tory as a spectrophotometric calibrator (see, e.g., Hayes &Latham 1975), it is a particularly well observed star.Ever since the IRAS discovery of a circumstellar disk (Au-mann et al. 1984), Vega has been a frequent target of imagingstudies. Though early detections of the dust around Vega ap-peared to show a clumpy, asymmetrical formation (Hollandet al. 1998; Koerner et al. 2001; Wilner et al. 2002; Marshet al. 2006), more recent data reveal that the disk is smootherthan originally thought (Su et al. 2005; Sibthorpe et al. 2010;Piétu et al. 2011; Hughes et al. 2012; Holland et al. 2017).ALMA observations have resolved the structure of Vega’souter dust belt, which extends to 150–200 au and has a steepinner edge at 60 −
80 au (Matrà et al. 2020).
Spitzer obser-vations detect mid-IR excess in the disk consistent with anasteroid belt located at 14 au (Su et al. 2013). And near-IRexcess has been detected close to the star, corresponding tohot dust (Absil et al. 2006; Defrère et al. 2011).While Yelverton et al. (2020) show that there are no clearor strong planet-debris disk correlations, systems such as HR8799 (Marois et al. 2008, 2010), β Pic (Lagrange et al. 2009,2010), and 51 Eridani (Macintosh et al. 2015) provide exam-ples of stars hosting both imaged planets and a disk. Further-more, features in a disk can be used to investigate the possi-ble presence of planets and their properties, and Vega’s diskis a complex system that contains features that could arisefrom a planetary system. For a star of Vega’s age, circum-stellar disks are maintained by debris from colliding plan-etesimals (Wyatt 2008). The warm and cold belts are po-tential sources for this debris, but radiation pressure, stellarwinds, and Poynting Robertson drag forces mean a high dustproduction rate is necessary to maintain the disk. Defrèreet al. (2011) conclude that major dynamic perturbations arenecessary to produce the quantities of dust observed, sug-gesting a system of giant planets migrating outwards. Ray-mond & Bonsor (2014) use dynamical simulations to find
Table 1.
Stellar Parameters of VegaParameter Value Units SourceR.A. 18 : : : : µ α − (1) µ δ − (1)Parallax 130.23 ± ± ± ± T eff (Apparent) 9660 ±
90 K (2) T eff (Pole) 10070 ±
90 K (2) T eff (Equator) 8910 ±
130 K (2) R pol ± R (cid:12) (2) R eq ± R (cid:12) (2)Mass 2.15 + − M (cid:12) (2)Upper Age Estimate 700 + − Myr (2)Lower Age Estimate 471 ±
57 Myr (3)Notes: (1) van Leeuwen (2007); (2) Monnier et al. (2012); (3)Yoon et al. (2010) that low-mass, closely-spaced planets could efficiently scat-ter exocomets inwards, accounting for the hot dust. A possi-ble configuration includes a system of planets between 5 and60 au, wherein the outermost planets have masses less thanabout 20 M ⊕ , and they suggest that a Jupiter mass planetbeyond 15 au would disrupt the inward-scattering chain.Gaps in the disk can also be used to infer the presence ofplanets. Observed depletion of dust between detected beltshas been suggested to indicate the presence of multiple long-period giant planets (Su et al. 2013), a single 3 M J planetat 75 au (Zheng et al. 2017), or a chain of low-mass planetsor a Saturn-mass planet (Bonsor et al. 2018). Matrà et al.(2020) argue that the steep inner edge of the cold belt cannotbe explained by collisional evolution, which would result ina shallow inner slope. It could be explained by a chain ofplanets in which the outermost is located near 70 au and hasa mass greater than 6 M ⊕ , or by a single planet with a massof 5 M J and an orbital radius of 50 −
60 au. Clearly not allof these architectures can be present simultaneously, but thehot dust, gap structures, and characteristics of the cold beltall allow for the existence of a system of planets.We view Vega approximately pole-on, allowing a copla-nar planet on a near-circular orbit to always be observednear its maximum separation, which further improves Vega’ssuitability for direct imaging. In the most recent publishedsearch, Meshkat et al. (2018) explored the inner 15 au usingthe P1640 instrument on Palomar’s 5.1-m Hale telescope andplaced mass detection limits of ∼ − M J . Heinze et al.(2008) provide MMT observations to constrain objects be- EGAN PLANETS AND STELLAR ACTIVITY R ad i a l V e l o c i t y ( m / s ) Figure 1.
Relative radial velocities of Vega, derived from TRES spectra. tween 20 and 80 au, finding an upper limit of ∼ − M J .And with Spitzer observations, Janson et al. (2015) rule outany planets with a mass greater than ∼ − M J between 100and 200 au. These represent the lowest mass limits in theliterature for objects orbiting Vega.The inner working angles of direct imaging instrumentsprevent good limits on the existence of planets for scales sim-ilar to or smaller than the inner solar system. Radial veloci-ties can be used to complement imaging at small separationsand for somewhat lower masses at large separations. Theproblem of rapid rotation remains, of course. Spectropolari-metric observations measure a rotation period of 0.678 + − days (Alina et al. 2012). A spectroscopic analysis by Böhmet al. (2015) indicates stellar activity modulated at the sameperiod. These results suggest a stellar rotational velocityof nearly 200 km s − , but the pole-on orientation leads toprojected rotation of only about 20 km s − , which does notseverely limit radial velocity precision. Indeed, velocitiesfrom Böhm et al. (2015) display scatter on the order of only Table 2.
