Thermal escape from extrasolar giant planets
TThermal escape from extrasolar giant planets
T. T. Koskinen , P. Lavvas , M. J. Harris , R. V. Yelle ABSTRACT
The detection of hot atomic hydrogen and heavy atoms and ions at high altitudesaround close-in extrasolar giant planets (EGPs) such as HD209458b imply that theseplanets have hot and rapidly escaping atmospheres that extend to several planetaryradii. These characteristics, however, cannot be generalized to all close-in EGPs. Thethermal escape mechanism and mass loss rate from EGPs depend on a complex inter-play between photochemistry and radiative transfer driven by the stellar UV radiation.In this work we explore how these processes change under different levels of irradi-ation on giant planets with different characteristics. We confirm that there are twodistinct regimes of thermal escape from EGPs, and that the transition between theseregimes is relatively sharp. Our results have implications on thermal mass loss ratesfrom different EGPs that we discuss in the context of currently known planets and thedetectability of their upper atmospheres.
Subject headings: extrasolar planets — hydrodynamics — atmospheric escape
1. Introduction
The upper atmospheres of three different EGPs HD209458b, HD189733b, and WASP-12bwere recently probed by UV transit observations obtained by the Hubble Space Telescope (HST)(Vidal-Madjar et al. 2003, 2004; Linsky et al. 2010; Fossati et al. 2010; Lecavelier des Etangs et al.2010, 2012). These observations indicate that close-in EGPs such as HD209458b are surroundedby a hot thermosphere composed of atomic hydrogen that extends to several planetary radii andprovides the required line of sight (LOS) optical depth in atomic resonance lines to explain largetransit depths (Koskinen et al. 2010, 2013a,b). It is also widely believed that the atmospheres ofclose-in EGPs undergo hydrodynamic escape (e.g., Lammer et al. 2003; Yelle 2004). Lunar and Planetary Laboratory, University of Arizona, 1629 E. University Blvd., Tucson, AZ 85721–0092;[email protected] Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK Groupe de Spectrométrie Moléculaire et Atmosphérique UMR CNRS 6089, Université Reims Champagne-Ardenne, 51687 Reims, France a r X i v : . [ a s t r o - ph . E P ] D ec ∼ X = GM p m / kTr exo is large,between 250–450, and thermal escape is firmly in the classical Jeans regime based on kinetic theory(Volkov et al. 2011a,b). In this case escape does not affect the temperature and density structure ofthe atmosphere significantly, and proceeds on particle by particle basis from the exobase into thenearly collisionless exosphere. Given this background, it is interesting to assess how the escapemechanism and thermal escape rates on different EGPs orbiting Sun-like stars vary with orbitaldistances. The upper atmospheres of close-in giant planets are heated by the stellar UV radiation,and at some orbital distance the flux should be high enough to cause a transition from kineticescape to hydrodynamic escape.Koskinen et al. (2007a,b) used results from a three-dimensional model for the thermospheresof EGPs to argue that this transition, which is controlled by the dissociation of H below theexobase and the subsequent lack of efficient infrared cooling by H + , occurs within a surprisinglynarrow range of orbital distances between 0.1 and 0.2 AU for Jupiter-type planets orbiting Sun-like stars. In other words there is a relatively sharp limit to the incoming UV flux that causes theatmosphere to expand and begin to undergo rapid escape. These calculations also indicate that theupper atmospheres of close-in EGPs are quite resilient – they remain relatively cool and stable atsurprisingly small orbital distances. The results provide an important perspective on the predictedproperties of the several hundreds of known EGPs, and can be used to guide statistical studies ofmass loss from EGPs (e.g., Lecavelier des Etangs 2007; Lammer et al. 2009) as well as to searchfor good targets for future observations of their upper atmospheres. 3 –Previous work by Koskinen et al. (2007a,b) relied on a model composed exclusively of hy-drogen and helium. However, recent calculations have shown that the photochemistry of carbonand oxygen species may play an important role in controlling the composition in the upper at-mosphere of HD209458b (Moses et al. 2011). In particular, complex photochemistry in a solarcomposition atmosphere can lead to significant dissociation of H by OH radicals at a relativelydeep pressure level of 1 µ bar. It should be noted that both on Jupiter and Saturn the thermosphereis composed mostly of H up to the exobase that is located at a pressure of a few pbar, so this isanother important difference between close-in EGPs and the giant planets in the solar system.In this paper we update the previous calculations of Koskinen et al. (2007a,b) to includemore complex photochemistry. More specifically, we study the dissociation chemistry of H asa function of orbital distance on EGPs by relying on existing thermal structure calculations andnew photochemical calculations. We use the results to assess the escape mechanism and mass lossrates under different levels of irradiation based on new theoretical results (Volkov et al. 2011a,b)and their application to close-in EGPs (Koskinen et al. 2013a,b). We then proceed to generalizethe results to a sample of known EGPs to make specific predictions about the nature of their upperatmospheres.
