Astronomy & Astrophysics manuscript no. atmosphere_erision ©ESO 2019 August 20, 2019 Erosion of an exoplanetary atmosphere caused by stellar winds J. M. Rodríguez-Mozos1 and A. Moya2; 3 1 University of Granada (UGR). Dept. Theoretical Physics and Cosmology. 18071. Granada. Spain 2 School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK 3 Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark e-mail: [email protected] Received September 15, 1996; accepted March 16, 1997 ABSTRACT Aims. We present a formalism for a first-order estimation of the magnetosphere radius of exoplanets orbiting stars in the range from 0.08 to 1.3 M . With this radius, we estimate the atmospheric surface that is not protected from stellar winds. We have analyzed this unprotected surface for the most extreme environment for exoplanets: GKM-type and very low-mass stars at the two limits of the habitable zone. The estimated unprotected surface makes it possible to define a likelihood for an exoplanet to retain its atmosphere. This function can be incorporated into the new habitability index SEPHI. Methods. Using different formulations in the literature in addition to stellar and exoplanet physical characteristics, we estimated the stellar magnetic induction, the main characteristics of the stellar wind, and the different star-planet interaction regions (sub- and super-Alfvénic, sub- and supersonic). With this information, we can estimate the radius of the exoplanet magnetopause and thus the exoplanet unprotected surface. Results. We have conducted a study of the auroral aperture angles for Earth-like exoplanets orbiting the habitable zone of its star, and found different behaviors depending on whether the star is in rotational saturated or unsaturated regimes, with angles of aperture of the auroral ring above or below 36◦, respectively, and with different slopes for the linear relation between the auroral aperture angle at the inner edge of the habitable zone versus the difference between auroral aperture angles at the two boundaries of the habitable zone. When the planet is tidally locked, the unprotected angle increases dramatically to values higher than 40◦ with a low likelihood of keeping its atmosphere. When the impact of stellar wind is produced in the sub-Alfvénic regime, the likelihood of keeping the atmosphere is almost zero for exoplanets orbiting very close to their star, regardless of whether they are saturated or not. Key words. Planets and satellites: magnetic fields – Planet-star interactions – Planets and satellites: atmospheres 1. Introduction ronment, but the presence of a strong planetary magnetic field does not necessarily protect a planet from losing its atmosphere. One of the characteristics that have received much attention in Thermal escape models suggest that exoplanetary atmo- the current effort of searching for potentially habitable exoplan- spheres around active KM stars undergo massive hydrogen es- ets is whether the planet is located in the habitable zone (HZ), cape. XUV radiation induces nonthermal heating through pho- allowing liquid water on its surface in first approximation (Kop- toabsorption and photoionization that increase the temperature parapu et al. 2014). Additional physics in this direction, such as of the exosphere. At high XUV fluxes, this process initiates hy- albedo or greenhouse effect, have also been taken into account. drodynamic atmospheric escape of neutral atmospheric species. However, little attention has been paid in comparison to the ef- Because it is the lightest component, hydrogen escapes faster fect of the space environment on the ability of the exoplanet to than any other species through this mechanism (Lammer et al. retain an atmosphere that is dense enough to protect any emerg- 2008) ing life at its surface from stellar radiation. Other nonthermal models (Airapetian et al. 2017) suggest Exoplanet atmospheres can be eroded by energetic radiation that the atmospheres of a significant fraction of Earth-like ex- (UV and X-ray) and stellar winds (Lammer et al. 2003; Cohen et oplanets orbiting M dwarfs and active K stars, which are ex- al. 2015; Garraffo et al. 2016). This is particularly important for posed to high XUV fluxes, will have a significant atmospheric arXiv:1908.06695v1 [astro-ph.EP] 19 Aug 2019 M-type and very low-mass (VLM) stars, where the HZ is located loss rate of oxygen and nitrogen, which will make them unin- very close to the star, the stellar activity is usually significant, habitable within a few tens to hundreds of megayears because and the stellar wind is very dense. of the low replenishment rate from volcanism or cometary bom- When a planet is magnetized, the magnetosphere is defined bardment. as the part of space that is dominated by the planetary mag- On the other