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Evolution of an early Titan atmosphere
Icarus 271 (2016) 202–206
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Evolution of an early Titan atmosphere R.E. Johnson a,b,∗, O.J. Tucker c, A.N. Volkov d a
Engineering Physics, University of Virginia, Charlottesville, VA 22904, United States Physics Department, New York University, New York, NY 10003, United States c Department of Climate and Space Sciences and Engineering, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109, United States d Department of Mechanical Engineering, University of Alabama, Tuscaloosa, AL 35487, United States b
a r t i c l e
i n f o
Article history: Received 2 November 2015 Revised 6 January 2016 Accepted 10 January 2016 Available online 21 January 2016 Keywords: Atmospheres, evolution Titan Atmosphere
a b s t r a c t Rapid escape from a proposed early CH4 /NH3 atmosphere on Titan could, in principle, limit the amount of NH3 that is converted by photolysis into the present N2 atmosphere. Assuming that this conversion occurred, a recent estimate of escape driven by the surface temperature and pressure was used to constrain Titan’s accretion temperature. Here we show that for the range of temperatures of interest, heating of the surface is not the primary driver for escape. Atmospheric loss from a thick Titan atmosphere is predominantly driven by heating of the upper atmosphere; therefore, the loss rate cannot be used to easily constrain the accretion temperature. We give an estimate of the solar driven escape rate from an early atmosphere on Titan, and then briefly discuss its relevance to the cooling rate, isotope ratios, and the time period suggested to convert NH3 to the present N2 atmosphere. © 2016 Elsevier Inc. All rights reserved.
1. Introduction The evolution of, and escape from, Titan’s atmosphere is still debated in spite of the large amount of Cassini data: >100 passes through Titan’s upper atmosphere (e.g., Mandt et al., 2014, 2015; Glein, 2015). There is agreement that the present H2 loss rate (e.g., Tucker et al., 2013) is roughly consistent with the rate of photolysis of CH4 and the subsequent precipitation of larger carboncontaining molecules (e.g., Atreya et al., 2006). However, the present escape rate for carbon and nitrogen containing molecules is small and still being studied (e.g., Tucker et al., 2013, 2016; Snowden and Yelle, 2014). Therefore, not much light has been shed on the early evolution of Titan’s atmosphere or on the possibility that nitrogen was initially present as NH3 and was subsequently converted to its present form N2 (e.g., Atreya et al., 1978; Strobel, 1982). Because the surface temperature following accretion (>∼300 K: Kuramoto and Matsui, 1994) was much higher than that at present (∼94 K), it was suggested that this parameter might determine the escape rate from an early Titan atmosphere (Gilliam and Lerman, 2014). Here we show that although the atmospheric temperature is important for the proposed nitrogen chemistry, the range of accretion temperatures of interest is a secondary effect in determining the escape rate, which is primarily driven by the solar energy absorbed in the upper atmosphere. We first give an
∗ Corresponding author at: Engineering Physics, University of Virginia, Charlottesville, VA 22904, United States. Tel.: +1 434 422 2424. E-mail address: [email protected] (R.E. Johnson).
http://dx.doi.org/10.1016/j.icarus.2016.01.014 0019-1035/© 2016 Elsevier Inc. All rights reserved.
estimate of the escape rate due only to the heating of Titan’s surface. We then discuss the heating of the upper atmosphere and give a new estimate of nitrogen loss from an early CH4 , NH3 atmosphere. 2. Escape driven by surface heating Molecular kinetic simulations have shown that the escape from a thick atmosphere can be simulated reasonably well by applying the Jeans escape rate iteratively as an upper boundary condition in a fluid dynamics simulation. This procedure is often referred to as a fluid-Jeans simulation (e.g., Erwin et al., 2013; Johnson et al., 2015). The Jeans escape rate in molecules per second (s−1 ) can be written as
J = π r2 n(r )v[1 + λ(r )] exp[−λ(r )] (1) where n(r), v, and λ(r) are the molecular density, mean thermal speed and Jeans parameter in the atmosphere at a radius r from the center of the planet. The Jeans parameter is λ(r) = U(r)/kT(r), the ratio of the gravitational binding energy of a molecule, U(r), to a measure of its thermal energy, kT(r), with k the Boltzmann constant and T(r) the local temperature. Here U(r) = GMm/r with G the gravitational constant, M the planet’s mass and m the molecular mass. By using Eq. (1) to calculate the escape rate, one assumes that molecular collisions, which might affect the escape rate, can be ignored above r. Therefore, it is typically evaluated at the nominal exobase (r = rx ). Since the surface temperature may be known but the exobase altitude and temperature require a detailed calculation, the escape rate is sometimes approximated by replacing
R.E. Johnson et al. / Icarus 271 (2016) 202–206
rx by the surface radius, r0 (e.g., Schaller and Brown, 2007). This is referred to as the surface-Jeans (SJ) approximation, which is appropriate for very thin atmospheres. A thick atmosphere heated only by the surface temperature typically decreases in temperature and pressure with altitude in the absence of upper atmosphere heating. Therefore, the SJ estimate can be orders of magnitude larger than the correct escape rate (e.g., Volkov et al., 2011a, 2011b; Volkov, 2015; Johnson et al., 2015). Escape driven only by the surface temperature and pressure has been simulated using the fluid-Jeans (FJ) model in which the escape rate in Eq. (1) is evaluated at the exobase with rx found iteratively. FJ simulations, which are accurate for large column densities, can be supplemented by molecular kinetic simulations for the lower column densities. Such simulations were recently carried out for atmospheres spanning a range of surface Jeans parameters [λ(r0 ) = λ0 = 10 to 30] and column densities [N(r0 ) = N0 = 1018 to 1031 molecules/m2 ] as shown in Fig. 2 of Johnson et al. (2015). Here N0 = Pvap /mg0 , with Pvap the vapor pressure and g0 = U(r0 )/r0 the surface gravity. In that paper the ratio, R, of the simulated escape rate to the SJ rate was roughly fit using the Knudsen number evaluated at the surface, Kn0 , defined in this paper as Kn0 = (λ0 N0 σ eff )−1 with σ eff the effective collision cross section between the atmospheric molecules. 1 The fit to that ratio is
R
−1
∼
R−1 1
+
R−1 2 , R1
∼
1/Kn00.09 ,
R2 ∼ 70[K n0 exp(λ0 )]/λ
2.55 0
(2)
