Mon. Not. R. Astron. Soc. 000, 1–11 (xx) Printed 10 November 2019 (MN LATEX style file v2.2)

Water loss from Earth-sized planets in the habitable zones ofultracool dwarfs:Implications for the planets of TRAPPIST-1

E. Bolmont1?, F. Selsis2,3, J. E. Owen4†, I. Ribas5, S. N. Raymond2,3, J. Leconte2,3,& M. Gillon61 NaXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur, Belgium2 Univ. Bordeaux, LAB, UMR 5804, F-33615, Pessac, France3 CNRS, LAB, UMR 5804, F-33615, Pessac, France4 Institute for Advanced Study, Einstein Drive, Princeton NJ 08540, USA5 Institut de Ciencies de l’Espai (CSIC-IEEC), Carrer de Can Magrans s/n, Campus UAB, 08193 Bellaterra, Spain6 Institut d’Astrophysique et de Geophysique, Universite de Liege, Allee du 6 Aout 19C, 4000 Liege, Belgium

Accepted xx xx xx. Received xx xx xx; in original form xx xx xx

ABSTRACT

Ultracool dwarfs (UCD) encompass the population of extremely low mass stars (laterthan M6-type) and brown dwarfs. Because UCDs cool monotonically, their habitable zone(HZ) sweeps inward in time. Assuming they possess water, planets found in the HZ of UCDshave experienced a runaway greenhouse phase too hot for liquid water prior to entering theHZ. It has been proposed that such planets are desiccated by this hot early phase and enterthe HZ as dry, inhospitable worlds. Here we model the water loss during this pre-HZ hotphase taking into account recent upper limits on the XUV emission of UCDs and using 1Dradiation-hydrodynamic simulations. We address the whole range of UCDs but also focus onthe planets b, c and d recently found around the 0.08 M� dwarf TRAPPIST-1.

Despite assumptions maximizing the FUV-photolysis of water and the XUV-driven es-cape of hydrogen, we find that planets can retain significant amounts of water in the HZ ofUCDs, with a sweet spot in the 0.04 – 0.06 M� range. With our assumptions, TRAPPIST-1band c can lose as much as 4 Earth Ocean but planet d – which may be inside the HZ dependingon its actual period – may have kept enough water to remain habitable depending on its ini-tial content. TRAPPIST-1 planets are key targets for atmospheric characterization and couldprovide strong constraints on the water erosion around UCDs.

Key words: stars: low-mass – (stars:) brown dwarfs – planets and satellites: terrestrial plan-ets – planet-star interactions – planets and satellites: atmospheres – planets and satellites:individual: TRAPPIST-1

1 INTRODUCTION

Earth-like planets have been detected in the HZs (Kasting, Whit-mire, & Reynolds 1993; Selsis et al. 2007a; Kopparapu et al. 2013)of early type M-dwarfs (e.g., Quintana et al. 2014). Here we ad-dress the potential habitability of planets orbiting even less massiveobjects: ultracool dwarfs (UCDs), which encompass brown dwarfs(BDs) and late type M-dwarfs. The first gas giant was detectedaround a BD by Han et al. (2013).Very recently, Gillon et al. (inpress) discovered 3 Earth-sized planets close to an object of mass0.08 M� (just above the theoretical limit of M? ∼ 0.075 M� be-

? E-mail: emeline.bolmont@unamur.be† Hubble Fellow

tween brown dwarfs and M-dwarfs, Chabrier & Baraffe 1997). Theplanets in this system have insolations between 4.25 and 0.02 timesEarth’s. The third planet may be in the HZ. The atmospheres ofthese planets could be probed with facilities such as the HST andJWST, which makes them all the more interesting to study.

BDs (i.e., objects of mass 0.01 6 M?/M� 6 0.07) do not fusehydrogen in their cores. They contract and become fainter in time.Their HZs therefore move inward in concert with their decreasingluminosities (Andreeshchev & Scalo 2004; Bolmont, Raymond, &Leconte 2011). Nonetheless, for BDs more massive than 0.04 M� aplanet on a fixed or slowly-evolving orbit can stay in the HZ for Gyrtimescales (Bolmont, Raymond, & Leconte 2011). In this study weconsider UCDs of mass up to 0.08 M�. A UCD of mass 0.08 M�is actually a late-type M-dwarf. As for a BD, its luminosity also

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2 E. Bolmont, F. Selsis, J. E. Owen, I. Ribas, S. N. Raymond, J. Leconte and M. Gillon

decreases with time but its mass is high enough so that it starts thefusion of Hydrogen in its core. From that moment on, the HZ stopsshrinking, allowing close-in planets to stay more than 10 Gyr inthe HZ. However, any planet that enters the HZ has spent time ina region that is too hot for liquid water. A planet experiencing arunaway greenhouse around a Sun-like star is expected to lose con-siderable amounts of water (one Earth ocean in less than one Gyr).This is due to H2O photolysis by FUV photons and the thermal es-cape of Hydrogen due to XUV heating of the upper atmosphere.This is the current scenario to explain the water depletion in the at-mosphere of Venus and its high enrichment in deuterium (Solomonet al. 1991). Could planets in the HZs of UCDs, like Venus, havelost all of their water during this early hot phase?

Barnes & Heller (2013) found that planets entering the BDhabitable zone are completely dried out by the hot early phase.They concluded that BDs are unlikely candidates for habitableplanets. Here we present a study of water loss using more recentestimates for the X-ray luminosity of very low mass stars andconfronting results obtained with energy-limited escape with 1Dradiation-hydrodynamic mass-loss simulations. We find that – evenin a standard case scenario for water retention – planets with aninitial Earth-like water reservoir (MH2O = 1.3 × 1021 kg) could stillhave water upon reaching the HZ. Once these planets enter the HZ,the water can condense onto the surface (as is thought happened onEarth, once the accretion phase was over; e.g. Matsui & Abe 1986;Zahnle, Kasting, & Pollack 1988). Observation of these objects,such as the TRAPPIST-1 planets, would probably lift this uncer-tainty.

2 ORBITAL EVOLUTION OF PLANETS IN THEULTRACOOL DWARF HABITABLE ZONE

The UCD habitable zone is located very close-in, at just a few per-cent of an AU (or less; Bolmont, Raymond, & Leconte 2011). Tidalevolution is therefore important. Due to UCDs’ atmospheres lowdegree of ionization (Mohanty et al. 2002) and the high densities,magnetic breaking is inefficient and cannot counteract spin-up dueto contraction. UCDs’ corotation radii – where the mean motionmatches the UCD spin rate – move inward.

Figure 1 shows the evolution of the HZ boundaries for twoUCDs: one of mass 0.01 M� and one of mass 0.08 M�. The timeat which a planet reaches the HZ depends on its tidal orbital evolu-tion as well as the cooling rate of the UCD. The tidal evolution of aplanet around a UCD is mainly controlled by its initial semi-majoraxis with respect to the corotation radius (in red and orange fulllines in Figure 1). A planet initially interior to the corotation radiusmigrates inwards due to the tide raised in the UCD and eventu-ally falls on the UCD. A planet initially outside corotation migratesoutward (Bolmont, Raymond, & Leconte 2011). There does exist anarrow region in which the moving corotation radius catches up toinward-migrating planets and reverses the direction of migration.The planet’s probability of survival is smaller the farther away itis from the corotation radius, which is illustrated by the coloredgradient area in Figure 1.

