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Home , 15 Cancri, 1 Cancri, HD 136118

Analysis of and Astrometric Signals in the Detection of Multi-Planet Extrasolar Planetary Systems Barbara McArthur Dominique Naef

Stephane Udry

Didier Queloz

Michel Mayor

Mike Endl

Tom Harrison Bill Cochran

Artie Hatzes

Geoff Marcy

R. Paul Butler Fritz Benedict Bill Jefferys Debra Fischer Barbara McArthur What is ? astrometry - the branch of astronomy that deals with the measurement of the position and motion of celestial bodies

It is one of the oldest subfields of the astronomy dating back at least to Hipparchus (130 B.C.), who combined the arithmetical astronomy of the Babylonians with the geometrical approach of the Greeks to develop a model for solar and lunar motions. Modern astrometry was founded by Friedrich Bessel with his Fundamenta astronomiae, which gave the mean position of around 3000 . Astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. Astrometric applications led to the development of spherical geometry. What is astrometry with the Hubble Space Telescope?

The Fine Guidance Sensors aboard HST are the only readily available white-light interferometers in space. The interfering element is called a Koester’s prism. Each FGS contains two, one each for the x and y axes, as shown in the following optical diagram.

FGS 1r Fringes

Fringe tracking extracts the position at which the fringe crosses zero.

We expect better fringe tracking performance from FGS 1r because the fringes are cleaner. How do we determine with astrometric measurements?

We measure a in a reference frame over time. We correct the positions for many instrumental effects, then we are left to derive the motions of the star.

As a planet tugs on a star with its gravitational pull, it causes the star to wobble in its path across the sky. By making careful, precise measurements of the star's position in the sky, we can detect wobble. But this tugging is not the only motion of the star…. So We find our astrometric But the parallax can disguise it And the can slinky it

-9.25 -9.25 -8.8

-8.9

-9.30 -9.30 -9.0

-9.1 -9.35 -9.35 -9.2

-9.3 -9.40 -9.40 -9.4

-9.45 -9.45 -9.5 53.30 53.35 53.40 53.45 53.50 53.30 53.35 53.40 53.45 53.50 53.4 53.6 53.8

53.50 53.50 53.8 53.45 53.45

53.40 53.40 53.6

53.35 53.35 53.4 53.30 53.30 6 6 6 2.4480 2.4490 2.4500x10 2.4480 2.4490 2.4500x10 2.4480 2.4490 2.4500x10 Julian Date Julian Date Julian Date What is Doppler Spectroscopy ? (the radial velocity method of planet detection)

As a planet orbits a star, it periodically pulls the star closer to and farther away from Earth (our observation point). This motion has an effect on the spectrum of light coming from the star. As the star moves toward the Earth, the light waves coming from it are compressed and shifted toward the blue (shorter-wavelength) end of the spectrum. As the star moves away from us, the light waves are stretched out toward the red (longer-wavelength) end of the spectrum. These shifts in the spectrum of light coming from the star are called Doppler shifts. By making measurements of the star's spectrum over time, we can detect shifts that would indicate the presence of a planet.

Astrometry works best when the star has a relatively low and the planet isn't too close to the star. In these cases, the star makes the greatest excursion across the sky and is easiest to detect. Think teeter- totter.

Doppler Spectroscopy has worked best detecting close-in short period planets. Why combine astrometry with doppler spectroscopy?

More bang for the buck! We can enhance limited amounts of HST astrometry with relatively ‘cheap’ ground-based doppler spectroscopy. And with a queue-scheduled instrument like the Hobby-Eberly High-Resolution spectroscope we can intensely monitor an object more efficiently than anyone else. AND more importantly The accuracy of our result is improved by the constraint that astromery and radial velocities should describe the same physical system. Why combine doppler spectroscopy with astrometry?

Without astrometry providing an inclination, any mass determined with doppler spectroscopy is only a . We need astrometry to determine the actual mass. So - how do we do this?

Use GaussFit, a computer program, written in the "C" programming language, which includes a full-featured programing language in which models can be built to solve least squares and robust estimation problems. It has a compiler which takes the user’s model, written in the GaussFit programming language, and converts it into an assembly language program for an abstract machine. This program is then interpreted. The interpreter relies on a built-in algebraic manipulator to calculate not only the value of every arithmetic operation, but also all of the required derivative information (which is therefore computed analytically, not numerically). We script models which can simultaneously solve for the orbital parameters from both astrometry and radial velocity and all other nuisance parameters (like parallax and proper motion (ha!). Any a priori knowledge can be entered In a quasi-bayseian approach where it is treated not as constant input but as an observation with error.

