Energy-limited escape revisited: A transition from strong planetary - - PDF document

Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold

Energy-limited escape revisited: A transition from strong planetary winds to stable thermospheres

• M. Salz1, P. C. Schneider2,1, S. Czesla1, J. H. M. M. Schmitt1

Talk given at OHP-2015 Colloquium

1Hamburger Sternwarte, Universit¨

at Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany (msalz@hs.uni-hamburg.de)

2European Space Research and Technology Centre (ESA/ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Nether-

lands Abstract Hot Jupiters are thought to suffer from mass loss through planetary winds powered by strong high-energy irradiation. These photoevaporative winds can affect planetary evolution. We carried

• ut photoionization-hydrodynamics simulations of the thermospheres of hot gas planets in the solar

neighborhood using our new interface between the PLUTO and CLOUDY codes called TPCI. These detailed simulations reveal efficient radiative cooling in the atmospheres of massive and compact Jo- vian planets, whose gravitational potential surpasses the critical limit of log10 (−ΦG) > 13.11 erg g−1. In contrast to widely-made assumptions, our modeling shows that planets like HAT-P-2 b host sta- ble thermospheres in radiative equilibrium, whereas smaller gas giants, indeed, show considerable mass-loss rates. Hence, the heating efficiency of the absorption of EUV radiation in the planetary thermospheres depends on the gravitational potential of the planet. We present a scaling law for the heating efficiencies that can be used in the well-known energy-limited escape formula and provides easily accessible mass-loss estimates for a wide range of irradiated planets from super-Earth type planets to the most massive hot Jupiters. The trend of the heating efficiency versus the gravitational potential is reflected in the planetary Lyα absorption and emission signals. These signals can be used to distinguish between two types of thermospheres in hot gas planets: strong, cool planetary winds with Lyα absorption and hot, stable thermospheres with Lyα emission.

1 Introduction

Planets on close orbits endure high irradiation levels. For example, CoRoT-2 b orbits an highly active host star at a distance of 0.028 au experiencing an high-energy irradiation level 105 times stronger than that of Earth today (Schr¨

• ter et al. 2011). This high-energy emission (X-rays and extreme ultraviolet radiation, XUV) is absorbed in

upper atmospheric layers creating a so-called thermosphere. The absorption causes ionizations with subsequent thermalization of the photoelectron’s energy. The resulting energy input heats the planetary thermospheres to up to 20000 K, increasing their scale height so that the atmosphere can even expand beyond the planetary Roche lobe. The continuous radiative energy input must be balanced by an equally strong energy sink. In the thermosphere of Jupiter itself, thermal conduction stabilizes the energy input through high-energy irradiation (Yelle & Miller 2004), but this channel is not sufficient for hot gas planets (Yelle 2004). If radiative cooling is small, the thermospheres of hot gas giants must expand to balance the radiative energy

• input. The expansion converts internal energy into gravitational potential energy by lifting material against the

gravitational attraction of the planet. Thus, the high-energy irradiation creates a planetary wind that carries off material into interplanetary space, where it interacts with the stellar wind and radiation pressure (Tremblin & Chiang 2013; Bourrier & Lecavelier des Etangs 2013). If hot gas planets maintain strong magnetic fields, atmospheric escape can be inhibited in regions of closed field lines, which also affects the planetary mass-loss rates (Trammell et al. 2014; Khodachenko et al. 2015), but currently our knowledge about exoplanetary magnetic fields is limited (e.g. Sirothia et al. 2014).

80

Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold Expanded planetary atmospheres have been found in the five systems HD 209458 b, HD 189733 b, WASP-12 b, 55 Cancri b, and GJ 436 b mostly through excess absorption in atomic lines (Vidal-Madjar et al. 2003; Lecavelier des Etangs et al. 2010; Fossati et al. 2010; Ehrenreich et al. 2012; Kulow et al. 2014). The spectrally resolved absorption signals often show strong blue shifts with velocity offset of up to −250 km s−1 (Lecavelier des Etangs et al. 2012), indicating that the detected material is indeed escaping from the planetary atmosphere. The presence

• f heavier atoms like carbon and oxygen in the upper atmospheres also requires the presence of strong winds to

prohibit mass segregation and the development of a planetary homosphere (Vidal-Madjar et al. 2004; Linsky et al. 2010; Ben-Jaffel & Ballester 2013). Models of the atmospheric escape are becoming more and more advanced, however, a complete picture of the complex environment is challenging. One class of simulations focuses on the interactions of the planetary wind with the stellar wind, radiation pressure, and the planetary magnetic field, however, without solving the energetics

