Skip to main content
SpringerLink
Log in

The Mass Distribution of Transit Exoplanets from the Mass–Radius Relationships: the Structurization within Planetary Systems

  • Published:
Solar System Research Aims and scope Submit manuscript

Abstract

Most transit exoplanets (85%) were discovered with the Kepler space telescope. However, the mass, which was measured mainly with the radial velocity method, is known only for ~15% of them. The mass of an exoplanet may be estimated by its radius from the statistical dependences based on the observational data, though no unambiguous interrelation between the mass and the radius of planets exists. Here, we calculate the earlier unknown masses of exoplanets from four statistical mass–radius relationships (Bashi et al., 2017; Chen and Kipping, 2017; Ning et al., 2018, and the averaged dependence derived) and added the results to the distribution of planets with known masses. The mass distributions of transit exoplanets obtained in this way are analyzed with taking into account the observational selection effect inherent in the transit method. The distributions are approximated by the power law ∂N/∂M ~ Mα, where the exponent (α < 0) is determined by the maximum likelihood estimation for the samplings acquired with four mass–radius relationships: α = –2.12 ± 0.03, –2.09 ± 0.03, –1.94 ± 0.03, and –2.27 ± 0.04. Moreover, for one of these distributions, we determine the parameters of the power law, the exponent of which differs on three intervals (with the boundaries at 0.025, 0.28, and 1.34 Jupiter masses): –1.99, –0.62, and –2.88. We also conclude that there is no evidence of the interrelation between the mass of an exoplanet and its average distance to the host star (the structurization within planetary systems), if this distance is smaller than 1 AU; besides, the dependence of the exponent α on the considered mass interval is analyzed. The above estimates appertain to exoplanets detected by the space telescopes: Kepler Space Telescope and Transiting Exoplanet Survey Satellite (TESS) (these exoplanets compose group 1). The masses of the other transit exoplanets, which were detected by ground-based instruments, were known (they compose group 2). For the latter group, the exponent α is estimated at –2.21 ± 0.04. In general, the results of our analysis agree with those of the earlier statistical and theoretic studies. A key idea of the present paper is to apply the model interrelations between the mass and the radius of exoplanets to the analysis of the mass distribution of exoplanets on the basis of the recent data of observations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.

Similar content being viewed by others

Notes

  1. This is such a mutual position of the observer and the orbital plane of an exoplanet that the passage of an exoplanet across the disc of a host star, i.e., the transit, can be observed.

  2. For the spectral class M, the mass distribution was obtained from the analysis of data on the radial velocities (Tuomi et al., 2019).

  3. Hereafter, the mass–radius relationship means the functional relationship between the statistic mass and the statistic radius, which makes it possible to estimate one of these parameters from the other one for a statistically average case.

  4. https://github.com/yko-v/exoplanets2020

  5. https://exoplanetarchive.ipac.caltech.edu/docs/API_exomultpars_columns.html

  6. The Kepler observations become incomplete starting from the planets with a period exceeding 400 days and a radius smaller than 0.178RJ (2RE) (Petigura et al., 2013). Most exoplanets with this radius (taken from the Archive or determined from the mass–radius relationship (see the section “The statistical mass–radius relationships…”)) correspond to the masses in a range of [0.01, 0.03]MJ.

  7. Or \(p\left( m \right) = {{C}_{1}}{{m}^{{ - {{\alpha }}}}}\), \({{\alpha }} > 0\). To compare the exponent to the results of the other papers, the version specified in Eq. (5) has been accepted.

  8. In the samples with calculated masses, the number of mass values taken from the Archive does not coincide with that in the Raw Data sample, since the latter includes only sufficiently reliable values (see the section “The statistical mass–radius relationships…”).

  9. In Fig. 4, the histograms are shown only for visualization of the considered distributions, the appearance of which depends on dividing into intervals; the power laws were obtained by the maximum likelihood estimation (6) rather than fitting.

