Unbiased Inference of the Masses of Transiting Planets from Radial Velocity Follow-up

ABSTRACT Radial-velocity follow-up of stars harbouring transiting planets detected by TESS is expected to require very large amounts of expensive telescope time in the next few years. Therefore, scheduling strategies should be implemented to maximize the amount of information gathered about the target planetary systems. We consider myopic and non-myopic versions of a novel uniform-in-phase scheduler, as well as a random scheduler, and compare these scheduling strategies with respect to the bias, accuracy and precision achieved in recovering the mass and orbital parameters of transiting and non-transiting planets. This comparison is carried out based on realistic simulations of radial-velocity follow-up with ESPRESSO of a sample of 50 TESS target stars, with simulated planetary systems containing at least one transiting planet with a radius below 4R⊕. Radial-velocity data sets were generated under reasonable assumptions about their noise component, including that resulting from stellar activity, and analysed using a fully Bayesian methodology. We find the random scheduler leads to a more biased, less accurate, and less precise, estimation of the mass of the transiting exoplanets. No significant differences are found between the results of the myopic and non-myopic implementations of the uniform-in-phase scheduler. With only about 22 radial velocity measurements per data set, our novel uniform-in-phase scheduler enables an unbiased (at the level of 1 per cent) measurement of the masses of the transiting planets, while keeping the average relative accuracy and precision around 16 per cent and 23 per cent, respectively. The number of non-transiting planets detected is similar for all the scheduling strategies considered, as well as the bias, accuracy and precision with which their masses and orbital parameters are recovered.

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Detection and Doppler monitoring of K2-285 (EPIC 246471491), a system of four transiting planets smaller than Neptune

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834001 ◽

2019 ◽

Vol 623 ◽

pp. A41 ◽

Cited By ~ 6

Author(s):

E. Palle ◽

G. Nowak ◽

R. Luque ◽

D. Hidalgo ◽

O. Barragán ◽

...

Keyword(s):

Bulk Composition ◽

Velocity Measurements ◽

Good Test ◽

Transiting Planets ◽

Atmospheric Escape ◽

Outer Planets ◽

Upper Limits ◽

The Masses ◽

Better Than

Context. The Kepler extended mission, also known as K2, has provided the community with a wealth of planetary candidates that orbit stars typically much brighter than the targets of the original mission. These planet candidates are suitable for further spectroscopic follow-up and precise mass determinations, leading ultimately to the construction of empirical mass-radius diagrams. Particularly interesting is to constrain the properties of planets that are between Earth and Neptune in size, the most abundant type of planet orbiting Sun-like stars with periods of less than a few years. Aims. Among many other K2 candidates, we discovered a multi-planetary system around EPIC 246471491, referred to henceforth as K2-285, which contains four planets, ranging in size from twice the size of Earth to nearly the size of Neptune. We aim here at confirming their planetary nature and characterizing the properties of this system. Methods. We measure the mass of the planets of the K2-285 system by means of precise radial-velocity measurements using the CARMENES spectrograph and the HARPS-N spectrograph. Results. With our data we are able to determine the mass of the two inner planets of the system with a precision better than 15%, and place upper limits on the masses of the two outer planets. Conclusions. We find that K2-285b has a mass of Mb = 9.68−1.37+1.21 M⊕ and a radius of Rb = 2.59−0.06+0.06 R⊕, yielding a mean density of ρb = 3.07−0.45+0.45 g cm−3, while K2-285c has a mass of Mc = 15.68−2.13+2.28 M⊕, radius of Rc = 3.53−0.08+0.08 R⊕, and a mean density of ρc = 1.95−0.28+0.32 g cm−3. For K2-285d (Rd = 2.48−0.06+0.06 R⊕) and K2-285e (Re = 1.95−0.05+0.05 R⊕), the upper limits for the masses are 6.5 M⊕ and 10.7 M⊕, respectively. The system is thus composed of an (almost) Neptune-twin planet (in mass and radius), two sub-Neptunes with very different densities and presumably bulk composition, and a fourth planet in the outermost orbit that resides right in the middle of the super-Earth/sub-Neptune radius gap. Future comparative planetology studies of this system would provide useful insights into planetary formation, and also a good test of atmospheric escape and evolution theories.