where R1 applies at small N0 (large Kn0 ) calculated using a molecular kinetic model and R2 applies at large N0 (small Kn0 ). A roughly equivalent theoretical equation for R2 was derived in Volkov (2015, Eq. (25)). One such result, relevant to the discussion below, is given in Fig. 1. This was calculated using parameters for an N2 atmosphere. Using Kn0 and λ0 , Eq. (2) can be scaled to approximate other compositions (Volkov et al., 2011b). Because the photolytic conversion of NH3 into N2 has been suggested to be efficient only if Titan’s atmospheric temperature is greater than ∼150 K (Atreya et al., 1978; Strobel, 1982) the postaccretion cooling rate of Titan’s surface is critical. Therefore, it is of concern whether or not the loss of NH3 occurred more rapidly than either the cooling to below 150 K and/or the conversion to N2 . With this in mind Gilliam and Lerman (2014) estimated simultaneous cooling and escape rates. Their suggested initial inventories of NH3 and CH4 are ∼1.62 × 1021 kg and ∼0.75 × 1021 kg with a small fraction in the atmosphere as determined by the surface vapor pressures. In their first model the surface starts with a post-accretion temperature of 355 K producing 5.8 bar of atmospheric NH3 (0.38 × 1020 kg) with λ0 = 20.3 and 19.6 bar of CH4 (1.2 × 1020 kg) with λ0 = 19.1. The total escape rate was then estimated as the surface cooled using a model roughly equivalent to Eq. (1). Applying Eq. (1) at Titan’s surface (r0 = rT = 2576 km) for an atmosphere in equilibrium with the suggested 355 K surface temperature gives an upward flux of molecules with sufficient energy to escape of ∼0.65 × 1035 NH3 /s and ∼6.8 × 1035 CH4 /s which is the SJ estimate discussed above. The initial loss rate in Gilliam and Lerman (2014), applied at one scale height above the surface, is about a factor of two larger, ∼1.4×1035 NH3 /s and 15 × 1035 CH4 /s, and is, therefore, roughly consistent with the SJ estimate. As the surface and, hence, the atmosphere cools, the estimated rate drops rapidly as indicated by the exponential dependence on λ(r) in Eq. (1). They note that for an initial 355 K surface the loss of the initial atmosphere is much faster than the NH3 to N2 conversion rate, so not enough NH3 could be converted into the amount of N2 required 1 The Knudsen number in a 1D atmosphere varying only with the radius, r, is the ratio of the mean free path for molecular collisions, lc , to the length scale over which the molecular density, n, changes, ∼|n/(dn/dr)|. Here we use Kn = lc /r; in other papers the atmospheric scale height, H, has been used.
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Fig. 1. Escape driven by the surface temperature and pressure: R is the ratio of the simulated loss rate to the SJ estimate shown for λ0 = 20 vs. Kn0 = (λ0 N0 σ eff )−1 with σ eff = 10−14 cm2 . Solid lines: FJ simulations for a diatomic gas with the viscosity index equal to 1; dashed line: approximate fit in Eq. (2); the difference at larger Kn0 (smaller N0 ) is estimated from molecular kinetic simulations which give a more accurate description of the exobase region (Johnson et al., 2015). Insert: column density N0 vs. r/r0 for λ0 = 20 and Kn0 = 10−15 , close to the conditions in GL for a 355 K early atmosphere: lines indicate a column N = 1018 /cm2 which gives a rough estimate of the absorption peak (ra ∼ 4.3r0 ) prior to the atmospheric expansion due to UV/EUV absorption; the nominal exobase, rx , at N(rx ) ∼ 1014 cm−2 , is seen to be rx 6r0 . Results can be very roughly scaled to Titan’s atmosphere using λ0 and Kn0 (Volkov, 2011b).
for the present atmosphere unless there was a continuous surface source of NH3 . Therefore, they suggested the initial accretion temperature might be lower, ∼300 K, significantly reducing their estimated loss rate. However, their estimates of the escape rate driven only by the surface temperature are much too large. Titan’s present exobase is well above Titan’s surface (∼1.6rT ) and was even higher for the proposed early Titan atmosphere. Therefore, applying a surface or near surface approximation for escape is incorrect. A good estimate for the escape rate driven by the surface pressure can be obtained using the ratio, R, in Eq. (2). Based on their NH3 and CH4 vapor pressures for the proposed 355 K early atmosphere, the average molecular mass is ∼16.2 amu giving λ0 = 19.3, close to the case shown in Fig. 1 for which rx 6rT . For the initial column density, N0 = 7 × 1027 molecules/cm2 and a collision cross section of σ eff ∼ 10−14 cm2 we obtain Kn0 = 7.5 × 10−16 . The resulting ratio of the simulated rate to the SJ rate using Eq. (2) is R ∼ 10−8 . Therefore, their initial loss rate is almost eight orders of magnitudes too large. In addition, the net escape rate integrated over the cooling process is also orders of magnitude too large as shown in Table 1. Their estimated net loss rate from their preferred atmosphere, having initial surface temperature of 300 K, is also many orders of magnitude too large. Therefore, such rates cannot be used to constrain Titan’s accretion temperature. 3. Escape driven by heating of the upper atmosphere Although the escape rate from an early Titan atmosphere is likely large, it is not driven by the near surface atmospheric temperature. Rather, as assumed in most studies, the energy deposited in the upper atmosphere dominates the loss rate. Escape due to heating of the upper atmosphere was recently modeled using
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Table 1 Mass loss rates from an early Titan atmospherea . Surface heating only b
GL GLb GLc This studyd Upper atmosphere heating This studye This studyf
Escape level (rT )
T0 (K)
Loss rate (kg/s)
∼1 ∼1 ∼1 >6 ra (rT ) ∼5 ∼2
355 300 300c 355 T0 (K) 355 150
4 × 1010 ∼109 ∼107 300 Loss rate (kg/s) 106 8 × 104
a Atmospheric content determined by the vapor pressures assumed in Gilliam and Lerner (2014, GL) for 355 K and 300 K models, using 5.82 bar of NH3 (∼0.4 × 1020 kg) and 19.58 bar of CH4 (1.2 × 1020 kg) out of an initial total inventory of NH3 (∼1.6 × 1021 kg) and CH4 (0.75 × 1021 kg): rT is Titan’s radius (2576 km). b Initial loss rate in GL using same total atmospheric mass for both T0 . c Loss rate averaged over the cooling of surface from T0 = 300 K until nitrogen content is equivalent to the present (∼0.5 Myr). d FJ loss rate from rx (>6rT ) obtained using R in Eq. (2) times the surface-Jeans rate (SJ: r = rT in Eq. (1)). e Initial loss rate due to UV/EUV absorption accounting for early solar enhancements averaged over 0.1–0.16 Gyr using Eq. (4). f Loss rate after rapid cooling (∼0.5 Myr) to 150 K due to UV/EUV absorption accounting for early solar enhancements averaged over 0.1–0.16 Gyr using Eq. (4).