2. Methods
We studied the dissociation chemistry of H by using the photochemical model of Lavvaset al. (2008a,b) that was recently modified to simulate the atmospheres of gas giant planets athigh temperatures (e.g., Koskinen et al. 2013a,b). In addition to the reaction rate coefficients, therequired inputs for the photochemical model are the stellar spectrum, a temperature-pressure (T-P) profile, and the eddy diffusion coefficient K zz that generally depends on altitude. In the loweratmosphere we used T-P profiles from Sudarsky et al. (2003) and Burrows et al. (2004) that werecalculated for EGPs at orbital distances ranging from 0.1 to 1 AU. We calculated the compositionat 1 AU, 0.5 AU, 0.4 AU, 0.3 AU, 0.2 AU, 0.1 AU, and 0.047 AU. For HD209458b we used the T-Pprofile from Showman et al. (2009). The T-P profiles above the 1 µ bar level of each simulation wereadopted from Koskinen et al. (2007a,b) for different orbital distances, and connected smoothly withthe T-P profiles at lower altitudes. We estimated the terminal values of K zz in the upper atmospherebased on the simple scaling proposed by Koskinen et al. (2010b). These values range from 10 to 10 m s − between 1 and 0.047 AU, respectively. The reader should note that these values aremore conservative than the relatively high values typically presented in the literature (e.g., Moseset al. 2011).We then proceeded to use the results from the photochemical model as lower boundary con-ditions for the escape model at the 1 µ bar level, and recalculated the temperature, density, and 4 –velocity profiles in the thermosphere. For this purpose, we used the one-dimensional escape modelof Koskinen et al. (2013a,b). We fixed the lower boundary temperature of this model to a valueconsistent with the T-P profiles above. The lower boundary was placed at 1 µ bar because most ofthe EUV radiation that powers escape in the model is absorbed above this level. The reader shouldnote that X-rays typically penetrate deeper than the 1 µ bar level and accounting for their heatingimpact on the atmosphere requires a model of radiative transfer that includes cooling by the abun-dant molecules. At the upper boundary we applied either the modified Jeans or Jeans conditions,depending on the value of X . In both cases we included the ambipolar electric potential that can beimportant in ionized atmospheres (e.g., Garcia Munoz 2007; Koskinen et al. 2013a). Our modelis self-consistent with regard to these boundary conditions in that the altitude of the exobase isupdated regularly during the simulation, and the Jeans conditions are applied slightly below theexobase where the Knudsen number Kn ≈
3. Results3.1. H dissociation chemistry The photochemical calculations constrain the mixing ratio of H at the 1 µ bar lower boundaryof the hydrodynamic escape model. The latter also includes the ion chemistry of H , H, andHe with a reaction scheme similar to that of Yelle (2004) and Koskinen et al. (2009). With anaccurate lower boundary constraint, the escape model can therefore update the H /H transitionlevel based on the temperature and chemistry in the thermosphere, as long as the homopause islocated reasonably near the 1 µ bar level. Our calculations show that the mixing ratio of H at the1 µ bar level varies from about 4.9 × − at 1 AU to about 1.7 × − at 0.1 AU, finally reachingabout 0.5 for HD209458b. As a point of comparison, the corresponding mixing ratio at Jupiter isabout 10 − (Seiff et al. 1998). Interestingly, H is mostly dissociated thermally at orbital distancesgreater than 0.1 AU.At close-in orbits, within 0.1 AU, H can also be dissociated by OH radicals that are releasedby the photolysis of water molecules (e.g., Moses et al. 2011). Because this dissociation mech-anism is primarily driven by FUV radiation, that penetrates past the EUV heating peak, it canpotentially dissociate H at deeper pressure level than thermal dissociation. We note, however, thatthe relative importance of thermal dissociation and photochemistry depends on the assumed T-Pprofile. The dayside T-P profile typically assumed for HD209458b, which was also used in this 5 –work is warm enough to dissociate thermospheric