• f the formation of the planetary wind (e.g., Bourrier & Lecavelier des Etangs 2013; Tremblin & Chiang 2013;

Trammell et al. 2014; Kislyakova et al. 2014). Another class focuses on the formation of a planetary wind in the thermosphere without solving further interactions (Yelle 2004; Tian et al. 2005; Garc´ ıa Mu˜ noz 2007; Murray-Clay et al. 2009; Koskinen et al. 2013; Shaikhislamov et al. 2014). Combined models are now emerging (Khodachenko et al. 2015), indicating the true complexity of the system, however, at the moment these models do not include the full extend of the chemical network in the planetary atmospheres (e.g., compare Garc´ ıa Mu˜ noz 2007; Koskinen et al. 2013).

2 Energy-limited escape

Neglecting all complexities, energy conservation provides a quick estimate for the planetary mass-loss rates by setting the radiative energy input equal to the gravitational potential energy gained through lifting atmospheric material from the planetary surface to the Roche lobe height (Erkaev et al. 2007). Adopting reasonable heating efficiencies for the absorption of high-energy radiation in the planetary thermospheres, this energy-limited mass- loss rate can indeed be reached in planetary atmospheres (Watson et al. 1981; Murray-Clay et al. 2009). The energy-limited mass-loss rate ˙ Mel is given by (Erkaev et al. 2007; Sanz-Forcada et al. 2010): ˙ Mel = 3 β2 ηFXUV 4 KG ρpl . (1) Here, β is a correction for the size of the planetary atmosphere that absorbs XUV radiation, η is the heating effi- ciency, FXUV is the combined X-ray plus extreme ultraviolet radiation flux at the planetary distance, K is a correc- tion for taking into account the limited size of the planetary Roche lobe (Erkaev et al. 2007), G is the gravitational constant, and ρpl is the mean planetary density.

3 Simulations

We have used a photoionization-hydrodynamics solver to simulate the escaping atmospheres of 18 hot gas plan- ets in the solar neighborhood on a spherically symmetric 1D grid including hydrogen and helium in the planetary atmospheres (Salz et al. 2015b). The code (TPCI) is an interface between the MHD code PLUTO and the photoion- ization equilibrium solver CLOUDY (Mignone et al. 2007, 2012; Ferland et al. 1998, 2013; Salz et al. 2015a). We focus on the formation of a planetary wind by accurately solving the energy conversion throughout the planetary

• thermosphere. The use of the photoionization solver was crucial for our results, because CLOUDY self-consistently

solves the absorption of XUV radiation and the emission of the planetary atmosphere. For example, the absorption

• f photoionizing radiation is solved by balancing the ionization ladder for each element, including photoionization

with wavelength dependent cross-sections, induced recombination, recombination, collisional ionization, Auger electrons, and collisional ionizations through supra-thermal electrons. TPCI further solves the emission of the planetary thermospheres, for example, line emission, free-free emission

• f electrons, and recombination cooling. The precise solution of the radiative heating and cooling rates throughout

the planetary thermosphere allows us to compute the heating efficiency in individual planetary atmospheres. While TPCI can be used to simulation the escaping atmospheres, it can also solve hydrostatic thermospheres, where the radiative energy input is completely re-emitted. Thus, the code is well suited to study the conditions under which a planetary atmosphere becomes hydrodynamically stable.

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Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold

4 The transition from strong winds to stable atmospheres

Figure 1 compares the thermospheres of HD 209458 b and HD 189733 b. While HD 189733 b experiences a 16 times higher irradiation level, the planet is heavier and more compact. According to Eq. 1, the energy limited mass-loss rate is 5 times higher than that of HD 209458 b (Salz et al. 2015b). However, our simulations show that HD 189733 b actually produces a weaker wind than HD 209458 b. Efficient radiative cooling brings the atmospheric layers below 1.5 Rpl close to radiative equilibrium, with only little energy remaining to accelerate the planetary wind (see Fig. 1 (d)). The average heating efficiency of only 8.3 × 10−3 is reduced by Lyα and free-free emission in the 3000 K hotter thermosphere. Comparing all our simulations, we find that a planet with a deeper gravitational potential well (ΦG = −GMpl/Rpl) has a hotter thermosphere that cools more efficiently. Therefore, the planetary wind becomes weaker.

