Atmosphere escape inferred from modelling the Hα transmission spectrum of WASP-121b
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ATMOSPHERE ESCAPE INFERRED FROM MODELLING THE H α TRANSMISSION SPECTRUM OFWASP-121B
Dongdong Yan,
1, 2, 3
Jianheng Guo,
1, 2, 3
Chenliang Huang, and Lei Xing
1, 2, 3 Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, Kunming 650011, People’s Republic of China School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, People’s Republic of China Key Laboratory for the Structure and Evolution of Celestial Objects, CAS, Kunming 650011, People’s Republic of China Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, US (Received November 5, 2020; Revised December 25, 2020; Accepted January 7, 2021)
Submitted to ApJLABSTRACTThe escaping atmospheres of hydrogen driven by stellar X-ray and extreme Ultraviolet (XUV) have been detectedaround some exoplanets by the excess absorption of Ly α in far ultraviolet band. In the optical band the excessabsorption of H α is also found by the ground-based instruments. However, it is not certain so far if the escape of theatmosphere driven by XUV can result in such absorption. Here we present the XUV driven hydrodynamic simulationcoupled with the calculation of detailed level population and the process of radiative transfer for WASP-121b. Ourfiducial model predicts a mass loss rate of ∼ × g/s for WASP-121b. Due to the high temperature and Ly α intensity predicted by the fiducial model, many hydrogen atoms are populated into the first excited state. As aconsequence, the transmission spectrum of H α simulated by our model is broadly consistent with the observation.Comparing with the absorption of H α at different observation times, the stellar XUV emission varies in the range of0.5-1.5 times fiducial value, which may reflect the variation of the stellar activity. Finally, we find that the supersonicregions of the planetary wind contribute a prominent portion to the absorption of H α by comparing the equivalentwidth of H α , which hints that a transonic outflow of the upper atmosphere driven by XUV irradiation of the host starcan be detected by the ground-based telescope and the H α can be a good indicator of escaping atmosphere. Keywords: planets and satellites: atmospheres – planets and satellites: composition– planets andsatellites: H α transmission spectrum – planets and satellites: individual(WASP-121b) Corresponding author: Jianheng Guo, [email protected] a r X i v : . [ a s t r o - ph . E P ] F e b Yan et al. INTRODUCTIONPlanetary atmosphere is the key interacting layer between planets and their host stars. For close-in planets, theiratmospheres can be photoevaporated by the strong irradiation of the host stars (Shaikhislamov et al. 2018; Yan & Guo2019; Shaikhislamov et al. 2020). The escape of the atmosphere can potentially modify the atmospheric compositionand structure and further influence the planetary evolution and distribution (Owen & Wu 2013; Howe & Burrows2015; Fulton et al. 2017). Transmission spectroscopy is a powerful method for the study of the atmosphere, thespectra detected by which provide a lot of physical and chemical information of the planetary atmosphere. Manyatoms and molecules, such as H, He, Na, Mg, Fe, and H O, have been detected in the planetary atmosphere by thismethod (Vidal-Madjar et al. 2003; Lecavelier des Etangs et al. 2010; Jensen et al. 2012; Ehrenreich et al. 2015; Tinettiet al. 2007; Spake et al. 2018; Allart et al. 2018; Alonso-Floriano et al. 2019; Seidel et al. 2020; Hoeijmakers et al. 2020;Stangret et al. 2020), which is crucial for studying the origin of planets.By detecting the excess absorption of Ly α , the extended hydrogen atmosphere has been found in HD 209458b,HD189733b and GJ 436b(Vidal-Madjar et al. 2003; Lecavelier des Etangs et al. 2010; Jensen et al. 2012; Ehrenreichet al. 2015). The Ly α absorption is caused by the hydrogen atoms in the ground state. Thus the absorption depth isrelatively higher compared to the line absorption caused by the hydrogen atoms in the excited states. However, the Ly α line can be quenched by the hydrogen in the ISM and also affected by the geoemissions, which limits its observationsto the space. Fortunately, the transmission spectroscopy in the optical band provides an alternative way to study theatmosphere from the ground. Ballester et al. (2007) firstly reported the detection of Balmer edge absorption in HD209458b, even though the absorption was relatively low. After that, the H α transmission spectroscopy springs up fordetecting hydrogen atmosphere around the exoplanets. So far, the excess absorption of H α have been observed inseven exoplanet systems (HD 189733b, KELT-9b, KELT-20b, WASP-12b, WASP-52b, WASP-121b and WASP-33b(Jensen et al. 2012; Yan & Henning 2018; Cauley et al. 2019; Casasayas-Barris et al. 2018; Jensen et al. 2018; Chen etal. 2020; Cabot et al. 2020; Borsa et al. 2020; Wyttenbach et al. 2020; Cauley et al. 2020; Yan et al. 2020)). All thesedetections of H α show