Surviving planets cross the shrinking HZ at different timesdepending on their orbital distance. Close-in planets tend to staylonger in the HZ because the UCDs’ luminosity evolution slows asit cools (Chabrier & Baraffe 1997). Bolmont, Raymond, & Leconte(2011) showed that for UCDs of mass higher than 0.04 M�, planetscan spend up to several Gyr in the HZ. Although their earlier tidalhistories vary, planets are on basically fixed orbits as they traverse

Age - t0 (yr)

Dis

tance

(au

)

Habitable zone M = 0.01 M⊙

Habitable zone M = 0.08 M⊙

Roche limit

Corotation radius

R

M = 0.08 M⊙

M = 0.01 M⊙

Figure 1. Evolution of the HZ limits for a UCD of 0.01 M� and of 0.08 M�.The full lines correspond to the corotation radius for the UCD of 0.08 M�in red and 0.01 M� in orange. With the same color coding, the dashed linescorrespond to the radius of the two objects and the thick dashed lines corre-spond to the Roche limit for the two objects. t0 is the initial time, named“time zero”. It corresponds to the time of protoplanetary disk dispersal,taken here as 1 Myr.

the UCD habitable zone. We computed the mass loss taking intoaccount the orbital tidal evolution, but we found that it has no ef-fect on the result1. For the rest of this study we therefore considerthe case of planets on fixed orbits. We consider planets at 0.01 AU.This value of semi-major axis is the average of the closest orbitwhich survives the evolution. For a fixed initial rotation period ofthe UCD, planets around low mass UCDs could survive at smallerinitial orbital radius, than around high mass UCDs. We choose thisvalue to be able to see the trends when the mass of the UCD isincreased.

3 MODELING WATER LOSS

3.1 Energy limited escape: an efficient process of water loss

In order to place the strongest possible constraints, we calculate wa-ter loss via energy-limited escape (Lammer et al. 2003). The mech-anism requires two types of spectral radiation: FUV (100–200 nm)to photo-dissociate water molecules and XUV (0.1–100 nm) to heatup the exosphere. This heating causes atmospheric escape when thethermal velocity of atoms exceeds the escape velocity. Non-thermalloss induced by stellar winds can in theory contribute significantlyto the total atmospheric loss, either by the quiescent wind or bythe coronal ejections associated with flares (Lammer et al. 2007;Khodachenko et al. 2007). For earlier type UCDs, this might be anissue, however we here consider UCDs of spectral type later thanM8 type, for which there is no indication of winds that could en-hance the atmospheric loss.

Energy-limited escape considers that the energy of incidentradiation with λ < 100 nm is converted into the gravitational energyof the lost atoms. We use the prescription of Selsis et al. (2007)linking the XUV flux FXUV(at d = 1 AU) to the mass loss rate m:

1 In the worst case, i.e. if the UCD is very dissipative, this would mean thatwe underestimate the mass loss by ∼ 1%.

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Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs 3

εFXUVπR2

p

(a/1AU)2 =GMpm

Rp, (1)

where Rp is the planet’s radius, Mp its mass and a its semi-majoraxis. ε is the fraction of the incoming energy that is transferredinto gravitational energy through the mass loss. This efficiency isnot to be confused with the heating efficiency, which is the fractionof the incoming energy that is deposited in the form of heat, asonly a fraction of the heat drives the hydrodynamic outflow (somebeing for instance conducted downward). This fraction has beenestimated at about 0.1 by Yelle (2004) and more recently at 0.1 orless in the limit of extreme loss by Owen & Wu (2013). Here we useε = 0.1 to place an upper limit on the mass loss rate.The left termof Equation 1, FXUVπR2

p/(a/1AU)2, corresponds to the fraction ofthe XUV flux intercepted by the planet.

Thus the mass loss rate is given by:

m = εFXUVπR3

p

GMp(a/1AU)2 . (2)

Taking into account that the planet might undergo orbital mi-gration or the evolution of the XUV flux the mass lost by the planetat a time t is of:

m = επR3

p

GMp

∫ t

0

FXUV

(a/1AU)2 dt. (3)

Venus probably lost its water reservoir by this mechanism.Radar observations of the Magellan satellite and ground-based ob-servations showed that the last traces of water on Venus date backat least 1 billion years (this corresponds to the age of the surface;Solomon et al. 1991). Although the Sun was fainter, this corre-sponds to the critical flux for energy-limited escape to occur (Kast-ing 1988). As UCDs are less bright than the Sun, we expect theirXUV flux to be lower than the Sun’s.

One could argue that the XUV cross section radius of theplanet is bigger than the planet’s radius and is probably similarthe Hill radius (as in Erkaev et al. 2007, which considered Jupiter-mass planets). This assumption would mean that the water massloss would be higher than what we propose to calculate here. In ahydrodynamic outflow the effect of the Roche Lobe is to weakenthe effect of gravity compared to the pressure force, its role is feltthrough the gradient of the potential. For transonic outflow the dis-tance of the sonic point from the surface of the planet dependson the gradient of the potential, with shallow gradients (i.e. closerto the Hill radius) pushing the sonic point closer to the planet in-creases the mass loss. We tested our hypothesis of taking the realradius of the planet with a hydrodynamical code (Owen & Alvarez2016). We find that, for the small rocky planets we consider here,this does not overestimate the mass loss as much as the work ofErkaev et al. (2007) would imply (taking the Roche radius), as theeffect is of the order of a few percent.

3.2 The joined escape of Hydrogen and Oxygen

The computed mass loss m is linked to a mass flux FM given by:FM = m/(4πR2

p). We consider here a mass loss, independently ofthe proportion of Hydrogen and Oxygen atoms lost. Losing justHydrogen atoms and losing Hydrogen and Oxygen atoms does nothave the same consequence for water loss. For example, if only Hy-drogen atoms are lost, losing an ocean means that the planet losesthe mass of Hydrogen contained in one Earth Ocean (9 times lower

that the mass of water in one Earth Ocean). This would change theproportion of H/O thus preventing an eventual recombination ofwater (e.g. for Venus, Gillmann, Chassefiere, & Lognonne 2009).In contrast, if the planet loses Hydrogen and Oxygen in stoichio-metric proportion, losing an ocean means that the planet is losingthe mass of water contained in one Earth Ocean. This is the morefavorable case for water retention because it necessitates a higherenergy to lose one ocean.

In the following, we show that it possible to estimate the pro-portion of escaping Hydrogen and Oxygen atoms. The mass lossflux FM (kg.s−1.m−2) can be expressed in terms of the particle fluxes(atoms.s−1.m−2):

FM = mHFH + mOFO. (4)

The ratio of the escape fluxes of Hydrogen and Oxygen insuch an hydrodynamic outflow can be calculated following Hunten,Pepin, & Walker (1987):

rF =FO

FH=

XO

XH

mc − mO

mc − mH, (5)

where mH the mass of one Hydrogen atom, mO the mass of oneOxygen atom and mc is called the crossover mass and is definedby:

mc = mH +kT FH

bgXH, (6)

where T is the temperature in the exosphere, g is the gravity andb is a collision parameter between Oxygen and Hydrogen. In theOxygen and Hydrogen mixture, we consider XO = 1/3, XH = 2/3,which corresponds to the proportion of dissociated water. Thisleads to XO/XH = 1/2.