REFERENCES

  1. Ananyeva, V.I., Ivanova, A.E., Venkstern, A.A., Shashkova, I.A., Yudaev, A.V., Tavrov, A.V., Korablev, O.I., and Bertaux, J.-L., Mass distribution of exoplanets considering some observation selection effects in the transit detection technique, Icarus, 2020a, vol. 346, art. id. 113773.

  2. Ananyeva, V.I., Ivanova, A.E., Venkstern, A.A., Tavrov, A.V., Korablev, O.I., and Bertaux, J.-L., The dependence of the mass distribution of exoplanets on the spectral class of host stars, Sol. Syst. Res., 2020b, vol. 54, no. 3, pp. 175–186.

    Article  ADS  Google Scholar 

  3. Bashi, D., Helled, R., Zucker, S., and Mordasini, C., Two empirical regimes of the planetary mass–radius relation, Astron. Astrophys., 2017, vol. 604, art. id. A83.

  4. Butler, R.P., Wright, J.T., Marcy, G.W., Fischer, D.A., Vogt, S.S., Tinney, C.G., Jones, H.R.A., Carter, B.D., Johnson, J.A., and McCarthy, C., Catalog of nearby exoplanets, Astrophys. J., 2006, vol. 646, p. 505.

    Article  ADS  Google Scholar 

  5. Chen, J. and Kipping, D., Probabilistic forecasting of the masses and radii of other worlds, Astrophys. J., 2017, vol. 834, pp. 17–30.

    Article  ADS  Google Scholar 

  6. Clauset, A., Shalizi, C., and Newman, M., Power-law distributions in empirical data, SIAM Rev., 2009, vol. 51, no. 4, pp. 661–703.

    Article  ADS  MathSciNet  Google Scholar 

  7. Cumming, A., Butler, R.P., Marcy, G.W., Vogt, S.S., Wright, J.T., and Fischer, D.A., The Keck planet search: detectability and the minimum mass and orbital period distribution of extrasolar planets, Publ. Astron. Soc. Pac., 2008, vol. 120, pp. 531–554.

    Article  ADS  Google Scholar 

  8. Howard, A.W., Marcy, G.W., Johnson, J.A., Fischer, D.A., Wright, J.T., Isaacson, H., Valenti, J.A., Anderson, J., Lin, D.N., and Ida, S., The occurrence and mass distribution of close-in super-Earths, Neptunes, and Jupiters, Science, 2010, vol. 330, pp. 653–655.

    Article  ADS  Google Scholar 

  9. Ida, S. and Lin, D. N. C., Toward a deterministic model of planetary formation. II. The formation and retention of gas giant planets around stars with a range of metallicities, Astrophys. J., 2004, vol. 616, no. 1, p. 567.

    Article  ADS  Google Scholar 

  10. Ivanova, A.E., Ananyeva, V.I., Venkstern, A.A., Shashkova, I.A., Yudaev, A.V., Tavrov, A.V., Korablev, O.I., Bertaux, J.-L., The mass distribution of transiting exoplanets corrected for observational selection effects, Astron. Lett., 2019, vol. 45, no. 10, pp. 687–694.

    Article  ADS  Google Scholar 

  11. Lemeshko, B.Yu., Neparametricheskie kriterii soglasiya (Nonparametric Goodness-of-Fit Tests), Novosibirsk: Novosibirsk Gos. Univ., 2014.

  12. Marcy, G., Butler, R.P., Fischer, D., Vogt, S., Wright, J.T., Tinney, C.G., and Jones, H.R., Observed properties of exoplanets: masses, orbits, and metallicities, Prog. Theor. Phys., 2005, vol. 158 Suppl., pp. 24–42.

    Article  Google Scholar 

  13. Mordasini, C., Alibert, Y., Georgy, C., Dittkrist, K.-M., Klahr, H., and Henning, T., Characterization of exoplanets from their formation II: The planetary mass–radius relationship, Astron. Astrophys., 2012, vol. 547, art. id. A112.