molecular kinetic simulations for Titan and Pluto (Tucker and Johnson, 2009; Tucker et al., 2012, 2013; Erwin et al., 2013) and is used as a guide here. Energy is deposited by the ambient plasma (e.g., Johnson, 2004; Ledvina et al., 2012; Sillanpaa and Johnson, 2015; Westlake et al., 2016) and by the short wavelength solar flux (e.g., Snowden and Yelle, 2014; Penz et al., 2005; Lammer et al., 2008). Molecular kinetic simulations for the UV/EUV driven escape from Titan’s present 1.5 bar atmosphere have led to very small rates for N2 loss (Tucker and Johnson, 2009; Tucker et al., 2013). But that is probably not the case for an early atmosphere dominated by species lighter than N2 and exposed to a higher solar particle and short wavelength solar flux. An accurate description of the loss rate by absorption of the solar UV/EUV flux requires a detailed description of the molecular physics, a program in progress. However, since thermal conduction and radiative cooling are often inefficient in the upper atmosphere, a large heating rate can be balanced by adiabatic cooling by escape. Using molecular kinetic simulations we have recently confirmed that is the case over a broad range of heating rates and planet sizes (Erwin et al., 2013; Johnson et al., 2013). When cooling by escape dominates, an approximation called energy limited (EL) escape can be used, as discussed below. When the EL approximation is valid it is often assumed that the gas flow goes through a sonic point. However, we have shown that adiabatic cooling by escape can dominate well below those heating rates for which sonic escape actually occurs (Erwin et al., 2013; Johnson et al., 2013). When this is the case, although the escape rate is large, it can be closer to Jeans-like than to sonic escape. Therefore, it is not necessarily correct to associate the EL estimates of the escape rate with, for instance, mass fractionation expressions for sonic escape (e.g., Mandt et al., 2014). When escape dominates the cooling of the upper atmosphere, the deposited energy primarily removes gravitationally bound molecules, so that the globally averaged mass loss rate, (dM/dt), can be roughly approximated as:
(dM/dt ) ∼ (dM/dt )EL ∼ c[mQ/U (ra )]
(3)
Here m is the molecular mass, Q is the globally-averaged heating rate of the upper atmosphere and U(ra ) is the gravitational binding energy of a molecule at a depth, ra , assumed to be at a radial distance just below the energy absorption peak (Erwin et al., 2013). The parameter c accounts for other effects, but it is often assumed that c ∼ 1. This assumption is reasonable when cooling by molecular outflow dominates, but breaks down at small heating
rates when downward conduction can dominate or if radiative cooling in the upper atmosphere is significant. It can also differ from one at very large heating rates above the sonic point when escape is limited by the supply of atmosphere from below ra , 2 as in Johnson et al. (2013). More detailed expressions for (dM/dt)EL have been discussed (e.g., Erwin et al., 2013; Lammer et al., 2009). The globally averaged heat flux deposited in Titan’s upper atmosphere is primarily due to Lyman-α absorption producing photolysis of CH4 . For average solar conditions and approximate heating efficiencies, this has been estimated to be ∼1.4×10-5 J/m2 /s with an EUV contribution of ∼20% due to photo-dissociation of N2 (Krasnopolsky, 2009). In the absence of N2 , an early CH4 /NH3 atmosphere also absorbs in the EUV but with somewhat smaller cross sections (e.g., Huebner, 2015). In the early Solar System the Lyman-α flux is enhanced by ∼(4.56 Gyr/t)0.72 and the EUV by ∼(4.56 Gyr/t)1.23 for t > 0.1 Gyr, where t is the time from after formation (Ribas et al., 2005). The suggested time required to convert ammonia to nitrogen is ∼0.16 Gyr (e.g., Atreya et al., 1978; Strobel, 1982). Since the estimate for early solar flux given above does not extend to <0.1 Gyr, we simply use an enhancement in the Lymanα flux of ∼13 and the EUV flux of ∼80 obtained by averaging from 0.1 to 0.16 Gyr, assuming the heating efficiencies are unchanged, and ignoring plasma heating in order to obtain a conservative estimate. Longer wavelength radiation is absorbed by NH3 producing dissociation. This initiates the chemistry that leads to the formation of N2 with a cross-section ∼5 × 10−23 cm2 below 2300 A˚ (Atreya et al., 1978; Strobel, 1982; Huebner 2015). Although direct absorption by NH3 contributes significantly to net atmospheric heating, it occurs, on average, much deeper into Titan’s atmosphere, as can be seen by comparing the cross section above to the CH4 absorption cross section for Lyman-α absorption, ∼1.8 × 10−17 cm2 . It is, therefore, much less efficient in driving escape, but likely contributes to maintaining a warm mesosphere while NH3 remains present. Since the early solar wind was also more intense, so that Titan likely spent much more time orbiting outside Saturn’s magnetopause, solar wind induced heating could also be important. Ignoring the solar wind enhancements and radiative cooling, but accounting for the UV/EUV enhancements discussed above, we combine the UV heating by methane absorption with a comparable contribution from the EUV to obtain an estimate of the global upper atmosphere heating rate averaged over 0.1– 0.16 Gyr: Q ∼ (4π ra2 )[4 × 10−4 J/m2 /s]. Here ra is the effective radius of the disk above which the relevant radiation is fully absorbed. Using Titan’s radius, rT , we write Q − (ra /rT )2 [3.3 × 1010 J/s] and U(ra )/m = 3.5 × 106 (rT /ra ) J/kg. Substituting into Eq. (3) with c ∼ 1,
(dM/dt )EL ∼ (ra /rT )3 × 104 kg/s
(4)
indicating the sensitivity of this estimate to the distance from the surface where the radiation is absorbed. Based on the size of the absorption cross sections, the UV/EUV are essentially fully absorbed above a column density ∼1018 cm−2 . Scaling the simulations reported in Johnson et al. (2015) to the relevant λ0 and pressure discussed earlier, the atmosphere is highly extended as seen in Fig. 1. For the atmosphere in Fig. 1, ra ∼ 4.3 2 Ignoring radiative cooling, the molecular kinetic simulations in Johnson et al. (2013) indicate that adiabatic cooling by escape dominates downward thermal conduction well below heating rates at which sonic escape is initiated. This validates Eq. (3) and is consistent with detailed simulations in Erwin et al. (2013). At very large Q, in the sonic regime, adiabatic cooling still dominates. But the molecular kinetic simulations in Johnson et al. (2013) show that the escape flux is limited by the fixed lower boundary conditions. Therefore, increased Q lead to an increase in the temperature of the escaping molecules and not an increased flux. Hydrodynamic simulations in the large Q sonic regime with more flexible lower boundary conditions are consistent with Eq. (3) in the absence of significant radiative cooling.
