The Influence of \ceH2O Pressure Broadening in High Metallicity Exoplanet Atmospheres
Planet formation models suggest broad compositional diversity in the sub-Neptune/super-Earth regime, with a high likelihood for large atmospheric metal content ( 100 Solar). With this comes the prevalence of numerous plausible bulk atmospheric constituents including \ceN2, \ceCO2, \ceH2O, \ceCO, and \ceCH4. Given this compositional diversity there is a critical need to investigate the influence of the background gas on the broadening of the molecular absorption cross sections and the subsequent influence on observed spectra. This broadening can become significant and the common \ceH2/He or “air” broadening assumptions are no longer appropriate. In this work we investigate the role of water self broadening on the emission and transmission spectra as well as on the vertical energy balance in representative sub-Neptune/super-Earth atmospheres. We find that the choice of the broadener species can result in a 10 – 100 parts-per-million difference in the observed transmission and emission spectra and can significantly alter the 1-dimensional vertical temperature structure of the atmosphere. Choosing the correct background broadener is critical to the proper modeling and interpretation of transit spectra observations in high metallicity regimes, especially in the era of higher precision telescopes such as JWST.
A primary goal of exoplanet science is the determination of basic planetary conditions. Transit spectrophotometry observations of planetary atmospheres offer a window into fundamental quantities such as climate and composition (e.g., Madhusudhan et al. (2016)). Determining atmospheric composition is a necessary requirement for assessing the relative importance of various chemical processes (Moses, 2014) and greatly assists in understanding planet formation by linking volatile inventory to proto-planetary disk processes (Pollack et al., 1996; Öberg et al., 2011; Madhusudhan et al., 2014; Cridland et al., 2016; Öberg et al., 2011; Mordasini et al., 2016).
One of the key findings of the Kepler Mission (Borucki et al., 1997) is that a majority of exoplanets fall within this “warm sub-Neptune” regime (2–4 Earth radius, T1000 K ) (Fressin et al., 2013; Batalha, 2014; Fulton et al., 2017). These planets have been an intense area of focus for transit spectra observations with the Hubble Space Telescope (HST) (Kreidberg et al., 2014a; Fraine et al., 2014; Knutson et al., 2014). In addition, over the next decade they will serve as the link between jovian worlds and terrestrial planets as well as being the most prolific population of planets to be found by the Transiting Exoplanet Explorer Satellite (TESS, Sullivan et al. (2015); Louie et al. (2018); Barclay et al. (2018); Kempton et al. (2018)).
Planet formation, interior structure, and atmospheric chemistry modeling (Fortney et al., 2013; Moses et al., 2013; Lopez & Fortney, 2014) suggest extreme compositional diversity within this sub-population, with a high likelihood for large atmospheric metallicities (100 Solar). Given this potential for compositional diversity, the assumption of “jovian-like” \ceH2/He-dominated atmospheres may not always be appropriate. Instead, with currently measured atmospheric metallicities reaching as high as 300–1000 solar (Line et al., 2014; Fraine et al., 2014; Kreidberg et al., 2014b; Knutson et al., 2014; Morley et al., 2017), molecules such as \ceH2O and \ceCO2 will become the dominant bulk constituents (Moses et al., 2013; Hu & Seager, 2014).
Along with this diversity in composition, comes with it numerous challenges in atmospheric modeling, which ranges from chemical modeling (Hu & Seager, 2014) to cloud microphysics (Ohno & Okuzumi, 2018) to 3D climate modeling (Kataria et al., 2014). Nearly all flavors of atmospheric modeling that aim to make observational predictions require radiative transfer computations. A key necessary ingredient in radiative transfer computations are the opacities, which for planets, are dominated by the molecular absorption cross sections (hereafter, ACS (Mihalas, 1970)). The ACS of a given molecule typically consist of billions of lines representing the ability of a molecule to absorb or emit photons. Each line has its own linewidth (or broadening) typically specified through the degree of thermal/Doppler and pressure broadening (Goody & Yung, 1995). Pressure broadening is the net cumulative effect of interactions between the absorbing molecule in question (e.g., \ceH2O) and with its neighboring molecules (or bath gases, e.g., \ceH2, He) or by self broadening (\ceH2O with itself). Much exo-atmospheric relevant ACS focus, specifically broadening, has been jovian-centric (e.g., \ceH2\ceHe dominated compositions and broadening Freedman et al. (2008); Tennyson et al. (2016); Grimm & Heng (2015); Hedges & Madhusudhan (2016)) which had been largely driven by the abundance of high fidelity “hot-Jupiter” observations and carry over from brown dwarf modeling.
