Combining Imaging + RV’s
Jus n R. Crepp
Frank M. Freimann Professor Department of Physics University of Notre Dame [email protected] Connec ng Two Dis nct Techniques Doppler Trends
30 HD 19467 20
10
0
ï10 dv/dt=é1.37+/é0.09 m/s/yr
Radial Velocity [m/s] ï20 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Mo va on • High detec on efficiency. • Break sin(i) degeneracy, construct 3d-orbits. • Dynamical masses of companions. • Calibrate evolu onary models.
Kappa Andromedae Determine fpl for wide orbits.
“b”
HR 8799 Marois et al. 2010 Carson et al. 2012 Par al Orbits
Isaac Newton What informa on can be gleaned? (1) Minimum dynamical mass (Torres 1999). (2) Physical separa on (Howard et al. 2010). Minimum Mass
2 ⎛ M ⎞ ⎛ d ρ ⎞ d(RV ) min⎜ B ⎟ =1.39E − 5 ⎜ ⎟ ⎝ MSun ⎠ ⎝ pc arcsec⎠ dt where RV accelera on is measured in m s-1 yr-1. € Physical Separa on
d(RV ) GMB ⎛ rAB ⎞ ρ = 2 cosθ, ⎜ ⎟ sinθ = dt rAB ⎝ AU⎠ π
where rAB is the instantaneous true physical separa on.
€ € 3d-Orbits and Dynamical Mass
Radial Velocities:
K, P, e, ω, tp Astrometry: * a, i, P, e, ω, tp, Ω
How much informa on do we need to calculate the orbit and mass? Murray & Dermo 1998 At What Point Can We Calculate the Orbit?
4π 2a3 p2 = G (M + m) * No ce that precise parallax is essen al (Dupuy & Kraus 2013) € When do constraints become interes ng? s “with accuracies of a few mas, it is possible to place strong constraints on KBO orbits even from very short (e.g., 24 hour) arcs … reflex mo on is easily σast detected giving a measure of distance to “Yes, of course the the target in less than an hour.” “I don’t trust anyone’s results inclina on falls out - Bernstein & Khushalani 2000 un l I see 2 phase wraps.” immediately.” - Andy Boden (Caltech) - Jessica Lu (IfA) Galac c Center Comets
PMS Binaries
100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 We are here. σast / s
How Do We Fit Observa ons?
• Bayesian sta s cal framework. (“Data Analysis: A Bayesian Tutorial” by Sivia) • Assume we understand uncertain es. • Keplerian orbit model. Single companion. • Markov-Chain Monte Carlo (MCMC) analysis. (“Quan fying the Uncertainty in the Orbits of Extrasolar Planets”, Ford 2005, AJ, 129, 1706) Markov Chain Monte Carlo
• Many degrees of freedom {P, e, i, ω, tp, Ω, …}. • Metropolis-Has ngs algorithm.
P
e X (Working in N-dimensional space) i
Metropolis-Hastings Pseudo-Code:
(1) Cull P, a, e, i, ω, tp, Ω, + nuissance parameters. (2) Calculate Likelihood, L, for parameters. Use both RV, Imaging data simultaneously.
(3) if (L > L0) record new chain entries. else
if (rand[0,1] < L / L0) record new chain entries. else record old chain entries. end end (4) Wash, Rinse, Repeat to determine posterior. Dynamical Masses
HR 7672 G0 primary L4 companion d=17.1 pc Liu et al. 2002
Crepp et al. 2012a, ApJ Direct Image, Keck/NIRC2 2011
2011.37 LiuLiu etet al.al. 20022002 BoccalettiBoccaletti etet al.al. 20032003 SerabynSerabyn etet al.al. 20092009 é0.5 presentNACO 279.C studyé5052(A)
present study Towards Star
é0.6
2007.73 North offset (") North offset (") é0.7 2006.69
2001.64 2002.54 2001.94
0.5 0.4 0.3 0.2 EastEast offsetoffset (")(") Crepp et al. 2012a, ApJ All Six Orbit Parameters 3d-Orbit and Dynamical Mass
More accurate and precise than Crepp et al. 2012a, ApJ theore cal evolu onary models(!) Mass of a Directly Imaged Brown Dwarf Crepp et al. 2012b, ApJ [K2, NIRC2] [K1, HIRES] California Planet Search (CPS)
Kappa CrB
MRVELS
trend=1.7 m/s/yr
Johnson et al. 2008
Astrometry Measurements
Doppler Measurements
m > 0.260+/-0.010Msun
Old and Cold T-Dwarf
30 HD 19467 20
10
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ï10 dv/dt=é1.37+/é0.09 m/s/yr
Radial Velocity [m/s] ï20 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Benchmark T dwarf
[Fe/H] = -0.15+/-0.04 Age > 4.6 Gyr
Mass > 52MJup Spectrum from Project 1640 now in hand. … Ar st Impression Methane Absorp on
CH4 Short
CH4 Long Can we detect planets? Yes!
80
min dynamical mass at 0.2" ) 70 min dynamical mass at 0.4"
Jup 60 min dynamical mass at 0.8" NIRC2 L’ mass sensitivity 50 0.8" 0.4" 40 0.2"
30
20
10 minimum mass (M
0 20 40 60 target star number ï4 Non-detec ons x 10
7 RV andOnly Imaging 6 100 ) ) Aperture 5 Masking Jup Jup 4
3 10 GPI mass (M mass (M 2 Determine giant planet occurrence rates(!) 1 oo 1 ii == 5050 0 10 100 1000 10000 period (yrs) The Frequency of Giant Planets around M-dwarfs
Montet et al. 2014, ApJ, 781, 28 Conclusion #1 6.5% +/- 3.0% of M-dwarfs host a giant planet between 0 < a < 20 AU.
Can explain why high-contrast imaging discoveries are found orbi ng more massive stars. Conclusion #2: Planet occurrence-metallicity correla on appears to hold for large orbital separa ons.
Evidence for core- accre on beyond the snow-line. Conclusion #3: Our results are consistent with gravita onal microlensing. Summary Combined RV+Imaging is more powerful than sum of individual parts. TRENDS high-contrast survey: - HD 114174 B [WD age discrepancy] - HD 19467 B [benchmark T-dwarf] Non-detec ons are Important: (i) M-dwarfs have few gas giant planets
(6.5%+/-3.0%) from 0-20 AU for 1-13MJup. (ii) Planet-metallicity correla on holds at wide orbit separa ons. (iii) First independent check of microlensing results for wide-separa on planets.