Radiation-Hydrodynamic multi-species escape from Hot Jupiters Matthäus Schulik1, Richard Booth1, James Owen1 1Imperial College London, Exhibition Rd, South Kensington, London SW7 2BX, United Kingdom

Abstract Photoevaporative models are an important tool for helping to understand the radius distribution of exoplanets. So far, those models have often focused on the escape of H/He mixtures, neglecting coupled escape with heavier species, or assumed a fixed hierarchy of major and minor species. In this work, we relax those assumptions by using a truly multi-species simulation framework, including radiation transport and friction. We present a set of tentative results aiming at understanding the behaviour of solutions we find for Hot Jupiter exoplanets. This will open the path for the investigation of other classes of exoplanets in the near-future. Project goal Methods We aim to study the transition to metal-dominated * We solve the hydrodynamic equations for multiple species, coupled via friction. The atmospheres in Sub-Neptune exoplanets via coupled fluids can radiate in several broad bands on a static, one-dimensional sperically- hydrogen-metal hydrodynamic escape. symmetric grid. As our model adds thermal heating and cooling as well as friction between individual species, we benchmark the The physics modules are solved operator-split according to the appropriate methods: physics first against established Hot Jupiter models. We * Hydrodynamics: HLLC (Toro 2009)+Well-balancing (Käppelli&Mishra 2016) * Friction between species: Implicit scheme by Benitez-Llambay+(2019) focus on comparing models of Hot Jupiters with m=224 me and d=0.05 AU around a G0-type star and leave the Sub- * Radiative transport: Multi-band flux-limited diffusion Inspired by Neptune exoplanets for a later project part. Commercon+(2011), Vaytet+(2012) and Bitsch+(2013)/Lega+(2014). 1. Thermally-driven winds 2. Transition to metal-dominated atmospheres We first investigate the impact of thermal solar irradiation and thermal Our nominal radiative simulation experiences strong hydrogen loss leading to cooling on the escape of hydrogen coupled to methane. No XUV luminosity its depletion around the tVIS=1-surface. Methane takes over as dominant is irradiated. The appearance of temperature minima is controlled by the atmospheric species at those altitudes, while a low-lying methane reservoir magnitude of the opacity kstar to solar irradiation (Guillot 2010). remains. Here we briefly characterize this process. 16 H m /m Fig. 4: Decrease of Hydrogen and methane mass-loss 4.75 Fig. 1: Influence of atmospheric temperature H CH4 CH4 with time, as the hydrogen reservoir is depleted. structures 14 4.50 ]

1 * Initially, both escape rates remain approx. constant,

] 4.25 s 12 K * In a two-species model, we keep the -5 [ g

[ as long as the hydrogen reservoir (m =10 m ) is not

e H e r x

u thermospheric temperature approx. constant by u

t 4.00 l a f significantly affected by escape r s 10

e keeping L x k constant. star star s p 3.75 a m M * Methane escape rates co-evolve with the hydrogen e 0 T * Additionally, one simulation is added with 1

0 8 g escape rates, but their ratio favours more and more

1 3.50 o g Quasi isothermal extremely high thermospheric temperature, but l o l methane escape. = nom, LUV = nom 3.25 constant stratospheric temperature. = 10 × nom, L = 10 1 × nom 6 * The flux ratio is proportional to the density ratio in the = 102 × nom, L = 10 2 × nom 3.00 * Those runs are compared to an isothermal = 102 × nom, L = 10 1 × nom outflow. Hence, while less hydrogen escapes, it remains model. 4 1 1.5 2 2.5 3 0 1 2 3 4 5 to be seen whether a non-zero hydrogen mixing ratio Radius [Rp] Time [yr] remains in the final state of the planet. Fig.2: Transport of a secondary atmospheric 1.9 H VIS UV 0.0 CH4 species 1.8 Fig. 5: Evolution of UV and visible t=1 radii with time 2.5

] 1.7 3 5.0 * Simulations start with adiabatic profiles for * The main absorber in the UV is hydrogen, which once ] m p c

both species. At r<1.3 r Methane is the R 1.6 g P [ depleted shrinks the planetary UV surface. [ 7.5 s y t u i dominant species, above it is hydrogen. i s d 1.5 n

10.0 a e r * The slight increase in visible t=1 radius, is a result of D * Hydrogen readily escapes at 10.000K 1 0 = 1 12.5 1.4 the coupled species dynamics: As hydrogen mass flux g

o temperature and is coupled via the Schunk & l shuts down, methane cannot escape from the upper 15.0 Nagy (1980) collision coefficients to Methane, 1.3 atmosphere anymore and accumulates there. 17.5 which would otherwise not escape. 1.2 This effect starts to reverse again, as methane drops into 20.0 the lower atmosphere. 1 1.5 2 2.5 3 1.1 Radius [Rp] Fig. 3: Mass-loss of primary and secondary species: 0 1 2 3 4 5 16 Time [yr] * Hydrogen mass-loss reduces linearly with the width ]