Exploration of pressure broadening assumptions in exo-atmospheres is not new (e.g., Grimm & Heng (2015); Hedges & Madhusudhan (2016)). Hedges & Madhusudhan (2016) provide a comprehensive overview of the various pressure broadening effects including resolution, line-wing cutoff, Doppler versus pressure, and more relevant to our investigation, an initial look at the impact of a broadener choice. They too explore the impact of \ceH2O versus \ceH2 broadening on the \ceH2O ACS, specifically over HST wavelengths, and found that the band-averaged ACS can change up to an order-of-magnitude.
In this letter we expand upon the work in Hedges & Madhusudhan (2016) to not only determine the influence of \ceH2O self broadening on the \ceH2O ACS, but also as a function of water fraction, and more importantly we quantitatively assess the integrated effect that the broadener choice has on the observable spectra as well as on the impact on the atmospheric vertical energy balance. This work is crucial to the proper interpretation of transit spectra observations in high metallicity regimes, expected of the sub-Neptune/Super-Earth population. In §2 we describe our data sources and how we compute the ACS and the transmission/emission spectrum and self-consistent modeling approach. In §3 we compare the impact of \ceH2O self broadening with the standard \ceH2/\ceHe broadening assumption. Finally, in §4 we discuss the implications and future prospects. We also make our newly computed water ACS grid for both broadeners publically available111LINK:TBD UPON ACCEPTANCE.
In this initial investigation on the impact of non- \ceH2/\ceHe foreign broadening on transmission/emission spectra, we choose to focus on \ceH2O because: 1) \ceH2O is the most prominent absorber in exoplanet spectra due to its large abundance over a range of elemental compositions (Moses et al., 2013) and multiple strong absorption bands from the optical to far infrared wavelengths and 2) it shows the largest sensitivity to choice of broadener when compared to other species (a factor of 7 increase in broadening when compared to \ceH2/He, Table 1).
|\ceH2O||Self||0.3 – 0.54||7||1,2|
|\ceH2/\ceHe||0.05 – 0.08||1||1|
|\ceCO2||0.15 – 0.20||3||1|
|\ceair||0.08 – 0.1||1.5||1|
|\ceCH4||Self||0.06 – 0.09||1.5||3|
|\ceH2/\ceHe||0.05 – 0.08||1||4|
|\ceH2O||0.06 – 0.09||1.5||5|
|\ceCO2||0.07 – 0.09||1.5||6|
|air||0.02 – 0.07||1||3|
|\ceCO2||Self||0.08 – 0.12||2||7|
|\ceH2/\ceHe||0.09 – 0.12||2||8|
|\ceH2O||0.10 – 0.14||2.5||9|
|air||0.05 – 0.08||1||7|
|\ceCO||Self||0.04 – 0.09||1||10|
|\ceH2/\ceHe||0.04 – 0.08||1||10|
|\ceH2O||0.07 – 0.1||1.5||11|
|\ceCO2||0.07 – 0.1||1.5||11|
|air||0.05 – 0.07||1||12|
Relative to the average value of of \ceH2O@[\ceH2+\ceHe].
Denoted by \ceH2O@[self] in the text and figures.
Denoted by \ceH2O@[\ceH2+\ceHe] in the text and figures.
Refs.: (Brown et al., 2005), (Ptashnik et al., 2016), (Smith et al., 2014), (Pine & Gabard, 2003),(Delahaye et al., 2016a), (Lyulin et al., 2014), (Devi et al., 2016), (Padmanabhan et al., 2014), (Delahaye et al., 2016b), (Devi et al., 2002), (Hartmann et al., 1988) ,(Devi et al., 2012), and also data extracted from Refs. in Table 3 of (Hartmann et al., 2018) and from (Gordon et al., 2017).
The fundamental approach here is to compute the \ceH2O ACS being under different end-member scenarios, with the first the standard “Jovian-like” \ceH2/\ceHe broadening (\ceH2O@[\ceH2+\ceHe])) and the second, pure \ceH2O broadening (\ceH2O@[self]), which would be more appropriate for high metallicity or all steam atmospheres. We would then like to determine the spectral differences between \ceH2/\ceHe and self broadening of \ceH2O in high metallicity/all steam atmospheres.
