HABITABLE ZONES AROUND MAIN-SEQUENCE STARS: NEW ESTIMATES

“These coefficients were later replaced (Mischna et al. 2000) by coefficients generated using the correlated-k technique (Mlawer et al. 1997; Kato et al. 1999).”

“Rayleigh scattering by water was also considered by Kasting (1988); Kasting et al. (1993), but these authors used the scattering coefficient for air because the coefficient for H2O was not available, or at least not known to them.”

“It is a program to produce high-resolution spectrum of any gas mixture, in any thermodynamical conditions, from line-by-line (LBL) databases such as HITRAN 2008 (Rothman et al. 2009) and HITEMP 20104 (Rothman et al. 2010).”

“As with the inner edge model, a more optimistic empirical limit on the OHZ can be estimated based on the observation that early Mars was warm enough for liquid water to flow on its surface (Pollack et al. 1987; Bibring et al. 2006).”

“Estimates of luminosities will be derived using photometric and spectroscopic distances for now (in cases where parallax measurements are absent), but eventually GAIA (Perryman et al. 2001) will yield very precise parallaxes (and by extension precise luminosities) for all these target stars.”

“In order to assess the potential habitability of recently discovered exoplanets, equilibrium temperature (Teq) has been used as a metric (Borucki et al. 2011; Batalha et al. 2012).”

“A δ two-stream approximation (Toon et al. 1989) was used to calculate the net absorbed solar radiation for each of the 101 layers, using separate eight-term, correlated-k coefficients for both CO2 and H2O to parameterize absorption in each of the 38 solar spectral intervals ranging from 0.2− 4.5µm.”

“The Kopparapu et al. (2013) inner optimistic, conservative, and outer optimistic habitable zones are shown in light, medium, and dark green, respectively.”

“In addition to the short–period ( P (cid:46) 10 days) transiting planets around nearby stars, there should also exist a large population of super-Earths that lie within their respective “Habitable Zones” (Kasting et al. 1993; Kopparapu et al. 2013).”

“…habitable terrestrial worlds; representative of early Earth, Mars, and Venus (Kasting 1993; Way et al. 2016; Wordsworth 2016); and expected on habitable exoplanets orbiting younger, fainter stars or at the outer edges of their habitable zones (e.g., TRAPPIST-1e; Kopparapu et al. 2013; Wolf 2017).”

“0 star that produced the Hazflare, the eventual main-sequence HZ lies 0.1–0.2 AU from the star (adopting a stellar mass of 0.4 M ; Kopparapu et al. 2013).”

“K2-18 b lies in the temperate zone of its host star (Kopparapu et al. 2013, 2014) and receives stellar irradiation similar to Earth.”

“Both act to lower the Bond albedo of an Earth-like planet around a206 cooler star relative to a hotter star (Kasting et al. 1993).207 Kopparapu et al. (2013) re-calculated the irradiance boundaries using a cloud-free208 climate model based on new H2O and CO2 absorption coefficients.”

“The non grey calculations from Kopparapu et al. (2013) also show that weak H2O lines in the visible and near IR included in the HITEMP spectral database could significantly lower the planetary albedo below the usual value of 0.4–0.5 to about 0.3.”

“…GCMs (Leconte et al. 2013b; Wolf & Toon 2015; Popp et al. 2016; Way et al. 2016b; Wolf et al. 2017), with all models finding inner edges that are at higher incident stellar flux relative to 1D models (e.g., Kopparapu et al. 2013) owing to the effects of clouds and reduced relative humidity.”

“…(1986), although it has been significantly modernized since then, and it was most recently updated and described in a recalculation of habitable zone boundaries around main sequence stars (Kopparapu et al., 2013) and in a study of the impact of organic haze in the Archean (Arney et al., 2016).”

“Cloud-free 1-Dmodels with saturated atmospheres predict that Earth will reach moist greenhouse conditions (Ts=340 K) when the solar constant increases by only 1.5% above its present level [Kopparapu et al., 2013].”

