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Estimating Physical Properties of Confirmed Exoplanets: I

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Estimating Physical Properties of Confirmed Exoplanets: I Original Research Papers Fundamental Journals Open Access Journals International Journal of Fundamental Physical Sciences (IJFPS) ISSN: 2231-8186 IJFPS, Vol 11, No 1, pp 17-29 March 2021 B. Nikouravan https://doi.org/10.14331/ijfps.2021.330146 Estimating Physical Properties of Confirmed Exoplanets: I. Calculation of essential planetary properties-Possible M-R cataloging of exoplanets Bijan Nikouravan Department of Physics, Islamic Azad University (IAU), Varamin - Pishva Branch, Iran Received March 2021 Received in revised: April 2021 Published: April 2021 ABSTRACT The discovery of extrasolar planets outside our solar system and around other stars is now well underway. In the presented paper, calculations of some physical properties for confirmed exoplanets have been done. We have estimated physical properties such as the semi-major axis for potentially habitable exoplanets, the mass of planets by applying Kepler's third law around the mass of solar, Jupiter, and Earth-mass, stellar luminosity, habitability zone for the inner center and outer regions, radial velocity amplitude, planetary equilibrium temperature (PET) or effective radiation emission temperature and planet density. The mass- radius (MR) relationship of planets was investigated for potentially habitable exoplanets of three different groups of extrasolar planets: Subterran (Mars-size), Terran (Earth-size), and Superterran (Super-Earths or Mini-Neptunes); introduced in PHL, and found well coefficient values for each group. The minimum and maximum values for the mass and radius of exoplanets have been selected from 0.1 < 푀 < 10 푀⊕ and 0.4 < 푅 < 2.5 푅⊕ . The same MR relationship has also estimated the same properties for a larger number of confirmed exoplanets with a mass and radius of 0.1< M < 100 푀⊕ and 0.4 < 푅 < 15 푅⊕ , respectively, resulting their classification within 7 groups of mass and radius, with good coefficient values for each group. This is a new, possible cataloging that may need more effort for concluding a better understanding of the properties and varieties of the exoplanets. Keywords: Planetary system - extrasolar planets - physical properties of exoplanets - Mass-Radius relationship - exoplanet classification ©2021 The Authors. Published by Fundamental Journals. This is an open-access article under the CC BY-NC https://creativecommons.org/licenses/by-nc/4.0/ INTRODUCTION systems and Exoplanets. Traditionally with the study of relations between these types of fundamental quantities, Fundamental quantities such as mass, radius, effective scientists can acquire more knowledge and information not temperature, semimajor axis, luminosity, etc., are essential to only about our solar system but also for other celestial objects study planets, stars, and widely for particular Extrasolar outside our solar system such as extrasolar systems and ISSN: 2231-8186/ ©2021 Published by Int. J. Fundam. Phys. Sci https://doi.org/10.14331/ijfps.2021.330146 17 IJFPS, Vol 11, No 1, pp 17-29, March, 2021 B. Nikouravan exoplanets. Depending on the improvements in theoretical and host stars (Akeson et al., 2013). The second is “The Habitable observational data, many relations have been developed and Exoplanets Catalog” which is also the next online source of modified many times from 20 years ago till today. data and catalog as PHL (Planetary Habitability Laboratory, Relatively recent studies on the subject are by (Bashi, Helled, 2021) for MR relationship. The PHL is managed by the Zucker, Mordasini, & Astrophysics, 2017; Malhotra, 2015; University of Puerto Rico at Arecibo. All data collected are Seager, Kuchner, Hier-Majumder, & Militzer, 2007; Weiss & updated by end of April 2021. Marcy, 2014). To date, quite several advances have been made on both sides; theoretical and observational. On the theoretical SEMI-MAJOR AXIS CALCULATION side, extrasolar planets (Baraffe, Chabrier, & Barman, 2009; One of the most important and essential physical properties is Perryman, 2000), and in theoretical vs observational the semi-major axis of planets. Here, the calculation of the uncertainties (Müller, Ben-Yami, & Helled, 2020), and semi-major axis of 35 confirmed and habitable exoplanets experimental, physical properties of extrasolar planets physics have been done. All data were necessary for this calculation, has undergone appreciable revision. So now the problem with collected from (NASA Exoplanet Archive, 2021). this huge amount of data and information is that we need to Newton's modification of Kepler's third law applied for the find out more related to these fundamental physical quantities host stars and