Astrometric Constraints on the Masses of Long-period Gas Giant Planets in the TRAPPIST-1 Planetary System

Since 2007, we have been engaged in a long-term program using the Carnegie Astrometric Planet Search Camera (CAPSCam) on the Las Campanas Observatory 2.5 m du Pont telescope to search for gas giant planets in orbit around nearby low-mass stars by the astrometric detection method. There are 21 known G stars within 10 pc of the Sun and at least 236 M dwarfs (Henry et al. 1997), with nearby late-M dwarfs continuing to be discovered (e.g., Reiners & Basri 2009). These abundant M dwarfs are a natural choice for astrometric planet searches, because low-mass primaries and close proximity to the Sun greatly enhance the detectability of planetary companions.

M dwarfs have become the favored targets for finding the closest habitable worlds, those most amenable to follow-up observations. M dwarf exoplanets are likely to be the primary targets to be searched by JWST, the James Webb Space Telescope, for atmospheric biosignatures (Deming et al. 2009) among the transiting super-Earths to be found by TESS, the Transiting Exoplanet Survey Satellite (Ricker et al. 2014). In fact, M dwarfs are estimated to harbor about 37% of the habitable-zone "real estate" within 10 pc of the Sun (Cantrell et al. 2013), and estimates of the frequency of habitable Earths around M dwarfs can be as high as 53% (Kopparapu 2013). The detection of a habitable-zone exo-Earth orbiting the M6V dwarf Proxima Centuari (Anglada-Escudé et al. 2016), literally the closest star to the Sun at 1.295 pc, has raised the stakes in the race for the first direct imaging and spectroscopy studies of nearby habitable worlds.

The detection of at first three (Gillon et al. 2016), and then a total of at least seven exoplanets (Gillon et al. 2017) orbiting the M8V dwarf TRAPPIST-1 (2M2306-05, 2MASS J23062928–0502285) has only added fuel to this race to discover and characterize potentially habitable exoplanets. Transit photometry has revealed that five of the seven known TRAPPIST-1 planets have radii and masses within factors of ∼1.1 and ∼2, respectively, of that of the Earth, and three of these appear to have stellar irradiation levels that might permit the existence of oceans of surface water, assuming Earth-like atmospheres (Gillon et al. 2017).

The near-resonant orbital periods of the six innermost TRAPPIST-1 planets suggests their formation at a greater orbital distance followed by inward coupled migration (Gillon et al. 2017). A number of the first hot and warm super-Earth exoplanets discovered by Doppler spectroscopy were found to have at least one longer-period gas giant sibling planet, with several having two (e.g., the M4V dwarf Gl 876 and the G8V star HD 69830) or even three such siblings (e.g., the G3V star Mu Ara and the G8V star 55 Cnc). HD 181433 is a K5V star with an inner 7.5 Earth-mass planet and two outer Jupiter-mass planets, while the G6V HD 47186 has an inner 22 Earth-mass planet and an outer Saturn-mass planet (Bouchy et al. 2009). Outer gas giants may thus accompany inner habitable worlds, a situation analogous to that of our own solar system.

The question then becomes, what other planets might be orbiting TRAPPIST-1 at greater distances than the seven known planets? The outermost one, TRAPPIST-1 h, has a semimajor axis of ∼0.063 au, leaving a large amount of orbital distance unexplored. Montet et al. (2014) combined Doppler and direct imaging results to estimate that about 6.5% of M dwarfs host one or more gas giants within 20 au. Gas giants orbiting M dwarfs may represent a challenge to the core accretion formation mechanism for gas giant planet formation (e.g., Koshimoto et al. 2014), but not for the competing disk instability mechanism (e.g., Boss 2006). The Very Large Telescope (VLT) FORS2 camera astrometric survey of Sahlmann et al. (2014) set an upper bound of about 9% on the occurrence of gas giants larger than five Jupiter masses orbiting at 0.01 to 0.8 au around a sample of 20 M8 to L2 dwarfs. The Gaia space telescope is presently searching about 1000 M dwarfs for long-period exoplanets (Perryman et al. 2014; Sozzetti et al. 2014).