“of rotation rate The first set of 3-D GCM HZ calculations were performed by Yang et al. [237,238]. Whereas previous 1-D calculations had implicitly assumed that all planets were rapid rotators (e.g., [1,26,129]), Yang et al. [237,238] found that the inner edge is closer in to the star than what the classical HZ predic…”

“…star 0.7 times the mass of the Sun (M⊙) with a radius (R⋆) of 0.64 solar radii (R⊙) (for Sun-like metallicity at an age of 1Gyr, following Bressan et al. 2012), and the planet- satellite system is placed into the center of the stellar HZ at 0.56AU (derived from the model of Kopparapu et al. 2013).”

“Kopparapu et al. (2013) made further revisions to the Kasting et al. (1993) model, using a 1-”

“Our 1D version of the LMD Generic inverse model is a single-column inverse radiative-convective climate model following the same approach (inverse modeling) as in Kasting et al. (1984) and more recently as in Kopparapu et al. (2013).”

“…al. (2014a), I used separate 8-term HITRAN and HITEMP coefficients for CO2 and H2O, respectively, truncated at 500 cm-1 and 25 cm1, respectively, computed over 8 temperatures (100, 150, 200, 250, 300, 350, 400, 600 K), and 8 pressures (105 – 100 bar) (Kopparapu et al. 2013; Ramirez et al. 2014ab).”

“Also, it has been found that three planets (TRAPPIST-1e, f and g) are in the habitable zone (HZ; Kopparapu et al., 2013) where surface temperatures would allow surface water to exist (Gillon et al., 2017; Wolf, 2017, 2018; Turbet et al., 2018).”

“The radiation field defines the habitable zone, a region in which orbiting planets could sustain liquid water at their surface (Huang 1960; Kopparapu et al. 2013).”

“Nearby M dwarfs are appealing targets for Doppler Radial Velocity (RV) and transit exoplanet searches because their low masses and luminosities make planets orbiting in their Habitable Zones (HZ Kasting 1993; Kopparapu et al. 2013, 2014) more easily detectable than those around higher-mass stars.”

“This work was significantly improved through subsequent studies, including the recent work by Kopparapu et al. (2013, 2014).”

“The search is now focused on detecting low mass planets, with great interest in those that orbit in a star’s habitable zone (HZ; Kasting et al. 1993; Selsis et al. 2007; Kopparapu et al. 2013).”

“From this, the so-called habitable zone (HZ) for rocky planets is defined, that is, the range of orbital distances over which liquid water may be possible on the surface (e.g. Hart, 1979; Kasting et al., 1993; Kopparapu et al., 2013).”

“Both planets receive far too much radiation from HD 7924 to be within the habitable zone as defined by Kopparapu et al. (2013) with incident stellar irradiation values 114, 28, and 15 times that received from the Sun by Earth for planets b, c, and d respectively.”

“Feeding this value into the Kopparapu et al. (2013) script resulted in the following HZ limits: conservative, 0.1128 – 0.2102 AU, optimistic, 0.0853 – 0.2197 AU.”

“…influence on a planet’s surface level atmospheric properties and (at temperatures cooler than those primarily probed in this paper) habitability (see Kopparapu et al. 2013; Rugheimer et al. 2013); our T should not be interpreted more deeply than as a useful shorthand for the amount of energy…”

“…exoplanets have mostly moved from the realm of 1D (e.g., Kasting et al. 1993; Forget 1998; Selsis et al. 2007; Pierrehumbert & Gaidos 2011; Kopparapu et al. 2013; Popp et al. 2013; Kopparapu et al. 2014; Ramirez & Kaltenegger 2014) to fully 3D coupled atmosphere and ocean general…”

“This indicates that the insolation needed at the outer limit of the HZ is higher (i.e., the HZ is narrower) than previous estimates (Kasting et al., 1993; Kopparapu et al., 2013) if a snowball planet is common.”

“For the latter, we take advantage of the information provided in the Habitable Zone Gallery* (HZG, Kane & Gelino 2012), regarding the optimistic and conservative calculations of the HZ (as defined in Kopparapu et al. 2013, 2014).”

“…et al. 2007; Khodachenko et al. 2007; Cohen et al. 2011; Lecavelier des Etangs et al. 2012; Khodachenko et al. 2014) if the planet orbits its host star at close distances, as it is the case for planets orbiting dM stars in the habitable zone which is located at ∼0.2 AU (Kopparapu et al. 2013).”