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Getting More For Your Money: Identifying and Confirming Long-Period Planets with Kepler

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308027208 ◽

2008 ◽

Vol 4 (S253) ◽

pp. 560-563

Author(s):

Jennifer C. Yee ◽

B. Scott Gaudi

Keyword(s):

Radial Velocity ◽

Circular Orbits ◽

Transiting Planets ◽

Long Period ◽

The Masses ◽

Better Than

AbstractKepler will monitor enough stars that it is likely to detect single transits of planets with periods longer than the mission lifetime. We show that by combining the Kepler photometry of such transits with precise radial velocity (RV) observations taken over ~3 months, and assuming circular orbits, it is possible to estimate the periods of these transiting planets to better than 20% (for planets with radii greater than that of Neptune) and the masses to within a factor of 2 (for planet masses mp ≥ MJup). We also explore the effects of eccentricity on these quantities.

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Simulating radial velocity observations of trappist-1 with SPIRou

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1953 ◽

2019 ◽

Vol 488 (4) ◽

pp. 5114-5126 ◽

Cited By ~ 6

Author(s):

Baptiste Klein ◽

J-F Donati

Keyword(s):

White Noise ◽

Radial Velocity ◽

Gaussian Process Regression ◽

Data Set ◽

Stellar Activity ◽

Sampling Schemes ◽

Activity Curve ◽

To Come ◽

The Masses

ABSTRACT We simulate a radial velocity (RV) follow-up of the TRAPPIST-1 system, a faithful representative of M dwarfs hosting transiting Earth-sized exoplanets to be observed with SPIRou in the months to come. We generate an RV curve containing the signature of the seven transiting TRAPPIST-1 planets and a realistic stellar activity curve statistically compatible with the light curve obtained with the K2 mission. We find a ±5 m s−1 stellar activity signal comparable in amplitude with the planet signal. Using various sampling schemes and white noise levels, we create time-series from which we estimate the masses of the seven planets. We find that the precision on the mass estimates is dominated by (i) the white noise level for planets c, f, and e and (ii) the stellar activity signal for planets b, d, and h. In particular, the activity signal completely outshines the RV signatures of planets d and h that remain undetected regardless of the RV curve sampling and level of white noise in the data set. We find that an RV follow-up of TRAPPIST-1 using SPIRou alone would likely result in an insufficient coverage of the rapidly evolving activity signal of the star, especially with bright-time observations only, making statistical methods such as Gaussian Process Regression hardly capable of firmly detecting planet f and accurately recovering the mass of planet g. In contrast, we show that using bi-site observations with good longitudinal complementary would allow for a more accurate filtering of the stellar activity RV signal.

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The CARMENES search for exoplanets around M dwarfs

Astronomy and Astrophysics ◽

10.1051/0004-6361/201935460 ◽

2019 ◽

Vol 627 ◽

pp. A49 ◽

Cited By ~ 30

Author(s):

M. Zechmeister ◽

S. Dreizler ◽

I. Ribas ◽

A. Reiners ◽

J. A. Caballero ◽

...

Keyword(s):

Radial Velocity ◽

Near Infrared ◽

Radial Velocities ◽

Slow Rotation ◽

M Dwarfs ◽

Photometric Variability ◽

Photometric Measurements ◽

The Masses ◽

Rule Out

Context. Teegarden’s Star is the brightest and one of the nearest ultra-cool dwarfs in the solar neighbourhood. For its late spectral type (M7.0 V), the star shows relatively little activity and is a prime target for near-infrared radial velocity surveys such as CARMENES. Aims. As part of the CARMENES search for exoplanets around M dwarfs, we obtained more than 200 radial-velocity measurements of Teegarden’s Star and analysed them for planetary signals. Methods. We find periodic variability in the radial velocities of Teegarden’s Star. We also studied photometric measurements to rule out stellar brightness variations mimicking planetary signals. Results. We find evidence for two planet candidates, each with 1.1 M⊕ minimum mass, orbiting at periods of 4.91 and 11.4 d, respectively. No evidence for planetary transits could be found in archival and follow-up photometry. Small photometric variability is suggestive of slow rotation and old age. Conclusions. The two planets are among the lowest-mass planets discovered so far, and they are the first Earth-mass planets around an ultra-cool dwarf for which the masses have been determined using radial velocities.