3 Fig. 6: Transition to a metal-dominated atmosphere 14 of the temperature minimum 9 m ] c 1 g [ s * Increasing the thermospheric temperatures does * At a fixed radius of 1.25 RP, just above the visible t=1 s 10 g [ u

12 i x not affect the hydrogen escape rates. This can be d radius, we plot the densities of both species. u a l r f s understood as ‘cold trap’ effect of the temperature d 11 s e a x i M 10 minimum. f * The hydrogen depletion is evident, as well as the t 0 a 1

g 12 y reason for the increase in visible tau=1 altitude. t o i l s

* The escape rates of the secondary species are n 8 e

D 13

sensitive to the thermospheric temperature (see 0 * Lower altitudes deplete even faster of hydrogen, as 1 g

H CH4 orange vs. green and blue curves). This is caused by o the relative abundance of methane there is higher. l 6 14 1 2 3 4 5 6 7 8 9 10 the hot thermospheric hydrogen escaping very fast H CH4 Radius [Rp] and hence dragging methane efficiently. 0 1 2 3 4 5 Time [yr] Conclusion: The temperature structure between the mass reservoir of potentially Conclusion: While those first results successfully show a proof-of-concept transition, escaping species and the sonic point does matter. A most interesting longer simulation times, or a snapshot appproach e.g. coupled with MESA, finding is the different sensitivity of the two species to the thermospheric will be needed to decide the final mixing ratio of hydrogen in metal- temperature. dominated atmospheres.

3. Literature comparison 4. Outlook * In the near-future we work to include the effects of Fig. 7: Hydrogen-only mass-loss rates with our full modell photoionization via C²-ray by Mellema+(2006). This will result in

13 models that are entirely comparable to the literature values and Nominal Murray-Clay et al. (2009) * Including thermal and UV heating and thermal cooling via should resolve remaining discrepancies in adiabatic simulations. P/10 No cooling Freedman+(2014) and Malygin+(2014) opacities, reduces ] 1 12 temperatures and hence escape rates drop drastically (blue curve), s * Individual species will need dedicated Planck and Rosseland g [ with a minimum escape rate given by thermal irradiation. e mean-opacities in order to correctly compute temperature t a r * Two variability regimes exist. At low FUV, individual gas pockets structures of mixed atmospheres s 11 s o

l cool, and loose pressure support, falling back, leading to intermittent s s a escape. At high FUV, the escaping mass is enough to change the UV * Sub-Neptunes and Super-Earths are the natural objects to study M

d 10 absorption altitude.

e 0 . next. 1 g ) a V r U

e F ( v a * As important check, we disable radiation transport which results as References 9 m

e in similar physics as in Murray-Clay+(2009) (cyan curve)

m doi:10.3847/1538-4365/ab0a0e

i Benitez-Llambay+(2019), T doi:10.1051/0004-6361/201220159 0 * Another test with reduced Planck-opacities mimicks a molecule- Bitsch+(2013), 1

g 8 Commercon+(2011), doi:10.1051/0004-6361/201015880 o l depleted upper atmosphere, which increases escape rates due to Freedman+(2014), doi:10.1088/0067-0049/214/2/25 Variability due Variability due to less efficient thermal cooling (green curve). Guillot (2010) doi:10.1051/0004-6361/200913396 to cooling r( = 1)-shift doi:10.1051/0004-6361/201527815 7 Käppeli / Mishra 2016, 2 4 6 8 10 Conclusion: Lega+(2014), doi:10.1093/mnras/stu304 log10 Ultraviolet flux F [erg cm 2 s 1] UV Including thermal cooling can shut down escape. However, the Malygin+(2014), doi:10.1051/0004-6361/201423768 doi:10.1016/j.newast.2005.09.004 tabulated opacities assume typically solar atom/molecule mixes Mellema+(2006), Murray-Clay+(2009), doi:10.1088/0004-637X/693/1/23 which should be reduced or destroyed in UV-irradiated Schunk & Nagy (1980), doi:10.1029/RG018i004p00813 heterospheres. Hence our nominal results probably underestimate Toro (2009), doi:10.1007/b79761 escape as they represent the maximum possible cooling rate. Vaytet+(2011), doi:10.1051/0004-6361/201219427