GaussFit was conceived by Bill Jefferys and implemented by Bill and myself. Mike Fitzpatrick and later James McCartney wrote the compiler.

GaussFit is available online from our website: http://clyde.as.utexas.edu/Software.html GaussFit has been a flexible platform where we can add another planet to the mix by adding a few lines of code, allowing us to respond immediately to additional patterns that require modeling.

{

if (file == marcyA) agamma = marcyAgamma; if (file == marcyB) agamma = marcyBgamma;

if (file == McD) agamma = McDgamma; if (file == elodie) agamma = elodiegamma; sinE = sin(E); cosE = cos(E); ecos = 1 - eccA * cosE; cosv = (cosE - eccA)/ecos; sinv = param*sinE/ecos; cosvw = cosv * coswrv - sinv * sinwrv; vorbA = agamma + K1A*(eccA*coswrv+cosvw); } Four Elements are common to the visual and Spectroscopic orbit. Solve for these with astrometry and radial velocity

P - period T - time of periastron passage ω - longitude of periastron passage ε - eccentricity •Solve for these with astrometry α - semiaxis major i - Ω - position angle of ascending node µ - proper motion π - parallax •Solve for these with radial velocity γ - offset K - semi-amplitude

•We apply a (Pourbaix & Jorrisen 2000) constraint Diagram of Orbital Elements So - what is out there?

As of January 17, 2006, around main-sequence stars

147 planetary systems 170 planets 17 multiple planet systems ρ1 Cancri ( = HD75732 = HIP 43587)

• G8V star, a bit lighter than the • V = 5.95 • Super metal-rich star ([Fe/H] = +0.27) • About 5 billion old • 41 light years away in the • A member of a double star system • No detectable circumstellar disk

• Mass estimates range from 0.88 - 1.08 Msun we adopt 0.95 Msun ± 0.08 (Allende-Prieto, private comm.) Why did we find ρ1 Cancri e?

• Because Melissa McGrath and Ed Nelan had taken HST FGS astrometric data of ρ1 Cancri that was public domain

• We realized we could get a mass for the outer planet

• We combined rv measurements with the astrometric measurements to get the mass of the outer planet. The accuracy of our result is improved by the constraint that astrometry and radial velocities should describe the same physical system. Element ρ1 Cancri e ρ1 Cancri b ρ1 Cancri c ρ1 Cancri d P (days) 2.808 ± 0.002 14.67 ± 0.01 43.93 ± 0.25 4517.4 ± 77.8 of periastron Ta 3295.31 ± 0.32 3021.08 ± 0.01 3028.63±0.25 2837.69 ±68.87 Eccentricity e 0.174 ± 0.127 0.0197 ± 0.012 0.44 ±0.08 0.327 ± 0.28 ω (deg) 261.65 ± 41.14 131.49 ± 33.27 244.39 ± 10.65 234.73±6.74 Velocity amplitude K (m s-1) 6.665 ± 0.81 67.365 ± 0.82 12.946 ± 0.86 49.786 ± 1.53 -1 V0 Lick (m s ) 21.166 ± 1.31 -1 V0 Elodie (m s ) 2727.448 ± 2.42 -1 V0 HET (m s ) 10.745 ± 0.59 Parameter ρ1 Cancri e ρ1 Cancri b ρ1 Cancri c ρ1 Cancri d

a (AU) 0.038 ± 0.001 0.115 ± 0.003 0.240 ± 0.008 5.257 ± 0.208

A sin i (AU) 1.694E-6± 0.19E-6 9.080e-5 ± 0.12e-5 4.695E-5 ± 0.14E-5 0.195E-1 ± 0.00E-1

M fraction (MSun) 8.225E-14 ± 2.33E-14 4.64E-10 ± 0.17E-10 7.15E-12 ± 0.54E-12 4.874E-8 ± 0.38E-8

a M sin i (MJ) 0.045 ± 0.01 0.784 ± 0.09 0.217 ± 0.04 3.912 ± 0.52

a M sin I (MN) 0.824 ± 0.17

a M sin I (ME) 14.210 ± 2.95

b,c M (MJ) 0.056 ± 0.017 0.982 ± 0.19 0.272 ± 0.07 4.9 ± 1.1

c,d M (MJ) 0.053 ± 0.020 0.982 ± 0.26 0.244 ± 0.07 4.64 ± 1.3

c,d M (MN) 1.031 ± 0.34

c,d M (ME) 17.770 ± 5.57 ρ1 Cancri e phased ρ1 Cancri e has a false alarm probability of 1.7 x 10 -9 ρ1 Cancri quadruple orbit plotted over HET ‘snapshot’ data Using Pourbaix’s constraint, the radial velocity, and the HST astrometry we find an actual mass for ρ1 Cancri e of only 17.7 Earth . ρ1 Cancri e - confirmed in the Lick data (Marcy, Pvt. Communication - no photometric period at 2.81 days (Greg Henry, Pvt. Communication) ρ1 Cancri (55 Cancri) Planetary System