R.E. Johnson et al. / Icarus 271 (2016) 202–206
due to surface heating alone and would increase due to the upper atmospheric heating (Erwin et al. (2013). For λ0 = 19.3 with a 335 K initial atmosphere produced only by surface heating this column density occurs at ra ∼ 5rT again ignoring the increase due to upper atmosphere heating. Although such extended atmospheres are certainly affected by the ambient plasma (Johnson, 2004), we ignore this as well as the fact that the enhanced flux is not well constrained at times earlier than 0.1 Gyr. Using (ra /rT ) ∼ 5 in Eq. (4) gives an early loss rate averaged over the UV/UV enhancements for 0.1–0.16 Gyr of ∼106 kg/s (∼4 × 1031 molecules/s). As the planet cools and the content of the atmosphere drops, then ra in Eq. (4) decreases, so that the net loss rate also decreases. In spite of the uncertainties, this loss rate is orders of magnitude larger than the correct escape rate due to surface heating alone, as seen in Table 1, confirming that upper atmosphere heating dominates. However, the rate above, which ignores the surface cooling, is an order of magnitude smaller than the ∼107 kg/s obtained by averaging the escape rates in Gilliam and Lerman (2014) over cooling from 300 K until the nitrogen content reaches present day levels (Table 1). 4. Discussion Scaling results from the simulations in Johnson et al. (2015) to conditions suggested for an early Titan atmosphere, we showed that surface heating alone cannot drive escape at rates that are faster than or comparable to the proposed cooling rates. Since the heating of the upper atmosphere dominates, the accretion temperature cannot be readily constrained using the escape rate and time scale for conversion to an N2 atmosphere. Based on earlier simulations (Erwin et al., 2013; Johnson et al., 2013) we also made a rough estimate of the initial mass loss rate from an early Titan atmosphere due to solar energy absorbed in its upper atmosphere. Averaging the enhancement in the shortwave length solar radiation over 0.1–0.16 Gyr gives the loss rate in Eq. (4). Although the surface cools rapidly after accretion, as long as there remains a column sufficient to absorb the short wavelength solar radiation, the mass loss rate is primarily sensitive to the surface temperature and pressure by the location of ra , that radius above which the short wavelength radiation is fully absorbed. Ignoring surface cooling and outgassing, and assuming that the atmosphere remains well mixed, then for the suggested 25.4 bar/355 K early CH4 /NH3 atmosphere we find (ra /rT ) ∼ 5 (Fig. 1) which gives an initial escape rate ∼106 kg/s in Table 1. If such a rate persisted, Titan would lose an amount equivalent to its initial atmosphere in ∼5 Myr. Although this rate, obtained by averaging the heating over 0.1–0.16 Gyr, is large, the amount of nitrogen lost is only a small fraction of the suggested total inventory. Therefore, the role of outgassing/venting (e.g., Glein, 2015) is critical in determining the net column of gas in the atmosphere as well as the effect of escape on the N14 /N15 isotope ratio. The possible conversion of Titan’s early NH3 component into N2 in ∼0.16 Gyr requires that the background temperature remains above ∼150 K (Atreya et al., 1978; Strobel, 1982). Ignoring venting and atmospheric heating, radiative cooling of Titan’s surface from ∼300 K to below ∼150 K has been estimated to occur in ∼0.6 Myr (e.g., Gillian and Lerner, 2014). However, venting, heating of the upper atmosphere, and absorption at longer wavelengths by both NH3 and the precipitating carbon species could in principal maintain the temperature above 150 K in the region where the chemistry is occurring, as discussed elsewhere (e.g., Atreya et al., 1978; Strobel, 1982; Gilliam and Lerman, 2014). At such a temperature in the lower atmosphere ra would decrease to ∼2rT , reducing the loss rate by over an order of magnitude (Table 1). However, Titan would still have lost the equivalent of its suggested initial atmosphere (Table 1) in a time much shorter than 0.16 Gyr. Assuming that the
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volatiles continue to outgas and the upper atmosphere remains well mixed then the short wavelength radiation will continue to be absorbed in the upper atmosphere. In that case Titan will have lost ∼10% of the suggested initial NH3 inventory (1.6 × 1021 kg) in 0.16 Gyr while converting a much smaller fraction of that inventory (∼1%) into the present 1.5 bar N2 atmosphere. Over the range of heating rates considered, sonic escape does not necessarily occur, especially at the lower rates discussed above (Johnson et al., 2013). Therefore, although the EL estimate of the escape rate applies, the mass fractionation calculated by assuming sonic escape can be incorrect. A detailed simulation of escape and concomitant isotope separation over the time that an early Titan atmosphere might evolve to the present N2 dominated is needed and is in progress. Acknowledgments REJ acknowledges support from ROSES PATM program of NASA, from the NASA’s CASSINI mission through SwRI; REJ & ANV acknowledge support from ROSES OPR program of NASA; OJT acknowledges support from the Grant NNH12ZDA001N from the ROSES OPR program of NASA. References Atreya, S.K., Donahue, T.M., Kuhn, W.R., 1978. Evolution of a nitrogen atmosphere on Titan. Science 201, 611–613. Atreya, S.K., Adams, E.Y., Niemann, H.B., et al., 2006. Titan’s methane cycle. Planet. Space Sci 54, 1177–1187. Erwin, J., Tucker, O.J., R.E. Johnson, R.E., 2013. Hybrid fluid/kinetic modeling of Pluto’s atmosphere. Icarus 226, 375–384. Gilliam, A.E., Lerman, A., 2014. Evolution of Titan’s major atmospheric gases and cooling since accretion. Planet. Space Sci. 93–94, 41–53. Glein, C.R., 2015. Noble gases, nitrogen, and methane from the deep interior to the atmosphere of Titan. Icarus 250, 570–586. Huebner, W., 2015. http://phidrates.space.swri.edu/ Accessed 27.01.15. Johnson, R.E., 2004. The magnetospheric plasma-driven evolution of satellite atmospheres. Astrophys. J. 609, L99–L102. Johnson, R.E., Volkov, A.N., Erwin, J.T., 2013. Molecular-kinetic simulations of escape from the ex-planet and exoplanets: Criterion for transonic flow. ApJ Lett. 768 (L4) 6p. Erratum: ApJ Lett. 774, 90 (1p.). Johnson, R.E., Oza, A., Young, L.A., et al., 2015. Volatile loss and classification of Kuiper Belt objects. Astrophys. J. 809 (43), 9 p. Krasnopolsky, V.A., 2009. A photochemical model of Titan’s atmosphere and ionosphere. Icarus 201, 226–256. Kuramoto, K., Matsui, T., 1994. Formation of a hot proto-atmosphere onthe accreting giant icy satellites: implications for the origin and evolution of Titan, Ganymede, and Callisto. J. Geophys. Res. 99, 21183–21200. Lammer, H., Kasting, J.F., Chassefière, E., et al., 2008. Atmospheric escape and evolution of terrestrial planets and satellites. Space Sci. Rev. 139, 399–436. Lammer, H., Odert, P., Leitzinger, M., et al., 2009. Determining the mass loss limit for close-in exoplanets: What can we learn from transit obervations? Astron. Astrophys. 506 (1), 399–410. Ledvina, S.A., Brecht, S.H., Cravens, T.E., 2012. The orientation of Titan’s dayside ionosphere and its effects on Titan’s plasma interaction. Earth Planets Space 64, 207–230. Mandt, K.E., Mousis, O., Lunine, J., et al., 2014. Protosolar ammonia as the unique source of Titan’s nitrogen. ApJ Lett. 788 (L24), 5p. Mandt, K., Mousis, O., Chassefière, E., 2015. Comparative planetology of the history of nitrogen isotopes in the atmospheres of Titan and Mars. Icarus 254, 259–261. Penz, T., Lammer, H., Kulikov, Y.N., et al., 2005. The influence of the solar particle and radiation environment on Titan’s atmosphere evolution. Adv. Space Res. 36, 241–250. Ribas, I., Guinan, E.F., Güdel, M., et al., 2005. Evolution of the solar activity over time ˚ Asand effects on planetary atmospheres. I. High-energy irradiances (1–1700 A). trophys. J. 622, 680–694. Schaller, E.L., Brown, M.E., 2007. Volatile loss and retention on Kuiper Belt objects. Astrophys. J. 659, L61–L64. Sillanpaa, I., Johnson, R.E., 2015. The role of ion-neutral collisions in Titan’s magnetospheric interaction. Planet. Space Sci. 108, 73–86. Snowden, D., Yelle, R.V., 2014. The thermal structure of Titan’s upper atmosphere, II: Energetics. Icarus 228, 64–77 http://dx.doi.org/10.1016/j.icarus.2013.08.027. Strobel, D.F., 1982. Chemistry and evolution of Titan’s atmosphere. Planet. Space Sci. 30, 839–848. Tucker, O.J., Johnson, R.E., 2009. Thermally driven atmospheric escape: Monte Carlo simulations for Titan’s atmosphere. Planet. Space Sci. 57, 1889–1894. Tucker, O.J., Erwin, J.T., Deighan, J.I., et al., 2012. Thermally driven escape from Pluto’s atmosphere: A combined fluid/kinetic model. Icarus 217, 408–415.
