[Paper Review] Finding Solar System Analogs With SIM and HIPPARCOS: A White Paper for the ExoPlanet Task Force

Rob P. Olling|ArXiv.org|Apr 23, 2007

Solar and Space Plasma Dynamics3 citations

TL;DR

This paper proposes a novel astrometric method to detect and characterize Solar System analogs (SOSAs) and heavy SOSAs (HOSAs) by combining historical HIPPARCOS astrometry with future SIM Quick-Look (SQL) survey data. Using SIM's high-precision position measurements (10–4 μas), the method enables detection of 1–10 M_J planets with periods up to 80–165 years, potentially identifying hundreds of long-period systems to constrain planet formation models.

ABSTRACT

The astrometric signature imposed by a planet on its primary increases substantially towards longer periods (proportinal to P^2/3), so that long-period planets can be more easily detected, in principle. For example, a one Solar-mass (M_Sun) star would be pulled by roughly 1 mas by a one Jupiter-mass (M_J) planet with a period of one-hundred years at a distance of 20 pc. Such position accuracies can now be obtained with both ground-based and space-based telescopes. The difficulty was that it often takes many decades before a detectable position shift will occur. However, by the time the next generation of astrometric missions such as SIM will be taking data, several decades will have past since the first astrometric mission, HIPPARCOS. Here we propose to use a new astrometric method that employs a future, highly accurate SIM Quick-Look survey and HIPPARCOS data taken twenty years prior. Using position errors for SIM of 4 muas, this method enables the detection and characterization of Solar-system analogs (SOSAs) with periods up to 240 (500) years for 1 (10) M_J companions. Because many tens of thousands nearby stars can be surveyed this way for a modest expenditure of SIM time and SOSAs may be quite abundant, we expect to find many hundreds of extra-solar planets with long-period orbits. Such a data set would nicely complement the short-period systems found by the radial-velocity method. Brown dwarfs and low-mass stellar companions can be found and characterized if their periods are shorter than about 500 years. This data set will provide invaluable constraints on models of planet formation, as well as a database for systems where the location of the giant planets allow for the formation of low-mass planets in the habitable zone. [Abridged]

Motivation & Objective

• To develop a method for detecting long-period planetary systems, including Solar System analogs (SOSAs), using existing and future astrometric data.
• To overcome the challenge of long orbital periods by leveraging historical HIPPARCOS data and future SIM Quick-Look (SQL) surveys.
• To estimate the frequency of HOSAs (1–13 M_J planets with periods up to 165 years) and assess their detectability with SIM-level precision.
• To provide a complementary dataset to radial-velocity and imaging surveys by targeting systems with giant planets in distant orbits.
• To guide future all-sky astrometric surveys by identifying optimal cadence and accuracy requirements for detecting long-period companions.

Proposed method

• The method uses a combination of past HIPPARCOS astrometry (1989–1993) and future SIM Quick-Look (SQL) survey data to model stellar motion and detect reflex motion from long-period companions.
• It fits SIM data with astrometric models (linear, quadratic) to predict the star's position at the HIPPARCOS epoch, then computes position differences (Δxy) between predicted and observed positions.
• The method employs two metrics: Δxy,μ (based on proper motion) and Δxy,μ+ḋμ (including acceleration), which help break the period-mass degeneracy in orbital parameter estimation.
• It assumes a conservative SIM position error of 10 μas per observation, with higher accuracy (4 μas) enabling extended detection limits.
• The approach uses the period-mass degeneracy-breaking power of second-order astrometric terms (acceleration and jerk) to constrain orbital parameters.
• Target selection focuses on non-binary stars from the ARIHIP catalog to prioritize systems likely to host sub-stellar or long-period stellar companions.

Experimental results

Research questions

• RQ1 Can long-period planetary systems, including Solar System analogs, be detected using a combination of historical HIPPARCOS data and future SIM Quick-Look surveys?
• RQ2 What is the maximum orbital period and minimum mass of a companion that can be detected using this astrometric method with SIM-level precision?
• RQ3 How does the inclusion of acceleration (ḋμ) improve the separation of orbital parameters compared to proper motion alone?
• RQ4 What is the expected yield of HOSAs (1–13 M_J planets) from a SQL survey of ~5,000 stars with SIM-level accuracy?
• RQ5 How does the detectability of long-period systems depend on the accuracy and cadence of future astrometric surveys?

Key findings

• With a conservative SIM position error of 10 μas, the method can detect and characterize 1 M_J planets with periods up to 80 years and 10 M_J planets up to 165 years.
• Using the expected SIM accuracy of 4 μas, the detectable period range for 1 M_J planets extends to 400 years, and for 10 M_J planets to 660 years.
• The method can detect 0.1 M_J planets in 10-year orbits when using follow-up high-accuracy SIM observations after SQL screening.
• A SQL survey of ~5,000 stars could detect approximately 400 HOSAs, given the predicted frequency of 7.9% for such systems around single stars.
• The limiting factor for detection is SIM’s position measurement accuracy, not HIPPARCOS’ error, making GAIA’s lower precision unsuitable for this method.
• The method effectively breaks the period-mass degeneracy in long-period systems by using second-order astrometric terms (acceleration and jerk).