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Integrating Imaging and RV Datasets

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Integrating Imaging and RV Datasets Combining Imaging + RV’s Jusn R. Crepp Frank M. Freimann Professor Department of Physics University of Notre Dame [email protected] Connec2ng Two Dis2nct 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 Mo2vaon • High detec2on efficiency. • Break sin(i) degeneracy, construct 3d-orbits. • Dynamical masses of companions. • Calibrate evolu2onary models. Kappa Andromedae Determine fpl for wide orbits. “b” HR 8799 Marois et al. 2010 Carson et al. 2012 Par2al Orbits Isaac Newton What informaon can be gleaned? (1) Minimum dynamical mass (Torres 1999). (2) Physical separaon (Howard et al. 2010). Minimum Mass 2 ⎛ M ⎞ ⎛ d ρ ⎞ d(RV ) min⎜ B ⎟ =1.39E − 5 ⎜ ⎟ ⎝ MSun ⎠ ⎝ pc arcsec⎠ dt where RV acceleraon is measured in m s-1 yr-1. € Physical Separaon d(RV ) GMB ⎛ rAB ⎞ ρ = 2 cosθ, ⎜ ⎟ sinθ = dt rAB ⎝ AU⎠ π where rAB is the instantaneous true physical separaon. € € 3d-Orbits and Dynamical Mass Radial Velocities: K, P, e, ω, tp Astrometry: * a, i, P, e, ω, tp, Ω How much informaon 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) * No2ce that precise parallax is essen2al (Dupuy & Kraus 2013) € When do constraints become interes2ng? 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 moon 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 inclinaon falls out - Bernstein & Khushalani 2000 unl I see 2 phase wraps.” immediately.” - Andy Boden (Caltech) - Jessica Lu (IfA) Galacc 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 Observaons? •! Bayesian stas2cal framework. (“Data Analysis: A Bayesian Tutorial” by Sivia) •! Assume we understand uncertain2es. •! Keplerian orbit model. Single companion. •! Markov-Chain Monte Carlo (MCMC) analysis. (“Quan2fying 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-Has2ngs algorithm. P e X (Working in N-dimensional space) i Metropolis-Hastings Pseudo-Code:! (1) Cull P, a, e, i, ω, tp, ", + 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 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 Benchmark T dwarf [Fe/H] = -0.15+/-0.04 Age > 4.6 Gyr Mass > 52MJup Spectrum from Project 1640 now in hand. … Ar2st Impression Methane Absorp2on 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-detecSons x 10 7 RV Onlyand 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 orbi2ng more massive stars. Conclusion #2: Planet occurrence-metallicity correlaon appears to hold for large orbital separaons. Evidence for core- accre2on beyond the snow-line. Conclusion #3: Our results are consistent with gravitaonal 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-detec2ons are Important: (i) M-dwarfs have few gas giant planets (6.5%+/-3.0%) from 0-20 AU for 1-13MJup. (ii) Planet-metallicity correlaon holds at wide orbit separaons. (iii) First independent check of microlensing results for wide-separaon planets. .
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