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Tucker, O.J., Johnson, R.E., Deighan, J.I., et al., 2013. Diffusion and thermal escape of H2 from Titan’s atmosphere: Monte Carlo Simulations. Icarus 222, 149–158. Tucker, O.J., Waalkes, W., Tenishev, V.M., et al., 2016. Examining the exobase approximation: DSMC models of Titan’s upper atmosphere. Icarus (in press). Volkov, A.N., 2015. A criterion for the validity of Parker’s model in thermal escape problems for planetary atmospheres. ApJ Lett. 812, L1.
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Note
Evolution of an early Titan atmosphere R.E. Johnson a,b,∗, O.J. Tucker c, A.N. Volkov d a
Engineering Physics, University of Virginia, Charlottesville, VA 22904, United States Physics Department, New York University, New York, NY 10003, United States c Department of Climate and Space Sciences and Engineering, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109, United States d Department of Mechanical Engineering, University of Alabama, Tuscaloosa, AL 35487, United States b
a r t i c l e
i n f o
Article history: Received 2 November 2015 Revised 6 January 2016 Accepted 10 January 2016 Available online 21 January 2016 Keywords: Atmospheres, evolution Titan Atmosphere
a b s t r a c t Rapid escape from a proposed early CH4 /NH3 atmosphere on Titan could, in principle, limit the amount of NH3 that is converted by photolysis into the present N2 atmosphere. Assuming that this conversion occurred, a recent estimate of escape driven by the surface temperature and pressure was used to constrain Titan’s accretion temperature. Here we show that for the range of temperatures of interest, heating of the surface is not the primary driver for escape. Atmospheric loss from a thick Titan atmosphere is predominantly driven by heating of the upper atmosphere; therefore, the loss rate cannot be used to easily constrain the accretion temperature. We give an estimate of the solar driven escape rate from an early atmosphere on Titan, and then briefly discuss its relevance to the cooling rate, isotope ratios, and the time period suggested to convert NH3 to the present N2 atmosphere. © 2016 Elsevier Inc. All rights reserved.
1. Introduction The evolution of, and escape from, Titan’s atmosphere is still debated in spite of the large amount of Cassini data: >100 passes through Titan’s upper atmosphere (e.g., Mandt et al., 2014, 2015; Glein, 2015). There is agreement that the present H2 loss rate (e.g., Tucker et al., 2013) is roughly consistent with the rate of photolysis of CH4 and the subsequent precipitation of larger carboncontaining molecules (e.g., Atreya et al., 2006). However, the present escape rate for carbon and nitrogen containing molecules is small and still being studied (e.g., Tucker et al., 2013, 2016; Snowden and Yelle, 2014). Therefore, not much light has been shed on the early evolution of Titan’s atmosphere or on the possibility that nitrogen was initially present as NH3 and was subsequently converted to its present form N2 (e.g., Atreya et al., 1978; Strobel, 1982). Because the surface temperature following accretion (>∼300 K: Kuramoto and Matsui, 1994) was much higher than that at present (∼94 K), it was suggested that this parameter might determine the escape rate from an early Titan atmosphere (Gilliam and Lerman, 2014). Here we show that although the atmospheric temperature is important for the proposed nitrogen chemistry, the range of accretion temperatures of interest is a secondary effect in determining the escape rate, which is primarily driven by the solar energy absorbed in the upper atmosphere. We first give an
∗ Corresponding author at: Engineering Physics, University of Virginia, Charlottesville, VA 22904, United States. Tel.: +1 434 422 2424. E-mail address: [email protected] (R.E. Johnson).
http://dx.doi.org/10.1016/j.icarus.2016.01.014 0019-1035/© 2016 Elsevier Inc. All rights reserved.
