MASSES of EXOPLANETS from ASTROMETRY. G. Fritz Benedict And, Barbara E

Protostars and Planets V 2005 8111.pdf

MASSES OF EXOPLANETS FROM ASTROMETRY. G. Fritz Benedict and, Barbara E. McArthur, McDonald Observatory, U. Texas, Austin, TX 78712, USA ([email protected], [email protected]).

Outline end we include in our modeling as much information as possible about each reference star. This information includes pho- While spectacularly successful at nding planets orbiting other tometry (at a minimum V from the FGS, JHK from 2MASS), stars, the radial velocity method cannot establish a precise spectral types when available or measured by our co-I’s, and companion mass. Planet type depends upon mass. As in proper motions from UCAC2 (Zacharias et al. 2004). Given the case of stars, mass critically determines most of the in- that luminosity class is at the same time the most dif cult stantaneous characteristics and future evolution of a planet. to determine and the most critical to reference star absolute Present instruments and techniques can distinguish between magnitude, we also employ an iterative reduced proper mo- brown dwarfs, gas giants, and rocky-cored Neptunes. As- tion technique to identify giant stars (Yong & Lambert 2003, trometry with Hubble Space Telescope Fine Guidance Sensors Gould & Morgan 2003), using proper motions primarily from (FGS) and the Allegheny Multi-aperture Astrometric Photome- UCAC2. With absolute magnitudes in hand we derive −(V −MV +5−AV )/5 ter (MAP) provides inclination, i, and perturbation size, α, πabs = 10 for each reference star, where which, when combined with an estimate of the stellar mass, interstellar absorption, AV is derived from the photometry provide a companion mass. We have applied this technique to and Schlegel et al. 1998. These and the proper motions from four candidate stars: GJ 876 (FGS), Eridani (FGS + MAP), UCAC2 enter our GaussFit (Jefferys et al. 1988) modeling as ρ1 Cancri (FGS), and υ Andromeda (FGS + MAP). Three of observations with error. The modeling yields estimated paral- these stars harbor known multi-planet systems. Invoking co- lax and proper motion for reference and target stars and per- planarity provides mass estimates for 10 exoplanets, including turbation orbital elements for the target stars. the lowest mass planet (actual mass, not Msini), ρ1 Cancri e, Our approach uses ground-based radial velocities to deter- a planet with M = 18 ± 3 M⊕, about the mass of Neptune. mine P, period, e, eccentricity, ω, longitude of periastron passage, T, time of periastron passage, and K1, the RV amplitude. Details FGS and MAP astrometry provides α, semi-major axis of perturbation, i, orbit inclination, Ω, position angle of ascending Our targets are listed in Table 1. To estimate exoplanet masses, node, πabs, absolute parallax of the system, and µ, proper mo- we apply the mixed astrometry and radial velocities approach tion of the system. Just as older, less-precise RVs assisted previously used to determine binary star masses (e.g., Bene- in pulling out the Erib planet signature in the original an- dict et al. 2001). We treat the exoplanet and the star as a nouncement paper (Hatzes et al. 2000), the lower-precision system with a very small fractional mass. Any astrometric ground-based MAP astrometry extends the time baseline to approach will be most effective on nearby systems with less better de ne the proper motion. Our epochs range for Eri, massive primaries. Hence, our rst exoplanet mass result was 1989 - present, and for υ And, 2000.7 - present. Finally, we for a companion to a nearby, low-mass star, GJ 876. Both carry out a simultaneous solution incorporating both astrom- discovery groups (Delfosse et al. 1998; Marcy et al. 1998) etry and radial velocities, constraining all plate constants to provided published and unpublished high-precision radial ve- those determined from astrometry-only, and constrain K, e, P, locities. We concentrated the FGS observations at peri- and and ω to values determined only from radial velocities. apastron, and completed the bulk of the observations within The perturbation periods of the outermost planets of the 61 days, the orbital period of GJ 876b. We obtained a few other three systems (see Table 2) are signi cantly longer than more observations over the next year to obtain the necessary the duration of our HST observation sequences (three years 1 precision for proper motion and parallax, nuisance parameters for Eri and υ And, a little over one year for ρ Cnc). How that must be determined and removed to establish perturbation do we establish inclination and perturbation size for systems orbital parameters. with periods far longer than our observation window, other than using MAP data where available? Pourbaix & Jorrisen Table 1 - Current Targets (2000) introduce a relation between parameters obtained from Star d π Sp. T. M astrometry and radial velocities. We use this relationship (pc) (”) ( ) α sin i PK sqrt(1 − e2) Gl 876 4.7 0.2146 M4V 0.32 A = 1 (1) π 2π × 4.7405 ρ1 Cnc 12.5 0.0798 G8V 0.95 abs Eri 3.2 0.3104 K2V 0.83 as a constraint, where quantities derived only from astrometry υ And 13.5 0.0730 F8V 1.1 (parallax, πabs, primary perturbation orbit size, αA, and inclination, i) are on the left, and quantities derivable from both The system parallax and proper motion are measured rela- (the period, P and eccentricity, e), or radial velocities only tive to a reference frame, each of whose members also exhibit (the radial velocity amplitude for the primary, K1), are on the those phenomena. To get at the far smaller planetary pertur- right. Typically, the errors of the right side quantities are quite bation, we must obtain and remove the parallax and proper small. Our simultaneous solution uses the Figure 1 curve re- motion as accurately as possible for each stellar host. To this lating perturbation size, α and perturbation inclination, i, as a Protostars and Planets V 2005 8111.pdf