We began observing TRAPPIST-1 with CAPSCam in 2011 as part of a long-term astrometric program to detect gas giant planets around approximately 100 nearby M, L, and T dwarf stars. Weinberger et al. (2016) published a trigonometric distance for TRAPPIST-1 of 12.49 pc ± 0.2 pc, slightly larger than the previous trigonometric distance of 12.1 pc ± 0.4 pc (Costa et al. 2006), but consistent within the error bars. Reiners & Basri (2009) found a spectrophotometric distance of 12.1 pc. The CAPSCam distance was based on the first 11 epochs of observations, spanning the 3 years from 2011 to 2014. Here, we re-analyze TRAPPIST-1, using the additional 4 epochs of observations taken in 2015 and 2016 to refine the trigonometric parallax and proper motions derived by Weinberger et al. (2016) and to search for any evidence of long-period gas giant companions to TRAPPIST-1.

The CAPSCam camera (Boss et al. 2009) employs a Hawaii-2RG HyViSi hybrid array (2048 × 2048) that allows the definition of an arbitrary Guide Window (GW), which can be read out (and reset) rapidly, repeatedly, and independently of the rest of the array, the Full Frame (FF). The GW is centered on the relatively bright target stars, with multiple short exposures to avoid saturation. The rest of the array then integrates for prolonged periods on the background reference grid of fainter stars. The natural plate scale for CAPSCam on the 2.5 m du Pont is 0.196 arcsec/pixel, a scale that allows us to avoid introducing any extra optical elements into the system that would produce astrometric errors. An astrometric quality (λ/30) dewar filter window with a red bandpass of 810 to 910 nm (similar to SDSS z) is the only other optical element in the system besides the du Pont primary and secondary mirrors. We take multiple exposures with CAPSCam, with small variations (2 arcsec) of the image position (dithering to four positions), in order to average out uncertainties due to pixel response non-uniformity.

Analysis of the star NLTT 48256 showed that an astrometric accuracy better than 0.4 mas can be obtained over a timescale of several years with CAPSCam on the du Pont 2.5 m (Boss et al. 2009). Anglada-Escudé et al. (2012) used CAPSCam to place an upper mass limit on the known Doppler exoplanet GJ 317b (Johnson et al. 2007). Analysis of the M3.5 dwarf GJ 317 showed that the limiting astrometric accuracy, at least for the brighter targets in our sample, is about 0.6 mas per epoch in Right Ascension (R.A.) and about 1 mas per epoch in Declination (decl.), based on the results of the preliminary data analysis pipeline available at the time. With 18 epochs, the overall accuracy in fitting the parallax of GJ 317 was about 0.15 mas (Anglada-Escudé et al. 2012). For comparison, VLT astrometry with SPHERE yields positional errors of about 1 mas (Zurlo et al. 2014). Hence, CAPSCam should be able to either detect or place significant astrometric constraints on the masses of any long-period gas giants in the TRAPPIST-1 system.

TRAPPIST-1 (R.A. = 23 06 29.283; Decl. = −05 02 28.59 [2000]) was observed at the 15 epochs listed in Table 1 between 2011 and 2016. TRAPPIST-1 is bright enough (I = 14.024, J = 11.354) that the GW mode was used, with either a 10 s or 15 s GW exposure (depending on the seeing conditions: the former for seeing of ∼1.0 arcsec, and the latter for seeing of ∼1.4 arcsec) and a 90 s FF exposure. At each epoch, there were typically 20 frames taken during a 40 minute time period as TRAPPIST-1 passed through the meridian. The data were analyzed using the same data pipeline that has been used for reducing the data for all previously published CAPSCam observations, the APTa pipeline developed by one of us (GAE). Details about ATPa may be found in Boss et al. (2009) and in Anglada-Escudé et al. (2012) and about the parallax, proper motions, and astrometric zero point corrections in Weinberger et al. (2016).