TRES Radial Velocities of VegaBJD RV σ ( m s − ) ( m s − )2456025.026123 -10.0 23.12456026.017315 -20.8 22.82456027.016471 -16.1 25.42456028.020389 -48.7 24.92456029.020685 17.2 24.42456030.020025 -69.8 21.32456031.019574 -37.6 19.82456033.007404 -59.8 19.72456034.010060 2.9 16.0N OTE —The full set of velocities is available as a machine-readabletable. A portion is shown here for form and content.
10 m s − . One concern is that because of the stellar orien-tation, radial velocities will be most sensitive to planets mis-aligned with the star. However, at least for giant planets onshort periods, misaligned orbits appear to be the rule ratherthan the exception for A-star hosts.In this work, we present our analysis of 1524 spectra ofVega, which can be used to study stellar activity and searchfor planets smaller than 1 M J on short periods and massiveplanets out to 15 au. In Section 2, we present the observa-tions and data reduction. In Section 3, we explore the radialvelocities for periodic signals and discuss their origin. InSection 4, we calculate detection limits. Lastly, in Section 5,we discuss our results. OBSERVATIONS2.1.
TRES Spectroscopy
We obtained high-resolution spectra of Vega with theTillinghast Reflector Echelle Spectrograph (TRES; F˝urész2008), which is mounted on the 1.5-m Tillinghast Reflectorat Fred L. Whipple Observatory on Mount Hopkins, AZ. Ithas a resolving power of R ∼
44, 000, and a wavelength cov-erage of 3850–9100 Å. We obtained a total of 1524 spectraspanning the 10-year period between UT 2009 June 13 and2019 October 24. Typical exposure times ranged from a fewseconds to a few tens of seconds, achieving signal-to-noiseratios (SNR) between about 300 and 1000 per resolution ele-ment.We optimally extracted and reduced the spectra followingthe procedures outlined in Buchhave et al. (2010), and whilewe begin by following the radial velocity measurement out-lined therein, our final velocity extraction includes a few keydifferences. We first cross-correlate each spectrum of Vegaagainst the strongest exposure, treating each spectral orderseparately. The relative RV for each exposure is taken to bethe location of the peak of the summed CCF (across all or-ders) from that spectrum. The internal RV uncertainty foreach observation is taken to be the standard deviation of the H
URT ET AL . ∆ F l u x ( pp m ) S14
S26
BJD (-2457000) N o r m a li z ed P o w e r σ ∆ F l u x ( pp m ) Figure 2.
Top: The
TESS light curve of Vega, after decorrelation against the spacecraft quaternion time series, as described in § 2.2. Individual30-minute cadence measurements are shown as small, light purple circles, while data in 6.5-hour bins are shown as large, dark purple circles.The median 6.5-hour standard deviation is 5.0 ppm. Lower Left: Lomb-Scargle periodogram of the
TESS light curve, showing a peak at 0.68days, consistent with the rotation period of the star. Lower Right: The binned, phase-folded
TESS light curve, which shows a total variation of ∼
10 ppm. locations of the CCF peak of each order for that spectrum.Next, we shift and median combine the 1524 spectra to gen-erate a master template spectrum. In the case of Vega, thetemplate SNR is 26,000 per resolution element. Though ex-posures of Vega are typically short enough that cosmic rayrejection is not very important, we identify outlier pixelsand replace them with the median spectrum at that location.Finally, we re-run the order-by-order cross-correlation, thistime against the high-SNR template.TRES was not designed for long-term stability at the levelof meters per second, and has at times experienced drifts andjumps in its instrumental zero point as large as a few tensof m s − . Changes of this magnitude can mimic or mask thepresence of long-period companions. To combat this prob-lem, we track the zero point with nightly observations of sev-eral RV standard stars, allowing us to measure and correct forzero point changes over time. From the standard deviation ofthe RV standards, we also estimate the instrumental RV noise floor, to be added in quadrature with the internal error es-timates described above. The TRES instrumental precisionat the beginning of our data set was ∼
50 m s − , but by theend of 2010 had improved to ∼ − , thanks in largepart to hardware upgrades. Though these introduced somezero point changes, they are corrected for in the same way asother zero point shifts. Our final, zero-point-corrected, rela-tive RVs are shown in Figure 1 and presented in Table 2.2.2. TESS Photometry
Vega was observed by NASA’s
TESS mission (Ricker et al.2015) in Sector 14, between UT 2019 July 18 and 2019 Au-gust 15, and in Sector 26, between UT 2020 June 8 and 2020July 04. The star is bright enough to fill the full well depthof hundreds of pixels, but the
TESS detector is designed topreserve the flux by spilling into neighboring pixels. As longas the star is not too close to the edge of the detector, the fullframe images (FFIs), returned at 30-minute cadence, can beused to extract photometry from an area encompassing all of
EGAN PLANETS AND STELLAR ACTIVITY
Kepler mission (Jenkins et al. 2010). We then per-formed photometry using apertures shaped to trace the distri-bution of charge on the
TESS images, including 3,625 pixelsin Sector 14 and 4,335 pixels in Sector 26. We correctedthe flux for sources within the aperture using
TESS magni-tudes listed in the
TESS
Input Catalog. To account for sys-tematics caused by the motion of the spacecraft, we followedthe procedure outlined in Vanderburg et al. (2019). Namely,we assumed that systematics caused by changes in spacecraftpointing can be corrected by decorrelating against the back-ground scattered light signal and combinations of the space-craft quaternions, which encode the pointing of the space-craft every 2 seconds. We produced quaternion time series bycalculating the standard deviation and mean quaternions dur-ing each 30-minute exposure. Ultimately, we found the bestperformance (i.e., lowest resulting light curve scatter) whendecorrelating against the scattered light signal and the first,second, and third order of these quaternion time series. Weexclude a few hours of data most strongly affected by scat-tered light at the beginning of each orbit in Sector 26, and weuse a spline to flatten remaining low frequency systematicsthat occur on the timescale of the spacecraft orbit.The resulting light curve is shown in Figure 2, and is re-markably quiet. The median standard deviation in 6.5-hourbins is only 5.0 ppm. We run
Transit Least Squares ( TLS , Hippke & Heller 2019) in search of transiting plan-ets but we find no evidence for transit-like features, and inSection 4.2 produce detection limits using transit injectionrecovery. The maximum power in a Lomb-Scargle peri-odogram occurs for a period of 0.68 days (Figure 2, lowerleft panel), which is consistent with previous measurementsof the rotation period of Vega. We do detect the signal in bothsectors individually at lower significance, but because of theyear-long gap between sectors we cannot confirm whetherthe signal is stable in phase for the full time span. It is inter-esting to note that while the period is still significant ( > σ )if we exclude photometric outliers, the significance is high-est when they are included. This suggests that the apparentoutliers vary in phase with the rest of the data and may be as-sociated with stellar activity rather than systematics relatedto the instrument or data processing. This could indicate thatsome surface features are evolving in brightness on very shorttimescales, while others appear more stable over the courseof a month, and perhaps over the full year spanned by the TESS data. ANALYSIS OF RADIAL VELOCITY SIGNALSIn this section, we present analyses of the TRES data tosearch for and characterize radial velocity signals arising
Table 3.