When mc < mO, only Hydrogen atoms are escaping and FH =

FM/mH. When mc > mO, Hydrogen atoms drag along some Oxygenatoms and:

FM = (mH + mOrF)FH. (7)

With Equations 5, 6 and 7, we can compute the mass flux ofHydrogen atoms:

FH =FM + mOXO (mO − mH) bg

kT

mH + mOXOXH

. (8)

In order to calculate the flux of Hydrogen atoms, we need anestimation of the XUV luminosity of the star considered, as well asan estimation of the temperature T .

3.3 Physical inputs

We first assume that protoplanetary disks around UCDs dissipateafter 1 Myr (Pascucci et al. 2009)2; this is our “time zero”. Weconsider that when the planet is embedded in the disk it is protectedand does not experience water loss.

We assume that at time zero planets have non-negligible wa-ter content. Planets are thought to acquire water during and afteraccretion via impacts of volatile-rich objects condensed at largerorbital radii. If planets form in-situ in the HZs of UCDs then it maybe difficult to retain water because of the rapid formation timescaleand very high impact speeds (Lissauer 2007; Raymond, Scalo, &

2 Note that this assumption is a strong one, it is very likely that disks livemuch longer than that, ∼ 10 Myr according to Pfalzner, Steinhausen, &Menten (2014).

c© xx RAS, MNRAS 000, 1–11

4 E. Bolmont, F. Selsis, J. E. Owen, I. Ribas, S. N. Raymond, J. Leconte and M. Gillon

Meadows 2007). However, if these planets or some of their con-stituent planetary embryos migrated inward from wider orbital dis-tances then they are likely to have significant water contents (Ray-mond, Barnes, & Mandell 2008; Ogihara & Ida 2009). Althoughthe origin of hot super-Earths is debated (see Raymond, Barnes,& Mandell 2008; Raymond & Cossou 2014), several known close-in planets are consistent with having large volatile reservoirs (e.g.,GJ 1214 b; Rogers & Seager 2010; Berta et al. 2012). We there-fore consider it plausible for Earth-like planets to form in the UCDhabitable zone with a water content comparable to Earth’s surfacereservoir3. Water can also be trapped in the mantle of the planet dur-ing the formation process and perhaps released in the atmosphereat later times through volcanic activity.

A key input into our model is the stellar flux at high ener-gies. There are no observations of the EUV flux of UCDs. We as-sume here that the loss rate of water is not limited by the photo-dissociation of water. This assumes that FUV radiation is suffi-cient to dissociate all water molecules and produce Hydrogen at arate higher than its escape rate into space. X-ray observations withChandra/ACIS-I2 exist for objects from M8 to L5 (e.g., Berger etal. 2010; Williams, Cook, & Berger 2014) for the range 0.1–10 keV(0.1–12.4 nm). This only represents a small portion of the XUVrange considered in Equations 2 and 3. For solar-type stars the fluxin the whole XUV range is 2 to 5 times higher than in the X-rayrange (Ribas et al. 2005). We thus multiply the value correspondingto the X-ray range by 5 and consider it can be used as a proxy for thewhole XUV range. Observations of objects of spectral types M0 toM7 show that the X-ray luminosity scales as 10−3 the bolometric lu-minosity Lbol (Pizzolato et al. 2003). More recent observations fromBerger et al. (2010) and Williams, Cook, & Berger (2014) show thatthe K luminosity of L dwarfs seems to scale as 10−5× Lbol. Some ofthese observations are actually non-detections, so the X-ray lumi-nosity of objects like 2M0523-14 (L2–L3), 2M0036+18 (L3–L4)and 2M1507-16 (L5) must be even lower than 10−5× Lbol. There isno indication of whether the X-ray luminosity varies in time.

We consider two limiting cases for our water loss calculation.In the first we adopt a value of 10−5× Lbol as an upper limit for theXUV luminosity of UCDs. As the bolometric luminosity changeswith time, we consider that the X-ray luminosity does as well. Inthe second case we assume that the X-ray luminosity does not varywith the bolometric luminosity but rather remains constant. Weadopt the value of 1025.4 erg.s−1 = 2.5 × 1018 W from Williams,Cook, & Berger (2014). This value corresponds to a X-ray detec-tion (0.1–10 keV) of the object 2MASS13054019-2541059 AB ofspectral type L2. For each case we then use Equation 3 to calculatethe water loss of a planet of 0.1 M⊕, 1 M⊕ and 5 M⊕.

We compared the XUV flux received by the planets of Figure1 to the one Earth receives. Before reaching the HZ, they are atleast a few times higher than Earth’s incoming XUV flux.

4 WATER LOSS OF PLANETS IN THE UCD HABITABLEZONE

In Section 4.1, we give estimates of the ratio of Hydrogen atomsand Oxygen atoms loss. In Section 4.2, we give the results obtainedby the method exposed in Section 3, then in Section 4.3 we com-pare them with 1D radiation-hydrodynamic mass-loss simulations(Owen & Alvarez 2016).

3 Note that Earth contains several additional oceans of water trapped in themantle (Marty 2012).

0.01 0.10 1 10 100

0.1

1

10

100

1000

���� /��

�����

(���)

0.01 0.10 1 10 1000.0

0.5

1.0

1.5

2.0

���� /��

� �/��

Figure 2. Top panel: Mass of Hydrogen lost as a function of the XUV lu-minosity for an Earth-like planet at 0.01 AU of a 0.08 M� dwarf. The massloss are in unit of Earth Ocean equivalent content of hydrogen (EOH). Theblue dashed line is for the limit case where only Hydrogen atoms escape,which is valid at low irradiation, when the escape is not strong enough todrag Oxygen atoms. The black line accounts for oxygen dragging in thecase where XO = XH/2 = 1/3. The gray line is the same for an atmosphereslightly depleted in Hydrogen (XO = 2XH = 2/3). Bottom panel: Ratio ofthe flux of Oxygen atoms over the flux of Hydrogen atoms. The colors arethe same as for the top panel. rF = FO/FH = 0.5 means that there is stoi-chiometric loss of Hydrogen and Oxygen For the baseline case, rF = 0.27.

4.1 Results on the stoichiometry of H and O loss

We assume ε = 0.1 as introduced in Section 3, we also assume thatthe XUV luminosity is here L0 = 5 × LX = 5 × 1025.4 erg/s andthe planet is at a = 0.01 AU. This is our baseline case. Using thesevalues and Equation 2, we calculate the mass loss flux FM = F0:

F0 =m

4πR2p

= εFXUVRp

4GMp(a/1AU)2 = 1.79 × 10−10 kg.s−1m−2. (9)

Using 1D radiation-hydrodynamic mass-loss simulations (see Sec-tion 4.3 and Owen & Alvarez 2016), we find that the temperatureT of the wind is of the order of 3000 K, which is much lower thanwhat is calculated for hot Jupiters (of the order of 104 K, e.g., Lam-mer et al. 2003; Erkaev et al. 2007; Murray-Clay, Chiang, & Mur-ray 2009).