estimate of the escape rate due only to the heating of Titan’s surface. We then discuss the heating of the upper atmosphere and give a new estimate of nitrogen loss from an early CH4 , NH3 atmosphere. 2. Escape driven by surface heating Molecular kinetic simulations have shown that the escape from a thick atmosphere can be simulated reasonably well by applying the Jeans escape rate iteratively as an upper boundary condition in a fluid dynamics simulation. This procedure is often referred to as a fluid-Jeans simulation (e.g., Erwin et al., 2013; Johnson et al., 2015). The Jeans escape rate in molecules per second (s−1 ) can be written as
J = π r2 n(r )v[1 + λ(r )] exp[−λ(r )] (1) where n(r), v, and λ(r) are the molecular density, mean thermal speed and Jeans parameter in the atmosphere at a radius r from the center of the planet. The Jeans parameter is λ(r) = U(r)/kT(r), the ratio of the gravitational binding energy of a molecule, U(r), to a measure of its thermal energy, kT(r), with k the Boltzmann constant and T(r) the local temperature. Here U(r) = GMm/r with G the gravitational constant, M the planet’s mass and m the molecular mass. By using Eq. (1) to calculate the escape rate, one assumes that molecular collisions, which might affect the escape rate, can be ignored above r. Therefore, it is typically evaluated at the nominal exobase (r = rx ). Since the surface temperature may be known but the exobase altitude and temperature require a detailed calculation, the escape rate is sometimes approximated by replacing
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rx by the surface radius, r0 (e.g., Schaller and Brown, 2007). This is referred to as the surface-Jeans (SJ) approximation, which is appropriate for very thin atmospheres. A thick atmosphere heated only by the surface temperature typically decreases in temperature and pressure with altitude in the absence of upper atmosphere heating. Therefore, the SJ estimate can be orders of magnitude larger than the correct escape rate (e.g., Volkov et al., 2011a, 2011b; Volkov, 2015; Johnson et al., 2015). Escape driven only by the surface temperature and pressure has been simulated using the fluid-Jeans (FJ) model in which the escape rate in Eq. (1) is evaluated at the exobase with rx found iteratively. FJ simulations, which are accurate for large column densities, can be supplemented by molecular kinetic simulations for the lower column densities. Such simulations were recently carried out for atmospheres spanning a range of surface Jeans parameters [λ(r0 ) = λ0 = 10 to 30] and column densities [N(r0 ) = N0 = 1018 to 1031 molecules/m2 ] as shown in Fig. 2 of Johnson et al. (2015). Here N0 = Pvap /mg0 , with Pvap the vapor pressure and g0 = U(r0 )/r0 the surface gravity. In that paper the ratio, R, of the simulated escape rate to the SJ rate was roughly fit using the Knudsen number evaluated at the surface, Kn0 , defined in this paper as Kn0 = (λ0 N0 σ eff )−1 with σ eff the effective collision cross section between the atmospheric molecules. 1 The fit to that ratio is
R
−1
∼
R−1 1
+
R−1 2 , R1
∼
1/Kn00.09 ,
R2 ∼ 70[K n0 exp(λ0 )]/λ
2.55 0
(2)
where R1 applies at small N0 (large Kn0 ) calculated using a molecular kinetic model and R2 applies at large N0 (small Kn0 ). A roughly equivalent theoretical equation for R2 was derived in Volkov (2015, Eq. (25)). One such result, relevant to the discussion below, is given in Fig. 1. This was calculated using parameters for an N2 atmosphere. Using Kn0 and λ0 , Eq. (2) can be scaled to approximate other compositions (Volkov et al., 2011b). Because the photolytic conversion of NH3 into N2 has been suggested to be efficient only if Titan’s atmospheric temperature is greater than ∼150 K (Atreya et al., 1978; Strobel, 1982) the postaccretion cooling rate of Titan’s surface is critical. Therefore, it is of concern whether or not the loss of NH3 occurred more rapidly than either the cooling to below 150 K and/or the conversion to N2 . With this in mind Gilliam and Lerman (2014) estimated simultaneous cooling and escape rates. Their suggested initial inventories of NH3 and CH4 are ∼1.62 × 1021 kg and ∼0.75 × 1021 kg with a small fraction in the atmosphere as determined by the surface vapor pressures. In their first model the surface starts with a post-accretion temperature of 355 K producing 5.8 bar of atmospheric NH3 (0.38 × 1020 kg) with λ0 = 20.3 and 19.6 bar of CH4 (1.2 × 1020 kg) with λ0 = 19.1. The total escape rate was then estimated as the surface cooled using a model roughly equivalent to Eq. (1). Applying Eq. (1) at Titan’s surface (r0 = rT = 2576 km) for an atmosphere in equilibrium with the suggested 355 K surface temperature gives an upward flux of molecules with sufficient energy to escape of ∼0.65 × 1035 NH3 /s and ∼6.8 × 1035 CH4 /s which is the SJ estimate discussed above. The initial loss rate in Gilliam and Lerman (2014), applied at one scale height above the surface, is about a factor of two larger, ∼1.4×1035 NH3 /s and 15 × 1035 CH4 /s, and is, therefore, roughly consistent with the SJ estimate. As the surface and, hence, the atmosphere cools, the estimated rate drops rapidly as indicated by the exponential dependence on λ(r) in Eq. (1). They note that for an initial 355 K surface the loss of the initial atmosphere is much faster than the NH3 to N2 conversion rate, so not enough NH3 could be converted into the amount of N2 required 1 The Knudsen number in a 1D atmosphere varying only with the radius, r, is the ratio of the mean free path for molecular collisions, lc , to the length scale over which the molecular density, n, changes, ∼|n/(dn/dr)|. Here we use Kn = lc /r; in other papers the atmospheric scale height, H, has been used.
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Fig. 1. Escape driven by the surface temperature and pressure: R is the ratio of the simulated loss rate to the SJ estimate shown for λ0 = 20 vs. Kn0 = (λ0 N0 σ eff )−1 with σ eff = 10−14 cm2 . Solid lines: FJ simulations for a diatomic gas with the viscosity index equal to 1; dashed line: approximate fit in Eq. (2); the difference at larger Kn0 (smaller N0 ) is estimated from molecular kinetic simulations which give a more accurate description of the exobase region (Johnson et al., 2015). Insert: column density N0 vs. r/r0 for λ0 = 20 and Kn0 = 10−15 , close to the conditions in GL for a 355 K early atmosphere: lines indicate a column N = 1018 /cm2 which gives a rough estimate of the absorption peak (ra ∼ 4.3r0 ) prior to the atmospheric expansion due to UV/EUV absorption; the nominal exobase, rx , at N(rx ) ∼ 1014 cm−2 , is seen to be rx 6r0 . Results can be very roughly scaled to Titan’s atmosphere using λ0 and Kn0 (Volkov, 2011b).
