Fast Rise of "Neptune-Size" Planets ($4-8 R_{\rm Earth}$) from $P\sim10$ to $\sim250$ days -- Statistics of Kepler Planet Candidates Up to $\sim 0.75 {\rm AU}$ (1212.4853v2)

Abstract: We infer the period ($P$) and size ($R_p$) distribution of Kepler transiting planet candidates with $R_p\ge 1 R_{\rm Earth}$ and $P < 250$ days hosted by solar-type stars. The planet detection efficiency is computed by using measured noise and the observed timespans of the light curves for $\sim 120,000$ Kepler target stars. We focus on deriving the shape of planet period and radius distribution functions. We find that for orbital period $P>10$ days, the planet frequency d$N_p$/d$\log$P for "Neptune-size" planets ($R_p = 4-8 R_{\rm Earth}$) increases with period as $\propto P^{0.7\pm0.1}$. In contrast, d$N_p$/d$\log$P for "super-Earth-size" ($2-4 R_{\rm Earth}$) as well as "Earth-size" ($1-2 R_{\rm Earth}$) planets are consistent with a nearly flat distribution as a function of period ($\propto P^{0.11\pm0.05}$ and $\propto P^{-0.10\pm0.12}$, respectively), and the normalizations are remarkably similar (within a factor of $\sim 1.5$ at $50 $ days). Planet size distribution evolves with period, and generally the relative fractions for big planets ($\sim 3-10 R_{\rm Earth}$) increase with period. The shape of the distribution function is not sensitive to changes in selection criteria of the sample. The implied nearly flat or rising planet frequency at long period appears to be in tension with the sharp decline at $\sim 100$ days in planet frequency for low mass planets (planet mass $m_p < 30 M_{\rm Earth}$) recently suggested by HARPS survey. Within $250$ days, the cumulative frequencies for Earth-size and super-Earth-size planets are remarkably similar ($\sim 28 %$ and $25%$), while Neptune-size and Jupiter-size planets are $\sim 7%$, and $\sim 3%$, respectively. A major potential uncertainty arises from the unphysical impact parameter distribution of the candidates.

Statistical Analysis of "Neptune-Size" Exoplanets in the Kepler Dataset

The paper under scrutiny presents a thorough statistical analysis of the distribution of transiting exoplanets with radii ranging from 1 to 8 Earth radii (denoted as $R_\oplus$) and orbital periods up to 250 days, leveraging data from the Kepler mission. The primary focus of Dong and Zhu's research is to infer the frequency distribution of these planets as a function of both their orbital periods and sizes, specifically targeting "Neptune-size" planets with radii between 4 to 8 $R_\oplus$.

Methodology and Findings

The researchers employed the Kepler data on approximately 120,000 solar-type stars to derive detection efficiencies, using the noise characteristics and observation spans of the light curves. They restricted their sample to stars with effective temperatures between 5000K and 6500K and optimized the selection criteria by excluding stars with poor gravity estimates, notably avoiding cool stars with unreliable parameters.

Key Findings:

• Frequency Trends by Size:
  • For "Neptune-size" planets (4-8 $R_\oplus$), the frequency d$N_p$/d$\log$P increases sharply with period ($\propto P^{0.7\pm0.1}$) for periods greater than 10 days.
  • "Super-Earth-size" (2-4 $R_\oplus$) and "Earth-size" (1-2 $R_\oplus$) planets exhibit a nearly flat distribution in terms of period, suggesting less dependence on orbital length ($\propto P^{0.11\pm0.05}$ and $\propto P^{-0.10\pm0.12}$ respectively).
• Cumulative Frequencies:
  • Within 250 days, the cumulative frequencies for Earth-size and super-Earth-size planets are nearly identical ($\sim 28\%$ and $\sim 25\%$ respectively). In contrast, the frequencies for Neptune-size and Jupiter-size planets are significantly lower ($\sim 7\%$ and $\sim 3\%$ respectively).
• Distribution Analysis:
  • The planet size distribution reveals significant evolution with period. Larger planets ($\sim 3-10 R_\oplus$) become relatively more prevalent at longer periods.
• Implications on Planetary Theories:
  • The results indicate a rising frequency of Neptune-size planets with increasing periods, challenging existing planet formation models that emphasize core-accretion and dynamical evolution processes.

Implications and Future Directions

The findings suggest a more nuanced understanding of planet formation and migration processes. The paper contradicts some of the trends previously observed in radial velocity surveys, specifically the HARPS survey, which suggested a decline in the frequency of low-mass planets with periods around 100 days. Kepler's data, in contrast, suggest a continued or increasing occurrence rate. This may encourage a re-evaluation of planetary system formation models and further investigations to reconcile these observational discrepancies.

Future Prospects:

The paper underscores the potential of extended planetary observations and analyses to provide insights beyond the now-constrained read of close-in exoplanets. Future missions with broader observation capabilities may utilize these findings to target specific planetary sizes and periods more accurately, further advancing planetary astrophysics.

In conclusion, Dong and Zhu's work importantly broadens our quantitative understanding of the distribution of Neptune-size exoplanets and sets the stage for refining theoretical models of planetary formation and distribution, as well as for the development of more tailored observational strategies in upcoming exoplanet surveys.