the existence of hydrogen in the excited state, although there are some controversies over theinterpretations of the H α signal in HD 189733b (Barnes et al. 2016; Cauley et al. 2017a,b).Among the seven systems, different assumptions are applied in explaining the H α signals. For HD 189733b, which hasa high gravitational potential, Christie et al. (2013); Huang et al. (2017) applied a hydrostatic model to fit the excessabsorption. However, the hydrostatic assumption can not be applicable for planets with an expanding atmosphereand a low mean density. For KELT-9b, it orbits a hot A-type star at 0.03368 AU (Borsa et al. 2019). Its equilibriumtemperature is higher than 4000 K so that many hydrogen atoms are in the first excited state (H(2)). In this situation,the intense near-ultraviolet (NUV) irradiation from its host star is the main source of heating in the atmosphere(Garc´ıa Mu˜noz & Schneider 2019). Although for hot stars, the irradiation of the NUV could be dominant in drivingthe escape of the atmosphere, the emission of the XUV should be more intense than that of NUV for late-type stars(Garc´ıa Mu˜noz & Schneider 2019).Therefore, this motivates us to explore the possibility that the H α transmission spectra are the signals of the escapingatmosphere driven by XUV. To this end, WASP-121b is an excellent target to study. Its mass and radius are 1.183 M J and 1.865 R J , respectively (Delrez et al. 2016). Therefore, one can expect a relatively expanding atmosphere owing toits low mean density and gravitational potential. In addition, WASP-121b is a hot Jupiter orbiting around a F6V starat a distance of 0.02544 AU. This means that the XUV irradiation received by the planet is about 1500 times higherthan that received at 1 AU. Using ESO-HARPS, Cabot et al. (2020) found that in the mid-transit the absorption ofH α at the line center was about 1.87%, along with a 5.82 km/s red-shift. Subsequently, Borsa et al. (2020) detectedabout 1.4% and 1.7% absorption depth of H α for 1-UT and 4-UT with ESO-ESPRESSO, respectively, both of whichalong with a blue-shift. In addition, other species such as Fe I, Fe II, MgII, and H O have also been found in itsatmosphere (Gibson et al. 2020; Hoeijmakers et al. 2020; Sing et al. 2019; Mikal-Evans et al. 2020; Evans et al. 2016).An expanding and potentially escaping hydrogen has been invoked to explain the H α absorption (Cabot et al. 2020;Borsa et al. 2020). However, a detailed model is still absent in explaining the excess absorption of H α . Thus, it isnot clear if the absorption in H α can be attributed to an escaping atmosphere driven by XUV irradiation of the hoststar. In this paper, our aim is to model the H α transmission spectrum of WASP-121b. In Section 2, we describe themethod. In Section 3, we display the results. In Section 4, we discuss the comparison with observations. In Section 5,we summarize the work and state our conclusions. METHOD he Astrophysical Journal Letters
Hydrodynamic atmosphere model
We used the hydrodynamic model (Yan & Guo 2019) to simulate the atmospheric structure of WASP-121b andobtained the atmospheric temperature, velocity and particle number densities. The planetary and stellar parametersare based on the observations (Delrez et al. 2016; Cabot et al. 2020). The equilibrium temperature (T eq ) is 2361 K,which is also the temperature at the bottom boundary in our model. The high temperature hints at the dissociationof H . The chemical composition of WASP-121b is assumed to be the same as that of WASP-121, which is calculatedby the solar abundance that is modified by [Fe/H] = 0.13 (Delrez et al. 2016). The integrated flux in XUV band isan important input in the simulations. Due to the lack of the stellar XUV observations, we used the age-luminosityrelation (Sanz-Forcada et al. 2011) to calculate the F XUV received by the planet. WASP-121b is about 1.5 Gigayear(Gyr), so the F XUV is about 37387 erg/cm /s at the orbital distance. In our calculation the value is divided by afactor of 4, which accounts for the uniform redistribution of the stellar radiation energy around the planet. Finally, theXUV SED is obtained by the XSPEC-APEC software (Arnaud 1996). In the simulations the pressure at the bottomboundary is 1 µ bar. The upper boundary is 7.6 R p , which covers the radius of the host star. The above input valuesare called the fiducial ones in this paper. In general, the escaping models assume that the photons of Ly α can freelyescape from the atmosphere (Murray-Clay et al. 2009). In the process of resonant scattering, the number of scatteringthat a Ly α photon takes to escape the atmosphere is comparable to its line center optical depth τ . In the atmosphereabove ∼ p where Ly α cooling is most efficient, τ (cid:28) /p abs , where p abs is the Ly α photon destroy probabilityper scattering (Huang et al. 2017). Thus, the Ly α cooling is included in the simulations. Furthermore, the stellar tidalforce is also considered in the model.2.2. Hydrogen populations in the excited state.