“We further note that a higher absolute burial flux of organic carbon would constitute a source of oxygen equivalents that would have needed to be balanced by reductants to maintain anoxic surface conditions in the Archean (Kasting, 2013).”

“The insolation optimistic habitable zone is the green region and the conservative zone extends between the two black vertical lines (Kopparapu et al., 2013; Kopparapu et al. 2014).”

“The habitable zone, as defined using the incident stellar flux (Kopparapu et al. 2013), should exist around 0.1 au (20 Re, 60 R*).”

“Further developments on the limits of the HZ for main-sequence stars are discussed elsewhere (e.g., Pierrehumbert & Gaidos 2011; Joshi & Haberle 2012; Kopparapu et al. 2013, 2014, 2016; Shields et al. 2013; Yang et al. 2013; Kitzmann 2016, 2017).”

“Using the Kopparapu et al. (2013) moist/max greenhouse HZ with the 5 Gyr Baraffe et al. (1998) stellar models, we calculate the semi-major axis of the inner and outer edge of the HZ and relate this to the IWA.”

“For example, the 33 d, 0.135 au orbit (Kopparapu et al. 2013) of an HZ planet hosted by 0.3 M early M dwarf would reduce to an 11 d, 0.045 au orbit for the sample planet hosted by a 0.1 M star.”

“Late-type M dwarf stars were favored as targets because these gave the best chance within the limited campaign duration to find small, temperate planets that may be rocky and lie in the surface liquid water “habitable zone” (Kasting et al. 1993; Kopparapu et al. 2013).”

“The best-fit orbital solution yields a planetary companion of mass mP sin i ≈ 25 M⊕ with an orbital semi-major axis a = 0.32 au and low eccentricity, which locates the planet inside the liquid-water temperate zone around HD 147379 (Kopparapu et al. 2013, 2014).”

“…equations from Kopparapu et al. (2013, 2014) for the Kepler-186 system results in an approximate inner boundary of the HZ (runaway greenhouse limit) of 0.20–0.23 AU, depending on the adopted stellar parameters and the choice of parameters (either Kopparapu et al. 2013 or Kopparapu et al. 2014).”

“Kasting et al. (1993) and Kopparapu et al. (2013) used a simple one-dimensional (1D) model with a saturated troposphere and an isothermal stratosphere to examine the response of the stratospheric water vapor mixing ratio to increased instellation (see also Kasting et al. 2015).”

“A conservative estimate for our solar system suggests that the HZ is between 0.95 and 1.67 AU (Kasting et al., 1993; Selsis et al 2007; Kopparapu et al., 2013, 2014; Leconte et al 2013).”

“…of the inner and outer boundariesof the HZ of a main sequence star with an eff ctive temperature of 2600K < TStar < 7200 K, we use equation (3) (see Kopparapu et al 2013a) lx−Star = lx−Sun L/LSun 1+ αx(Ti) l2x−Sun 1/2 (3) In this equation,lx = (l in, lout) is in AU, Ti(K) = TStar(K)…”

“…to recent studies with radiative–convective climate models with an HITEMP database, Rayleigh scattering of H2O is found to be not so effective: the planetary albedo increases with the surface temperature but is less than that previously thought (Goldblatt et al. 2013; Kopparapu et al. 2013).”

“Notably, we find that our prognostic H mixing ratios are almost never twice the amount of H2Ov, as assumed in previous studies (e.g., Kasting et al. 1993; Kopparapu et al. 2013, 2017).”

“The inner edge of the habitable zone was estimated using a 1D climate model by Kasting et al. (1993) and Abe (1993), and recently this work was updated by Kopparapu et al. (2013, 2014) and Kasting et al. (2014).”

“Also, this range of host star angular sizes spans those for the Habitable Zones of M and K dwarf stars (Kopparapu et al. 2013).”

“Radiative transfer calculations of the atmospheric response of an Earthlike planet to insolation (Kasting et al. 1993; Kopparapu et al. 2013, 2014) allow the identification of planetary orbits that permit surface liquid water.”

“…that the self continuum absorption of water vapor is underestimated in a MT CKD 2.4 model, which was used by Goldblatt et al. 17 (2013), especially in a wavenumber range from 2000 to 3000 cm−1, compared with the MT CKD 2.5 model used in our model and a BPS formalism used by Kopparapu et al. (2013).”