H anyway.At 1 AU the H /H transition occurs above the 0.2 nbar level i.e., above the thermosphericheating peak that is located at 1–10 nbar. Near the exobase at 2.4 pbar, the mixing ratio of H isclose to unity. This means that there is a rather sharp H /H transition at low pressures near theexobase, but that H is the dominant species in most of the thermosphere. Moving inward from 1AU to 0.4 AU, the H /H dissociation front moves down to the 3 nbar level. By 0.3 AU, it reachesdown to the 20 nbar level i.e., below the EUV heating peak. At this point the thermosphere alsoheats up and expands dramatically (see Section 3.2 below). At 0.2 AU the exobase is above the 16 R p upper boundary and the maximum temperature is 10,300 K. At 0.1 AU the H /H transition islocated near the 50 nbar level and, as we pointed out above, for HD209458b this transition takesplace near the 1 µ bar level. Figure 1 shows the T-P profiles from our new calculations for different orbital distances abovethe 1 µ bar level. These calculations are based on the planetary parameters of HD209458b. Theresults are compared with the model T-P profile for HD209458b (Koskinen et al. 2013a,b) and themeasured equatorial T-P profile for Jupiter (Seiff et al. 1998). At 1 AU the exospheric temperatureis T ∞ ≈ + is also important near the heating and ionization peak. Contrary to HD209458b,cooling by adiabatic expansion or advection are negligible.The exospheric temperature at 1 AU is comparable to the exospheric temperature on Earth.The model T-P profile at 1 AU is also similar to the observed T-P profile on Jupiter. In particular,our temperature profile agrees well with the Jovian profile below the 20 nbar level. It is wellknown that the temperatures on Jupiter and other giant planets in the solar system are higher thanexpected from solar heating alone (e.g., Miller et al. 2005), and the heating mechanism responsiblefor this is currently unknown. In this regard it is interesting that the correct T-P profile in the lowerthermosphere can be obtained by moving Jupiter from 5 AU to about 1 AU i.e., by multiplying thesolar flux by a factor of 25.It is not easy to predict the degree to which the atmospheres of EGPs might also be warmerthan expected from solar heating. The situation in the solar system may provide some guidanceon this though. The leading suggestions for the missing heating mechanism on Jupiter and Saturn 6 –Fig. 1.— Simulated temperature-pressure profiles for EGPs with planetary parameters ofHD209458b at different orbital distances (solid lines). The T-P profiles are shown up to the exobasewhen it exists (at orbital distances greater than 0.3 AU). Also shown are the T-P profiles for Jupiter(Seiff et al. 1998) and the simulated profile for HD209458b (Koskinen et al. 2013a,b). 7 –include redistribution of auroral energy from the poles to the equator or, given the rapid rotationof these planets and polar ion drag that may constrain the auroral energy to high latitudes, directheating by breaking gravity waves (e.g., Müller-Wodarg et al. 2006; Smith et al. 2007). Both ofthese phenomena are observed on Earth, but solar EUV heating is still the most important overallenergy source in the thermosphere and the temperature in the Earth’s thermosphere can easily beexplained. It may thus be argued that stellar heating simply overtakes any secondary heat sourceswithin 1 AU. We rely on this assumption in this work, and present results within 1 AU based onstellar heating only.Adiabiatic cooling or advection that are associated with the escape of the atmosphere do notaffect the energy balance at 1 AU. The ‘critical’ thermal escape parameter at the exobase ( r ∞ = 1.09R p ) is X ∞ = 72, and near the EUV heating peak X = 190. These values imply a negligible mass lossrate of ˙ M ≈ × − kg s − . We note that the thermospheric heating efficiency at 1 AU, whichis based on the balance of radiative (photoelectron) heating and cooling, is about η eff = 0.48. Thisvalue is not very different from η eff = 0.44 that we estimated for HD209458b . Thus the energy-limited mass loss rate at 1 AU is about 10 kg s − . This means that the escape rate that we calculatedat 1 AU is