Significant Periodogram Signals (FAP < 0.1%)Period Frequency Notes Amplitude FAP(days) (days − ) ( m s − )0.105 9.48 F rot + · · · rot + rot + rot + rot + | F rot − | rot + · · · | F rot − | rot + | F rot − | rot + rot rot − from rotation and orbiting companions. We begin our searchfor periodic signals in the radial velocity data using a gen-eralized Lomb Scargle periodogram (GLS, Zechmeister &Kürster 2009) and the window function, shown in Figure 3.The periodogram contains many significant peaks with falsealarm probabilities (FAPs) below 0.001, most of which fallat short periods. The window function reflects our nightlyobserving cadence, with strong power at a sampling rateof 1 day − . Given that the majority of signals in the peri-odogram fall below 1 day, the true frequency of variabilityis likely above the Nyquist frequency of .5 days − , and therest of the peaks are aliases. We discuss identification of thetrue peak below and then model this signal and others withGaussian processes and Keplerians.3.1. A Signal Arising from the Rotation of Active Regions
Detection of the Activity Signal
One of the strongest peaks in the RV periodogram is lo-cated at 0.677 days, which corresponds to the previously re-ported rotation period (Alina et al. 2012; Böhm et al. 2015).Table 3 lists all of the significant peaks in the periodogram,and shows how they relate to the rotation period. Nearly ev-ery signal is an alias of the 0.677-day periodicity, with har-monics also present but at lower significance. While we havegood reason to suspect that this value corresponds to the truesignal, we conduct a more rigorous test of the aliases usingthe methodology of Dawson & Fabrycky (2010). This pro-cedure simulates a sinusoidal signal at the candidate periodusing the time stamps of the observed data. The amplitudesand phases of each peak in the periodogram are then com-pared between the synthetic and actual data. The simulated H
URT ET AL . P o w e r Figure 3.
GLS periodogram (top) and window function (bottom) for TRES radial velocities. The horizontal lines in the periodogram correspondto FAPs of 0.05, 0.01, and 0.001. The peak located at 0.677 days, corresponding the the rotational period, is marked in red. signal that best reproduces the results from the observationsis chosen as the true period. While the signal we observe islikely caused by activity, and therefore is somewhat irregu-lar, this test does confirm 0.677 days as the best match to theobserved periodogram.A useful diagnostic for distinguishing between activity andorbiting companions is the stacked periodogram, which is de-scribed by Mortier & Collier Cameron (2017). As the num-ber of observations included in a periodogram increases, thepower of a peak corresponding to a planetary signal should
Figure 4.
Stacked periodogram of the TRES RVs, showing the pe-riodicity at 0.677 days. The strength of the peak falls off around1000 observations, after which multiple peaks emerge, suggestingthat this signal originates from active surface regions rather than anorbiting companion. monotonically increase, within the limits of the noise, whilethe power of a peak corresponding to rotation of features onthe stellar surface may not, due to changes in the phase ofthe signal driven by the evolution of active regions. In Fig-ure 4, we present a stacked periodogram for our TRES ra-dial velocities. For the first ∼ Modeling the Activity Signal
We first attempt to model the stellar activity with a Kep-lerian orbit using the radvel
Python package (Fulton et al.2018). However, Markov chain Monte Carlo (MCMC) sam-ples failed to converge. Additionally, a periodogram of theresiduals to the best fit showed significant power remain-ing near 0.677 days. This suggests that a Keplerian modeldoes not adequately fit the signal, which is expected giventhe structure seen in the stacked periodogram. It would havebeen surprising for the stellar surface to be described well bya single Keplerian (corresponding to a single active region)over the span of a decade.We next consider a model in which active regions are verylong-lived, but multiple regions may exist with slightly dif-ferent periods due to differential rotation. For this exercise,we follow an iterative whitening procedure in which we fita Keplerian with initial conditions determined from the peri-odogram following Delisle et al. (2016). After refining that
EGAN PLANETS AND STELLAR ACTIVITY < radvel , we model the correlated stellar noisewith a kernel matrix whose elements are defined as C i j = η exp − (cid:12)(cid:12) t i − t j (cid:12)(cid:12) η − sin (cid:16) π | t i − t j | η (cid:17) η , (1)where t i and t j are observations made at any two times; η is the amplitude hyperparamter; η is the exponential decaytimescale, which is physically related to the lifetime of theactive regions; η is the period of the variability, correspond-ing to the rotational period; and η is the length scale of theperiodic component, describing the high-frequency variationin the stellar rotation. It is important to note, however, thatthese physical interpretations are often not straightforward,particularly given the degeneracies between the hyperparam-eters.No trend is apparent in our data or the residuals of earlyfits and we choose to exclude a linear or quadratic term inour model. However, we do include offset and jitter termsto account for instrumental offset and noise. Priors are onlyplaced on parameters to keep them within physically possiblelimits. The complete log-likelihood of this model isln L = − r T K − r −
12 ln ( det K ) − n ( π ) , (2)where r is the vector of residuals, K is the covariance matrix,and n is the number of data points.We perform an affine-invariant Markov chain Monte Carlo(MCMC) exploration of the parameter space using the Table 4.
