[Paper Review] A Statistical Analysis of The Extrasolar Planets and The Low-Mass Secondaries

T. Mazeh, S. Zucker|arXiv (Cornell University)|Jan 21, 2002

Stellar, planetary, and galactic studies3 citations

TL;DR

This paper challenges the claim that extrasolar planet candidates have non-random orbital orientations, showing Hipparcos astrometric data lack statistical significance for detecting orbital inclinations. Using a maximum-likelihood mass estimation method (MAXLIMA), it reveals two distinct populations—giant planets and low-mass stellar secondaries—separated by the 'brown-dwarf desert', with similar logarithmic period and eccentricity distributions, suggesting a scale-free formation mechanism common to both, despite differing formation pathways.

ABSTRACT

We show that the astrometric Hipparcos data of the stars hosting planet candidates are not accurate enough to yield statistically significant orbits. Therefore, the recent suggestion, based on the analysis of the Hipparcos data, that the orbits of the sample of planet candidates are not randomly oriented in space, is not supported by the data. Assuming random orientation, we derive the mass distribution of the planet candidates and show that it is flat in log M, up to about 10 Jupiter masses. Furthermore, the mass distribution of the planet candidates is well separated from the mass distribution of the low-mass companions by the 'brown-dwarf desert'. This indicates that we have here two distinct populations, one which we identify as the giant planets and the other as stellar secondaries. We compare the period and eccentricity distributions of the two populations and find them surprisingly similar. The period distributions between 10 and 1650 days are flat in log period, indicating a scale-free formation mechanism in both populations. We further show that the eccentricity distributions are similar - both have a density distribution peak at about 0.2-0.4, with some small differences on both ends of the eccentricity range. We present a toy model to mimic both distributions. We found a significant paucity of massive giant planets with short orbital periods. The low frequency of planets is noticeable for masses larger than about 1 Jupiter Mass and periods shorter than 30 days. We point out how, in principle, one can account for this paucity.

Motivation & Objective

• To assess the statistical significance of orbital inclinations derived from Hipparcos astrometric data for planet candidates.
• To determine whether the observed orbital orientations of planet candidates are isotropically distributed in space.
• To derive the true mass distribution of planet candidates under the assumption of random orbital orientations.
• To compare the period and eccentricity distributions of giant planets and low-mass stellar secondaries to identify common formation mechanisms.
• To explain the observed paucity of massive giant planets with short orbital periods (P < 30 days, M > 1 M_Jup).

Proposed method

• Applied a permutation test to Hipparcos astrometric data to evaluate the statistical significance of derived orbital orbits.
• Used the MAXLIMA algorithm—a maximum-likelihood method for inferring mass distributions from minimum mass estimates (M2 sin i) under random inclination assumption.
• Compared the derived mass distribution of planet candidates with that of low-mass secondaries in spectroscopic binaries to identify the 'brown-dwarf desert' gap.
• Analyzed the logarithmic period and eccentricity distributions of both populations to detect scale-free features.
• Developed a toy model with Gaussian radial and tangential velocity scatters added to circular Keplerian orbits to mimic observed eccentricity distributions.
• Evaluated migration and instability formation scenarios to explain the observed paucity of massive short-period planets.

Experimental results

Research questions

• RQ1 Is the claimed anisotropy in orbital orientations of planet candidates statistically supported by Hipparcos astrometric data?
• RQ2 What is the true mass distribution of planet candidates when assuming random orbital inclinations?
• RQ3 Are the period and eccentricity distributions of giant planets and low-mass stellar secondaries significantly different?
• RQ4 Can the observed paucity of massive planets with short orbital periods be explained by current formation models?
• RQ5 What common physical mechanism could produce the observed scale-free logarithmic period distributions in both populations?

Key findings

• The Hipparcos astrometric data do not provide statistically significant evidence for non-random orbital orientations; the derived orbits are consistent with measurement noise.
• The mass distribution of planet candidates is flat in log M up to ~10 M_Jup, indicating a scale-free distribution.
• A clear separation exists between planet candidates and low-mass secondaries at masses around 13–15 M_Jup, defining the 'brown-dwarf desert'.
• The period distributions of both populations are flat in log P over 10–1650 days, indicating a scale-free formation process.
• The eccentricity distributions of both populations peak at ~0.2–0.4 and are remarkably similar, with minor differences at extreme eccentricities.
• A significant paucity of massive planets (M > 1 M_Jup) with orbital periods shorter than 30 days is observed, which can be explained by migration or instability models.