hand, it has been found that the atmospheric netic field, and the magnetopause as the outer boundary of the mass escape rate occurs in two areas. The first corresponds to magnetosphere. The polar caps are the regions around the mag- polar cap escape and is dominant for hydrogen, while the sec- netic poles where the magnetic field lines are open; that is to say, ond area is dominated by cusp escape (Gunell et al. 2018). In where they have one end in the ionosphere and the other in in- the polar cap of a magnetized planet, magnetic field lines are terplanetary space (Gunell et al. 2018). The magnetic field is a opened, which allows the penetration of charged particles that physical barrier that shields the exoplanet from this stellar envi- are transported by the stellar wind, including cosmic rays, which Article number, page 1 of 14 A&A proofs: manuscript no. atmosphere_erision can interact directly with the atmosphere of the planet. We call These authors propose the following formulation for the an- the fractional area of the planetary surface that has open mag- gular momentum loss with time: netic field lines the unprotected surface. When a star increases the magnetic and dynamic pressure on a planet, it not only pro- dJ 2 2 ˙ (1−2m) (2+4m) 4m Ω∗ duces a reduction of the radius of the magnetopause, but also = K1 M R∗ B0 m ; (2) dt 3 2 2 2 2 an increase in unprotected surface of the planet (Vidotto et al. K2 νesc + Ω∗R∗ 2013). where K , K , and m are unknown constants, B is the stellar We here present a formalism based on current models for a 1 2 p 0 magnetic induction, ν = GM =R is the stellar escape ve- first-order estimation of the magnetosphere radius of the exo- esc ∗ ∗ locity, M is the stellar mass, and G is the gravitational constant. planet as a function of its orbit, its rotation period, its internal ∗ One of the main assumptions for deriving this expression is that structure, and the stellar properties. With this radius, we can es- the stellar wind is isotropic, that is, timate the unprotected surface (Vidotto et al. 2013). We have analyzed this unprotected surface for the most extreme environ- ment for exoplanets: GKM-type and VLM stars at the two limits M˙ = 4π r2 ρ(r) u(r); (3) of the corresponding HZ. In addition, we have also studied some real cases. where r is the distance from the stellar center, ρ(r) is the stellar Recently, Rodríguez-Mozos & Moya (2017) have proposed wind density, and u(r) the stellar wind velocity. a new statistically significant planetary habitability index where Although we can find some alternative expressions for the the exoplanet magnetic field plays a major role. The estimated stellar rotation breaking (see, e.g., van Saders & Pinsonneault unprotected surface together with some assumptions related to 2013; Matt et al. 2012, 2015; Garraffo et al. 2018), we have de- the ability of the Earth to retain its atmosphere with time makes it cided to follow the expression in Sadeghi Ardestani et al. (2017) possible to define a likelihood function that can be incorporated in coherence with the rest of our work. The results shown in Sec- into the index. This likelihood is related only to the atmosphere tion 4 validate this assumption. Sadeghi Ardestani and collab- erosion caused by the stellar environment. It should be borne in orators have empirically calibrated the unknown constants and mind that the thickness of the atmosphere has not yet been taken obtained K1 = 6:43, K2 = 0:0506, and m = 0:2177. Matt et into account. al. (2012) proposed a similar angular frequency evolution law, and they also empirically calibrated their unknown constants. In both cases, K2 and m account for the same functional depen- dence, and both teams reach the same empirical values for these 2. Theoretical framework two constants. ˙ The study of the effect of stellar winds on exoplanetary atmo- For M and B0, Pallavicini et al. (1981) found a relation be- spheres is the study of the interaction of three physical quanti- tween the stellar X-ray emission relative to the bolometric lu- ties. These are the stellar magnetic field and its translation into minosity (LX=Lbol) and its rotation. This relation was the origin a stellar wind and radiation, the exoplanet magnetic field and its of the relation of stellar activity to rotation and its connection translation into a protective environment for the exoplanetary at- with stellar dating, which has been widely studied since then. For rapid rotators, that is, stars with a Rossby number lower than 0.1, mosphere, and the distance of the star to the exoplanet and its −3 translation into a regime of sub-Alfvénic or super-Alfvénic, su- this relation breaks and remains constant around LX=Lbol ≈ 10 personic or subsonic stellar wind when it hits the magnetopause (Vilhu 1984; Micela et al.