On the Habitability of Teegarden's Star planets

TL;DR

This study evaluates the habitability of two Earth-mass planets orbiting Teegarden's Star, suggesting they could host surface liquid water and be promising for bio-signature detection, based on analytical habitability modeling.

Contribution

First assessment of habitability potential for Teegarden's Star planets using analytical models, highlighting their suitability for future bio-signature searches.

Findings

Both planets could sustain surface liquid water across various atmospheric conditions.

Planets are within the habitable zone and are tidally locked.

They are among the most Earth-like exoplanets discovered to date.

Abstract

We study the habitability of the two 1-2 Earth-mass planets, recently detected by the CARMENES collaboration, around the ultra-cool nearby M dwarf Teegarden's Star. With orbital periods of 4.9 and 11.4 days, both planets are likely to be within the Habitable Zone and tidally locked. They are among the most Earth-like exoplanets yet discovered. Applying an analytical habitability model we find that surface liquid water could be present on both planets for a wide range of atmospheric properties, which makes them attractive targets for bio-signature searches. The prospects of the planets retaining such an atmosphere over their history are discussed.

Tables

Table 1. Table 1: Habitable H a ​ t ​ m subscript 𝐻 𝑎 𝑡 𝑚 H_{atm} ranges for each planet, for different choices of f 𝑓 f and T m ​ a ​ x subscript 𝑇 𝑚 𝑎 𝑥 T_{max} .

$T_{max}$	$f=0.5$, TGb	$f=0.5$, TGc	$f=1.0$, TGb	$f=1.0$, TGc
$340$ K	$0.32-3.7$	$1-12$	$0.8-1.9$	$2.5-5.8$
$373$ K	$0.32-5.6$	$1-17$	$0.8-2.8$	$2.5-8.6$
$400$ K	$0.32-8.0$	$1-25$	$0.8-4.0$	$2.5-12$

Equations

$$H=(1-A)H_g\alpha S/S_{\oplus }=H_{atm}s,$$

$$T_{min}=278(Hf{)}^{1/4}\mathrm{K},\mathrm{and}$$

$$T_{max}=394H^{1/4}(1-\frac{3}{4}f{)}^{1/4}K.$$

$$T(\theta )=415[HF(\theta ){]}^{1/4}\mathrm{K},$$

$$F(\theta )=\{\begin{array}{ll}f/4+(1-f)\cos (\theta )& 0\le \theta \le 90\\ f/4& 90\le \theta \le 180.\end{array}$$

$$0.23(1-\frac{3}{4}f{)}^{-1}<H<3.2f^{-1}.$$

$$500a^2<H_{atm}<8770a^2.$$

$$0.23(1-\frac{3}{4}f{)}^{-1}{s}^{-1}<H_{atm}<3.2f^{-1}{s}^{-1}.$$

Full text

stars: individual (Teegarden’s Star) — planets and satellites: atmospheres

1 Introduction

The CARMENES collaboration has recently announced (Zechmeister et al. 2019, hereafter Z19) the detection of two planet candidates, each with $1.0$–$2.0$ M*⊕* mass, orbiting the ultra-cool (M7V) nearby ($3.83$ pc) Teegarden’s Star (hereafter TG). Assuming the estimated host’s mass of $0.089\pm 0.009$ M*⊙*, their periods, $4.91$  and $11.4$ days, correspond to an orbital distance of $0.025$ and $0.044$ AU, $\pm 3$ $\%$, respectively. At these distances, with the estimated host’s age of $>8$ Gyr (Z19), both planets are most probably tidally locked (e.g., Griessmeier et al. 2009).

We investigate the habitability of the exoplanets Teegarden’s Star b and c (hereafter TGb and TGc, respectively), and their potential to have an atmosphere that would support surface liquid water, using an atmospheric habitability model for locked planets (Wandel 2018, hereafter W18). We derive the dependence of the surface temperature of the planets on circulation and greenhouse heating, as well as their habitability regime in the atmospheric parameter space.