Weinberger et al. (2016) used the same first 11 epochs of observations as are used here to determine an absolute parallax π_abs = 80.09 ± 1.17 mas and proper motions in R.A. and decl., respectively, of 922.02 ± 0.61 mas yr⁻¹ and −461.88 ± 0.94 mas yr⁻¹. This absolute parallax is based on a relative parallax of π_rel = 79.10 ± 1.11 mas and a zero point correction of −0.99 ± 0.36 mas. Note that the proper motions are not corrected for any bias in the reference frame and that Weinberger et al. (2016) used only a portion of the ATPa data analysis pipeline and developed new routines to fit for the parallax and proper motion. When all 15 epochs listed in Table 1 are included in the solution, the absolute parallax becomes π_abs = 79.59 ± 0.78 mas and the proper motions in R.A. and decl., respectively, become 922.64 mas yr⁻¹ and −462.88 mas yr⁻¹. Now the absolute parallax is based on a relative parallax of π_rel = 78.51 ± 0.75 mas and a zero point correction of −1.08 ± 0.22 mas, as described below. Clearly, the revised values for the parallax and proper motion are consistent with each other and are well within the error bars. TRAPPIST-1 thus has a revised trigonometric parallax distance of 12.56 ± 0.12 pc.

The correction to absolute parallax was based on a comparison of the photometric distance to five reference stars with good catalog photometry at V, I, J, H, and Ks and with fit effective temperatures ≥4000 K. Our CAPSCam measurements of these stars yield nominal parallaxes, which in this case are all smaller than their uncertainties. We averaged the offset between the nominal parallaxes and the photometric parallaxes obtained by fitting Kurucz stellar atmosphere models to the broad-band photometry and find a correction to absolute parallax of 1.08 ± 0.22 mas. Note that this correction is irrelevant to the determination of the residuals to the five-parameter fit to the astrometry and therefore does not contribute to the upper limit on any giant planet companion to the star.

Figure 1 displays the CAPSCam TRAPPIST-1 field image that served as the reference plate for the ATPa astrometric analysis. TRAPPIST-1 itself lies within the central GW, while the stars labeled with blue numbers were used as the reference stars for the ATPa analysis. Red vectors depict the inferred proper motions of the stars.

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Table 1 lists the ATPa residuals in R.A. and decl. for the apparent motion of TRAPPIST-1 with respect to the background reference stars that remain after the parallax and proper motion have been removed from the solution. Table 1 also lists the individual epoch statistical uncertainties, computed as the root mean square (rms) of the offsets of the individual frames that are taken at each epoch. We note that the standard deviation of the residuals (∼1.2 mas in R.A.) is much larger than the typical individual epoch statistical uncertainty (∼0.6 mas), and we attribute the difference to systematic sources that we are working to resolve.

The ATPa pipeline searches for periodicities in these Table 1 residuals that could be caused by a companion object on a circular orbit, with a minimum orbital period of 80 days and maximum orbital period of 4000 days. Figure 2 shows the resulting power spectrum for a possible long-period companion to TRAPPIST-1. The power spectrum yields no hints of any long-period planets, as it is dominated by a large number of short-period peaks with rather low amplitudes, with little power at periods longer than about 1500 days.

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Figures 3 and 4 plot the ATPa residuals (δ_R.A., δ_Decl.) from Table 1, allowing a visual search for any suspected periodicity. These figures confirm what is evident from Figure 2, namely that the only way to fit the residuals with an astrometric wobble would be to use an orbit with a period of order a year or less. Given that the 15 CAPSCam observations spanning a little over 5 years average out to only about 3 epochs per year, orbital periods of a year or less are likely to be spurious. Ongoing work on developing the CAPSCam date pipeline will allow us to further refine the astrometric analysis.