Stellar activity RV modelsParameter Units ValueMultiple Keplerians P days 0.676682 ± T c BJD 2457187.123 ± e · · · ± ω deg 344 ± K m s − ± P days 0.676086 ± T c BJD 2457187.195 ± e · · · ± ω deg 179 ± K m s − ± γ m s − − ± σ jit m s − ± η m s − + − η days 179 + − η days 0.6764 + − η · · · + − γ m s − − + − σ jit m s − ± ensemble sampler emcee (Foreman-Mackey et al. 2013,2019). Our MCMC analysis used 8 ensembles of 50 walkersand converged after 4950000 steps, achieving a maximumGelman-Rubin statistic (Gelman & Rubin 1992) of 1.006.The resulting posterior distributions are shown in Table 4.We do note that this model is over-fitting the data, with a re-duced χ statistic of 0.869; either the model is fitting noiseor our cadence is not sufficient to constrain high-frequencyvariations in the rotation signal. In either case, the Gaus-sian process is likely too complex of model for our data. Wecheck our results with a second GP fit of the radial velocitiesusing a quasi-periodic kernel with the PyMC3
Python pack-age (Salvatier et al. 2016), which returns results well within1 σ of those in Table 4.3.2. Additional Signals of Interest
The activity signal at the period of stellar rotation is by farthe strongest we observe, but other candidate signals havebeen reported in previous Vega data sets, and we also searchfor signals of lower significance in the TRES RVs.3.2.1.
Previously Suggested Signals
Böhm et al. (2015) used their SOPHIE spectra to search foradditional short-period signals and reported a possible detec-tion at 1.77 d − (0.56 days) with an amplitude of 6 m s − . H URT ET AL .If it has a planetary origin, it would correspond to roughly aSaturn-mass planet well aligned with the stellar spin near theco-rotation radius of the star. However, no such periodicityappears in our TRES observations. When we inject this sig-nal into our data, we find that it would have been clearly de-tected, which suggests that the signal in the SOPHIE data setdoes not correspond to a planet. While we cannot concludewith certainty what the source of that signal was, the SOPHIEdata only span 5 nights and cover about 7 hours each night,so one possibility is that it may have resulted from a combi-nation of short-timescale stellar variability and the sampling.3.2.2.
Signals at Long Periods
Because our Gaussian process model of the 0.677-day sig-nal over-fits the data, it is difficult to use the residuals ofthat model to search for—or to jointly fit—additional signals.However, we note that in the original periodogram of ourradial velocities, the strongest peak with a timescale longerthan a few days is located at 197.3 ± ± Table 5.
Candidate Planetary Companion to Vega
Parameter Units ValueEccentric Circular P days 2.42977 ± ± T c BJD 2457186.51 ± ± e ··· ± ω deg 304 ± ··· K m s − ± ± γ m s − − ± − ± σ m s − ± ± m p sin i M ⊕ ± ± originate from activity; the timescale of evolution of the for-mer (179 + − days) derived from the GP fit is consistent withthe latter. Because the GP activity model is flexible enoughto absorb the long-period signal even if it is real, we exam-ine the effect of the multiple-Keplerian model on this signal.If active regions are long-lived and exist with very slightlydifferent periods due to differential rotation, then beating be-tween the two frequencies will lead to evolution of the ob-served variation on long timescales. Modeling and removingthe signal from the static active regions should reduce the sig-nificance of signals related to the beat frequency, but shouldnot generally absorb unrelated signals like the GP does. Af-ter fitting the two dominant activity signals near 0.677 days,the FAP of the peak at 194 days is reduced (to ∼ P rot /
2) removes the 194-day sig-nal completely.Given the very modest significance of the 194-day sig-nal, the existence of plausible alternative explanations, andits disappearance when removing Keplerians associated withthe rotation period, we do not consider this to be a planetarycandidate. There are no other long-period signals of note inour RVs. 3.2.3.
A Candidate Planetary Companion
Interestingly, after removing two Keplerian signals asso-ciated with the stellar rotation, the strongest remaining peakhas a period of 2.43 days and a formal FAP of only < EGAN PLANETS AND STELLAR ACTIVITY R ad i a l V e l o c i t y ( m / s ) Figure 5.
Left : TRES RVs (small light blue circles) phase-foldedto the 2.43-day period of a candidate planet orbiting Vega after re-moval of activity signal by fitting Keplerians at the rotation period.Data binned in phase are shown as orange circles.