technically not in the energy-limited regime – instead it is many orders of magnitudelower than the energy-limited rate. We argue in Section 3.3 that this apparent discrepancy arisesfrom a confusion about the definition of heating efficiency rather than any new insight into thephysics of evaporation.Moving inward from 1 AU to 0.5 AU, the exospheric temperature increases from 1440 Kto about 2630 K. With this increase in temperature the exobase extends to about 1.8 R p wherethe pressure is about 7 × − nbar. Such a low pressure for the exobase is possible because thethermosphere is mostly ionized at radii higher than about 1.4 R p , and the cross section for Coulombor ion-neutral collisions is much larger than the cross section for neutral-neutral collisions. This isin contrast to 1 AU where the electron-neutral mixing ratio at the exobase is only x e = 6 × − .As shown in Figure 1, the temperature profile at 0.5 AU is isothermal near the exobase, indicatingthat heating is balanced by conduction. Similarly to 1 AU, escape has a negligible impact on theT-P profile, and the modified Jeans outflow velocity at the exobase is only v J ∞ = 1.9 × − m s − .The critical escape parameter in this case is X ∞ = 26. In addition to conduction, cooling from H + plays a substantial role in the lower thermosphere. This can be seen in the shape of the T-P profile(Figure 1) near the 10 nbar level and below where infrared cooling is comparable to the stellarheating rate.At 0.4 AU the exospheric temperature is 2840 K i.e., only slightly higher than at 0.5 AU,and the critical escape parameter is X ∞ = 20. Inward from 0.4 AU, the atmosphere undergoes an Note that these efficiencies are defined in terms of the stellar flux at wavelengths shorter than 912 Å. p , and formally the exobase is located above the 16R p upper boundary of the model. Above 1.4 R p the temperature also decreases with altitude. Thisis because heating at high altitudes is no longer balanced by conduction – instead it is balancedby ‘adiabatic’ cooling that is associated with the expansion and escape of the atmosphere. In thissense the model at 0.2 AU is qualitatively similar to HD209458b where the same behavior hasbeen predicted by several previous models (e.g., Yelle 2004; Garcia Munoz 2007; Koskinen et al.2013a,b). Based on these changes in the location of the exobase and the energy balance, we arguethat the transition to ‘hydrodynamic’ escape occurs near 0.3 AU. We note that a similar transitionwas identified before by Tian et al. (2008a,b) in the context of the early terrestrial atmosphere. The energy-limited loss rate in the context of extrasolar planets is often formulated as (Erkaevet al. 2007; Lammer et al. 2009): ˙ L = ηπ r F EUV Φ (1)where r EUV is the radius of the EUV heating peak, F EUV is the stellar EUV flux, Φ is the grav-itational potential, and η is referred to as the ‘heating efficiency’. We believe that the use of‘heating efficiency’ here can be misleading . For instance, the peak midday heating efficiencyof the Earth’s thermosphere is 50–55 % (Torr et al. 1981) but only a tiny fraction of the energythat heats the thermosphere powers escape. Instead, the heating is mostly balanced by downwardheat conduction, radiative cooling and to some degree by circulation. Under these circumstancesa reasonable estimate of the temperature profile can be derived analytically from a simple balancebetween stellar heating and conduction (e.g., Gross 1972; Lammer et al. 2003). Naturally theseconsiderations are different on Earth in any case because the escape of lighter species such as Hand H is diffusion-limited, but the discussion here illustrates the general limitations of the energylimit.With a proper choice of η , r EUV and Φ , equation (1) is always accurate and with η = 1 ityields an upper limit on thermal escape rates. It is thus be better to call η ‘mass loss efficiency’rather than ‘heating efficiency’. This better reflects the fact that equation (1) describes a balancebetween external heating and cooling by adiabatic expansion (e.g., Yelle 2004). It also removesany apparent disagreement between equation (1) and our results at 0.4–1 AU in Section 3.2. Ifone