Using Equation 8 and the estimation of T , we can computethe flux of Hydrogen atoms FH as a function of the XUV lumi-nosity LXUV compared to our baseline case luminosity L0. Figure2 shows the behavior of the mass loss of the atmosphere in unit ofEarth Ocean equivalent content of Hydrogen (EOH) with respect tothe ratio LXUV/L0. This behavior is plotted for two cases: a stoichio-metric mixture of Hydrogen and Oxygen atoms (XO = XH/2 = 1/3)and a mixture slightly depleted in Hydrogen (XO = 2XH = 2/3).We can see that the mass loss is a monotonous function of the

c© xx RAS, MNRAS 000, 1–11

Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs 5

total XUV luminosity, and for both cases it saturates much be-low our baseline case. For a stoichiometric mixture, at a ratioLXUV/L0 ∼ 0.08, the Oxygen atoms start to be dragged along there-fore consuming energy. For a mixture depleted in Hydrogen, Oxy-gen atoms start to be dragged along for lower incoming XUV lu-minosity LXUV/L0 ∼ 0.04.

Here however, for LXUV = L0, we find that one Oxygen atomis lost for about 3.7 Hydrogen atoms: rF = FO/FH = 0.27. Toconclude, for a X-ray luminosity of 1025.4 erg/s, there is no stoi-chiometric loss of Hydrogen and Oxygen. However, the situationis not as catastrophic as it would be if only Hydrogen escaped. Inthe following, we give the Hydrogen lost by the planet. We assumethat rF is constant and the Hydrogen mass loss is given by:

MH = mmH

mH + rFmO, (10)

where m is obtained with Equation 3 and is given in unit of themass of Hydrogen in one Earth Ocean (EOH , which correspondsto ∼ 1.455 × 1020 kg). Hydrogen is the limiting element for therecombination of water, so that the remaining content of Hydro-gen in EOH actually represents the ocean portion we can expect toprecipitate once in the HZ.

4.2 Results with energy limited escape

Figure 3 shows the evolution of the Hydrogen loss from an Earth-mass planet orbiting a 0.04 M� BD as a function of both time andorbital radius (assumed to remain constant). We assumed here sto-ichiometric loss of Hydrogen and Oxygen atoms, i.e., rF = 0.5.Let us consider that the planet has an initial water content compa-rable to Earth’s surface water (MH2O = Mocean = 1.3 × 1021 kg,corresponding to a Hydrogen quantity of ∼ 1.455 × 1020 kg) andis located at 0.01 AU from a 1 Myr-old BD. Figure 3 shows that itwould lose 0.55 EOH in ∼60 Myr (vertical red dashed line). Thus,there would be sufficient water for 45% of an Earth Ocean to pre-cipitate when the planet reaches in the HZ. As the bolometric lumi-nosity decreases with time, the mass loss is more efficient for youngages. This planet could therefore be considered a potentially habit-able planet, assuming an appropriate atmospheric composition andstructure.

Figure 4 shows the water loss for planets of 0.1 M⊕, 1 M⊕ and5 M⊕ orbiting UCDs of different masses at 0.01 AU. The figureshows how much water was lost by the time each planet reachedthe HZ. This time is ∼ 3 Myr for a BD of 0.01 M� and ∼ 300 Myrfor a dwarf of 0.08 M�. The calculations were done for both cases:LX/Lbol = 10−5 (red symbols) and LX = 1025.4 erg/s (blue symbols)and for two assumptions about the escape of Hydrogen and Oxygenatoms: a) rF = 0.5 (stoichiometric loss) and b) rF = 0.27, which iswhat is calculated for the baseline case (see Section 3).

Assuming LX = 1025.4 erg/s, we find that planets orbiting moremassive UCDs lose more water. This is mainly because of the muchlonger time spent by those planets interior to the HZ. For LX/Lbol =

10−5, planets lose even more water than for LX = 1025.4 erg/s be-cause their hosts were more luminous at earlier age.

We also find that lower-mass planets lose their water at ahigher rate than higher-mass ones: for an Earth-like composi-tion (Fortney, Marley, & Barnes 2007), the quantity R3

p/Mp(∝1/density) decreases when Mp increases, so Equation 2 tells usthat less water is lost for more massive planets. In other words, theincrease of gravitational energy is not compensated by the highercross section.

Figure 4a) provides a best case scenario for water retention

0.1 EOH

0.5 EOH

1 EOH

HZ inner edge

Figure 3. Map of Hydrogen loss (in EOH) as a function of the age of theBD (0.04 M�) and the orbital distance of the planet. We assumed here sto-ichiometric loss of Hydrogen and Oxygen atoms (rF = 0.5). White linescorrespond, from left to right, to a loss of 1 EOH , 0.5 EOH et 0.1 EOH . Thegrey line corresponds the inner edge of the HZ: the HZ lies above this line.Here the X-ray luminosity evolves as 10−5 × Lbol and ε = 0.1.

(rF = 0.5). This calculation assumes LX/Lbol = 10−5 and an initialwater surface water budget of one Earth Ocean for all planets. Wefind that 1 M⊕ planets orbiting BDs of mass lower than 0.05 M�reach the HZ with a non-negligible water content. For planets moremassive than 1 M⊕, this limit can be pushed to 0.06 M�. However,assuming LX = 1025.4 erg/s allows to push this limit for the rangeof planetary mass considered here to 0.08 M�.

Figure 4b) represents a more likely scenario than a). In thisscenario, the escape is not quite strong enough to drag along ev-ery Oxygen atoms: around an atom of Oxygen is lost with ev-ery 3.7 atoms of Hydrogen (rF = 0.27). It shows us that assum-ing LX/Lbol = 10−5 and an initial Earth’s ocean content, 1 M⊕planets orbiting BDs of mass lower than 0.04 M� reach the HZwith a non-negligible water content. For planets more massive than1 M⊕, this limit can be pushed to 0.05 M�. However, assumingLX = 1025.4 erg/s allows to push this limit for the range of planetarymass considered here to 0.07 M�.

The ratio of loss of Oxygen atoms with respect to Hydrogenatoms was calculated for LX = 1025.4 erg/s and the results dis-played in Figure 4b) do not take into account that as time passesthe atmosphere is getting depleted in Hydrogen atoms. This hasseveral consequences. First, as Figure 2 shows, the escape rate islower when the atmosphere is depleted in Hydrogen. So, our re-sults in Figure 4b) for LX = 1025.4 erg/s (blue circles, squares andtriangles) actually overestimate the mass loss. The results shouldbe somewhere between what was calculated for rF = 0.5 and forrF = 0.27. Second, for LX/Lbol = 10−5, LXUV is initially larger thanL0, so the ratio of loss of Hydrogen and Oxygen atoms is initiallycloser to stoichiometry (see Figure 2) than what was calculated forLX = 1025.4 erg/s. Furthermore, as was discussed in the first point,the escape rate also decreases due to the depletion in Hydrogenatoms. Consequently, for LX/Lbol = 10−5, the results obtained withan energy limited escape calculation are again overestimated. Andthe mass loss should be somewhere in between what was calculatedfor rF = 0.5 and for rF = 0.27.