2 Habitability ranges for the planets of Teegarden’s Star

2.1 The analytic climate-habitability model

Planets within the habitable zone (HZ) of late M-dwarfs are tidally locked (Griessmeier et al. 2009). Without atmosphere the surface temperature would be determined only by the irradiation from the host star and the angular distance from the substellar point. W18 puts together an analytic 1D model, in which the atmosphere’s impact on the surface temperature distribution is evaluated, taking into account (a) the irradiation from the host star (insolation), (b) atmospheric transmission (screening and greenhouse effect), and (c) horizontal heat transport due to circulation, convection, and advection. The values (b) and (c) can in principle be calculated, given the planet’s data (specific gravity, rotation) and the atmospheric properties (composition, pressure, heat capacity, wind speed, global circulation patterns, etc.). However, as these data are difficult to obtain and disentangle in exoplanets, they are parameterized using the atmospheric heating and the global redistribution factors, respectively. The model combines elements from previous analytic temperature models of locked planets (e.g., Haberle et al. 1996; Koll and Abbot 2016), but the model’s novelty and strength is in being independent of the specific atmospheric composition and of the details of the energy transport mechanism, both being represented in a parametric form: the former by the atmospheric heating factor and the latter by the global heat redistribution parameter. This, of course, is also a weakness, when it comes to subjects like 2D and 3D effects, flow patterns like cells and vertical transport, and more complex feedback mechanisms that depend on the composition, like clouds (e.g., Yang et al. 2013). The analytic expression of the surface temperature is combined with the temperature boundaries of the HZ, to define a habitability range in the two-dimensional parameter plane, namely, atmospheric heating and circulation (e.g., Fig. 2). This will be discussed in more detail in subsection 2.3.

2.2 Surface temperature distribution

Following W18 we define the dimensionless heating factor $H$ which is a measure of the surface heating, combining the host’s irradiation with the albedo ($A$), the atmospheric screening ($\alpha$), and the greenhouse heating factor ($H_{g}$),

[TABLE]

where $s=S/S_{\oplus}$ is the insolation relative to Earth. The product $(1-A)H_{g}\alpha=H_{atm}$ is defined as the atmospheric heating factor. $H_{g}$ is also related to the atmospheric optical depth in the lower wavelength band (IR) by $H_{g}\approx\tau_{\rm LW}+1$. Typical values of the heating parameter for the solar system are: $H\sim 1$ (Earth), $\sim 0.3$ (Mars), and $\sim 50$ (Venus). For a locked planet, the surface temperature distribution can be calculated for each ”latitude” (angular distance from the substellar point) by equating the local heating and cooling. In the model this is combined with the global heat redistribution, described by a parameter $f$, which is related to the atmospheric circulation and varies between $f=0$ (no heat distribution) and $f=1$ (full distribution, leading to an isothermal surface). While rocky planets with no or little atmosphere, like Mercury, have an extremely high day–night temperature contrast, planets with a thick, Venus-like atmosphere tend to be nearly isothermal. Intermediate cases, with up to $10$ bar atmospheres, conserve significant surface temperature gradients (e.g., Selsis et al. 2011). For a locked planet the highest and lowest temperatures occur at the substellar point (denoted in this work by $\theta=0$) and at its antipode ($\theta=180$), respectively. These temperatures can be written as (W18)

[TABLE]

[TABLE]

The surface temperature distribution with a uniform global heat redistribution is given by (W18; Fig. 1 therein)

[TABLE]

where

[TABLE]

Including local heat transport (e.g., by advection) leads to a differential equation, similar to the heat equation (Eq. 5 in W18) with a smoothed temperature distribution (see Fig. 1). If the advective heating is small, compared to the radiative heating due to the host star (e.g., on Earth at sea level advective heat transport is less than 1% of the solar irradiation), the values of the substellar and antipode temperatures are approximately still given by Eqs. 2 and 3, respectively.