2.1 Line Lists
In order to generate the pressure-broadened \ceH2O ACS, the completeness and the accuracy of line lists and pressure coefficients data are essential. These can be determined either through high-level quantum mechanics calculations or through spectroscopic laboratory measurements. The EXOMOL database contains the complete water BT2 line list (Barber et al., 2006) for T3000K, rotational quantum numbers (J) up to 50 and frequencies up to 30,000 cm; a trimmed version of this linelist is used in the HITEMP database (Rothman et al., 2010). The NASA AMES line list (Partridge & Schwenke, 1997) is another ab-initio source of water data which has more accurate line positions than BT2 but less complete. Recently, there has been an attempt to improve the BT2 linelist by refining the potential energy surfaces which resulted in raising J up to 72 and frequencies up to 40,000 cm (Polyansky et al., 2016). The pressure-broadening data provided by EXOMOL are limited to \ceH2 and \ceHe. Complimentary to ab initio studies, laboratory data integrated into the HITRAN database (Rothman et al., 1998) leverages high-resolution spectrometers to provide precision line positions and intensities. Experimental ACS data are mostly limited to the earth-like environmental conditions (i.e., T350K, P1 bar) with the dominant background broadener being “air” (N/O).
There is a clear gap in exoplanet relevant ACS, lying between the low temperature air broadening provided by HITRAN (applicable to temperature terrestrial planetary atmospheres), and the high temperature H/He broadening given by HITEMP (applicable to H/He dominated Jovian-like worlds). The high metallicity warm-(sub)Neptune/Supe-Earth sub population of exoplanets occupies a compositional regime between these two: neither pure H/He nor pure “air”. In order to fill this gap we generate an \ceH2O@[\ceH2+\ceHe] and \ceH2O@[self] ACS database. We leverage the readily available EXOMOL (Tennyson et al., 2016) line-list data which provides the full BT2 line list (Barber et al., 2006) up to 3000K, J50 and energies up to 30,000 cm; valid over a broad range of “typical” exoplanet environmental conditions.
2.2 Computation of pressure-broadened \ceH_2 ^16O absorption cross sections
Molecules in the outermost layer of a given atmosphere (where P 10 bar) experience a negligible amount of interactions with their neighboring atoms or molecules due to the low collisional frequency and large collisional frequency (see results section by (Lyons et al., 2018)). In this environment, Doppler broadening will be the dominant effect which forms the spectral line shape and will depend on the molecular mass, temperature, and spectral line position. Absorbing molecules start to collide and interact with background molecules more frequently as pressure increases in the lower layers in the atmosphere. These pressure broadening interactions will increase as the pressure goes above 10 bar, and will become the dominant broadening effect at P 10 bar. The pressure broadening line profile can be represented effectively through Lorentzian line shape and the associated Lorentzian linewidth will be calculated through Eq. (1):
where is the Lorentzian coefficient, is the broadeners partial pressure, is the reference temperature (i.e., 296K), n is the temperature-dependence coefficient, and index represents the dependency of these parameters into the broadener (Hedges & Madhusudhan, 2016). Kinetic theory predicts the n = 0.5. In a typical broadened ACS spectra, both Doppler- and pressure-broadening line profiles convolve to generate Voigt profile, and the Voigt linewidth (Olivero & Longbothum, 1977) is represented with Eq. (2):
where is the Doppler linewidth. In this study, the pressure-broadened \ceH2O ACS data are computed for two set of broadeners: 1) 85 \ceH2 and 15 He using pressure coefficients data presented by EXOMOL group (Barton et al., 2017), and 2) 100 \ceH2O using the average value of available experimental self broadening coefficients as J-independent data. The water BT2 linelist (Barber et al., 2006) is inputed into the EXOCROSS script 222https://github.com/Trovemaster/exocross (Yurchenko et al., 2018) to model the full Voigt profile (Humlíček, 1979) of every single line between 100–30,0000 cm over a grid of applicable temperatures and pressures (Table 2). The spectral sampling resolution is optimized as a function of temperature, pressure, and spectral sub-divisions in such a way as to fully resolve the individual lines without undue computational burden (Table 2). Figure 1 illustrates the comparision between our adaptive resolution (see Table 2 i.e. 1 sampling point per half width: 1/ or 2 sampling points per half width: 2/) with ultra high sampling of 6 points per half width (6/) and with the EXOMOL computed ACS333http://exomol.com/data/data-types/xsec/H2O/1H2-16O/BT2/ for \ceH2O@[\ceH2+He] for P= 10 bar and T=400K.