At larger orbital radius less water is lost, for two reasons. First,as the planet is farther from the UCD, the mass loss rate is lower

c© xx RAS, MNRAS 000, 1–11

6 E. Bolmont, F. Selsis, J. E. Owen, I. Ribas, S. N. Raymond, J. Leconte and M. Gillon

Mp = 5.0 M⊕

Mp = 0.1 M⊕

Mp = 1.0 M⊕

Hyd

rogen

loss

(EO

H)

BD mass (M⊙)

0.00 0.02 0.04 0.06 0.08

0.0

0.5

1.0

1.5

2.0

LX = 1025.4 erg/s

LX/Lbol = 10-5

Energy limited escape

Mp = 1.0 M⊕ Hydrodynamical code

BD mass (M⊙)

0.00 0.02 0.04 0.06 0.08

a) rH = 0.5 (stoichiometric loss) b) rH = 0.27

Figure 4. Water mass loss (in units of Earth’s ocean) as a function of the mass of the BD for a planet of different masses at 0.01 AU. A mass loss superiorto 1 Earth’s ocean means that the planet considered here has lost all of its water. The results obtained with the energy limited escape calculations for 1 M⊕are compared with those obtained with the 1D radiation-hydrodynamic code (red and blue crosses; Owen & Alvarez 2016). In panel a), we assumed astoichiometric loss of Hydrogen and Oxygen atoms and in panel b) we assumed rF = 0.27 as calculated in Section 3.

(see Equation 2). Second, a more distant planet reaches the HZ ear-lier in the UCD’s evolution (see Figure 3). For planets around BDs,this means that the planet will stay less time in the HZ. However,for a M-dwarf of 0.08 M�, the HZ does not continue to shrink in-definitely (see Figure 1). In this case, the mass of the dwarf is highenough that late in its evolution, its core reaches a high enoughtemperature to initiate Hydrogen fusion. Bolmont, Raymond, &Leconte (2011) therefore showed that such a planet would remainin the HZ up to 10 Gyr. For example, a planet at a semi-major axisof 0.019 AU around a 0.08 M� dwarf, would enter the HZ at anage of 55 Myr, with 0.43 EOH if LX/Lbol = 10−5 and 0.95 EOH ifLX = 1025.4 erg/s. These objects are therefore interesting targets forastrobiology.

As the maximum of the water loss occurs around an UCD of0.08 M�, we can also estimate the minimum semi-major for whichplanets can still have a fraction of their initial Earth Ocean. ForLX/Lbol = 10−5, we find that planets farther away than 0.017 AUcan retain a fraction of their initial water reservoir whatever theirmass (Mp > 0.1 M⊕) and whatever the assumption made on theratio of the molecules escape (rF > 0.27). For LX = 1025.4 erg/s, wefind that planets farther away than 0.0103 AU can retain a fractionof their initial water reservoir whatever their mass (Mp > 0.1 M⊕)and whatever the assumption made on the ratio of the moleculesescape (rF > 0.27).

4.3 Results with a hydrodynamical code

In order to guide our calculations, we perform a set of 1D radiation-hydrodynamic mass-loss simulations based on the calculations ofOwen & Alvarez (2016). The simulations are similar in setup tothose described by Owen & Alvarez (2016), where we perform1D spherically symmetric simulations using a modified version ofthe zeus code (Stone & Norman 1992; Hayes et al. 2006), along astreamline connecting the star and planet. We include tidal gravity,but neglect the effects of the Coriolis force as it is a small while

the outflow remains sub-sonic (Murray-Clay, Chiang, & Murray2009; Owen & Jackson 2012). In order to get a sense of the relia-bility of our simple calculations, we consider only the case of the1 M⊕, 1 R⊕ planet at an orbital separation of 0.01 AU. The radialgrid is non-uniform and consists of 192 cells, the flow is evolvedfor 40 sound crossing times such that a steady state is achieved(which is checked by making sure the pseudo-Bernoulli potentialand mass-flux are constant). We explicitly note that these simula-tions do not include line cooling from Oxygen that maybe impor-tant in these flows, and as such these calculations should be consid-ered as a guide with which to compare the standard energy-limitedcalculations. Line cooling from Oxygen would necessarily reducethe temperature and mass-loss rate. We can use the simulations tocalculate the efficiency (ε) parameter along with the correspond-ing mass loss. Figure 5 shows the variation of ε with the incomingXUV flux, we note that the tidal gravity places a negligible role inchanging the mass-loss rates with stellar mass. At high fluxes theefficiency drops off due to the increased radiative cooling that canoccur as the flows get more vigorous and dense. The drop off at lowfluxes is simply caused by the fact that the heating rate is not strongenough to launch a powerful wind. At high fluxes the temperaturepeaks at a radii ∼ 1.2−1.4 R⊕, indicating some of the XUV photonsare absorbed far from the planet, increasing its effective absorbingarea, but at low fluxes the temperature peaks close to 1 R⊕. Figure 5shows that for a X-ray luminosity of LX = 1025.4 erg/s (correspond-ing to a flux in XUV of ∼ 450 erg/s/cm2), we slightly overestimatedε by a factor of ∼ 1.17.

Figure 4 shows that the results obtained with a simple energy-limited escape calculation are of the same order of magnitude aswith those obtained with an explicit hydrodynamic model (crossesin Figure 4). However, Figure 4 also shows that our model overes-timates mass loss by a factor of ∼ 1.17 (for LX = 1025.4 erg/s, inagreement with Figure 5) to ∼ 2 (for LX/Lbol = 10−5).

When we assume a stoichiometric loss of Hydrogen and Oxy-gen atoms (rF = 0.5), we find that only the 1 M⊕ planet orbiting the

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Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs 7

10 -2 10 -1 10 0 10 1 10 2 10 3 10 4

Flux [erg s -1 cm -2 ]

10 -3

10 -2

10 -1

10 0

ϵ

Lx = cst

Lx � Lbol

Figure 5. Variation of the efficiency ε with respect to the incoming fluxobtained with the model from Owen & Alvarez (2016), we note the stel-lar mass makes very little difference in the obtained mass-loss rates. Thehorizontal dashed line represents the value of ε used in our energy-limitedescape calculations. The vertical dotted line represents the XUV flux corre-sponding to LX = 1025.4 erg/s for an orbital distance of 0.01 AU.

UCD of 0.08 M� loses more than one EOH (for LX/Lbol = 10−5, seeFigure 4a), red cross). For a BD of mass 0.04 M�, the planet onlyloses about 0.30 EOH , which means that about 70% of an EarthOcean could precipitate when reaching the HZ.

When we assume that rF = 0.27, we find that planets aroundBDs of mass inferior to 0.05 M� can retain a fraction of their initialwater reservoir. For a BD of mass 0.04 M�, the planet now losesabout 0.50 EOH , which means that about 50% of an Earth Oceancould precipitate when reaching the HZ. We remind here that dueto the depletion of Hydrogen in the atmosphere, the more probablewater loss would between what we obtain for rF = 0.5 and forrF = 0.27. We thus expect this planet to have between 50% and70% of its initial water reservoir when reaching the HZ.

Consequently, the conclusions remain the same as in Section4.2: close-in planets orbiting at 0.01 AU around a BD of mass∼ 0.04−0.05 M� are the good candidates for the search of habitablecandidates: they lose less than an Earth Ocean before reaching theHZ, they can stay in the HZ a non-negligible time and they are eas-ily detectable and characterizable. If the planets are located fartheraway, the best candidates would orbit UCDs of 0.08 M�.