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In Table 1, the mean absolute value of the ATPa residuals in R.A. is 1.17 mas, while that for the residuals in decl. is 1.46 mas. For the detection of an astrometric amplitude A (in mas) in the presence of astrometric uncertainties of σ (in mas) with N_obs observations, a conservative estimate of the signal to noise ratio (S/N) is given by

$$\begin{eqnarray*}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{A}{\sigma }\sqrt{{N}_{\mathrm{obs}}}.\end{eqnarray*}$$

Taking the larger of the two residuals, namely those in decl., as σ = 1.46 mas, N_obs = 15, and requiring S/N = 5 yields a conservative estimate of the largest amplitude that could be hidden in our CAPSCam data of A = 1.9 mas.

We then use 1.9 mas as an upper limit on any wobble of TRAPPIST-1, allowing us to place upper limits on the mass of any long-period gas giant companions, as a function of their orbital periods. The angular semimajor axis (Θ) of the displacement of a star about the common center of mass of a star–planet system is given (e.g., Boss 1996) by

$$\begin{eqnarray*}&&{\rm{\Theta }}=\displaystyle \frac{{M}_{p}a}{{M}_{s}r}=\displaystyle \frac{{M}_{p}{P}^{2/3}}{{M}_{s}^{2/3}r},\end{eqnarray*}$$

where Θ is in arcsec, M_p is the planet mass (in solar masses), M_s is the stellar mass (in solar masses), M_p is assumed to be negligible in mass compared to M_s, a is the orbital semimajor axis (in astronomical unit) and is equal to the radius of an assumed circular orbit, P is the orbital period (in years), and r is the distance to the star–planet system (in pc). For example, with only Jupiter orbiting around the Sun, the solar wobble is ±1 mas when viewed from 5 pc. Note that in the case of TRAPPIST-1, where the primary has a mass of only about 80 M_Jup (Gillon et al. 2017), neglecting the planet mass is not strictly a good approximation when considering possible planetary masses in the multiple Jupiter-mass range, but this approximation is adequate for the constraint considered here.

Figure 5 displays the possible long-period planet masses that appear to be ruled out by our non-detection at the 1.9 mas level for the TRAPPIST-1 system, compared to the six TRAPPIST-1 planets with known masses, and all of the confirmed exoplanets currently contained in the NASA Exoplanet Archive. We assumed a mass for TRAPPIST-1 of 0.08 M_⊙ (Gillon et al. 2017). We halt the astrometric constraint at an orbital period of five years, the length of our CAPSCam observations. It can be seen from Figure 5 that our astrometric constraint still leaves a large area of discovery space to be explored for additional planets in the TRAPPIST-1 system. While the plethora of confirmed exoplanets shown in Figure 5 is suggestive of the possibility of other planets to be found around TRAPPIST-1, it should be noted that most of those confirmed planets orbit stars of an earlier type than the M8 dwarf TRAPPIST-1, and planetary demographics can be expected to depend on stellar masses.

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Tanner et al. (2012) performed Keck II NIRSPEC Doppler spectroscopy of 23 late-M dwarfs, including 2M2306-05 = TRAPPIST-1. Their data consisted of three epochs, one in 2006 and two more in 2010 taken on consecutive nights, a sequence chosen to search for both short-period hot Jupiters and long-period cold Jupiters. They obtained radial velocities for 2M2306-05 with an uncertainty of 130 m s⁻¹. Following Boss (1996), the radial velocity amplitude in km s⁻¹ for an edge-on planetary orbit is

$$\begin{eqnarray*}&&{v}_{r}=30\displaystyle \frac{{M}_{p}}{{P}^{1/3}{M}_{s}^{2/3}},\end{eqnarray*}$$

using the same units that were previously. Figure 5 shows the resulting upper limit on the mass of any undetected companions to TRAPPIST-1, based on the conservative estimate of a maximum Doppler wobble of 380 m s⁻¹. This estimate assumes that S/N = 5 (Mayor & Queloz 1995), σ = 130 m s⁻¹, and N_obs = 3. It can be seen that this Doppler upper mass limit, in combination with our astrometric upper mass limit, rules out a large portion of possible discovery space, though an equally large and interesting portion remains to be explored. Orbital stability of the TRAPPIST-1 system appears to be assured even in the presence of a 15 M_⊕ planet, provided that it orbits beyond 0.37 au (Quarles et al. 2017), yielding another constraint on any undiscovered planets in this system.