• a Jupiter sized planet at a Jupiter distance (Marcy et al., 2002)

• a 0.2 M Jupiter planet at 0.24 au (Marcy et al., 2002) • a close-in Hot Jupiter planet (Butler, et al., 1997) thought to be in a 3:1 resonance with the smaller middle planet

• a 14.2 Msini Earth massed planet at 0.038 au (McArthur et al., 2004

• first extrasolar quadruple system, the closest analog we have to our own solar system ρ1 Cancri e - Where was it formed? - How big was it when it was formed? - Is it rocky? Comfirming the planet around Epsilon Eridani

In 2000, the discovery of a planet orbiting Epsilon Eridani was announced by Hatzes et al. which combined data from 6 instruments spanning 24 years. It was met with come critical response because ε Eridani is an active star A Planet Around Epsilon Eridani? Revised 12 February 2002

Velocity versus Time for Epsilon Eridani (Data from Lick Observatory) Epsilon Eridani is a chromospherically active star, rich in emission lines in the Ultraviolet (Prieto et al. 2000). Its spectral line shapes, magnetic field, and photospheric temperature vary with time much more than most main sequence stars (Gray and Baliunas 1995). Its abundance of heavy elements is slightly less than Solar, despite being only 1 Gyr old (Drake & Smith 1993). Moreover, the Doppler shift of Epsilon Eridani varies quickly (within a ) by ~15 m/s, constituting a "noise" in the search for a planet. From the California & Carnegi Planet Search page: www..org Is it activity or a planet?

So . . an HST proposal was submitted and accepted to look for the astrometric signal of the planet. The perturbation that could be detected depended upon the observed inclination. The smallest perturbation that could be created at a 90 degree inclination was around 0.8 milliarcsecond, significantly above our precision level. Therefore, we would Not get an ambiguous result with good quality astrometry. Astrometric Perturbation vs. Orbital Inclination

2 " sin i P K1sqrt( 1$ e ) A = # abs 2# % 4.705

! The residuals to the astrometric fit (scale, parallax, proper motion, calibrations) of the HST data revealed the orbit of the planet!

Large circles represent normal points of the tiny dots (actual data). A 1.53 Jupiter mass planet! We found the inclination the be 25.3 degrees from HST astrometry - ε Eri b has the same inclination as the circumstellar dust (Greaves 2005), assuming the dust (at 850m) has a circular distribution.

Greaves et al. 2005, ApJL, 619, L187 Table of the planetary masses we have determined with HST astrometry combined with radial velocities. Coplanarity assumed on multi-planet systems. Table 2 - Masses

Companion a(AU) P(d) eccentricity M (M Jup) Gl 876 b 0.21 30 0.10 1.9 ± 0.4 Gl 876 c 0.13 61 0.27 0.6

!1 Cnc b 0.12 14.7 0.02 0.98 !1 Cnc c 0.24 43.9 0.44 0.24 !1 Cnc d 5.26 4517 0.33: 4.6 ± 1.3 !1 Cnc e 0.04 2.8 0.17 0.056

" Eri b 3.29 2390 0.48 1.5 ± 0.3 The FUTURE and near FUTURE We are awaiting additional HST data for υ And and we have started getting data for the targets listed below.

Table 3 - Future Targets

Companion M * (M O) Sp.T. d(pc) ecc M sini (M Jup) !sini (mas) P(d) HD 47536 b 1.1 K1 III 12.1 0.2 7 0.8 712 HD 136118 b 1.21 F9 V 52.3 0.36 11.8 0.4 1209 HD 168443 c 1.05 G6 IV 37.9 0.2 17.4 1.3 1739 HD 145675 b 1.00 K0 V 18.1 0.38 4.9 0.8 1796 HD 38529 c 1.45 G4 IV 42.4 0.33 13.1 0.8 2207 HD 33636 b 1.02 G0 V 28.7 0.53 9.4 1.1 2447 The question:

As radial velocity instrumentation improves and we find and investigate systems with many planets how can we best model the interactions of the planets to get dynamical orbits when we don’t know the masses only the mass limits of the planets?

It will be years before SIM (Space Interferometry Mission) is available to measure these planets astronomically and some of these planet cannot even be measured directly with the micro-arcsecond precision of SIM.