Density (cm-3) HD 209458 b HD 189733 b 107 1010 1013 (a)

• Temp. (1000 K)

2 6 10 (b) Velocity (km s-1) 10-3 10-1 101 (c)

Heating fraction

Radius (Rpl) 0.0 0.5 1 2 3 4 5 (d)

Figure 1: Comparison of the thermospheres of HD 209458 b and HD 189733 b. We show the number density, temperature, veloc-

ity, and heating faction, which is defined as radiative heating minus cooling divided by heating. The atmosphere of HD 189733 b is 3000 K hotter and the planetary wind strength, which is density times velocity, is smaller. The weaker wind is a result of stronger radiative cooling in the hotter atmosphere.

Indeed, the decrease of the heating efficiency in massive planets can hardly be avoided. To overcome the higher gravitational attraction a massive planets requires a higher thermospheric temperature, but the strong increase of radiative cooling with temperature hinders the thermosphere to heat up sufficiently. Therefore, the atmospheric scale height is smaller in massive planets, resulting in a reduced thermospheric density. This lower density reflects the weaker planetary wind, because the velocity of an isolated planetary wind is always slightly supersonic, which is close to 10 km s−1 in all planetary thermospheres.

5 Evaporation efficiencies

For each simulated planetary wind, we computed the individual evaporation efficiency given by the fraction of the simulated mass-loss rate to the energy-limited value (Salz et al. 2015c). In contrast to the heating efficiency, the evaporation efficiency includes the conversion of radiative energy into kinetic and thermal energy (Lopez et al. 2012). The values are plotted versus the planetary gravitational potential in Fig. 2. We find that for planets with log10 (−ΦG) > 13.11 erg g−1 the evaporation efficiency declines rapidly and when the logarithm of the gravitational

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Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold potential exceeds a value of 13.6 in units of erg g−1 the efficiency drops below 10−5. At this point the planetary at- mospheres become collisionless before any significant acceleration of a planetary wind occurs. Such thermospheres are hydrodynamically stable and re-emit nearly the complete XUV radiative energy input through Lyα and free-free emission.

• 5
• 4
• 3
• 2
• 1

12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 log10 (ηeva) log10 (-ΦG) (erg g-1)

WASP-12 b GJ 3470 b WASP-80 b HD 149026b HAT-P-11 b HD 209458 b 55 Cnc e GJ 1214 b GJ 436 b HD 189733 b HD 97658 b WASP-77 b WASP-43 b CoRoT-2 b

Figure 2: Dependency of the evaporation efficiency on the planetary gravitational potential (Salz et al. 2015c). The simulated

systems are marked by crosses with names indicated; circles represent artificial systems. The solid line is a fitted broken power

• law. The evaporation efficiency decreases quickly for massive planets and the most massive planets have hydrodynamically stable

atmospheres.

We fitted a broken power law to the the simulation results (see Fig. 2). The fit provides evaporation efficiencies for any planet with a hydrogen dominated atmosphere based on its gravitational potential (Salz et al. 2015c). These efficiencies can be used in the energy-limited mass-loss equation (Eq. 1) to provide quick mass-loss estimates based on the results of our detailed simulations. While the scatter of the values around the fit results from further influences on the simulated mass-loss rates, (e.g., boundary conditions, see Salz et al. 2015b), the values for the evaporation efficiency drop by several orders of magnitude depending only on the gravitational potential. These results can also be combined with the recombination limited mass-loss rates of Murray-Clay et al. (2009).

