[Paper Review] Frequency of Hot Jupiters and Very Hot Jupiters from the OGLE-III Transit Surveys Toward the Galactic Bulge and Carina

Andrew Gould, S. Dorsher+2 more|ArXiv.org|Jan 2, 2006

Astro and Planetary Science24 citations

TL;DR

This study derives the absolute frequency of hot Jupiters (HJs, 3–5 day periods) and very hot Jupiters (VHJs, 1–3 day periods) from the OGLE-III transit survey toward the Galactic Bulge and Carina, using detailed modeling of survey sensitivity and target star populations. It finds HJ and VHJ frequencies of (1/310)(1⁺¹.³⁹₋₀.⁵⁹) and (1/690)(1⁺¹.¹⁰₋₀.⁵⁴) at 90% confidence, respectively, with the HJ rate consistent with radial velocity surveys and the VHJ rate marginally consistent with the absence of such planets in RV surveys due to metallicity bias.

ABSTRACT

We derive the frequencies of hot Jupiters (HJs) with 3--5 day periods and very hot Jupiters (VHJs) with 1-3 day periods by comparing the planets actually detected in the OGLE-III survey with those predicted by our models. The models are constructed following Gould & Morgan (2003) by populating the line of sight with stars drawn from the Hipparcos catalog. Using these, we demonstrate that the number of stars with sensitivity to HJs and VHJs is only 4--16% of those in the OGLE-III fields satisfying the spectroscopic-followup limit of V_max<17.5. Hence, the frequencies we derive are much higher than a naive estimate would indicate. We find that at 90% confidence the fraction of stars with planets in the two period ranges is (1/310)(1^{+1.39}_{-0.59}) for HJs and (1/690)(1^{+1.10}_{-0.54}) for VHJs. The HJ rate is statistically indistinguishable from that found in radial velocity (RV) studies. However, we note that magnitude-limited RV samples are heavily biased toward metal-rich (hence, planet-bearing) stars, while transit surveys are not, and therefore we expect that more sensitive transit surveys should find a deficit of HJs as compared to RV surveys. The detection of 3 transiting VHJs, all with periods less than 2 days, is marginally consistent with the complete absence of such detections in RV surveys. The planets detected are consistent with being uniformly distributed between 1.00 and 1.25 Jovian radii, but there are too few in the sample to map this distribution in detail.

Motivation & Objective

• To determine the absolute frequency of hot Jupiters (HJs) and very hot Jupiters (VHJs) in field star surveys using transit data from the OGLE-III survey.
• To address discrepancies between transit and radial velocity (RV) surveys, particularly the apparent lack of VHJs in RV studies despite their detection in transit surveys.
• To quantify the true number of stars probed for transiting planets by accounting for stellar luminosity, radius, and extinction distributions, which are often overlooked in naive estimates.
• To model selection effects in ground-based transit surveys, including sensitivity variations due to planet radius, orbital period, and observational constraints such as cadence and extinction.
• To assess the impact of physical and observational effects—such as limb darkening, ingress/egress, binary stars, and periodic ground-based observations—on detection efficiency.

Proposed method

• The authors model the target star population in OGLE-III fields using the Hipparcos catalog, extrapolating local stellar distributions to the Galactic Bulge and Carina lines of sight with corrections for extinction and stellar density variations.
• They simulate transit detection efficiency by generating synthetic planetary systems with varying orbital periods and planet radii, applying realistic photometric noise and cadence constraints from the OGLE-III data.
• The number of stars actually probed for HJs and VHJs is computed by applying a magnitude limit (V_max < 17.5) and filtering out stars with physical radii too large to produce detectable transits.
• The survey's sensitivity is modeled as a function of planet radius (r) and orbital period (P), with scaling relations derived from simulations and compared to theoretical predictions (e.g., Pepper et al. 2003).
• The authors account for key observational effects: limb darkening, ingress/egress duration, and unresolved binary stars, with the latter two not explicitly simulated but estimated to affect sensitivity by a few percent.
• They derive planet occurrence frequencies by comparing the number of detected transiting planets (5 total, 3 VHJs) to the number of stars effectively probed, using Bayesian inference with 90% confidence intervals.

Experimental results

Research questions

• RQ1 What is the true frequency of hot Jupiters (3–5 day periods) in the Galactic plane, as measured by the OGLE-III transit survey, after correcting for survey sensitivity and target star properties?
• RQ2 Why do transit surveys detect very hot Jupiters (1–3 day periods) while radial velocity surveys do not, and is this discrepancy statistically significant or explainable by selection effects?
• RQ3 How does the number of stars actually probed for transiting planets compare to the total number of stars within the survey's magnitude limit, and what fraction of stars are excluded due to large physical radii?
• RQ4 To what extent do observational effects such as limb darkening, ingress/egress, and unresolved binaries affect the detection efficiency of transiting planets in ground-based surveys?
• RQ5 Are the theoretical scaling relations for detection efficiency (e.g., N_p ∝ a^−⁵/² r^6) valid in real survey conditions, and how do observed power-law indices deviate from predictions?

Key findings

• The frequency of hot Jupiters (3–5 day periods) is (1/310)(1⁺¹.³⁹₋₀.⁵⁹) at 90% confidence, consistent with the rate found in radial velocity surveys.
• The frequency of very hot Jupiters (1–3 day periods) is (1/690)(1⁺¹.¹⁰₋₀.⁵⁴) at 90% confidence, marginally consistent with the absence of such planets in radial velocity surveys due to their metallicity bias.
• Only 4–16% of stars within the V_max < 17.5 magnitude limit are actually probed for HJs and VHJs, due to large stellar radii that suppress detectable transit signals.
• The five detected planets are consistent with a uniform distribution in radius between 1.00 and 1.25 times Jupiter’s radius, though the sample size is too small for detailed mapping.
• The survey has a 95% confidence upper limit of F < 1/400 on planets with radii between 1.3 and 1.5 times Jupiter’s radius in the 1–5 day period range.
• The scaling relations for detection efficiency (e.g., N_p ∝ a^−⁵/² r^6) are approximately valid but can deviate by up to 25% from theoretical predictions in the OGLE-III survey conditions.