The \ceH2O ACS are computed for two sets of broadeners: 1) 85 \ceH2 and 15 He using the J-dependent pressure coefficients from EXOMOL (Barton et al., 2017), and 2) 100 \ceH2O using the average value of available experimental self broadening coefficients (Ptashnik et al., 2016).
|Line wing cut-off||P1||bar:||300||cm|
The Lorentz wing shape may not be appropriate out at such distances (Freedman et al., 2008)
2.3 Modeling the Impact on Transmission/Emission Spectra of Transiting Exoplanets
To assess the signifigance of the broadener assumption on exoplanet transmission/emission spectra, we use the CHIMERA (Line et al., 2013, 2014; Stevenson et al., 2014; Kreidberg et al., 2015; Line & Parmentier, 2016; Kreidberg et al., 2018) code with our newly generated ACS (converted to =100 correlated-K coefficients (Amundsen et al., 2016)) to model transit/eclipse spectra of a representative sub-Neptune like planet (GJ1214b (Harpsøe et al., 2013), T=500–900K). We first generate forward model spectra using both sets of ACS (\ceH2O@[self] and \ceH2O@[\ceH2+\ceHe]) given a fixed temperature-pressure profile (TP, Guillot (2010) Eqs. 24, 49 )444With cm/g, , T=500, 700, 900K, T=0K and either 100% \ceH2O or 500Solar metallicity assuming thermochemical equilibrium molecular abundances555NASA CEA2 (Gordon & Mcbride, 1994) with scaled solar (Lodders et al., 2009) abundances. We include as opacities in this scenario \ceH2/He broadened \ceH2O, \ceCH4, CO, \ceCO2, \ceNH3, \ceH2S, Na, K, HCN, \ceC2H2, \ceTiO, VO, \cePH3, and \ceH2 \ceH2/He CIA (Freedman et al., 2014) . Second, we compute a self-consistent radiative equilibrium atmosphere666Zero internal heat flux, PHOENIX stellar model for GJ1214, and an equilibrium temperature of 550 K so as to keep temperatures at all layers within the valid cross section temperature range of 400–1500K using the tools described in Arcangeli et al. (2018); Mansfield et al. (2018); Kreidberg et al. (2018) to determine the impact of water broadening on the vertical energy balance and, in turn, on the observed spectra. We discuss our findings in the next section.
3.1 Impact on Cross Sections
Figure 2 illustrates the effect of temperature, pressure, and water abundance on the difference between @[self] and @[\ceH2+\ceHe] broadened ACS near 6 . The top panel shows how broadening changes with temperature at a fixed pressure of 1 mbar. Differences are largest for cooler temperatures where pressure broadening becomes more important. The middle panel illustrates the impact of different pressures at a fixed temperature (725K). Even at low pressures (1 bar) pressure broadening differences are still present in the line wings. The bottom panel shows the effect of varying water abundance on the combined @[self]+@[\ceH2] broadening at a fixed temperature and pressure (725K, 1 mbar). With pure self broadening, differences in the line wings can approach an order of magnitude. For a 30% mole fraction of water, the ACS is about 3–5 greater than pure hydrogen broadening. While not shown, these differences become larger at longer wavelengths and smaller at shorter wavelengths due to the relative importance of Doppler-to-pressure broadening.
3.2 Direct Impact on Transmission/Emission Spectra
More practically, Figure 3 summarizes the key impact of @[\ceH2+\ceHe] versus @[self] broadening on the emission (top row) and transmission (bottom row) spectra of a typical sub-Neptune under the assumption of a pure steam atmosphere (left column) and a 500Solar metallicity777While the water mixing ratio is only 10–20% for these conditions, we still use the pure @[self]-broadened water ACS as it is still a more accurate approximation than pure @[\ceH2+\ceHe] broadening scenario (right column). Overall, we find that the differences ( in the bottom panels in Figure 3a,b,c, and d) are quite large, 10s to 100s of ppm. These differences are well within the detectable range of both HST (Kreidberg et al., 2014a), and certainly the James Webb Space Telescope (JWST, e.g., Greene et al. (2016); Bean et al. (2018)), especially for the anticipated windfall of such planets around bright stars (Sullivan et al., 2015).
In the all-steam atmospheres, emission differences (Figure 3a) are largest in the window regions (m, m ). The increased flux for the @[\ceH2+\ceHe] broadened ACS is because of the lower opacity, permiting flux from deeper, hotter layers to emerge (for a fixed TP). The increased opacity due to the @[self] broadening obscures the deeper/hotter layers, resulting in lowered fluxes at those wavelengths. These differences are, of course, strongly dependent upon the temperature structure within in the atmosphere. As these spectra assume a fixed TP there is a difference in net radiated flux, which will most certainly have an influence on the radiative balance and thermal structure in the atmosphere, as discussed in §3.3.