orbital period of planets. Here 푀 is the mass of to answer our unknown questions not only about the solar 푠 a star, 푀 is the mass of exoplanets, 푃 is the orbital period of system but also for outside of our solar system as extrasolar 푝 planets and extrasolar systems. a planet moving around the center of mass of its star, and To do this, we first consider the calculation of some physical finally, 푎 is the semi-major axis of the planet in the AU unit as properties of exoplanets such as the Semi-major axis for 35 shown in Equation (1). potentially habitable exoplanets, the mass of planets by 2 3 applying Kepler's third law, around the mass of solar, Jupiter, (푀푠 + 푀푝)푃 = 푎 (1) and Earth-mass, stellar luminosity, and radial velocity amplitude. The MR relationship is the next aim of this paper Typically, the mass of planets is very small in comparison with for potentially habitable exoplanets of the suggested three the mass of stars (푀푝 ≪ 푀푠) therefore equation (1) reduces to, groups in the Planetary Habitability Laboratory (PHL) 2 3 (Planetary Habitability Laboratory, 2021). The minimum and 푀푠푃 = 푎 (2) maximum values for the mass and radius of exoplanets have been selected from 0.1 < 푀 < 10 푀⊕ and 0.4 < 푅 < By rearranging Equation (2) the semi-major axis is can find as 2.5 푅⊕. below. 3 2 DATA 푎 = √푀∗푃 (3) All data used in this paper is from two data centers. The first one is “The NASA Exoplanet Archive” (NASA Exoplanet Table (1) shows a very well correlation between calculated and Archive, 2021) which is an online directory and astronomical observed values of the semi-major axis. In addition, we found planet and data service that collects and provides public data 12 unknown values of the semi-major axis in AU (Table 1). that supports the search and description of exoplanets and their Table 1 Calculation of Semi-major axis with applying Kepler's Third Law for confirmed Exoplanets. The mass of planets is between 0.5 and 5 푀⊕ or with radii between 0.8 and 1.5 푅⊕ for Terran planets. Calculated Parameters No Planets Name Host Name M (M ) M (M ) R (R ) P(day) a(AU) s ⊙ p ⊕ p ⊕ P (year) a (AU) 1 KOI-55 c KOI-55 0.5 0.655 0.867 0.343 0.0076 0.0009 0.0076 2 GJ 1252 b GJ 1252 0.38 2.09 1.193 0.518 0.0092 0.0014 0.0091 3 TOI-561 b TOI-561 0.79 1.59 1.423 0.447 0.0106 0.0012 0.0106 4 TRAPPIST-1 b TRAPPIST-1 0.08 0.85 1.086 1.511 0.0111 0.0041 0.0111 5 Kepler-407 b Kepler-407 1 3.2 1.07 0.669 - 0.0018 0.0150 6 TRAPPIST-1 c TRAPPIST-1 0.08 1.38 1.056 2.422 0.0152 0.0066 0.0152 7 GJ 1132 b GJ 1132 0.18 1.66 1.13 1.629 0.0153 0.0045 0.0153 8 Kepler-10 b Kepler-10 0.91 4.60853 1.481 0.837 0.0172 0.0023 0.0169 9 GJ 486 b GJ 486 0.32 2.82 1.305 1.467 0.0173 0.0040 0.0173 10 L 168-9 b L 168-9 0.62 4.6 1.39 1.402 0.0209 0.0038 0.0209 11 L 98-59 b L 98-59 0.31 1.01 0.8 2.253 0.0228 0.0062 0.0228 12 K2-36 b K2-36 0.79 3.9 1.43 1.423 0.0223 0.0039 0.0229 13 TOI-178 b TOI-178 0.65 1.5 1.152 1.915 0.0261 0.0052 0.0262 14 LHS 1140 c LHS 1140 0.18 1.81 1.282 3.778 0.0268 0.0104 0.0268 15 TRAPPIST-1 e TRAPPIST-1 0.08 0.62 0.918 6.100 0.0282 0.0167 0.0282 16 L 98-59 c L 98-59 0.31 2.42 1.35 3.690 0.0317 0.0101 0.0316 ISSN: 2231-8186/ ©2021 Published by Int. J. Fundam. Phys. Sci https://doi.org/10.14331/ijfps.2021.330145 18 IJFPS, Vol 11, No 1, pp 17-29, March, 2021 B. Nikouravan 17 GJ 357 b GJ 357 0.34 1.84 1.217 3.931 0.0350 0.0108 0.0340 18 Kepler-97 b Kepler-97 0.94 3.51 1.48 2.587 - 0.0071 0.0361 19 Kepler-408 b Kepler-408 1.08 5 0.82 2.465 - 0.0068 0.0367 20 TRAPPIST-1 f TRAPPIST-1 0.08 0.68 1.045 9.207 0.0371 0.0252 0.0371 21 GJ 9827 c GJ 9827 0.61 0.84 1.241 3.648 0.0393 0.0100 0.0394 22 TRAPPIST-1 g TRAPPIST-1 0.08 1.34 1.127 12.353 0.0451 0.0338 0.0451 23 Kepler-406 c Kepler-406 1.07 2.71 0.85 4.623 - 0.0127 0.0556 24 Kepler-101 c Kepler-101 1.17 3.78 1.25 6.030 0.0684 0.0165 0.0683 25 HD 21749 c GJ 143 0.73 3.7 0.892 7.790 0.0695 0.0213 0.0693 26 Kepler-105 c Kepler-105 0.96 4.6 1.31 7.126 - 0.0195 0.0715 27 Kepler-107 d Kepler-107 1.24 3.8 0.86 7.958 0.0838 0.0218 0.0838 28 Kepler-102 d Kepler-102 0.8 3.8 1.18 10.312 - 0.0283 0.0861 29 Kepler-138 c Kepler-138 0.52 1.97 1.197 13.781 - 0.0378 0.0905 30 HD 136352 b HD 136352 0.91 4.62 1.482 11.578 0.0969 0.0317 0.0971 31 Kepler-595 c Kepler-595 0.93 3.3 1.009 12.386 - 0.0339 0.1023 32 Kepler-36 b Kepler-36 1.03 3.83 1.498 13.868 - 0.0380 0.1141 33 Kepler-128 b Kepler-128 1.09 0.77 1.43 15.090 - 0.0413 0.1230 34 Kepler-138 d Kepler-138 0.52 0.64 1.212 23.088 - 0.0633 0.1277 35 Kepler-128 c Kepler-128 1.09 0.9 1.34 22.804 - 0.0625 0.1620 Figure (1), shows a-P relation for 23 confirmed and potentially Figure (2), also shows a-P a relationship for calculated 35 habitable exoplanets with masses from 0.5 to 5 푀⊕ with the confirmed and potentially habitable exoplanets with masses 2 2 value of 푅 = 0.8101.
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