accounts for the fact that heating is mostly balanced by downward conduction, the mass loss Note that heating efficiency is often understood as the fraction of solar energy that heats the atmosphere. η , equation (1) is actually not very useful unless adiabatic cooling really is important.It may always be possible to tune the mass loss efficiency to force the equation to agree withmodeled or observed mass loss rates, but this does not capture the relevant physics in all cases.Thus the escape mechanism must also be studied in detail before energy-limited escape can beassumed.The globally averaged mass loss rates are 3.4 × − kg s − and 6.3 × − kg s − at 0.5 AU and0.4 AU, respectively. Needless to say, these mass loss rates are irrelevant to the long term evolutionof the atmosphere. At 0.2 AU the mass loss rate is 8 × kg s − . In this case the heating efficiencyis comparable, although not identical, to the mass loss efficiency. According to our simulations,the heating efficiency is about 8.5 % at 0.2 AU. This relatively low value arises because coolingfrom H + is important in the lower thermosphere below the H /H transition. The T-P profile at 0.1AU is qualitatively similar to the T-P profile at 0.2 AU, and the maximum temperature is about10,900 K. The mass loss rate at 0.1 AU is about 6 × kg s − . The heating efficiency at 0.1AU is only 22 % because H + still cools the lower thermosphere. As we argue below, this coolingeffect becomes negligible within 0.1 AU and thus the heating efficiency for HD209458b increasesto 44 %. As before, we obtained a mass loss rate of 4.1 × kg s − from our reference model ofHD209458b (Koskinen et al. 2013a,b).Our results show that heavy species such as C, O, and Si that collide frequently with H andH + escape the atmosphere of HD209458b with nearly uniform mixing ratios in the thermosphere(Koskinen et al. 2013a,b). There is an obvious interest in estimating the degree to which this is trueon other EGPs because escape can affect the composition and thus the evolution of the atmosphere.For example, the thermal mass loss rate predicted by us and previous models of HD209458b (e.g.,Yelle 2004) implies that the planet has lost less than 1 % of its mass during the lifetime of thestellar system. However, it also implies that HD209458b loses the equivalent mass of its wholeatmosphere above the 1 bar level approximately every 800,000 years.The crossover mass equation given by Hunten et al. (1987) can be used to derive a roughestimate of the limiting mass loss rate ˙ M lim that is required for a species with mass M c (in units of m H ) to escape with H due to neutral-neutral collisions: ˙ M lim = 4 π m GM p ( M c − nD c kT (2)where D c is the mutual diffusion coefficient for species c with H. At a temperature of 7,200 K(Koskinen et al. 2013a,b), the mass loss rate required to mix He is about 10 kg s − , while themass loss rate required to mix C and O is 4–6 × kg s − . Given that we estimate a mass lossrate of 6 × kg s − at 0.1 AU, progressively heavier neutral species escape the atmosphere withdecreasing orbital distance from 0.1 AU. Because carbon species are effective in removing H + , this 10 –is another indication that infrared cooling is not effective in the lower thermospheres of close-inEGPs. Instead H is dissociated near the 1 µ bar level and the temperature increases rapidly withaltitude above this level. The escape mechanism depends on the gravitational potential Φ through its dependence on X . The energy-limited escape rate given by equation (1) and the crossover mass loss rate given byequation (2) also depend on the gravitational potential. For example, Koskinen et al. (2009) pointedout that the atmosphere of heavy planets such as HD17156b is not likely to undergo rapid escapeeven at close-in orbits. We explored the effect of Φ in more detail by generating models at the sameorbital distances as before but with different values of the surface potential ranging from 0.1 Φ J to3 Φ J , where Φ J is the surface potential of Jupiter. In order to illustrate the results, we discuss themin the context of a few well known transiting EGPs. For instance, GJ3470b is a nearby Neptune-size