We have also performed a more involved analysis of the companion masses ruled out by the Tanner et al. (2012) Doppler RV observations. To assess the detectability of RV companions, we followed the procedure described in Kohn et al. (2016). We calculated orbits for 482 million putative binary systems for masses of the secondary of 0.6 to 12.6 M_Jup and periods up to 1550 days. The mass of the primary was assumed to be 0.08 M_⊙. For each period and mass-ratio pair, we calculated the radial velocities that would be observed given a single epoch precision of 130 m s⁻¹ for an ensemble of binaries with orbital elements drawn from the eccentricity distribution for known planets as described by the Beta distribution in Kipping (2013), a uniform distribution of sin i (inclination i), a uniform distribution of time of periastron passage over the period, and a uniform distribution of the longitude of periastron. We define a binary to be observable at a given period and mass-ratio if, in 67% of the calculated orbits, the rms of its calculated RV exceeded 225 m s⁻¹. We plot the resulting RV constraint as a blue curve in Figure 5 as well.

Given that about two transits occur every day in the TRAPPIST-1 system (Gillon et al. 2017), and that the transits last for at least a half-hour apiece, transits should be occurring on average for one hour every day. Each CAPSCam epoch lasted for roughly one hour on target, so 15 epochs observed meant that CAPSCam had observed TRAPPIST-1 for a total of about 15 hr, or 0.6 day. Hence, there is a reasonable chance that at least one transit occurred during our astrometric observations.

We thus decided to check to see if any transits were obvious in our CAPSCam data. The deepest transit depth for a TRAPPIST-1 planet is about 0.782% (for TRAPPIST-1 g), while the shallowest depth is about 0.352% (for TRAPPIST-1 h), so detecting a transit requires millimag photometry from the ground. CAPSCam was not designed to be a photometric camera, and our astrometric observations do not require photometric seeing, and as a consequence, our photometric precision has not been measured or developed. A quick look at a total of 356 CAPSCam images of TRAPPIST-1 found that when the photometric flux in TRAPPIST-1 was normalized by that of the brighter reference stars in the 6.63 arcmin ×6.63 arcmin field of view, variations of order unity occurred in an irregular manner. Even larger variations were evident when normalized to fainter reference stars. As a result, we abandoned our search for transits in the CAPSCam data.

The TRAPPIST-1 system is a fascinating example of a planetary system that will continue be a focus of intensive research in the coming decades. Our ongoing astrometric observations with CAPSCam have refined the trigonometric distance to TRAPPIST-1, with the new value being 12.56 pc. In addition, the absence of any clear, long-period signals in the residuals, once the parallax and proper motions have been removed, places strong upper limits on the masses of any gas giant planets orbiting well beyond the seven known transiting planets: no planets more massive than ∼4.6 M_Jup orbit with a 1 year period, and none more massive than ∼1.6 M_Jup orbit with a 5 year period. A large region of discovery space intermediate between these long-period orbits and the short-period orbits of the TRAPPIST-1 planets, however, remains to be explored by other means.

One of us (T.L.A.) is presently working on further developing ATPa, with the goal of reducing sources of systematic errors, such as those caused by differential chromatic refraction and by distortions of the entire optical system that might change with time. The latter is being addressed by taking multiply dithered (4 × 4) CAPSCam images of rich stellar fields at multiple epochs and generating a pixel-by-pixel correction function. We plan to continue our astrometric observations of TRAPPIST-1, and we look forward to learning what an improved analysis of our data might reveal about the TRAPPIST-1 planetary system.

We thank the David W. Thompson Family Fund for support of the CAPSCam astrometric planet search program, the Carnegie Observatories for continued access to the du Pont telescope, and the telescope operators and technicians at the Las Campanas Observatory for making these observations possible. We also thank the referee for several suggestions for improvements. The development of the CAPSCam camera was supported in part by NSF grant AST-0352912.