Bayesian prior, sliding along it until the astrometric and radial This work has been supported through multiple grants from velocity residuals are minimized. Gross deviations from the the Space Telescope Science Institute which is operated by curve are minimized by the low errors of the right-side quan- AURA for NASA. tities. Table 2 presents our masses, where those determined as- References suming coplanarity have no stated errors. We note that a perturbation size due to Eri b (α = 1.5 ± 0.4 mas) was rst re- Benedict et al. 2001, AJ, 121, 1607 ported by Gatewood (2000) in abstract form. Our preliminary combined FGS/RV solution yields α = 1.8 ± 0.4 mas, used to Benedict et al. 2002, ApJL, 581, L115 obtain the Table 2 mass. We also note that Mazeh et al. (1999) Delfosse et al. 1998, A&A, 338, L67 obtained a mass (that agrees with ours within the error bars) for υ And d, Md = 10 ± 5MJup, using HIPPARCOS. Our Gatewood, G. 2000, DPS Meeting, abstract 32.01, BAAS, upper limit for υ And will improve as we analyze additional 32, 1051 Cycle 13 observations. Gould, A. & Morgan, C. W. 2003, ApJ, 585, 1056 Table 2 - Exoplanet Masses Hatzes, A. P. et al. 2000, ApJ, 544, L145 Planet a P ecc M (AU) (days) (Jup) Jefferys, W., Fitzpatrick, J., & McArthur, B. 1988, Ce- Gl 876 b 0.21 30 0.10 1.9 ± 0.4 lest. Mech. 41, 39. Gl 876 c 0.13 61 0.27 0.6 Marcy, G. et al. 1998, ApJL, 505, L147 ρ1 Cnc b 0.12 14.7 0.02 0.98 ρ1 Cnc d 5.26 4517 0.33: 4.6± 1.3 Mazeh, T. et al. 1999, ApJL, 522, L149 1 ρ Cnc e 0.04 2.8 0.17 0.056 McArthur et al. 2004, ApJL, 614, L81 υ And b 0.06/sini 4.6 0.01 <1.7 υ And c 0.83/sini 241.5 0.28 <2.9 Pourbaix, D. & Jorrisen, A. 2000, A&A, 145, 161 υ And d 2.53/sini 1284 0.27 <9 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, Eri b 3.14 2363 0.7 1.5± 0.3 ApJ, 500, 525

Future Work Yong, D. & Lambert, D. L. 2003, PASP, 115, 796 Zacharias et al. 2004, AJ, 127, 3043 The HST Cycle 14 Time Allocation Committee awarded us or- bits over the next two years to carry out similar investigations on the 6 additional systems listed in Table 3. With the plausi- ble assumption of i = 30◦, some of these objects may reside 7.0 in the brown dwarf desert. ε Eri 5.5 M = 0.83 M 6.0 * O 5.0 Table 3 - Future HST Targets π = 0.3106 ± 0.0004 arcsec Planet M ∗ Sp.T. d M a aa P 4.5 ( ) (pc) (Jup) (mas) (days) 5.0 ε Eri b 4.0 M = 1.5 ± 0.3MJup HD 47536 b 1.1 K1III 12.1 7 0.8 712 p 3.5 M 4.0 HD 136118 b 1.2 F9V 52.3 11.8 0.4 1209 Jup 3.0 HD 168443 c 1.0 G6IV 37.9 17.4 1.3 1739 HD 145675 b 1.0 K0V 18.1 4.9 0.8 1796 3.0 2.5 HD 38529 c 1.5 G4IV 42.4 13.1 0.8 2207 2.0 2.0 HD 33636 b 1.0 G0V 28.7 9.4 1.1 2447 1.5

a Eri Astrometric Perturbation (mas) 1.0 Minimum values modulo sini. ε 1.0 0.5 Summary 0.0 0 10 20 30 40 50 60 70 80 90 While it will be years before astrometric missions (SIM Plan- Orbital Inclination (°) etQuest and GAIA) will be able to measure the astrometric perturbations of all the planets in these systems (and directly Figure 1: This curve relates perturbation size and inclina- test the assumption of co-planarity), we have been and will tion for the Eriperturbation through the Pourbaix & Jorrisen be able to use a combination of high-precision radial veloc- (2000) relation (Equation 1). In a quasi-bayesian sense we use ity and HST astrometric data to estimate the inclination of the the curve as a prior. outer-most known planet in each system. Successful comple- tion of our HST Cycle 14-15 project will result in an additional 8 planetary masses, again, assuming co-planarity.