Right : The sameorbit on a different velocity scale to better show the binned data. Thepurple open circles represent phased, binned data from the interme-diate steps of whitening the RVs by removing Keplerians associatedwith the rotation period. A consistent orbit is seen when removing0, 1, 2, 3, 4, or 5 activity signals. lar orbit with a period of 2.43 days has an RV semi-amplitudeof about 6 m s − , corresponding to a minimum mass of about20 M ⊕ . According to the difference in the Bayesian Infor-mation Criterion ( ∆ BIC), a circular orbit is statistically pre-ferred, but we present both eccentric and circular solutionsin Table 5. Figure 5 shows the phase folded RVs of the can-didate planetary signal. While we cannot conclusively ruleout false positive scenarios, we discuss in Section 5 ways inwhich we might confirm the candidate with future observa-tions and analyses. DETECTION LIMITS4.1.
TRES Radial Velocities
Isotropic Orbits
We begin the calculation of our detection limits by ran-domly generating ∼ models corresponding to planetswith semi-major axes between 0 and 15 au and masses rang-ing from 0 to 100 M J . Each orbit is assigned an inclina-tion (drawn from a uniform distribution in cos i ), eccentricity(drawn from a beta distribution described by Kipping 2013,with parameters a = b = radvel , we calculate the expected radial velocitiesfor each orbit at our times of observation. We then add noisescaled to the observed uncertainties at each time stamp. Us-ing radvel , we fit a flat line to the synthesized RVs andcalculate the χ statistic and its associated p value for thismodel. Low p values indicate that the synthesized signal isunlikely to arise from white noise—i.e., it is distinguishable from a flat line and we therefore consider it detected. To set athreshold for detection, we follow Latham et al. (2002), whodemonstrate that p < p < ∆ BIC be-tween the detected signal and a flat line model be greater than10—yield more sensitive limits, we adopt the conservative p ( χ ) < M J at 6 au, which corresponds to an orbital period of 10years around Vega. Beyond 6 au, our detection limits de-grade more quickly, as our data no longer cover an entire or-bit. Nonetheless, we are sensitive to the most massive giantplanets all the way out to 15 au. Given the roughly isotropicdistribution of stellar obliquities for hot stars hosting tran-siting hot Jupiters, the decision to draw inclinations from anisotropic distribution may be the most realistic assumptionfor short periods. However, it is unclear whether the same istrue at long periods. We therefore also explore our detectionlimits for well-aligned orbits in the following section.4.1.2. Well-Aligned Orbits
For our purposes, we will consider a well-aligned orbit tofall within 5° of the stellar spin axis. Assuming Vega hasan inclination of 6.5°, this means that a well aligned planetwould have an inclination between 1.5° and 11.5°. To cal-culate detection limits for well-aligned orbits, we follow thesame steps as in the previous section, but instead assign incli-nations drawn from a uniform distribution between 1.5° and11.5°. The resulting detection probabilities are shown in themiddle panel of Figure 6. While drawing from a distributionof well aligned orbits (highly inclined to the line of sight)clearly reduces detection probabilities, we are still sensitiveto the most massive giant planets as widely separated as 6 au;beyond this distance, we are only sensitive to brown dwarfsor stars. 4.1.3.
Including Direct Imaging Limits
The direct imaging limits from Meshkat et al. (2018) alsoexplore the inner 15 au around Vega for planets. While ourRV detection limits fall off exterior to ∼ interior to this boundary.We also note that direct imaging and radial velocities aremost sensitive to planets at opposite inclinations. Conse-quently, a brown dwarf that is missed by RVs because it ishighly inclined to the line of sight may be detected by direct0 H URT ET AL . Figure 6.
Top: TRES detection probabilities for objects in isotrop-ically distributed orbits. Middle: Detection probabilities for objectsin orbits well-aligned with Vega’s spin-axis. Bottom: TRES de-tection probabilities combined with Palomar P1640 detection limitsfrom Meshkat et al. (2018) for objects in well-aligned orbits. imaging; one that is too close in projection for direct imag-ing can be detected by RVs. By combining our results, we areable to provide a more comprehensive limit on the presenceof widely separated companions. We calculate the projected separation for each randomlydrawn sample in Sections 4.1.1 and 4.1.2 on UT 2016 Aug19 and 2017 June 05 (two of the observing times in Meshkatet al. 2018) using Equation (7) in Kane & Gelino (2011). Weconsider the planet to be detectable in the data presented byMeshkat et al. (2018) if its mass falls above the five-sigmaH-band mass limits for either of the observation times. Wethen use the same criterion as before to determine if it is de-tectable in our radial velocities. For isotropically distributedorbits, our RVs are more sensitive than the imaging at allseparations, but for long-period orbits aligned with the stel-lar spin, imaging is more sensitive. The detection probabili-ties for well-aligned orbits using RVs and direct imaging areshown in the bottom panel of Figure 6.4.2.
TESS Photometry
Using the Python package batman (Kreidberg 2015), werandomly generate ∼ transit models for planets with pe-riods ranging from 0.5 to 30 days and radii between 1 and 8 R ⊕ . Each orbit is assumed to be circular and semi-major axesare calculated using Kepler’s law, assuming that the planet’smass is negligible compared to Vega. Transit times are ran-domly assigned from a uniform distribution and inclinationsare drawn from a uniform distribution in cos i such that0 < cos i < R (cid:63) − R p a , (3)where a is the semi-major axis and R (cid:63) and R p are respectivelythe stellar and planetary radii, ensuring that the planet tran-sits. Additionally, each synthetic transit follows quadraticlimb darkening laws for an A0 star in the TESS bandpasswith u = u = TLS . We consider a transit to be de-tectable if the best period recovered by
TLS is within 1% ofthe injected period and if at least one of the transit times iswithin the same margin of an injected transit. Additionally,because a transit could appear within the gaps of our lightcurve, any recovered integer multiples of the injected periodare considered detectable.We also require a transit to be distinguishable from a falsepositive to be considered a true recovery, ensuring that thesignal would not be dismissed due to low signal in a realsearch. Using synthetic light curves and transits, Hippke &Heller (2019) find that a signal detection efficiency (SDE)threshold of 7 corresponds to a false positive rate of 1% for
TLS . Therefore, for a transit to be detectable, we also requirethat the best period have an SDE of 7 or greater.The results of our injection recovery test are shown in Fig-ure 7. At the shortest periods, we are sensitive to transitingplanets as small as 2 R ⊕ , and as small as 3 R ⊕ for orbitalperiods similar to the duration of a TESS orbit ( (cid:46)
14 days).For periods longer than a couple weeks, our formal sensitiv-
EGAN PLANETS AND STELLAR ACTIVITY R a d i u s [ E a r t h R a d ii ] F r a c t i o n o f R e c o v e r e d O r b i t s Figure 7.