5 IMPLICATION FOR THE TRAPPIST-1 PLANETS

The three planets of the TRAPPIST-1 system (Gillon et al. in press)are Earth-size planets, and thus probably rocky (Weiss & Marcy2014; Rogers 2015). They orbit a M8-type dwarf of 0.08 M�.TRAPPIST-1b is located at ab = 0.01111 AU, TRAPPIST-1c atac = 0.01522 AU. The orbit of TRAPPIST-1d is poorly con-strained, however it is farther away than ad = 0.022 AU. The irra-diation of the planets are respectively: 4.25 S ⊕, 2.26 S ⊕ and 0.02–1 S ⊕, where S ⊕ is the insolation received by the Earth. ThereforeTRAPPIST-1d could be in the HZ. The age of the system has beenestimated to be more than 500 Myr. The structural evolution gridswe use for a dwarf of 0.08 M� (Chabrier & Baraffe 1997) show thatthe luminosity and radius of TRAPPIST-1 correspond to a body of

Hyd

rogen

loss

(EO

H)

Age (Myr)

4

0

1

2

3

4

0

1

2

3

0 200 400 600 800 1000

Hyd

rogen

loss

(EO

H)

Trappist 1d

Trappist 1b

Trappist 1c

Trappist 1d

Trappist 1b

Trappist 1c

THZ, d

LX = 1025.4 erg/s

LX/Lbol = 10-5

Figure 6. Hydrogen loss (colored regions) as a function of time for theplanets of TRAPPIST-1. The colored regions are delimited by what is ob-tained with rF = 0.27 (upper line) and rF = 0.5 (lower line) for planet bin full lines, planet c in dashed lines and planet d in dashed-dotted lines.The top panel corresponds to LX/Lbol = 10−5 and the bottom panel toLX = 1025.4 erg/s. The results were obtained with the energy limited es-cape calculations for the radiuses and semi-major axes of the planets givenby Gillon et al. (in press). The long- dashed line shows the lower limit of theestimation of the age of the star (Gillon et al. in press). The dashed dotteddotted dotted line represents the time for which our model of the 0.08 M�dwarf has the same luminosity and radius as the observed stellar valuesfrom Gillon et al. (in press). The dashed-dotted vertical line represents thetime TRAPPIST-1d reaches the HZ.

∼ 400 Myr, which is lower than the estimated age of the system, butnonetheless of the same order of magnitude. This is consistent withthe fact that evolution models seem to under-estimate the luminos-ity of low-mass objects (Chabrier, Gallardo, & Baraffe 2007).

Figure 6 shows the mass loss of the TRAPPIST planets as afunction of time, as calculated in the energy limited escape sce-nario. The colored regions delimit the water loss calculated withrF = 0.27 and rF = 0.5 and thus delimit the regions where thevalue of the expected Hydrogen loss should be. We assumed thatthe semi-major axes of the planets remain constant throughout theevolution.

Tables 1 and 2 summarize the results for different ages of thedwarf: the age THZ, d = 37.2 Myr at which TRAPPIST-1d entersthe HZ, the age of the dwarf as estimated with the evolution grids,the estimated lower limit of the age of the dwarf of Gillon et al.(in press) and an age of 1000 Myr. Assuming LX/Lbol = 10−5, wefind that the two inner planets of the system are completely des-

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8 E. Bolmont, F. Selsis, J. E. Owen, I. Ribas, S. N. Raymond, J. Leconte and M. Gillon

Table 1. Remaining percentage of an initial EOH for TRAPPIST-1 planetsfor LX/Lbol = 10−5.

Age (Myr) TRAPPIST-1b TRAPPIST-1c TRAPPIST-1d

THZ, d < 12% 18–51% 63–78%400 0% 0% 19–52%500 0% 0% 14–49%

1000 0% 0% 0–38%

Table 2. Remaining percentage of an initial EOH for TRAPPIST-1 planetsfor LX = 1025.4 erg/s.

Age (Myr) TRAPPIST-1b TRAPPIST-1c TRAPPIST-1d

THZ, d 90–94% 94–97% 98–99%400 < 33% 37–63% 72–84%500 < 16% 21–54% 65–79%

1000 0% < 7% 30–59%

iccated at the possible ages of the dwarf (400 and 500 Myr). As-suming that TRAPPIST-1d stops losing its water when it reachesthe HZ, it should still have between 63 and 78% of its initial EarthOcean. However, even if we assume that the planet continues los-ing its water in the HZ, it would still have more than 20% of itsinitial Earth Ocean at the estimated ages of the dwarf. AssumingLX = 1025.4 erg/s, the situation is much more favorable. The twoinner planets could have retained a small fraction of their poten-tial initial Earth Ocean at the possible ages of the dwarf. The ob-servation with transit spectroscopy of the atmospheres of the twoinner planets with facilities such as the JWST would therefore al-low us to constrain the XUV luminosity of the dwarf. AssumingLX = 1025.4 erg/s, we find that TRAPPIST-1d is very likely to havea non-negligible water content. Indeed, if we consider that it stopslosing its water when it reaches the HZ, it should still have morethan 98% of an initial Earth Ocean. If we assume that it continueslosing its water in the HZ, it would still have more than 70% of itsinitial Earth Ocean at the estimated ages of the dwarf. Even if thestar is 1 Gyr old, it would still have a minimum of 30% of its initialEarth Ocean. Note here, that the mass loss calculated with the hy-drodynamical code would give us results between 1.17 and 2 timeslower than what is given here. The estimations of Tables 1 and 2are therefore an underestimation of the expected water reservoir.

The orbit of TRAPPIST-1d is not well constrained, but thereis a high probability that it is in the HZ. This calculation showsthat there is a non-negligible probability that this planet was ableto retain a high fraction of an eventual water reservoir of one EarthOcean, which makes it a very interesting astrobiology target. As-suming rF = 0.27, we can calculate the maximum amount ofDioxygen O2 left on the planet. For LX = 1025.4 erg/s, the pres-sure of O2 is respectively PO2 = 3, 27, 34 and 69 bar at t = THZ, d,400 Myr, 500 Myr and 1000 Myr. For LX/Lbol = 10−5, the pressureof O2 left on the planet is respectively PO2 = 36, 79, 84 and 97 barat t = THZ, d, 400 Myr, 500 Myr and 871 Myr, i.e. when all Hy-drogen escaped. Belu et al. (2013) showed that the atmosphere ofthe planets of TRAPPIST-1 could be characterizable with facilitieslike JWST. The observation of these planets could therefore bringus informations on water delivery during the formation processesand their capacity to retain water.

Hyd

rogen

(EO

H)

Age (Myr)

Hyd

rogen

(EO

H)

LX = 1025.4 erg/s

LX/Lbol = 10-5

Hydrogen lost

Hydrogen available from photolysis

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

ε!=0.10

ε!=0.18

ε!=0.30

ε!=0.50

ε!=1.00

ε!=0.10

ε!=0.18

ε!=0.30ε!=0.50

ε!=1.00

0 10 20 30 40 50 60

Figure 7. Hydrogen loss (as calculated in Section 4.2; colored regions de-limited with full lines: top line rF = 0.27, bottom line rF = 0.50) andHydrogen created by photolysis (dashed lines) as a function of time for anEarth-mass planet orbiting a 0.04 M� BD at 0.01 au. The top panel corre-sponds to LX = 1025.4 erg/s and the bottom panel to LX/Lbol = 10−5. TheHydrogen quantity created by photolysis was calculated assuming a differ-ent efficiency of the photolysis process εα.