planet orbiting an M dwarf that has a gravitational potential of about 0.1 Φ J . The gravitationalpotential of HD209458b is 0.5 Φ J i.e., similar to Saturn, whereas the gravitational potential ofHD189733b is identical to Jupiter. The gravitational potential of HD17156b, on the other hand, is2.9 Φ J Φ = Φ J the atmosphere enters the rapid escape regimebetween 0.2 AU and 0.3 AU i.e., slightly inward from the corresponding transition for a planetwith Φ = 0.5 Φ J . We note that the previous calculations of Koskinen et al. (2007b), that also used Φ = Φ J , placed this transition between 0.1 AU and 0.2 AU. The difference between the calculationshere and the previous results could be due to circulation. With a slow rotation rate approachingtidal synchronization that was assumed by Koskinen et al. (2007b), the GCM at 0.2 AU developsstrong day-night circulation at high altitudes that leads to upwelling in the dayside. This upwellingreplenishes H and helps to maintain the stability of the atmosphere. However, a faster rotationrate with a period of 24 hours or less disturbs this type of circulation and leads to a transition tothe rapid escape regime between 0.2 AU and 0.3 AU (Koskinen et al. 2008), in agreement with the1D globally averaged simulations presented here. It should be noted that while close-in EGPs areassumed to be rotationally synchronized with their orbital periods (e.g. Guillot et al. 1996), thereis no reason to assume that this is the case farther out between 0.2 and 0.3 AU.With the surface potential increased to Φ = 3 Φ J , the atmosphere at 0.2 AU does not undergohydrodynamic escape. Instead, the exospheric temperature is only 2,820 K with an exobase at 11 –1.08 R p and X ∞ = 207. At 0.1 AU, H dissociates rapidly above the 1 µ bar level and the exospherictemperature increases to 12,400 K. However, even in this case the exobase is at 1.5 R p with X ∞ = 33and the atmosphere does not escape hydrodynamically. At 0.05 AU, the exospheric temperatureis 14,340 K and X ∞ = 25. These results confirm the finding of Koskinen et al. (2009) that heavyplanets such as HD17156b do not undergo rapid escape even at close-in orbits, despite the fact thatH is dissociated in their upper atmospheres.Escape is less effective on heavier planets partly because radiative cooling offsets the stellarXUV heating near the heating peak. In our new calculations we include cooling due to recombina-tion but H Lyman α cooling can also contribute (Murray-Clay et al. 2009), keeping the temperaturein the thermosphere close to 10,000 K. These cooling effects play a more significant role in theenergy balance on planets with higher gravity because the temperature in the thermosphere on suchplanets is not high enough for adiabatic cooling to become important. Further research is requiredto study the role of these cooling mechanisms in detail though as they are rarely included in mod-els of giant planet atmospheres. In any case, our results show that a high speed wind containingpotassium atoms from the exosphere of another similar planet HD80606b, as proposed by Colonet al. (2012), is unlikely to be realistic. The same considerations do not apply to planets such asGJ3470b with Φ = 0.1 Φ J . We found that such planets undergo a transition to rapid escape muchfarther out, and the exobase extends to very high altitude even at 1 AU.Naturally, surface gravity also affects ˙ M lim , which is directly proportional to the mass of theplanet. Thus the mass loss rate required to mix, say, C into the thermosphere of HD189733b is1.7 times higher than on HD209458b. On HD17156b the corresponding rate is 4.6 times higherthan on HD209458b and on GJ3470 it is 16 times lower than on HD209458b. Thus the collisionalmixing of heavy species is much more likely on planets with a low surface gravity than on heavyplanets such as HD17156b. Given that the escape rates on HD17156b or HD80606b are likely tobe comparable to the Jeans escape rate even at the periastron near 0.05 AU, we do not expect thatsubstantial abundances of heavy elements escape from their atmospheres. Instead, heavy specieson these planets are likely to be diffusively separated below the exobase.