Transit detection limits for
TESS observations of Vega.For periods shorter than a few days, we can rule out most transitingplanets with radii greater than 2 R ⊕ , and for periods out to 15 days,planets with radii greater than 3 R ⊕ . Planets with longer periods donot transit frequently enough to be consistently ruled out. However,we note that for many of the larger injected planets not recoveredaccording to our criteria, single transit events would be easily visibleby eye, so our detection map should be viewed as a conservativelimit. ity drops, as fewer transits are expected; some planets mayexhibit only one or two transits total, and some might noteven be observed once by TESS due to data gaps between or-bits. Many of these will not pass our automated TLS criteriafor detection. On the other hand, the transits of even rela-tively small planets orbiting Vega would be easily visible byeye in the quiet
TESS light curve. A 4 R ⊕ transit, for ex-ample, would be about 180 ppm. It is clear that there are noNeptune-sized planets transiting in the TESS data even once.While the formal detection limits shown in Figure 7 are illus-trative of the types of transiting planets we could detect mosteasily, they should be taken as a conservative estimate. DISCUSSION5.1.
Stellar Activity
Rotational modulation has consistently been found in spec-troscopic observations of Vega (Böhm et al. 2015; Petit et al.2017), providing evidence for active regions on the surfaceof the star. While chemically peculiar A stars are known tohave star spots, normal A stars conventionally do not exhibitthe same traits. Vega is the first normal A-type star observedto have a weak surface magnetic field (Lignières et al. 2009;Petit et al. 2010), accounting for the rotational modulation.However, the origins of these magnetic fields are uncertain.One possible mechanism is dynamo action, where thin con-vective layers host a dynamo driven by convective motion,generating a magnetic field. On the other hand, the fieldscould be ‘failed fossils,’ which are generated in the earlyphases of a star’s life and dynamically evolve towards fos- sil equilibrium (e.g., Braithwaite & Cantiello 2013). Thesemodels can be distinguished by the time variation of the mag-netic field. Dynamos are intrinsically variable, leading tospot lifetimes similar to the rotation period. In contrast, failedfossil fields would evolve much more slowly.Vega appears to have a very complex magnetic field. Böhmet al. (2015) find no evidence for rapid variability consistentwith dynamo action in their data, suggesting the presenceof star spots that last for over five days. However, apply-ing Doppler imaging techniques to the same data set, Pe-tit et al. (2017) do find rapidly evolving surface features incombination with stable structures. Cantiello & Braithwaite(2019) suggest that this rapid variation is a sign of dynamo-generated magnetic fields.While our spectroscopic observations are likely not high-cadence enough to characterize the short term evolution ofco-rotating structures, they stretch over a span of time muchlonger than the five consecutive nights used by Böhm et al.(2015) and Petit et al. (2017), which may provide insight re-garding the long-term evolution. In Section 3, we describedthat our RVs can be modeled by either a Gaussian processwith a quasi-periodic kernel or the combination of Kepleriansignals very close to the rotation period. In both cases, theimplied timescale for evolution is long: the GP fit suggestsan exponential decay timescale of half a year, while the Ke-plerian model that adequately reproduces the signal seen inour ten-year data set suggests that some surface features maybe even more long-lived. It is hard to distinguish between thetwo models, but both imply the presence of surface featureswith lifetimes longer than expected for dynamo fields. Evenso, this is not necessarily at odds with the complex and time-varying reconstructed surface map presented by Petit et al.(2017), who identified both variable and stable surface fea-tures in their data. We speculate that their stable features maybe the ones responsible for our long-lived RV signal, whiletheir rapidly varying features contribute high frequency noiseto our data that we cannot characterize due to our limited ob-serving cadence. We do, however, measure stellar jitter witha magnitude comparable to that of the coherent modulation,which may arise from rapidly varying surface features. Ifboth types of features exist, it may imply magnetic structuresinfluenced both by a failed fossil field and a subsurface dy-namo. However, long term spectropolarimetric observationsof Vega are necessary to conclusively determine the behaviorof its active regions.Another interesting feature of Vega’s activity is its lowphotometric variation, particularly given its maximum radialvelocity amplitude of 14.4 + − m s − . A dark spot inducing a10 m s − variation on a star rotating with v sin i (cid:63) =
20 km s − should also induce a photometric signal of A RV / v sin i (cid:63) ∼ URT ET AL . Figure 8.