for the present atmosphere unless there was a continuous surface source of NH3 . Therefore, they suggested the initial accretion temperature might be lower, ∼300 K, significantly reducing their estimated loss rate. However, their estimates of the escape rate driven only by the surface temperature are much too large. Titan’s present exobase is well above Titan’s surface (∼1.6rT ) and was even higher for the proposed early Titan atmosphere. Therefore, applying a surface or near surface approximation for escape is incorrect. A good estimate for the escape rate driven by the surface pressure can be obtained using the ratio, R, in Eq. (2). Based on their NH3 and CH4 vapor pressures for the proposed 355 K early atmosphere, the average molecular mass is ∼16.2 amu giving λ0 = 19.3, close to the case shown in Fig. 1 for which rx 6rT . For the initial column density, N0 = 7 × 1027 molecules/cm2 and a collision cross section of σ eff ∼ 10−14 cm2 we obtain Kn0 = 7.5 × 10−16 . The resulting ratio of the simulated rate to the SJ rate using Eq. (2) is R ∼ 10−8 . Therefore, their initial loss rate is almost eight orders of magnitudes too large. In addition, the net escape rate integrated over the cooling process is also orders of magnitude too large as shown in Table 1. Their estimated net loss rate from their preferred atmosphere, having initial surface temperature of 300 K, is also many orders of magnitude too large. Therefore, such rates cannot be used to constrain Titan’s accretion temperature. 3. Escape driven by heating of the upper atmosphere Although the escape rate from an early Titan atmosphere is likely large, it is not driven by the near surface atmospheric temperature. Rather, as assumed in most studies, the energy deposited in the upper atmosphere dominates the loss rate. Escape due to heating of the upper atmosphere was recently modeled using
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Table 1 Mass loss rates from an early Titan atmospherea . Surface heating only b
GL GLb GLc This studyd Upper atmosphere heating This studye This studyf
Escape level (rT )
T0 (K)
Loss rate (kg/s)
∼1 ∼1 ∼1 >6 ra (rT ) ∼5 ∼2
355 300 300c 355 T0 (K) 355 150
4 × 1010 ∼109 ∼107 300 Loss rate (kg/s) 106 8 × 104
a Atmospheric content determined by the vapor pressures assumed in Gilliam and Lerner (2014, GL) for 355 K and 300 K models, using 5.82 bar of NH3 (∼0.4 × 1020 kg) and 19.58 bar of CH4 (1.2 × 1020 kg) out of an initial total inventory of NH3 (∼1.6 × 1021 kg) and CH4 (0.75 × 1021 kg): rT is Titan’s radius (2576 km). b Initial loss rate in GL using same total atmospheric mass for both T0 . c Loss rate averaged over the cooling of surface from T0 = 300 K until nitrogen content is equivalent to the present (∼0.5 Myr). d FJ loss rate from rx (>6rT ) obtained using R in Eq. (2) times the surface-Jeans rate (SJ: r = rT in Eq. (1)). e Initial loss rate due to UV/EUV absorption accounting for early solar enhancements averaged over 0.1–0.16 Gyr using Eq. (4). f Loss rate after rapid cooling (∼0.5 Myr) to 150 K due to UV/EUV absorption accounting for early solar enhancements averaged over 0.1–0.16 Gyr using Eq. (4).
molecular kinetic simulations for Titan and Pluto (Tucker and Johnson, 2009; Tucker et al., 2012, 2013; Erwin et al., 2013) and is used as a guide here. Energy is deposited by the ambient plasma (e.g., Johnson, 2004; Ledvina et al., 2012; Sillanpaa and Johnson, 2015; Westlake et al., 2016) and by the short wavelength solar flux (e.g., Snowden and Yelle, 2014; Penz et al., 2005; Lammer et al., 2008). Molecular kinetic simulations for the UV/EUV driven escape from Titan’s present 1.5 bar atmosphere have led to very small rates for N2 loss (Tucker and Johnson, 2009; Tucker et al., 2013). But that is probably not the case for an early atmosphere dominated by species lighter than N2 and exposed to a higher solar particle and short wavelength solar flux. An accurate description of the loss rate by absorption of the solar UV/EUV flux requires a detailed description of the molecular physics, a program in progress. However, since thermal conduction and radiative cooling are often inefficient in the upper atmosphere, a large heating rate can be balanced by adiabatic cooling by escape. Using molecular kinetic simulations we have recently confirmed that is the case over a broad range of heating rates and planet sizes (Erwin et al., 2013; Johnson et al., 2013). When cooling by escape dominates, an approximation called energy limited (EL) escape can be used, as discussed below. When the EL approximation is valid it is often assumed that the gas flow goes through a sonic point. However, we have shown that adiabatic cooling by escape can dominate well below those heating rates for which sonic escape actually occurs (Erwin et al., 2013; Johnson et al., 2013). When this is the case, although the escape rate is large, it can be closer to Jeans-like than to sonic escape. Therefore, it is not necessarily correct to associate the EL estimates of the escape rate with, for instance, mass fractionation expressions for sonic escape (e.g., Mandt et al., 2014). When escape dominates the cooling of the upper atmosphere, the deposited energy primarily removes gravitationally bound molecules, so that the globally averaged mass loss rate, (dM/dt), can be roughly approximated as:
(dM/dt ) ∼ (dM/dt )EL ∼ c[mQ/U (ra )]
(3)
Here m is the molecular mass, Q is the globally-averaged heating rate of the upper atmosphere and U(ra ) is the gravitational binding energy of a molecule at a depth, ra , assumed to be at a radial distance just below the energy absorption peak (Erwin et al., 2013). The parameter c accounts for other effects, but it is often assumed that c ∼ 1. This assumption is reasonable when cooling by molecular outflow dominates, but breaks down at small heating
rates when downward conduction can dominate or if radiative cooling in the upper atmosphere is significant. It can also differ from one at very large heating rates above the sonic point when escape is limited by the supply of atmosphere from below ra , 2 as in Johnson et al. (2013). More detailed expressions for (dM/dt)EL have been discussed (e.g., Erwin et al., 2013; Lammer et al., 2009). The globally averaged heat flux deposited in Titan’s upper atmosphere is primarily due to Lyman-α absorption producing photolysis of CH4 . For average solar conditions and approximate heating efficiencies, this has been estimated to be ∼1.4×10-5 J/m2 /s with an EUV contribution of ∼20% due to photo-dissociation of N2 (Krasnopolsky, 2009). In the absence of N2 , an early CH4 /NH3 atmosphere also absorbs in the EUV but with somewhat smaller cross sections (e.g., Huebner, 2015). In the early Solar System the Lyman-α flux is enhanced by ∼(4.56 Gyr/t)0.72 and the EUV by ∼(4.56 Gyr/t)1.23 for t > 0.1 Gyr, where t is the time from after formation (Ribas et al., 2005). The suggested time required to convert ammonia to nitrogen is ∼0.16 Gyr (e.g., Atreya et al., 1978; Strobel, 1982). Since the estimate for early solar flux given above does not extend to <0.1 Gyr, we simply use an enhancement in the Lymanα flux of ∼13 and the EUV flux of ∼80 obtained by averaging from 0.1 to 0.16 Gyr, assuming the heating efficiencies are unchanged, and ignoring plasma heating in order to obtain a conservative estimate. Longer wavelength radiation is absorbed by NH3 producing dissociation. This initiates the chemistry that leads to the formation of N2 with a cross-section ∼5 × 10−23 cm2 below 2300 A˚ (Atreya et al., 1978; Strobel, 1982; Huebner 2015). Although direct absorption by NH3 contributes significantly to net atmospheric heating, it occurs, on average, much deeper into Titan’s atmosphere, as can be seen by comparing the cross section above to the CH4 absorption cross section for Lyman-α absorption, ∼1.8 × 10−17 cm2 . It is, therefore, much less efficient in driving escape, but likely contributes to maintaining a warm mesosphere while NH3 remains present. Since the early solar wind was also more intense, so that Titan likely spent much more time orbiting outside Saturn’s magnetopause, solar wind induced heating could also be important. Ignoring the solar wind enhancements and radiative cooling, but accounting for the UV/EUV enhancements discussed above, we combine the UV heating by methane absorption with a comparable contribution from the EUV to obtain an estimate of the global upper atmosphere heating rate averaged over 0.1– 0.16 Gyr: Q ∼ (4π ra2 )[4 × 10−4 J/m2 /s]. Here ra is the effective radius of the disk above which the relevant radiation is fully absorbed. Using Titan’s radius, rT , we write Q − (ra /rT )2 [3.3 × 1010 J/s] and U(ra )/m = 3.5 × 106 (rT /ra ) J/kg. Substituting into Eq. (3) with c ∼ 1,
(dM/dt )EL ∼ (ra /rT )3 × 104 kg/s
(4)
indicating the sensitivity of this estimate to the distance from the surface where the radiation is absorbed. Based on the size of the absorption cross sections, the UV/EUV are essentially fully absorbed above a column density ∼1018 cm−2 . Scaling the simulations reported in Johnson et al. (2015) to the relevant λ0 and pressure discussed earlier, the atmosphere is highly extended as seen in Fig. 1. For the atmosphere in Fig. 1, ra ∼ 4.3 2 Ignoring radiative cooling, the molecular kinetic simulations in Johnson et al. (2013) indicate that adiabatic cooling by escape dominates downward thermal conduction well below heating rates at which sonic escape is initiated. This validates Eq. (3) and is consistent with detailed simulations in Erwin et al. (2013). At very large Q, in the sonic regime, adiabatic cooling still dominates. But the molecular kinetic simulations in Johnson et al. (2013) show that the escape flux is limited by the fixed lower boundary conditions. Therefore, increased Q lead to an increase in the temperature of the escaping molecules and not an increased flux. Hydrodynamic simulations in the large Q sonic regime with more flexible lower boundary conditions are consistent with Eq. (3) in the absence of significant radiative cooling.