6 WHY THIS RESULT LIKELY OVERESTIMATESWATER LOSS

In this section, we show that the thought process we performed inthe previous section, both following the standard way of computingmass loss (as in Barnes & Heller 2013) and using simple radiation-hydrodynamics calculations (as in Owen & Alvarez 2016) may ac-tually be overestimating the mass loss.

• The time of the disk dispersal we consider here might be tooshort for such low mass objects. The evolution of disks aroundUCDs is not well constrained, however it is reasonable to assumethey dissipate between 1 Myr and 10 Myr (disks around low massstars tend to have longer lifetimes, e.g. Pascucci et al. 2009; Liu etal. 2015; Downes et al. 2015). Disks around UCDs could very welldissipate at an age of 10 Myr. As young UCDs are brighter than oldUCDs, a later dissipation of the disk would mean that a planet isexposed less time and to a weaker XUV radiation, meaning that theplanet would lose less water than what was calculated in this work.

For example, using the energy limited escape calculation and as-suming a stoichiometric loss of Hydrogen and Oxygen atoms, aplanet orbiting a 0.04 M� BD at 0.01 AU would only lose 25% ofits initial Earth Ocean by the time it reaches the HZ if the disk dis-sipates at 10 Myr (instead of 55% if the disk dissipates at 1 Myr,see Figure 4, for LX/Lbol < 10−5). And a planet orbiting a 0.06 M�BD at 0.01 AU would lose only 77% of its initial Earth Ocean if thedisk dissipates at 10 Myr (instead of being totally desiccated if thedisk dissipates at 1 Myr). Under this assumption of a longer livedprotoplanetary disk, this planet could therefore have surface liquidwater when in the HZ.• UCDs might be too cold to emit the FUV radiations needed to

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Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs 9

photo-dissociate water molecules. This would mean that the waterloss would be less efficient. Recent observations of 11 M-dwarfsby France et al. (2016) showed that the estimated energy flux inthe Lyman-alpha band is equal to the flux in the XUV range. Usingthis constraint, we can estimate the quantity of Hydrogen producedby photodissociation. Figure 7 shows the quantity of Hydrogen lostaccording to our calculations of Section 4.2 and the quantity ofHydrogen available.

If all the incoming FUV photons do photolyse H2O moleculeswith a 100% efficiency (εα = 1) and all the resulting Hydrogenatoms remain available for the escape process then photolysis doesnot appear to be limiting the loss process. The production rate ofHydrogen atoms exceeds by a factor of ∼ 4 the computed thermalloss assuming an Hydrogen and Oxygen mixture and rF = 0.27.In reality, however, only a fraction of the incoming FUV actuallyresults in the loss of an Hydrogen atom. Part of the incoming pho-tons are absorbed by other compounds (in particular Hydrogen inthe Lyman alpha line) or backscattered to space. Then, productsof H2O photolysis (mainly OH and H) recombine through variouschemical pathways. If the efficiency εα is less than about 20% thenthe loss rate becomes photolysis-limited. Although efficiency cal-culations would require detailed FUV radiative transfer and photo-chemical schemes, we can safely argue that efficiencies much lowerthan 20% can be expected.

It is important to stress that the loss is likely to be photolysis-limited, which would allow us to calculate upper limits of the losswithout the need of complex thermal and non-thermal escape mod-els. At this point the FUV flux, which is the key input for H2O pho-tolysis, is only estimated based on the XUV/FUV ratio measuredon earlier-type stars. Measuring the FUV of UCDs could allow usto put strong constraints on the water erosion on their planets.

• The XUV flux considered here might be much higher thanwhat is really emitted by UCDs. Indeed, all Chandra observationsof X-ray emissions of low mass objects (e.g. Berger et al. 2010;Williams, Cook, & Berger 2014) are actually non-detection for theUCD range. New estimations from Osten et al. (2015) show thatfound upper limits for the X-ray luminosity for the object Luh-man 16AB (WISE J104915.57–531906.1, L7.5 and T0.5 spectraltypes) are lower than what we used in this study: LX < 1023 erg/sor LX/Lbol < 10−5.7. Besides, Mohanty et al. (2002) show that inBDs’ cool atmospheres the degree of ionization is very low so it isvery possible that the mechanisms needed to emit X-rays are notefficient enough to produce the fluxes considered in this work. Inwhich case, the computed mass loss would be lower than what wecalculated here.

• We consider that the planets have an initial content of oneEarth’s ocean, but it might be more. Both on the observational andtheoretical side, it has been shown that planets could even havea large portion of their bulk made out of water (Ocean planets,hypothesized by Kuchner 2003; Leger et al. 2004). For example,Kaltenegger, Sasselov, & Rugheimer (2013) have identified Kepler-62e and 62f to be possible ocean planets. Furthermore, as discussedin Marty (2012), a large part of water can be trapped in the man-tle to be released by geological events during the evolution of theplanet, allowing a replenishment of the surface water content.

• Johnson, Volkov, & Erwin (2013) showed using molecular-kinetic simulations that the mass loss saturates for high incomingenergy, which could mean that in our case the mass loss would besmaller than what we calculated. However, their results should beapplied to our specific problem in order to be sure.

7 CONCLUSIONS

Unlike Barnes & Heller (2013), we find that planets in the HZsof UCDs should in most cases be able to retain their water. Themain differences between Barnes & Heller (2013) and our workare the following. First, they used for the XUV radiation an ob-served upper limit for early-type M-dwarfs (Pizzolato et al. 2003,which was the only available study at the time) for which the XUVluminosity scales as 10−3 times the bolometric luminosity. We usedhere more recent estimates of X-ray emission of later-type dwarfs,which show that UCDs emit much less X-rays than earlier-type M-dwarfs (Berger et al. 2010; Williams, Cook, & Berger 2014; Os-ten et al. 2015). Second, in addition to the standard method used inBarnes & Heller (2013), we also tested the robustness of our resultsobtained with an energy-limited escape model with those obtainedwith 1D radiation-hydrodynamic mass-loss simulations (Owen &Alvarez 2016). We found a good agreement between the two meth-ods. This allowed us to have a better estimate of the fraction ofthe incoming energy that is transferred into gravitational energythrough the mass loss (ε). Thanks to this estimation of ε, we foundthat a standard energy-limited escape model gives actually an over-estimate of the water loss (by a factor 1.17 to 2). Third, Barnes& Heller (2013) used a larger XUV cross-section for the planets.However, using our hydrodynamical model, we found that for suchsmall planets the XUV cross-section is very similar to the radiusof the planet and only causes a difference of a few percents in thequantity of water lost. Fourth, they considered a loss of only Hydro-gen atoms, while in this work we estimated the ratio of the escapefluxes of both Hydrogen and Oxygen atoms. We found that in theconfiguration considered here, Oxygen atoms are dragged away bythe escaping Hydrogen atoms, which is more favorable for waterretention.