6 Planetary Lyα absorption and emission signals

Four of the five detected expanded planetary atmospheres have been detected through Lyα absorption during the planetary transit. A planetary wind transports large amounts of neutral hydrogen into the upper atmosphere and beyond the planetary Roche lobe (unbound hydrogen), and the more neutral hydrogen is present, the more ab- sorption can be expected. Further interactions with radiation pressure or with the stellar wind can result in large radial velocity shifts but do not create additional neutral hydrogen. We compute the equivalent width of the Lyα absorption signals from our simulations (following Cauley et al. 2015). This is a measure for the total strength of the planetary absorption signal. We do not compute spectrally resolved signals, because of the approximation of spherical symmetry and the omission of further interactions in the simulations. Figure 3 shows that the clear trend of the evaporation efficiencies versus the planetary gravitational potential is reflected in the Lyα absorption signals. Massive planets with hot and almost stable atmospheres produce very little Lyα absorption. Smaller planets with strong, cool, and highly neutral winds can produce very large absorption signals. These results reflect the trend seen in observations. GJ 436 b was detected with the largest Lyα absorption signal (Kulow et al. 2014; Ehrenreich et al. 2015) and in our simulations this planet hosts one of the strongest and most neutral winds, causing strong Lyα absorption. HD 209458 b also produces a strong signal, while in HD 189733 b the wind is weaker and more highly ionized causing less absorption. Again this corresponds with the observations, where in HD 209458 b strong Lyα absorption was detected repeatedly (Vidal-Madjar et al. 2003, 2004; Ehrenreich et al. 2008), but in HD 189733 b the absorption is time-variable and possibly occurs only when the planetary wind is enhanced by strong stellar activity (Lecavelier des Etangs et al. 2012, and Wheatley 2015, see this conference proceedings). The simulation results also agree with the non-detection of Lyα absorption during the transit of the super-Earth 55 Cnc e (Ehrenreich et al. 2012). This planet can produce a strong hydrogen dominated wind, but the

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Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold extreme irradiation level quickly ionizes hydrogen limiting the extend of the neutral hydrogen cloud to values that are challenging for a detection. 12.5 13 13.5 14 10−5 10−4 10−3 10−2 10−1 (φpl/φst)max 100 1000 Lyα absorption equivalent width (mÅ) log10 (ΦG) (erg g−1)

WASP-12 GJ 3470 WASP-80 HD 149026 HAT-P-11 HD 209458 55 Cnc e GJ 1214 GJ 436 HD 189733 HD 97658 WASP-77 WASP-43 CoRoT-2 WASP-10 WASP-8 HAT-P-20 HAT-P-2

10−5 10−4 10−3 10−2 10−1 (φpl/φst)max 100 1000 Lyα absorption equivalent width (mÅ) Figure 3: Planetary Lyα absorption and emission signals plotted versus the planetary gravitational potential (Salz et al. 2015b).

Green dots give the equivalent width of the absorption signal and blue crosses indicate the maximal planet-to-star Lyα flux ratio. Small planets cause strong absorption but little emission and massive planets cause little absorption but strong emission.

While the hot and almost stable atmospheres of massive planets produce little absorption, they efficiently con- vert stellar XUV emission into Lyα radiation. This strongly enhances the contrast of the planetary Lyα emission compared to the stellar flux. Menager et al. (2013) found that the Lyα emission of HD 189733 b could be detectable during the orbital phases 0.25 and 0.75, when the planetary emission has a radial velocity offset from the stellar emission by the orbital velocity. We follow these authors and compute the maximal planet-to-star Lyα flux ration during these phases in all our simulations by assuming that only the illuminated half the planetary surface is emit- ting (Salz et al. 2015b). Figure 3 shows that the trend of the decreasing evaporation efficiency is reflected by an increasing Lyα brightness of massive planets. Small planets with cool and strong winds do not strongly emit or reflect Lyα emission, but massive planet are Lyα bright and reach flux ratios of several percent compared to their host star. Such high flux ratios are possibly detectable with the Hubble Space Telescope today.

7 Conclusions

The evaporation efficiencies in the thermospheres of hot gas planets differ by several orders of magnitude depending

• n the gravitational potential of the planet. Smaller planets like GJ 436 b efficiently use the XUV irradiation to

power a planetary wind. For such planets we find an average evaporation efficiency of ηeva = 0.23. In contrast, the XUV irradiation is almost completely re-emitted in massive planets like HAT-P-2 b via Lyα and free-free emission, leading to hot and stable thermospheres. Planetary Lyα absorption and emission signals can be used to distinguish between the two types of thermo- spheres in hot gas planets. Smaller planets produce powerful, cool, and neutral planetary winds that cause large Lyα absorption signals. Massive hot Jupiters host hot, highly ionized, and almost stable thermospheres that cause little Lyα absorption but are strong Lyα emitters. A detection of planetary Lyα emission can be seen as clear indi- cation of a stable thermosphere, because only the conversion of XUV irradiation into Lyα emission results in high planet-to-star Lyα flux ratios. Acknowledgments: Thank you to the organizers of this great conference.