The H α absorption is caused by the hydrogen atoms in the first excited state (n=2, where n is the principal quantumnumber). Because of the coupling of spin and orbital angular momentum, this state is split to 2s and 2p substate. Inthe upper thermosphere, both the collisions among particles and the radiation process affect the population of H(2).Thus, we used a non-local thermal equilibrium (NLTE) scheme to calculate the hydrogen populations based on thehydrodynamic results. Assuming that the atmosphere is in a stationary state, the production rates of H(2) are equalto their loss rates. We find that the Ly α mean intensity ( ¯ J Lyα ) is dominant in determining the number density ofH(2p) (as shown by Equation (1)), which is consistent with that of Christie et al. (2013) and Huang et al. (2017).Therefore, it can be approximately expressed as: n p ≈ B s → p ¯ J Lyα A p → s n s (1)where n(1s) and n(2p) are the number densities of H(1s) and H(2p), B s → p and A p → s are the Einstein coefficients(Rybicki & Lightman 2004). The number density of H(2s) is solved in the meantime. The source of H(2s) is mainlyfrom l -mixing; and the sink of H(2s) is mostly due to the l -mixing ( < p ) and photoionization ( > p ). Therefore,it can be approximately expressed as: n s ≈ C p → s ( p ) n p n p + C p → s ( e ) n p n e C s → p ( p ) n p + C s → p ( e ) n e + Γ s (2)where C p ↔ s ( p ) and C p ↔ s ( e ) are the protons’ and electrons’ collisional transition rates (Seaton 1955) between 2pand 2s, n p and n e are the number densities of protons and electrons, and Γ s is the photoionization rate of H(2s).Although n p and n s can be estimated by Equation (1) and (2), in the simulations we solved the equation of rateequilibrium for H(2p) and H(2s) by including the reactions of radiative excitation and de-excitation, collision excitationand de-excitation, photoionization and recombination, etc. The equations of rate equilibrium are the same to that ofHuang et al. (2017).Because there is currently no available Ly α profile of the host star, in our model we took the Ly α flux of ζ Dor(Linsky et al. 2013) to replace that of WASP-121. ζ Dor is a F7V star whose spectral type is similar to that ofWASP-121 (F6V). The Ly α profile of ζ Dor is referenced from Wood et al. (2005). Based on this, we constructed adouble Gaussian profile with the full width at half maximum (FWHM) = 0.7 ˚A, and the two centers being 1215.5˚A and 1215.9 ˚A (Ly α , see the solid black line in Figure.1(a)). The Ly α integrated flux is about 71900 erg cm − s − . The ¯ J Lyα is then calculated by the Ly α resonant scattering method of Huang et al. (2017). Since the stellar Yan et al. Ly α profile is an important physical input in calculating H(2p) population but can not be measured precisely, weinvestigated another Ly α profile (Ly α , see the dashed red line in Figure.1(a)) with the same integrated flux and twocenters but with a different FWHM = 0.45 ˚A. The Ly α intensity is higher around the line center of Ly α profile,which leads to higher Voigt line profile weighted mean intensity (see Figure.1(b) for ¯ J Lyα of Ly α and Ly α ). TheH α absorption (see Figure.1(c); for more details, see Method below) is slightly deeper for Ly α case compared to thatof Ly α . The difference of absorption at the H α line center is less than 0.2% and it is indistinguishable at the linewings. Our results show that the FWHM of Ly α input profile in the range of 0.45 to 0.7 ˚A has minor influence on thefinal results. Therefore, we use Ly α in our models.Finally, the ionization of H(2s) and H(2p) is an important process which is caused by the photons in the wavelengthrange of 912-3646 ˚A. The spectrum in this wavelength range is taken from the stellar atmosphere model of Castelli &Kurucz (2003). The photoionization cross-sections of H(2s) and H(2p) are cited from TOPbase of The Opacity Project(Cunto & Mendoza 1992; Cunto et al. 1993). 2.3. H α radiative transfer After we obtained the hydrogen populations, we simulated the H α radiative transfer as the stellar H α line travelsalong the ray path in the planetary atmosphere during transit (Yan & Guo 2019). The transmission spectrum isdefined by Equation (3) as a function of wavelength, T S ( λ ) = F IT F OT ( λ ) − . − T S ( λ )”, where F IT and F OT are the in- and out-oftransit flux. H α absorption is a bound-bound transition whose line center is at 6562.8 ˚A (in air). The calculation ofcross-section of H α absorption is similar to that of Ly α RESULTS3.1.