SOAP 2.0 simulations of the radial velocity and photometric variation induced by spots (blue) and plages (red) at different latitudes.The top row simulates a spot or plage on Vega’s equator, the second row a latitude of 15°, the third a latitude of 45°, and the last a latitude of80°. Dark spots deviate from Vega’s effective temperature by 750 K and the sizes of active regions are varied to obtain an RV amplitude similarto the observed values of ∼
15 ms − . While spots and plages are both able to reproduce the RV variation, the change in flux is much lower forplages. Vega’s surface may be more complicated than this toy model, but this suggests that plages are more likely the dominant driver of theradial velocity signal and the quiet TESS light curve. dominate the surface. To explore this further, we use
SOAP2.0 (Dumusque et al. 2015) to compare the effects of starspots and plages at different latitudes on a Vega-like star (Fig-ure 8). We vary the size of the active region to reproduce anRV signal with an amplitude of ∼
15 m s − and compare theexpected photometric signals. We find that a dark spot wouldinduce photometric variations ranging from a hundred to over700 ppm. On the other hand, a high-latitude plage can re-produce photometric variations less than 10 ppm, consistentwith the observed TESS light curve. This is because plagesare only marginally hotter than the rest of the stellar sur-face, resulting in little flux variation, but are still surroundedby local magnetic fields that suppress convective blueshiftand cause regions to appear redshifted, creating an RV sig-nal (Dumusque et al. 2015). Given that Petit et al. (2017)detected many bright and dark regions on Vega’s surface,the picture is clearly not as simple as our simulations, butit suggests that the observed variations are primarily drivenby plages. 5.2.
Candidate Planets Orbiting Vega
Any planetary signals in our radial velocities may be dif-ficult to detect, since the dominant signal arises from stellar activity and its removal is not straightforward. Nevertheless,we are able to rule out the presence of a candidate signal near0.53 or 0.56 days previously reported by Böhm et al. (2015),and we do identify two signals worthy of further investiga-tion. The first, with a period of 196.4 + − days, would havea semi-major axis of 0.853 + − au and a minimum massof 0.252 ± M J , falling well below the detection limitsof previous direct imaging surveys. The power of the sig-nal monotonically increases with the addition of new data,which is what one would expect for a real orbiting compan-ion. However, it is not formally significant, is located neara small peak in the window function, and its significance isreduced further when the activity signal is modeled. We con-clude that there is not good evidence for a planet at this pe-riod.The second interesting signal emerged from the velocityresiduals when modeling the activity with multiple Kepleri-ans near the rotation period. We identify a short-period signalwith a formal false alarm probability less than 1%, a best-fitperiod of 2.43 days, and a semi-amplitude of 6 m s − , imply-ing a minimum mass of ∼ M ⊕ . A true mass this low wouldrequire a polar orbit, but A stars hosting short-period plan-ets do display a wide range of stellar obliquities, and even a EGAN PLANETS AND STELLAR ACTIVITY i = ∼ M J ). Continued radial velocity observations couldprovide further insight into the presence of a planet orbit-ing Vega, but more work needs to be done to account forthe activity signal; further spectroscopic observations shouldbe planned carefully, for example to achieve a cadence thatresolves the rotational and orbital periods, allowing better si-multaneous modeling of planet and stellar activity.If there is a planet with a period of 2.43 days orbiting Vega,there are a few ways one might confirm its existence. TESS data rule out transits of objects larger than about 2 R ⊕ atthis period, so unless it is very dense, this candidate planetdoes not transit. It has taken 1500 spectra obtained over 10years to detect the RV signal at low significance, so it mayrequire a large investment of spectroscopic resources to in-crease the SNR of the detection even if it is real. A high ca-dence campaign spanning many orbital periods (ideally frommultiple longitudes to achieve uninterrupted data) might bebest suited for mitigating stellar activity and limiting its evo-lution during observations. Alternatively, it may be possi-ble to directly detect the planet using high resolution spec-troscopy and cross-correlation against a template of elemen-tal or molecular species in the planetary atmospheres (e.g.,Snellen et al. 2010). With such a short period around sucha hot star, the planet would have an equilibrium temperatureof ∼ ∼ R J ), so 1 R J wouldbe a conservative estimate. As outlined in Birkby (2018), thesignal to noise of the planetary signal is described bySNR planet = (cid:18) S p S (cid:63) (cid:19) SNR star (cid:112) N lines , (4)where S p / S (cid:63) is the planet-to-star contrast ratio. Adopting R p = R J and assuming blackbody radiation, the planet-to-star contrast ratio for the candidate Vega planet wouldbe 2 × − . As a reference, assuming 1 R J for tau Boötisb (the first non-transiting planet with a detection using thistechnique; Brogi et al. 2012), we would estimate a contrastof 2.6 × − . The total SNR of our Vega spectra is about26,000, implying SNR planet ∼ √ N lines . If we can resolve ∼
100 lines in the planetary spectrum, it is possible that wecould detect such a planet with our TRES data. However,a high confidence detection may have to wait for a data set better suited to this purpose. The SOPHIE data obtained byBöhm et al. (2015) have higher resolving power and totalSNR than our TRES data but cover a narrower wavelengthrange. TRES covers the red optical where contrasts are notas extreme and where lines from molecules such as TiO, CO,and H O may be present in the planetary atmosphere. On theother hand, Fe I has been detected on the daysides of ultra-hot Jupiters like KELT-9b and WASP-33b, so direct detectionof the planet is possible even in the blue optical. Ultimately,it may be necessary to move to the near infrared where con-trasts are further reduced and the presence of strong molecu-lar bands of CO and H O can boost the SNR.5.3.