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Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold

References

Ben-Jaffel, L. & Ballester, G. E. 2013, A&A, 553, A52 Bourrier, V. & Lecavelier des Etangs, A. 2013, A&A, 557, A124 Cauley, P. W., Redfield, S., Jensen, A. G., et al. 2015, ApJ, 810, 13 Ehrenreich, D., Bourrier, V., Bonfils, X., et al. 2012, A&A, 547, A18 Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, 459 Ehrenreich, D., Lecavelier Des Etangs, A., H´ ebrard, G., et al. 2008, A&A, 483, 933 Erkaev, N. V., Kulikov, Y. N., Lammer, H., et al. 2007, A&A, 472, 329 Ferland, G. J., Korista, K. T., Verner, D. A., et al. 1998, PASP, 110, 761 Ferland, G. J., Porter, R. L., van Hoof, P. A. M., et al. 2013, Rev. Mexicana Astron. Astrofis., 49, 137 Fossati, L., Haswell, C. A., Froning, C. S., et al. 2010, ApJ, 714, L222 Garc´ ıa Mu˜ noz, A. 2007, Planet. Space Sci., 55, 1426 Khodachenko, M. L., Shaikhislamov, I. F., Lammer, H., & Prokopov, P. A. 2015, ApJ, 813, 50 Kislyakova, K. G., Holmstr¨

• m, M., Lammer, H., Odert, P., & Khodachenko, M. L. 2014, Science, 346, 981

Koskinen, T. T., Harris, M. J., Yelle, R. V., & Lavvas, P. 2013, Icarus, 226, 1678 Kulow, J. R., France, K., Linsky, J., & Loyd, R. O. P. 2014, ApJ, 786, 132 Lecavelier des Etangs, A., Bourrier, V., Wheatley, P. J., et al. 2012, A&A, 543, L4 Lecavelier des Etangs, A., Ehrenreich, D., Vidal-Madjar, A., et al. 2010, A&A, 514, A72+ Linsky, J. L., Yang, H., France, K., et al. 2010, ApJ, 717, 1291 Lopez, E. D., Fortney, J. J., & Miller, N. 2012, ApJ, 761, 59 Menager, H., Barth´ elemy, M., Koskinen, T., et al. 2013, Icarus, 226, 1709 Mignone, A., Bodo, G., Massaglia, S., et al. 2007, ApJS, 170, 228 Mignone, A., Zanni, C., Tzeferacos, P., et al. 2012, ApJS, 198, 7 Murray-Clay, R. A., Chiang, E. I., & Murray, N. 2009, ApJ, 693, 23 Salz, M., Banerjee, R., Mignone, A., et al. 2015a, A&A, 576, A21 Salz, M., Czesla, S., Schneider, P. C., & Schmitt, J. H. M. M. 2015b, ArXiv e-prints Salz, M., Schneider, P. C., Czesla, S., & Schmitt, J. H. M. M. 2015c, ArXiv e-prints Sanz-Forcada, J., Ribas, I., Micela, G., et al. 2010, A&A, 511, L8+ Schr¨

• ter, S., Czesla, S., Wolter, U., et al. 2011, A&A, 532, A3+

Shaikhislamov, I. F., Khodachenko, M. L., Sasunov, Y. L., et al. 2014, ApJ, 795, 132 Sirothia, S. K., Lecavelier des Etangs, A., Gopal-Krishna, Kantharia, N. G., & Ishwar-Chandra, C. H. 2014, A&A, 562, A108

85

Twenty years of giant exoplanets - Proceedings of the Haute Provence Observatory Colloquium, 5-9 October 2015 Edited by I. Boisse, O. Demangeon, F. Bouchy & L. Arnold Tian, F., Toon, O. B., Pavlov, A. A., & De Sterck, H. 2005, ApJ, 621, 1049 Trammell, G. B., Li, Z.-Y., & Arras, P. 2014, ApJ, 788, 161 Tremblin, P. & Chiang, E. 2013, MNRAS, 428, 2565 Vidal-Madjar, A., D´ esert, J.-M., Lecavelier des Etangs, A., et al. 2004, ApJ, 604, L69 Vidal-Madjar, A., Lecavelier des Etangs, A., D´ esert, J.-M., et al. 2003, Nature, 422, 143 Watson, A. J., Donahue, T. M., & Walker, J. C. G. 1981, Icarus, 48, 150 Yelle, R. V. 2004, Icarus, 170, 167 Yelle, R. V. & Miller, S. 2004, Jupiter’s thermosphere and ionosphere, ed. F. Bagenal, T. E. Dowling, & W. B. McKinnon, 185–218

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