“…respectively, which are truncated at 500 and 25 cm−1, respectively, computed over eight temperatures (100, 150, 200, 250, 300, 350, 400, 600 K) and eight pressures (10−5–100 bar) (Kopparapu et al., 2013a, 2013ab; Ramirez, Kopparapu, Zugger, et al., 2014; Ramirez, Kopparapu, Lindner, et al., 2014).”

“Habitable-Zone (HZ) boundaries (Kopparapu et al. 2013) are also much closer to the host stars in M-dwarf systems than larger solar-type stars, making them ideal candidates for surveys designed to detect potentially habitable planets.”

“However, although it lies outside the Teff range studied by Kopparapu et al. (2013), it certainly orbits too close to the star, with S ≈ 5S0 (five times the solar incident flux).”

“…ones, will affect the regions close to the stars; for M dwarfs, this includes the socalled Habitable Zone (HZ), a region at a distance from the star in which water on the planetary surface would be liquid (Kasting et al. 1993; Kane & Gelino 2012; Kopparapu et al. 2013, 2014; Kasting et al. 2014).”

“In particular, the cloud-free habitable zone for a star like LP 791- 18 extends from approximately P=10–30 days (Kopparapu et al. 2013, 2014), a range only poorly sampled by the existing TESS photometry.”

“Their surface temperatures are low enough to enable the existence of liquid water (Stevenson, 1999; Kopparapu et al., 2013; Leconte et al., 2013).”

“The stellar irradiance on the planet, in turn: • Provides an estimate as to whether or not the planet is inside the HZ (e.g., Kopparapu et al. 2013); • Is needed to infer the reflectivity of the planet from its apparent brightness relative to the star; and • Is a main input in atmospheric modeling…”

“Whereas habitable planets around G stars reside on wide orbits with periods ∼ 100 days, habitable zones around M stars are located much closer in, with periods of ∼ few days, enhancing the crucial repeatability of observations (Kopparapu et al. 2013, 2016). ar X iv :1 90 7.”

“In order to estimate the HZ limits we use the recently updated values calculated by Kopparapu et al. (2013).”

“The liquid water habitable zone of M dwarfs is typically at ∼0.1 AU (Kasting et al. 1993; Kopparapu et al. 2013).”

“Runaway greenhouse planets like early Venus would be suspect because of their position near or inside the inner edge of the habitable zone (Kasting 1988; Kopparapu et al. 2013; Kane et al. 2014; Way et al. 2016).”

“5, the thermal radiation from the top of the atmosphere decreases along with decrease in the surface temperature or increase in the atmospheric mass, but finally approaches ∼ 280 W/m2 (Abe and Matsui 1988; Kasting 1988; Goldblatt et al. 2013; Kopparapu et al. 2013).”

“Indeed, the 39-day rotation period and the 112-day activity signal roughly enclose the optimistic habitable zone of GJ 176 according to Kopparapu et al. (2013).”

“In this scenario, the planet-moon system is close to the inner edge of the stellar HZ (Kopparapu et al. 2013).”

“N 2 atmosphere 7 .”

“The “habitable zone” is the circumstellar region where an Earth-like planet can support liquid water on its surface (Kasting et al. 1993; Kopparapu et al. 2013; Kasting et al. 2014), which is essential for Earth-like life.”

“Our 1D climate model calculates the limits for a grid of stars with effective temperatures between 2600 and 10,000 K (the model for 2600–7200 K is discussed in detail in Kasting et al. 1993; Kopparapu et al. 2013, 2014; Ramirez et al. 2014b).”

“…thus providing powerful evidence that our solar system is not an exception but simply one out of countless others in the Universe (e.g., Borucki et al., 2010; Kopparapu et al., 2013; Seager, 2013; Batalha, 2014; Gaidos et al., 2014; Hatzes, 2014; Quintana et al., 2014; Macintosh et al., 2015).”

“Our parameterizations are valid for a larger spectral range than that in previous work (e.g., Kopparapu et al. 2013), expanded to include A spectral classes (TEFF=2600–10,000 K).”