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Testing exoplanet evaporation with multitransiting systems

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3435 ◽

2019 ◽

Vol 491 (4) ◽

pp. 5287-5297 ◽

Cited By ~ 15

Author(s):

James E Owen ◽

Beatriz Campos Estrada

Keyword(s):

Radial Velocity ◽

Excellent Agreement ◽

Minimum Mass ◽

Mass Measurements ◽

Evolutionary Pathway ◽

X Ray ◽

Transiting Planets ◽

Formation History

ABSTRACT The photoevaporation model is one of the leading explanations for the evolution of small, close-in planets and the origin of the radius-valley. However, without planet mass measurements, it is challenging to test the photoevaporation scenario. Even if masses are available for individual planets, the host star’s unknown EUV/X-ray history makes it difficult to assess the role of photoevaporation. We show that systems with multiple transiting planets are the best in which to rigorously test the photoevaporation model. By scaling one planet to another in a multitransiting system, the host star’s uncertain EUV/X-ray history can be negated. By focusing on systems that contain planets that straddle the radius-valley, one can estimate the minimum masses of planets above the radius-valley (and thus are assumed to have retained a voluminous hydrogen/helium envelope). This minimum mass is estimated by assuming that the planet below the radius-valley entirely lost its initial hydrogen/helium envelope, then calculating how massive any planet above the valley needs to be to retain its envelope. We apply this method to 104 planets above the radius gap in 73 systems for which precise enough radii measurements are available. We find excellent agreement with the photoevaporation model. Only two planets (Kepler-100c and 142c) appear to be inconsistent, suggesting they had a different formation history or followed a different evolutionary pathway to the bulk of the population. Our method can be used to identify TESS systems that warrant radial-velocity follow-up to further test the photoevaporation model. The software to estimate minimum planet masses is publicly available at https://github.com/jo276/EvapMass.

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The TROY project: Searching for co-orbital bodies to known planets

Astronomy and Astrophysics ◽

10.1051/0004-6361/201730652 ◽

2018 ◽

Vol 609 ◽

pp. A96 ◽

Cited By ~ 18

Author(s):

J. Lillo-Box ◽

D. Barrado ◽

P. Figueira ◽

A. Leleu ◽

N. C. Santos ◽

...

Keyword(s):

Radial Velocity ◽

Planetary Systems ◽

Occurrence Rate ◽

Velocity Data ◽

Transiting Planets ◽

Extrasolar Systems ◽

Upper Limits ◽

And Migration ◽

The Masses ◽

Radial Velocity Data

Context. The detection of Earth-like planets, exocomets or Kuiper belts show that the different components found in the solar system should also be present in other planetary systems. Trojans are one of these components and can be considered fossils of the first stages in the life of planetary systems. Their detection in extrasolar systems would open a new scientific window to investigate formation and migration processes. Aims. In this context, the main goal of the TROY project is to detect exotrojans for the first time and to measure their occurrence rate (η-Trojan). In this first paper, we describe the goals and methodology of the project. Additionally, we used archival radial velocity data of 46 planetary systems to place upper limits on the mass of possible trojans and investigate the presence of co-orbital planets down to several tens of Earth masses. Methods. We used archival radial velocity data of 46 close-in (P < 5 days) transiting planets (without detected companions) with information from high-precision radial velocity instruments. We took advantage of the time of mid-transit and secondary eclipses (when available) to constrain the possible presence of additional objects co-orbiting the star along with the planet. This, together with a good phase coverage, breaks the degeneracy between a trojan planet signature and signals coming from additional planets or underestimated eccentricity. Results. We identify nine systems for which the archival data provide >1σ evidence for a mass imbalance between L4 and L5. Two of these systems provide >2σ detection, but no significant detection is found among our sample. We also report upper limits to the masses at L4/L5 in all studied systems and discuss the results in the context of previous findings.

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Distribution of RV- and transiting exoplanets by masses and orbital periods taking into account observational selection

10.5194/epsc2021-802 ◽

2021 ◽

Author(s):

Vladislava Ananyeva ◽

Alexander Tavrov ◽

Oleg Korablev ◽

Jean-Loup Bertaux

Keyword(s):