The fiducial model
We define the model with the fiducial inputs as our fiducial model (OFM). The mass loss rate of WASP-121b is1.28 × g/s for the fiducial model. The number density of hydrogen atoms is obtained from the hydrodynamicsimulation. The atmospheric structures are showed in Figure.2(a-c). As we can see, the highest temperature is higherthan 10000 K. The velocity becomes supersonic when the altitude is larger than 1.7 R p , and reaches 100 km/s beyond 7R p . By solving a detailed equation of statistical equilibrium, we obtained the number densities of H(2s) and H(2p) (seeFigure.2(a)). The number density of H(2s) plus H(2p) is about a few 10 − times H(1s). The ratio of H(2p) to H(2s)changes significantly with the increase of r/R p , mainly due to the large photoionization of the n=2 state hydrogen,which especially affects H(2s). The optical depth of H α line center is shown in Figure.2(d), which is larger than unitywhen r/R p is less than 1.1.We compared the simulated transmission spectrum with the observation of Borsa et al. (2020) (B20) . In theirwork, they reported the observations in 1-UT and 4-UT mode, the observation time of which is 06 Jan 2019 and 30Nov 2018. The H α absorption depth was about 1.4% and 1.7% for 1-UT and 4-UT mode, with a blue shift of 4.64and 3.9 km/s, respectively. B20S is obtained by shifting the observed transmission spectrum of Borsa et al. (2020)towards the red side by the corresponding blue shift for 1-UT and 4-UT.To investigate the contribution of different atmospheric regions to the H α absorption, we calculated the H α absorptionfor different altitudes of the atmosphere until the altitude reaches 7.6 R p . Figure.3(a) shows the results of the fiducialmodel, in which the gray dots with errorbars are B20S. The lightgray and darkgray points are for 1-UT and 4-UT,respectively. The different lines represent the absorption of H α produced in different atmospheric altitudes. Oursimulations show that different altitudes of the atmosphere contribute differently to the final transmission spectrumof H α . The increase of the altitude leads to a deeper absorption. From 3 R p to 4 R p , the absorption at H α line centeronly increases by 0.05%. The H α absorption of WASP-121b by the atmosphere above 4 R p is negligible because theH(2) are sparse. In addition, we compared the equivalent width (EW) of the model transmission spectrum with that Note the data of B20 used in this paper was extracted from Figure.9 of Borsa et al. (2020) by “WebPlotDigitizer”, a tool for extractingthe data points (https://automeris.io/WebPlotDigitizer/index.html). he Astrophysical Journal Letters σ ) and lower (- 1 σ ) limit of the observations. One can see that the EW of the fiducialmodel increases with the increase of the atmospheric altitude. For 1-UT, an atmosphere higher than 1.7 Rp can fit theobservation in the three passbands. For 4-UT, a supersonic atmosphere beyond the Roche lobe (1.86 R p ) is required tofit the EW in 0.75 and 1.0 ˚A. For example, an atmosphere at least up to 6 R p can fit the lower limit of the observationin passband 1.0 ˚A. The EW of the model in passband 1.5 ˚A, however, can not reach the lower limit of the 4-UTobservation, because our model can not reproduce the relatively high absorption at the H α line wings.The results above show that the absorption of H α close to the line center can be well fitted by our model and thecontribution of supersonic regions can not be neglected. However, the strong absorption in the wings of H α for 4-UTshould be investigated in the future. Furthermore, the 1D simulation can not reproduce the blue-shift found by B20.A blue- or red- shift has also been found in other absorption lines in exoplanetary atmosphere (Casasayas-Barris etal. 2018; Allart et al. 2018; Gibson et al. 2020; Bourrier et al. 2020; Cabot et al. 2020), which can be led by theatmospheric winds or the circulations from the day-side to night-side (Guo 2013).3.2. XUV integrated flux