  14. NASA Exoplanet Archive, 2020. Accessed July 25, 2020. https://doi.org/10.26133/NEA1

  15. Ning, B., Wolfgang, A., and Ghosh, S., Predicting exoplanets mass and radius: A nonparametric approach, Astrophys. J., 2018, vol. 869, no. 1.

  16. Otegi, J.F., Bouchy, F., and Helled R., Revisited mass–radius relations for exoplanets below 120 Earth masses, Astron. Astrophys., 2019, vol. 634, art. id. A43.

  17. Petigura, E.A., Howard, A.W., and Marcy, G.W., Prevalence of Earth-size planets orbiting Sun-like stars, Proc. Natl. Acad. Sci. USA, 2013, vol. 110, no. 48, pp. 19273–19278.

    Article  ADS  Google Scholar 

  18. Tuomi, M., Jones, H.R.A., Butler, R.P., Arriagada, P., Vogt, S.S., Burt, J., Laughlin, G., Holden, B., Shectman, S.A., Crane, J.D., Thompson, I., Keiser, S., Jenkins, J.S., Berdinas, Z., Diaz, M., Kiraga, M., and Barnes, J.R., Frequency of planets orbiting M dwarfs in the Solar neighbourhood, Earth Planet. Astrophys., 2019. https://arxiv.org/abs/1906.04644.

  19. Seager, S. and Mallén-Ornelas, G. A., Unique solution of planet and star parameters from an extrasolar planet transit light curve, Astrophys. J., 2002, vol. 585, no. 2.

  20. Weiss, L.M., Marcy, G.W., Rowe, J.F., Howard, A.W., Isaacson, H., Fortney, J.J., Miller, N., Demory, B.-O., Fischer, D.A., and Adams, E.R., The mass of KOI-94d and a relation for planet radius, mass, and incident flux, Astrophys. J., 2013, vol. 768, no. 14.

  21. Winn, J., Transits and occultations, Earth and Planetary Astrophysics, 2014. https://arxiv.org/abs/1001.2010v5.

  22. Wolfgang, A., Rogers, L.A., and Ford, E.B., Probabilistic mass–radius relationship for sub-Neptune-sized planets, Astrophys. J., 2016, vol. 825, no. 19.

  23. Zeng, Li., Sasselov, D.D., and Jacobsen, S.B., Mass-radius relation for rocky planets based on PREM, Astrophys. J., 2016, vol. 819, no. 2.

Download references

ACKNOWLEDGMENTS

In this paper we used the NASA Exoplanet Archive (2020), which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

Funding

The study was supported by the Government and the Ministry of Education and Science of Russia (grant no. 075-15-2020-780 (N13.1902.21.0039)).

Author information

Authors and Affiliations

  1. Space Research Institute, Russian Academy of Sciences, 117997, Moscow, Russia

    O. Ya. Yakovlev, A. E. Ivanova, V. I. Ananyeva, I. A. Shashkova & A. V. Tavrov

  2. Moscow State University, 119992, Moscow, Russia

    O. Ya. Yakovlev

  3. Moscow Institute of Physics and Technology, 141701, Dolgoprudnii, Moscow oblast, Russia

    A. V. Yudaev & A. V. Tavrov

  4. LATMOS-IPSL, 78280, Guyancourt, France

    J.-L. Bertaux

Authors
  1. O. Ya. Yakovlev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. E. Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Ananyeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. I. A. Shashkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. V. Yudaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J.-L. Bertaux
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. V. Tavrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Ya. Yakovlev.

Additional information

Translated by E. Petrova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yakovlev, O.Y., Ivanova, A.E., Ananyeva, V.I. et al. The Mass Distribution of Transit Exoplanets from the Mass–Radius Relationships: the Structurization within Planetary Systems. Sol Syst Res 55, 200–217 (2021). https://doi.org/10.1134/S0038094621030084

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0038094621030084

Keywords:

Search

Navigation