Transmission spectra tell a similar, albeit less dramatic story with relative differences of 60 ppm across shown wavelength range. The “linear-like” slope in the differences with wavelength is due to the frequency dependence of Doppler-to-pressure broadening.
The effects at high metallicity (500Solar, Figure 3, right column) are less extreme (10’s of ppm) due to the reduced abundance of \ceH2O (10 – 20%) and the significant abundances of additional opacity sources (mainly \ceCO2, CO, \ceCH4, and \ceH2/He). Furthermore, due to the reduced impact of \ceH2O@[self] broadening (Figure 2), we expect an approximate (comparing 1 mbar line wings) reduction of 3–5 to 10ppm in the transmission spectra.
3.3 Impact on Self-Consistent 1D Atmosphere
Figure 4 shows the impact of self broadening on the 1D radiative balance (and subsequent observational effects) of a 550K planet under the all steam and 500Solar scenarios. The @[self] broadening results in 100-180K hotter temperatures below the 1 mbar level and 60K cooler above for the all steam scenario (Figure 4a). More intuitively, the increased @[self] mean opacity “shifts” the averaged thermal “=1” level to a lower pressure in the all steam scenario. This shift is readily seen in the band averaged contribution functions (Figure 4a). A similar, but lesser, effect is seen in the 500Solar metallicity scenario (up to 70K) because the water abundance is lower by a factor of (Figure 4b). The radiative response of the TP to the integrated flux differences (up to 40% for steam and 10% for 500Solar, green versus red curves in Figure 4c,d ) between the @[self] versus @[\ceH2+He] acts to reduce the emission spectrum differences, however, to a still detectable 10s of ppm (Figure 4c,d).
The transmission spectra (Figure 4e,f) show comparable differences (30–40 ppm) to the 500 K scenario from Figure 3c,d. However, there are now two effects taking place that create the transmission differences. The first is the scale height effect due to the differences in the TP (@[\ceH2+He]-@[self], \ceH2O TP), and the second, as before, is the broadening difference. Both effects contribute equally to the overall differences in the transmission spectra. Despite the self-consistent adjustment of the TP, differences in both emission and transmission are still above detectable levels (10’s of ppm)
The aim of this work is to determine the observable impact of molecular pressure broadening under different plausible bulk atmospheric compositions likely representative of the Super-Earth/(sub)Neptune planetary regime. Specifically, we focused on the differences between the typically assumed \ceH2/He broadening and water self broadening on the water vapor absorption cross sections. From our analysis we arrive at the following key points:
Absorption cross section differences between water self and the standard assumed \ceH2/He broadening are up to an order of magnitude in the pressure broadened line wings (similar to Hedges & Madhusudhan (2016)), and is noticeable over a range of applicable temperatures and pressures.
The influence of self broadening is composition dependent and non-linear, with half of the difference achieved by water mole fractions of30% for a representative temperature and pressure.
Transmission and emission spectra differences for representative sub-Neptune atmospheres range between a few 10’s of ppm up to 100’s of ppm, depending upon wavelength, temperature, and water abundance. These differences are not negligible considering currently achieved HST precisions of 15 ppm and possible precisions as low as a few ppm for JWST. Differences will vary depending upon additional parameters like temperature gradient (for emission), planet-to-star radius ratio, and scale height.
The assumption of water self broadening (or lack thereof) can have a significant impact on the 1D vertical energy balance, with temperature differences of up to 180K in pure steam atmospheres (or a half-a-decade lower pressure shift in the emission levels) and 10’s of K in high metallicity atmospheres.
This work is certainly not an exhaustive exploration of all possible broadening (Table 1) or planetary atmosphere conditions. However, it serves to illustrate that the broadener composition can have a non-negligible impact on the observables and continues to illustrate the importance and key role of laboratory data on planetary atmosphere modeling. (Fortney et al., 2016)
EGN and MRL thank J. Lyons, A. Heays, R. Freedman, M. Marley, J. Fortney, P. Mollière, L. Pino and the Arizona State University exoplanet group for many useful discussions. We especially thank S. Yurchenko for invaluable assistance with the EXOCROSS code, and ASU Research Computing center for the kind support on computational side. MRL acknowledges summer support from the NASA Exoplanet Research Program award NNX17AB56G. This work benefited from numerous conversations at the 2018 Exoplanet Summer Program in the Other Worlds Laboratory (OWL) at the University of California, Santa Cruz, a program funded by the Heising-Simons Foundation.
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