Since the XUV integrated flux was calculated by the age-luminosity relation of Sanz-Forcada et al. (2011), therecould be some uncertainties due to the uncertainty of the stellar age (Delrez et al. 2016). Here we investigated towhat extent the F XUV will influence the H α transmission spectrum. We adopted 0.5, 0.75, 1.5, 2.0, 3.0 and 4.0 timesthe value of fiducial F XUV ( F ), and the mass loss rates are 8.20 × g/s, 1.07 × g/s, 1.58 × g/s, 1.84 × g/s,2.29 × g/s and 2.68 × g/s accordingly. The energy-limited theory (Lammer et al. 2003; Erkaev et al. 2007)proposes that the mass loss rates of the atmosphere are proportional to the F XUV . However, our results found thatthey do not increase linearly with the increase of the F XUV because the escape of Ly α photons takes away a portion ofthe heat from the atmosphere. The H α absorption increases moderately with F XUV (see Figure.4(a), the transmissionspectra are calculated within 7.6 R p ). For instance, an increase of a factor of 8 in F XUV only increases the absorptionat line center by ∼ F XUV , the corresponding temperatureof the atmosphere becomes higher at the bottom of the atmosphere but will drop dramatically with the increase ofatmospheric altitude. The high temperature occurs in the relatively high pressure and is close to the bottom of theatmosphere, so that the Ly α photons will spend a longer time to be scattered out of the atmosphere. Therefore, the¯ J Lyα will be more intense and then will excite more hydrogen atoms into the n=2 state. However, the atoms can beionized easily owing to higher F XUV . The combined effect is to increase the H α absorption slightly. It is clear fromFigure.4(a) that a higher F XUV is needed to fit the 4-UT data, while a relatively lower F XUV is preferable for thedata of 1-UT. This can be verified by Figure.4(b), which shows the χ as a function of F XUV . The χ is calculatedin passband 1.5 and 3.6 ˚A for 1-UT and 4-UT, respectively. The minimum χ for 1-UT and 4-UT occurs at F XUV =F * 0.5 and F XUV = F * 1.5, respectively. Borsa et al. (2020) reported that log R (cid:48) HK = -4.87 ± R (cid:48) HK =-4.81 ± F XUV levels for 1-UT and 4-UT may reflect the different stellar activities of WASP-121 in thetwo observations. A higher F XUV of 4-UT could probably attributes to its higher activity level compared to that of1-UT.We also simulated the H α transmission spectra for the cases of F XUV = F * 0.5 and F XUV = F * 1.5 as a functionof different altitudes. Figure.5(a) shows the case of F XUV = F * 0.5. The absorption caused by the atmospherebelow the sonic point (1.7 R p ) is shallower compared with 1-UT of B20S. Figure.5(b) shows the equivalent width as afunction of different altitudes. It shows when WASP-121b receives 0.5 times the fiducial XUV irradiation of the hoststar, the EW produced by the atmosphere lower than 2.5 R p can not reach the lower limit of the observation. Above2.5 R p , the more the atmosphere expands, the better the fit to the observation of 1-UT. Figure.5(c) and (d) are thesame to Figure.5(a) and (b), respectively, but for the case of F XUV = F * 1.5 and in comparison with 4-UT of B20S. Yan et al.
