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Extrasolar planet radial velocities

The CASt dataset


Astronomical background

Until 1995, astronomers had direct evidence for only one planetary system orbiting a normal star, our Solar System. Protostars were known to have dusty protoplanetary disks consistent with the formation mechanism developed for our Solar System, but the planets themselves were elusive because they are so small and faint. However, extremely accurate (parts in a million) spectroscopy of bright, nearby solar-type stars have recently revealed small periodic Doppler (radial velocity) shifts indicating the star is wobbling back-and-forth as some unseen object orbits.  The first case was the wobble of 51 Pegasi reported by Swiss astronomers Michel Mayor and Didier Queloz.   Knowing the period and velocity amplitude of the wobble, and the mass of the primary star, standard theory based on Newton's laws are applied to infer the mass and orbit of the orbiting object. Typical inferred masses are around the mass of Jupiter -- thus the discovery of exoplanets has emerged.

Today (mid-2006), nearly 200 planets have been found around nearby stars, most found using the Doppler wobble method.  An updated list with inferrred properties is provided by The Extrasolar Planets Encyclopaedia.  Masses range from 0.02 to 15 Jupiters, orbital periods range from 1 day to a decade,  and eccentricities range from zero to 93%.   The findings have opened up many new astrophysical investigations concerning the origin and evolution of planetary systems.  Many observational programs are underway, including space-based observatories, to detect and characterize more exoplanets.


The detection of a periodicity and estimation of orbital parameters from typical radial velocity datasets is statistically challenging.  The observations are sparse, unevenly spaced, and with heteroscedastic measurement errors (of known variance).  The periodic behavior is non-sinusoidal if the orbital eccentricity is non-zero.  Methods considered include: simple Fourier analysis, the Lomb-Scargle periodogram for unevenly spaced data, maximum-likelihood estimation, and Bayesian inference. 

We give here three radial velocity datasets.  The following table summarized the datasets.  HD refers to the 19th century Henry Draper catalog of bright stars.  Mass estimates assume an edge-on orbit (inclination 90o). N gives the number of radial velocity measurements.  Period (in days), Mass (in Jupiter masses) and Eccentricity give the published derived parameters from The Extrosolar Planets Encyclopaedia.  Reference gives the discovery paper (see the Encyclopaedia for full references).  The figure below show a periodogram for part of the HD 3651 data, and the radial velocities with best-fit orbital model folded with the P=62.23 day period. 

Fischer et al. 2005, ApJ 620, 481-486
Vogt et al. 2005, ApJ 632, 638-658



Fischer et al. 2003, ApJ 590, 1081-1087

HD 3651 periodogram

HD 3651 radial velocities & model

The columns are:

  1. Day of observation (in modified Julian days)
  2. Radial velocity (RV, in meters/second, after heliocentric correction)
  3. RV standard deviation (in meters/second). This is determined from detailed analysis of the spectrum from which the RV is measured.
  4. For HD 4651, this column gives the observatory at which the observation was made
Statistical exercises
  • Recover the published periodicities in the datasets.  Compare various methods.  Estimate the reliability and confidence intervals for the periods and eccentricities. Evaluate an optimal observational strategy for improving the orbital determinations for each system.
These datasets were generously provided by Eric Ford (University of Florida) for the Exoplanets Working Group of the 2006 SAMSI Astrostatistics Program.

NSFDepartment of StatisticsEberly College of ScienceDepartment of Astronomy and Astrophysics