Figure 1 shows the surface temperature distribution for the two planets TGb and TGc, for several values of the atmospheric heating as indicated on the legend on the right. In the range $0.3<H_{atm}<17$ there is a habitable region on some part of the surface of one or both planets. At $H_{atm}=1$ TGc has a narrow habitable region at the substellar (permanent day) point, at $H_{atm}=4$ TGb has a narrow habitable region at the substellar antipode (permanent night), and at $H_{\rm atm}=2$ both planets have a wide range of habitable latitudes, TGb between $60$–$180$ and TG [math]–$80$. The upper and lower curves also represent the two extreme ends of the habitability range of the atmospheric heating in the Teegarden’s Star system. The upper dashed curve is also the temperature distribution of TGc with $H_{\rm atm}=17$, while the lower dotted curve also represents TGb with $H_{\rm atm}=0.32$. These numbers agree with the boundaries indicated in Table 1 and Fig. 2, for $f$=0.5.

2.3 The habitability range of the atmospheric heating

The range of temperatures allowing liquid water on at least part of the planet surface could vary between freezing and the minimal moist greenhouse temperature ($\sim 340$ K) or higher, according to the atmospheric pressure and composition. The results do not strongly depend on this choice (W18), so we take this range as $273K<T<373$ K. This temperature range defines the ”habitability range” of the heating parameter. It extends between the lowest value, for which the substellar temperature is $273$ K, and the highest value for which the substellar antipode is at $373$ K (or $\sim 340$ K for a more conservative range). This gives (W18)

[TABLE]

Equations 1 and 6 give a relation between the planet’s distance from the host star ($a$, in units of astronomical unit) and the atmospheric heating factor. For TG’s luminosity ($7.3\,10^{-4}$ L*⊙*, Schweitzer et al. 2019) and $f=0.5$ we get

[TABLE]

Equation 6 may also be written in terms of the insolation and the atmospheric heating,

[TABLE]

The corresponding ranges of the atmospheric heating factor can be seen in Fig. 2, which shows the habitability boundaries of the atmospheric heating vs. the insolation (calculated with TG’s luminosity). The biohabitable ranges for the planets are marked by vertical stripes. For a given insolation, the range corresponding to Eq. 6 is the vertical span between the lines of the highest habitable atmospheric heating factor (red curves) and the minimal value (blue) for a given value of the redistribution parameter $f$. Higher $f$ values (more atmospheric circulation causing heat distribution) narrow the range of habitability, as they either make the substellar point of planets at the HZ outskirts too cold, or make the substellar antipode of planets inward of the ”traditional” HZ too hot.

The stellar flux on the two planets is $S({\rm TGb})\sim 1.15$ S*⊕* and $S({\rm TGb})\sim 0.37$ S*⊕*, with an uncertainty of $\sim 10$ %. This uncertainty comes mainly from the large systematic uncertainty (of $\sim 10$ %) on $T_{\rm eff}$ of the star (Z19). Table 1 shows the habitability ranges in $H_{\rm atm}$ for each of the planets for two choices of heat circulation: $f=1$ (isothermal surface) and $f=0.5$, and for three cases of greenhouse upper limit: conservative, $T_{max}\sim 340$ K, corresponding to maximal moist greenhouse runaway (Kasting et al. 1993), optimistic, $T_{max}\sim 373$ K, and the highest bio-habitability limit (W18), $T_{max}\sim 400$ K. For $T_{max}\sim 340$ K the upper limits on $H_{\rm atm}$ will be smaller than those for $T_{max}\sim 373$ K by a factor of $\sim(340/373)^{4}=0.69$. Similarly, $T_{max}\sim 400$ K, applicable to a higher atmospheric pressure, gives the upper $H_{\rm atm}$ limits larger by a factor of $\sim 1.32$.