The EW of the model can not reach the lower limit of the EW of 4-UT, because our model can not reproduce therelatively high absorption at the H α line wings. 3.3. XUV SEDs
XUV SEDs can also influence the photoionization process in the atmosphere(Guo & Ben-Jaffel 2016). Accordingto Owen & Jackson (2012), X-ray can solely drive hydrodynamic escape of planetary atmosphere. Here we study theeffect of different SEDs on the transmission spectra by introducing a modified spectral index β m , defined as F(1-100˚A)/F(1-912 ˚A), where F(1-100 ˚A) is the integrated flux in the band of X-ray and F(1-912 ˚A) is the integrated fluxof the whole XUV band. For the fiducial model, the value is 0.1475. We tested the cases of 0.03 (almost no X-raybut all EUV), 0.103, 0.221, and 0.5 (half X-ray and half EUV, which could be not real according to the evolutionof XUV radiation of late-type stars, and it is for model experiment), while the XUV integrated flux F XUV = F .Figure.4(c) shows the transmission spectra (calculated within 7.6 R p ). One can see that a larger X-ray proportionwill lead to deeper H α absorption. The main reason is that more hydrogen atoms will be retained instead of beingionized, due to the lower photoionization cross section (inversely proportional to the cube of the frequency) in X-rayband in comparison with that in EUV. To compare with the observations, Figure.4(d) shows the χ as a function of β m . For 1-UT, the minimum χ appears at β m = 0.003. For 4-UT, the χ decreases with the increase of β m . A higher β m is required to fit the absorption at H α line wings for 4-UT. However, the variation of χ is less than 1 for β m from0.103 to 0.5. In addition, for the case of β m = 0.5 the absorption at H α line center exceeds the upper limit (+ 1 σ ) ofthe observation. Thus, a high β m can not be applicable for 4-UT although the value of the χ is smaller. Thus, wesuggest that β m should be confined to a relatively low level in order to fit the observation at different times, which isconsistent with the evolution of XUV radiation of late-type stars (Sanz-Forcada et al. 2011). DISCUSSIONIn addition to the observation of H α transmission spectroscopy conducted by Borsa et al. (2020), there is anotherobservation made by Cabot et al. (2020) (C20). According to C20, the observed transmission spectrum can be fittedwith a Gaussian profile, of which the full width at half maximum (FWHM) is 0.75˚A and the line center is at 6562.93˚A. C20S is the transmission spectrum obtained by shifting the Gaussian fitted spectrum towards the blue side by 5.82km/s. The average absorption depths (ADs) in different passbands are also shown in their work (see Table.3 of Cabotet al. (2020)).For comparison with C20, we calculated the ADs of the simulated transmission spectra in different passbands asshown in Figure.6. The passbands are 0.188, 0.375, 0.75, 1.5 and 3 ˚A, which are the same to that used in C20. In theirwork, they used the photo noise and readout noise from the observed spectrum to calculate the weight (Casasayas-Barris et al. 2017) for the mean absorption depth. Here, we evaluated the ADs of C20S for the above passbands byan equally weighted method (i.e., the spectral points are weighted equally despite different errors) and found that theresults did not deviate much from C20. We also calculated the χ of the ADs in different passbands for the models ofdifferent F XUV and XUV SEDs with respect to that of C20.Figure.6(a) shows the the χ as a function of F XUV for different passbands. The minimum χ appears at 0.5, 0.75and 1.0 F for the given passbands, indicating that the F XUV is not larger than the fiducial value. The F XUV valuesin the range of 0.5-1.0 times F reflect that the stellar activity may be between that of 1-UT and 4-UT of B20. We alsosimulated the H α transmission spectra for the cases of 0.5, 0.75 and 1.0 times F and found that the H α absorptioncaused by the atmosphere below the sonic points for the three F XUV cases is not enough to match C20S, especially forthe absorption at line center (see Figure.6(b)), which shows that the supersonic regions are not negligible in explainingthe excess absorption of H α of WASP-121b.Figure.6(c) shows the χ as a function of β m for different passbands. For the cases of 0.188, 0.375 and 1.5 ˚A, theminimum χ appears at β m = 0.103; for the cases of 0.75 and 3.0 ˚A, the model of β m = 0.03 is closest to the observation.This is consistent with the conclusion of B20S that β m is confined to a lower level. SUMMARYIn this paper, we presented the XUV driven hydrodynamic simulation including the detailed hydrogen populationcalculation and the process of radiative transfer to model the H α transmission spectrum of WASP-121b. Our modelsare in agreement with the observations. We found that the supersonic regions of planetary wind contribute a prominentportion to the absorption of H α . We also performed a broad parameter study to evaluate the affects of the input stellar he Astrophysical Journal Letters F XUV can be in the range of0.5-1.5 times the fiducial value and the different F XUV level inferred from the independent observations may reflect thestellar activities of the host star. It also showed that the X-ray portion in the XUV radiation should be at a low level,which is consistent with the evolution of XUV radiation of late-type stars (Sanz-Forcada et al. 2011). The parameterstudy enhanced the conclusion of the fiducial model that the supersonic regions are indispensable in the interpretationof the excess absorption of H α for WASP-121b, which clearly expresses the requirement of a transonic hydrodynamicatmosphere. The consistence of our simulations and the observation of H α transmission spectrum suggested that thereis an expanding hydrogen atmosphere around this planet. These findings are helpful for the future detection of theescaping planetary atmosphere around F-type stars by using the ground telescope. Acknowledgement.