Current and Future Limits on Planetary Companions
Using 1524 TRES RVs, we are able to place new detec-tion limits on planets orbiting within 15 au of Vega, a re-gion in which direct imaging surveys have only ruled outbrown dwarfs. Assuming no preference for the orientationof the orbital plane—consistent with the observed distribu-tion for short-period planets orbiting hot stars—we can ruleout nearly all hot Jupiters. We are sensitive to Saturn-massobjects at 0.1 au, Jupiters at 1 au, 5 M J at 10 au, and 13 M J at 15 au. For a planet well aligned with the stellar spin,these masses increase by a factor of about 8 and even massiveplanets would therefore be difficult to detect beyond ∼ ∼ M J at 5–10 au toNeptune masses at tens of au could replenish the hot dust inthe inner belt. Our data are not quite sensitive enough to con-strain planets this small at these distances, with our detectionprobabilities falling off steeply below about 2 M J at 5 au,even for planets drawn from an isotropic inclination distribu-tion.With TESS data, we are able to place constraints on thesize of any transiting planets. While most planets wouldnot transit, requiring both a very high stellar obliquity and asemi-major axis (cid:46)
TESS results in very sensitive detection limits,despite the large stellar radius. We can rule out any tran-siting hot Jupiters, along with most other planets with radiigreater than 3 R ⊕ . Further observations could place evenmore extensive limits on transiting planets while helping usto better understand the active regions on the star. The TESS extended mission will return to the northern hemisphere in itssecond year of operations, which may be the next opportunityfor additional uninterrupted measurements at a similar preci-sion. The 10-minute full frame images used in the extendedmission will also improve the time resolution by a factor of4 H
URT ET AL .three, opening the possibility of further characterization ofhigh frequency stellar variations.Current and future space telescopes offer additional op-portunities to search for planets around Vega. Meshkatet al. (2018) show that planned James Webb Space Tele-scope (JWST) NIRCam GTO observations of Vega (Beich-man et al. 2010) will have greater sensitivity than previoussurveys, perhaps extending to Saturn-mass planets. Addi-tionally, MIRI GTO observations are expected to resolve thepotential asteroid belt analog (Beichman et al. 2017), pro-viding further insight into the disk structure of Vega and itsimplications for a planetary system. However, JWST willonly be able to search the region beyond 1.5 (cid:48)(cid:48) (11 au) fromVega for planets; any closer, and the star will saturate theinstrument. The Nancy Grace Roman Space Telescope coro-nagraph instrument (CGI) is more promising for close com-panions, as it is intended to observe small fields around brightstars. Because Vega is so bright, Roman would not need toobserve a bright PSF reference star, potentially allowing bet-ter CGI stability and improving contrast for point sources.On the other hand, the CGI is optimized for stars with an-gular diameters less than ∼ (cid:48)(cid:48) (close to 1 au) (Nemati et al. 2017; Krist et al.2018). Combining Roman and JWST observations, futurespace missions promise to place new direct imaging limitson planets throughout the entire Vega system.As a nearby star, Vega is also an interesting candidatefor astrometric detection of companions, though the bestprecision—i.e., with Gaia—may not be possible. Sahlmannet al. (2016, 2018) describe protocols to observe very brightstars with Gaia, but Vega is far beyond the bright limit forstandard Gaia processing and they do not quantify what theuncertainties for such measurements may be. If astrometricprecision for Vega were to rival the typical performance (e.g.,35 µ as per measurement), we might expect Gaia to be sen-sitive to Jupiter masses beyond about 1.5 au (Ranalli et al.2018). However, we do not know the precision with whichGaia can observe a star like Vega, and it is unlikely to beclose to the instrumental floor.Radial velocities remain the most sensitive technique forcompanions within 1 au for the foreseeable future. CONCLUSIONSUsing 1524 TRES spectra and two sectors of
TESS pho-tometry, we search for planets orbiting Vega. We do notdiscover any transiting planets, but do detect a candidate inour radial velocities with a period of 2.43 days and a semi-amplitude of 6 m s − , implying a minimum mass of about 20 M ⊕ . Further observations and analysis will be requiredto confirm or refute this candidate. We use our data to derivelimits on the presence of transiting planets within 0.2 au andnon-transiting planets within 15 au. For orbits well alignedto the stellar spin, we are only sensitive to the most massiveplanets inside about 1 au, but for misaligned orbits, we aresensitive to sub-Saturn masses at small separations and themost massive planets out to about 10 au. Combining our ra-dial velocity limits with those from previous direct imaging,we place new detection limits on brown dwarfs out to 15 au.The TESS light curve is remarkably quiet and shows no signsof a transiting planet. With transit injection recovery tests,we can rule out most planets with radii greater than 3 R ⊕ and periods between 0.5 and 15 days.We also identify rotational modulation in our data, whichdominates the radial velocities but is weak in our photometry,consistent with variation driven primarily by bright plages,rather than dark spots. We model this signal with a quasi-periodic Gaussian process and with multiple Keplerians, bothof which suggest that the structures on Vega’s surface evolveon timescales much longer than the rotation period, implyingthat at least some of the surface features may be fueled by afailed fossil magnetic field.Future high resolution spectroscopy offers a path forwardfor the direct or indirect detection of short-period planetsorbiting Vega while simultaneously characterizing the stel-lar surface features and the underlying mechanisms drivingthem. Future photometry––such as the extended TESS mis-sion will further constrain the presence of transiting planets.At wider separations, JWST and the Nancy Grace RomanSpace Telescope promise to provide new constraints on plan-ets via direct imaging.
EGAN PLANETS AND STELLAR ACTIVITY
Software: astropy (Astropy Collaboration et al.2018), batman (Kreidberg 2015), emcee (Foreman-Mackey et al. 2013), matplotlib (Hunter 2007), numpy (Harris et al. 2020),
PyMC3 (Salvatier et al. 2016), radvel (Fulton et al. 2018),
SOAP 2.0 (Dumusque et al. 2015),
Transit Least Squares (Hippke & Heller 2019)
Facilities:
FLWO:1.5m (TRES),
TESS
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