Considering a very unfavorable scenario for water retention– complete dissociation of water molecules and energy limited es-cape – and assuming that the X-ray luminosity of the UCD scalesas 10−5 its bolometric luminosity, we find that planets orbiting at0.01 AU around BDs of mass lower than 0.05 M� can retain aninitial Hydrogen reservoir (here equal to the Hydrogen reservoir inone Earth Ocean) when interior to the HZ. When reaching the HZ,the remaining Hydrogen can recombine with Oxygen to form watermolecules that can then condense. Using a hydrodynamical model,this limit is pushed to 0.07 M�. Assuming a constant X-ray lumi-nosity of 1025.4 erg/s, we find that for both models, planets aroundall BDs could retain a non-negligible fraction of their initial waterreservoir. Even a planet at 0.01 AU around M-dwarf of 0.08 M�could retain a small fraction of its initial water reservoir.

Bolmont, Raymond, & Leconte (2011) showed that the moremassive the BD, the longer a close-in planet spends in the HZ. Thiswork therefore shows that, at worst, there is still a sweet spot forpotential life around BDs: planets orbiting BDs of masses between∼ 0.04 M� and ∼ 0.06 M� could have surface liquid water ANDhave it for a long time (& 1 Gyr, according to Bolmont, Raymond,& Leconte 2011). Of course, if one of the mechanisms consideredhere does not take place, or if the real XUV flux of BDs is lowerthan the upper value we considered, as we discussed in the previousSection 6, the sweet spot for life could widen towards the massiveBDs. The low-mass BDs will always suffer from the fact that theycool down very fast and that at best, planets spend a few 100 Myrin the HZ. Even though this could be enough time for life to appear,its potential detectability would be a rare event. The high mass BDsare interesting targets but in this scenario, planets at 0.01 AU couldhave a rather small water reservoir when entering the HZ. However

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10 E. Bolmont, F. Selsis, J. E. Owen, I. Ribas, S. N. Raymond, J. Leconte and M. Gillon

planets farther away (> 0.017 AU for Earth-size planets around a0.08 M�) could have a non-negligible water reservoir when enter-ing the HZ.

We considered here close-in planets. Due to the planets prox-imity to the star, they are likely to be tidally locked when reachingthe HZ. As was shown in Yang, Cowan, & Abbot (2013), due to thepresence of clouds at the substellar point of tidally-locked planets,planets could host surface liquid water at distances closer than theusual HZ inner edge. Consequently, according to Bolmont, Ray-mond, & Leconte (2011), planets closer than 0.01 AU might beeven better targets (they would stay in the HZ for a longer time).However, these planets being slightly closer, they are expected tolose more water than what was calculated for 0.01 AU. For exam-ple, an energy-limited escape calculation for a planet with an initialsemi-major axis of 0.007 AU around a 0.04 M� BD would give awater loss of about 70% of Earth’s ocean (see Figure 3, assumingrF = 0.5). The more reliable 1D radiation-hydrodynamic simula-tions would therefore calculate a loss of about 0.35 EOH , whichmeans that the planet could retain a non-negligible fraction of itsinitial water content and have liquid water when in the HZ. Fur-thermore, as the inner edge of the HZ is closer to the BD for thesetidally-locked planets (Yang, Cowan, & Abbot 2013), it also meansthat they reach the HZ earlier, so that they would probably lose evenless water.

We only consider here quiescent energetic emissions. How-ever BDs could emit energetic flares for a significant fraction oftheir lifetime in the Hα emission line and in the U-band (Schmidtet al. 2014; Schmidt 2014). This would also endanger the survivalof a water reservoir. Gizis et al. (2013) showed that these flares canbe as frequent as 1-2 times a month (e.g., the L1 dwarf W1906+40).W1906+40 experienced a white flare during ∼ 2 hours, which re-leased an energy of 1031 erg (in a band 400–900 nm). Let us con-sider here that the flare released in the XUV range 20% of the en-ergy it released in the 400–900 nm band (this proportion has beenmeasured for Sun flares in Kretzschmar 2011). This flare wouldthen correspond to an energy ∼ 20 times what we considered forthe quiescent emission in the case of the constant XUV emission.Using the energy limited escape formula, we find that if such a flarehappened during 2 hours every months (as could be the case forW1906+40), a 1 M⊕ planet at 0.01 AU would lose an Earth’s oceanin ∼ 1 Gyr (assuming stoichiometric loss of Hydrogen and Oxy-gen atoms). Taking flares into account would then reduce slightlythe lifetime of the water reservoir: instead of entering the HZwith 0.85 EOH , the 1 M⊕ planet at 0.01 AU (MBD = 0.04 M�,LX = 1025.4 erg/s, blue squares on Figure 4a), would enter with0.79 EOH . Taking into account the flares therefore do not changesignificantly the results.

Of course, water retention is not synonymous with habitabil-ity. Given that BD’s HZs are very close-in, HZ planets feel strongtidal forces. This may affect their ability to host surface liquid wa-ter. For example, a lone planet would likely be in synchronous ro-tation. One can imagine that all liquid water might condense ontothe night side (cold trap). However, this can be avoided if the atmo-sphere is dense enough to efficient redistribute heat (e.g., Leconte etal. 2013). In multiple-planet systems, a HZ planet’s eccentricity canbe excited and lead to significant tidal heating (Barnes et al. 2009,2010; Bolmont et al. 2013; Bolmont, Raymond, & Selsis 2014). Insome cases tidal heating could trigger a runaway greenhouse state(Barnes & Heller 2013). In other situations, such as in the outerparts of the HZ or even exterior to the HZ, tidal heating may bebeneficial by providing an additional source of heating and perhapseven by helping to drive plate tectonics (Barnes et al. 2009).

Despite the lack of knowledge about escape mechanisms, inparticular about the way Hydrogen and Oxygen conjointly escape(or not), we find that there are possibilities that planets aroundUCDs might arrive in the HZ with an important water reservoir.As shown in Section 6, there might be even more possibilities if theloss of Hydrogen is photolysis-limited, which would happen if theefficiency of this process is below 20%. We also find that the twoinner planets of the system TRAPPIST-1 (Gillon et al. in press)might be desiccated (the presence of water would actually bring usinformations about the dwarf’s XUV luminosity) but that the thirdplanet might still have an important water reservoir. Furthermore,planets in the HZs of BDs may be easy to detect in transit due totheir large transit depths and short orbital periods (at least for suffi-ciently bright sources; Belu et al. 2013; Triaud et al. 2013). Giventheir large abundance in the Solar neighborhood (∼1300 have beendetected as of today according to http://DwarfArchives.org),such planets may be among the best nearby targets for atmosphericcharacterization with the JWST.

ACKNOWLEDGMENTS

The authors would like to thank Rory Barnes and Rene Heller forbringing this subject to their attention.

I. R. acknowledges support from the Spanish Ministryof Economy and Competitiveness (MINECO) through grantESP2014-57495-C2-2-R.

S. N. R. and F. S. acknowledge support from the ProgrammeNational de Planetologie (PNP). S. N. R. thanks the Agence Na-tionale pour la Recherche for support via grant ANR-13-BS05-0003-002 (project MOJO).

J. E. O. acknowledges support by NASA through Hubble Fel-lowship grant HST-HF2-51346.001-A awarded by the Space Tele-scope Science Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., for NASA, undercontract NAS 5-26555.

E. B. acknowledges that this work is part of the F.R.S.-FNRSExtraOrDynHa research project.

M. G. is Research Associate at the F.R.S.-FNRS.

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