We thank the anonymous reviewers for their constructive comments to improve themanuscript. We also thank Z. W. Han and G. Chen for their helpful discussions about the observation data. Theauthors also acknowledge supports by the Strategic Priority Research Program of Chinese Academy of Sciences, GrantNo. XDB 41000000 and from National Natural Science Foundation of China though grants 11973082 to JG.REFERENCES
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Figure 2. Atmospheric structures.
This structure is plotted as a function of r/Rp, r is the distance from the planetarycenter and Rp is the planetary radius. (a) The number density for H(1s), H(2p) and H(2s). (b) The atmospheric temperature.(c) The particles’ velocity. (d) Optical depth of H α line center as a function of impact parameter. he Astrophysical Journal Letters (a) (b)(c) (d) Figure 3. H α transmission spectrum and the equivalent width (EW). (a) H α transmission spectrum. The gray dotswith errors are the H α transmission spectrum of B20S, with the lightgray for 1-UT and darkgray for 4-UT. The red dashedline represents the absorption within the sonic point (SP). Other lines represent the absorption within the labeled atmosphereregions. (b) The equivalent width calculated in passband 0.75 ˚A as a function of atmospheric altitude. The black line representsthe EW of the fiducial model, in which the sonic point is marked by the purple cross. The orange and cyan horizontal solidlines represent the mean EW of 1-UT and 4-UT, respectively. The corresponding dashed lines are + 1 σ and - 1 σ of the meanEW. (c) and (d) are the same as (a), but for the passbands 1.0 and 1.5 ˚A, respectively. Yan et al. (a) (b)(c) (d)
Figure 4. H α transmission spectrum and the comparison of models with observations. (a) H α transmissionspectrum. The gray dots with errors are the H α transmission spectrum of B20S, with the lightgray for 1-UT and darkgray for4-UT. Different lines represent models of different F XUV , calculated within 7.6 R p . (b) χ as a function of different F XUV .The black line represents the χ for 1-UT, calculated in passband 1.5 ˚A. The red line represents the χ for 4-UT, calculated inpassband 3.6 ˚A. (c) The same as (a), but for the models of different XUV SEDs while F XUV = F , calculated within 7.6 R p .Note that the black and green lines are almost overlapped. (d) The same as (b), but for the models of different XUV SEDswhile F XUV = F . he Astrophysical Journal Letters (a) (b)(c) (d) Figure 5. H α transmission spectrum and the comparison of models with observations for F XUV = F ∗ . and F XUV = F ∗ . . (a) H α transmission spectrum as a function of altitudes for F XUV = F ∗ .
5, in comparison with the observationof 1-UT. (b) The equivalent width calculated in passband 1.5 ˚A as a function of atmospheric altitude, in comparison with theobservation of 1-UT. The orange horizontal solid line represents the mean EW of 1-UT and the dashed lines are + 1 σ and - 1 σ of the mean EW. The sonic point is marked by the purple cross. (c) The same as (a), but for F XUV = F ∗ . F XUV = F ∗ . Yan et al. (a)(b)(c)
Figure 6. Comparison with C20. (a) χ as a function of different F XUV . Different colors represent the χ calculated byusing different passbands. (b) Transmission spectrum for 0.5, 0.75 and 1.0 times F . The Green solid line represents C20S.Other solid lines are calculated within 7.6 R p , and the dashed lines are calculated within the sonic points. (c) χ as a functionof different XUV SEDs, which are characterised by β mm