4. Discussion and Conclusions
The study of extrasolar planet atmospheres is still an emerging field. This means that there aremany uncertainties in both the models and even the interpretation of the observations. For instance,we used T-P profiles in the lower atmosphere that are based on models that make many simplify-ing assumptions about the composition and radiative transfer (Sudarsky et al. 2003; Burrows etal. 2004). Although these models account for condensation, cloud formation and the scattering ofradiation, they ignore the effects of photochemistry and non-LTE radiative transfer that can, for 12 –instance, produce strong emission features on close-in planets (Swain et al. 2010; Waldmann et al.2012). The temperature profile in the thermosphere, on the other hand, depends on the photoelec-tron heating efficiencies and the H + infrared cooling rates. Fully self-consistent calculations of theheating efficiency do not yet exist, and H + emissions have not been detected on EGPs. In fact, ourestimates indicate that these emissions are undetectable with current instruments despite the factthat they can play a substantial role in the energy balance of EGPs.The composition and T-P profiles are also affected by dynamics and turbulent mixing. Thereare no observational constraints on the impact of dynamics on the composition, and only a fewconstraints on circulation in general. Yet dynamics can play a large role in the atmosphere, con-trolling processes such as cloud formation and the mixing ratios of heavy elements in the upperatmosphere. Photochemistry, dynamics, and thermal structure are all driven by the stellar flux. It issurprising how little is known about the properties of the host stars and the details of their spectra.The activity cycle of even other Sun-like stars is not well understood although it is likely to affectboth the atmospheres and the interpretation of transit observations. Even less is known about starsof other spectral type. For instance, M stars exhibit a range of activity levels in general, and can behighly variable even on short time scales (France et al. 2012).Despite the uncertainties, we are able to identify some robust qualitative results. First, thereare two distinct regimes of atmospheric escape that are separated by a relatively sharp transitioncontrolled by the stellar flux. In the ‘stable’ regime, stellar heating is balanced by downwardconduction and/or radiative cooling. In this case the mass loss rate is typically many orders ofmagnitude smaller than the energy-limited escape rate that is based on the thermospheric heatingefficiency. In the ‘unstable’ regime stellar heating is efficient enough to cause a significant ex-pansion of the atmosphere. As a result, stellar heating is balanced by adiabatic cooling and thetemperature decreases with altitude above the EUV heating peak. In this regime the mass loss rateis comparable to the energy-limited mass loss rate that is based on the thermospheric heating effi-ciency. The transition between these two regimes on close-in EGPs is sharp because it is in manycases driven by the dissociation of H . The H /H dissociation front is sharp both as a function ofaltitude in the atmospheric models and in terms of orbital distance.In addition to stellar flux and composition, the escape mechanism depends on the surfacegravitational potential. We find that planets such as HD209458b with Φ = 0.5 Φ J are stable atorbital distances greater than about 0.3 AU. In our calculations this corresponds to an integratedEUV flux of F lim = 44 mW m − at wavelengths shorter than 912 Å. For planets like Jupiter this limitis closer at 0.2 AU ( F lim = 0.1 W m − ). The atmospheres of heavier planets such as HD17156b arestable even at 0.05 AU ( F lim = 1.6 W m − ), and unstable only near 0.01 AU. The atmospheresof planets such as GJ3470b are much more likely to escape hydrodynamically, even near 1 AU.The escape of heavy species is controlled by the escape rate of hydrogen. For a planet such as 13 –HD209458b, the energy-limited escape rate is high enough to cause species more massive than Cto escape within 0.1 AU. The escape of heavy species from planets such as HD17156b is unlikelywhereas planets such as GJ3470b can start losing heavy species within 1 AU. We note here that wedid not calculate photochemistry in the lower atmosphere for planets with different Φ , assumingthat the changes in the mass and radius of the planet do not affect the H /H transition significantly.To illustrate the results, Figure 2 shows the gravitational potential Φ = GM p / R p of currentlyknown transiting EGPs (planets with a mass higher than 10 M E ) as a function of effective orbitaldistance. This is the orbital distance in the Solar System where the planets would receive thesame EUV flux as they do currently, given an estimate of the EUV flux of their host stars. For Gstars, we used the solar flux (4 mW m − Φ , the limits given in Figure 2 can be used todetermine the thermal escape mechanism for different EGPs. We note, however, that the limitsfor the different escape regimes here are based on models with a relatively few values of a eff and Φ , and we recommend that interested readers contact the authors for separate models of specifictargets if more accurate results are required. We also stress that only a detailed comparison of thesimulations with actual observations can validate the models, and future efforts in characterizingthe upper atmospheres of EGPs should concentrate on obtaining multiple observations of both thehost stars and the planets in different systems, and designing new techniques and instruments tomake these observations possible. 14 –Fig. 2.— Surface potential of EGPs with known radius, mass, and the spectral type of the host staras a function of effective orbital distance (see text). The dashed line shows the transition betweenunstable escape-dominated (to the left) and stable (to the right) regimes as defined in the text. Thestars show the values of Φ for which simulations were performed. 15 –The calculations in this paper relied on the High Performance Astrophysics Simulator (HiPAS)at the University of Arizona, and the University College London Legion High Performance Com-puting Facility, which is part of the DiRAC Facility jointly funded by STFC and the Large Fa-cilities Capital Fund of BIS. SOLAR2000 Professional Grade V2.28 irradiances are provided bySpace Environment Technologies. This research was supported by the National Science Founda-tion (NSF) grant AST1211514. REFERENCES