Radial Velocity ◽

Mass Distribution ◽

Power Law ◽

Planetary Systems ◽

Similar Distribution ◽

Statistical Distributions ◽

Population Synthesis ◽

Transiting Planets ◽

Orbital Periods

More than 95% of the known exoplanets were discovered by the transit- and radial velocity techniques. However, the observed distributions of planets by their masses and by their orbital periods are significantly distorted by numerous observational selections, different for these techniques and different surveys. We found and studied the de-biased statistical distributions of exoplanets by masses and by orbital periods for three groups of exoplanets: I. transiting planets discovered by Kepler ST, whose masses were measured by the follow-up radial velocity technique, II. transiting planets discovered by ground-based surveys (SuperWASP, HATNet, NGTS, XO, KELT, etc.), III. planets discovered by the radial velocity technique. The synthetic projective-mass distribution of RV planets obeys the piecewise power law with the breakpoints at ~0.14MJ and ~1.7MJ. The distribution of RV-planets with m = (0.011-0.087)MJ (or (3.5-28)ME) accurately obeys the power law with an exponent of -2, dN/dm &#8733; m^-2. The distribution of RV planets with m = (0.21-1.7)MJ follows the power law with an exponent ranging from -0.7 to -0.8, dN/dm &#8733; m^(-0.7&#8230;-0.8). The distribution of RV planets with m = (1.7-13)MJ is fitted by a power law with an exponent ranging from -1.7 to -2.0, dN/dm &#8733; m^(-1.7&#8230;-2.0). In general, the synthetic projective-mass distribution of RV planets well agrees with the predictions of the population synthesis theory (Mordasini, 2018) and includes more detailed features to be discussed. The exoplanets distribution by periods generally follows a power law with an exponent of -0.75 and indicates a predominant (averaged) structuring of the planetary systems. De-biased mass distribution of RV-planets with orbital periods of 2-58 days is well consistent with a similar distribution of the Kepler planets. The mass distribution of the transit exoplanets detected by ground-based surveys is consistent with the similar distribution of RV planets with periods of 1-20 days.

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DEMONEX: The DEdicated MONitor of EXotransits

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308026793 ◽

2008 ◽

Vol 4 (S253) ◽

pp. 408-411 ◽

Cited By ~ 1

Author(s):

J. D. Eastman ◽

B. S. Gaudi ◽

D. L. DePoy

Keyword(s):

Radial Velocity ◽

Signal To Noise Ratio ◽

Low Cost ◽

Signal To Noise ◽

Data Set ◽

Transiting Planets ◽

Readout Time ◽

Robotic Telescope ◽

Homogeneous Data

AbstractDEMONEX is a low-cost, 0.5 meter, robotic telescope assembled mostly from commercially available parts dedicated to obtaining precise photometry of bright stars with transiting planets. This photometry will provide a homogeneous data set for all transits visible from its location at Winer Observatory in Sonoita, Arizona. We will also search for additional planets via transit timing variations, measure or place limits on the albedos from secondary eclipses, systematically search known radial velocity planets for those that transit, and follow up promising KELT candidates. Despite its modest size, the signal-to-noise ratio per transit is comparable to that obtained with larger, 1m-class telescopes because of its short readout time and high z-band quantum efficiency. However, its main strength is that it will be used every night for transit follow-up and gather an unprecedented data set on transiting planets. With the 24 known transiting planets and 112 radial velocity planets visible from Winer Observatory, over 90% of all nights have at least one full event to observe.

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Exoplanet mass estimation for a sample of targets for the Ariel mission

Experimental Astronomy ◽

10.1007/s10686-021-09758-0 ◽

2021 ◽

Author(s):

J. R. Barnes ◽

C. A. Haswell

Keyword(s):

Radial Velocity ◽

Input Parameter ◽

Noise Sources ◽

Time Commitment ◽

Low Mass ◽

Time Required ◽

Fixed Input ◽

The Impact ◽

Quadrature Sampling

AbstractAriel’s ambitious goal to survey a quarter of known exoplanets will transform our knowledge of planetary atmospheres. Masses measured directly with the radial velocity technique are essential for well determined planetary bulk properties. Radial velocity masses will provide important checks of masses derived from atmospheric fits or alternatively can be treated as a fixed input parameter to reduce possible degeneracies in atmospheric retrievals. We quantify the impact of stellar activity on planet mass recovery for the Ariel mission sample using Sun-like spot models scaled for active stars combined with other noise sources. Planets with necessarily well-determined ephemerides will be selected for characterisation with Ariel. With this prior requirement, we simulate the derived planet mass precision as a function of the number of observations for a prospective sample of Ariel targets. We find that quadrature sampling can significantly reduce the time commitment required for follow-up RVs, and is most effective when the planetary RV signature is larger than the RV noise. For a typical radial velocity instrument operating on a 4 m class telescope and achieving 1 m s−1 precision, between ~17% and ~ 37% of the time commitment is spent on the 7% of planets with mass Mp < 10 M⊕. In many low activity cases, the time required is limited by asteroseismic and photon noise. For low mass or faint systems, we can recover masses with the same precision up to ~3 times more quickly with an instrumental precision of ~10 cm s−1.

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