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due to surface heating alone and would increase due to the upper atmospheric heating (Erwin et al. (2013). For λ0 = 19.3 with a 335 K initial atmosphere produced only by surface heating this column density occurs at ra ∼ 5rT again ignoring the increase due to upper atmosphere heating. Although such extended atmospheres are certainly affected by the ambient plasma (Johnson, 2004), we ignore this as well as the fact that the enhanced flux is not well constrained at times earlier than 0.1 Gyr. Using (ra /rT ) ∼ 5 in Eq. (4) gives an early loss rate averaged over the UV/UV enhancements for 0.1–0.16 Gyr of ∼106 kg/s (∼4 × 1031 molecules/s). As the planet cools and the content of the atmosphere drops, then ra in Eq. (4) decreases, so that the net loss rate also decreases. In spite of the uncertainties, this loss rate is orders of magnitude larger than the correct escape rate due to surface heating alone, as seen in Table 1, confirming that upper atmosphere heating dominates. However, the rate above, which ignores the surface cooling, is an order of magnitude smaller than the ∼107 kg/s obtained by averaging the escape rates in Gilliam and Lerman (2014) over cooling from 300 K until the nitrogen content reaches present day levels (Table 1). 4. Discussion Scaling results from the simulations in Johnson et al. (2015) to conditions suggested for an early Titan atmosphere, we showed that surface heating alone cannot drive escape at rates that are faster than or comparable to the proposed cooling rates. Since the heating of the upper atmosphere dominates, the accretion temperature cannot be readily constrained using the escape rate and time scale for conversion to an N2 atmosphere. Based on earlier simulations (Erwin et al., 2013; Johnson et al., 2013) we also made a rough estimate of the initial mass loss rate from an early Titan atmosphere due to solar energy absorbed in its upper atmosphere. Averaging the enhancement in the shortwave length solar radiation over 0.1–0.16 Gyr gives the loss rate in Eq. (4). Although the surface cools rapidly after accretion, as long as there remains a column sufficient to absorb the short wavelength solar radiation, the mass loss rate is primarily sensitive to the surface temperature and pressure by the location of ra , that radius above which the short wavelength radiation is fully absorbed. Ignoring surface cooling and outgassing, and assuming that the atmosphere remains well mixed, then for the suggested 25.4 bar/355 K early CH4 /NH3 atmosphere we find (ra /rT ) ∼ 5 (Fig. 1) which gives an initial escape rate ∼106 kg/s in Table 1. If such a rate persisted, Titan would lose an amount equivalent to its initial atmosphere in ∼5 Myr. Although this rate, obtained by averaging the heating over 0.1–0.16 Gyr, is large, the amount of nitrogen lost is only a small fraction of the suggested total inventory. Therefore, the role of outgassing/venting (e.g., Glein, 2015) is critical in determining the net column of gas in the atmosphere as well as the effect of escape on the N14 /N15 isotope ratio. The possible conversion of Titan’s early NH3 component into N2 in ∼0.16 Gyr requires that the background temperature remains above ∼150 K (Atreya et al., 1978; Strobel, 1982). Ignoring venting and atmospheric heating, radiative cooling of Titan’s surface from ∼300 K to below ∼150 K has been estimated to occur in ∼0.6 Myr (e.g., Gillian and Lerner, 2014). However, venting, heating of the upper atmosphere, and absorption at longer wavelengths by both NH3 and the precipitating carbon species could in principal maintain the temperature above 150 K in the region where the chemistry is occurring, as discussed elsewhere (e.g., Atreya et al., 1978; Strobel, 1982; Gilliam and Lerman, 2014). At such a temperature in the lower atmosphere ra would decrease to ∼2rT , reducing the loss rate by over an order of magnitude (Table 1). However, Titan would still have lost the equivalent of its suggested initial atmosphere (Table 1) in a time much shorter than 0.16 Gyr. Assuming that the
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volatiles continue to outgas and the upper atmosphere remains well mixed then the short wavelength radiation will continue to be absorbed in the upper atmosphere. In that case Titan will have lost ∼10% of the suggested initial NH3 inventory (1.6 × 1021 kg) in 0.16 Gyr while converting a much smaller fraction of that inventory (∼1%) into the present 1.5 bar N2 atmosphere. Over the range of heating rates considered, sonic escape does not necessarily occur, especially at the lower rates discussed above (Johnson et al., 2013). Therefore, although the EL estimate of the escape rate applies, the mass fractionation calculated by assuming sonic escape can be incorrect. A detailed simulation of escape and concomitant isotope separation over the time that an early Titan atmosphere might evolve to the present N2 dominated is needed and is in progress. Acknowledgments REJ acknowledges support from ROSES PATM program of NASA, from the NASA’s CASSINI mission through SwRI; REJ & ANV acknowledge support from ROSES OPR program of NASA; OJT acknowledges support from the Grant NNH12ZDA001N from the ROSES OPR program of NASA. References Atreya, S.K., Donahue, T.M., Kuhn, W.R., 1978. Evolution of a nitrogen atmosphere on Titan. Science 201, 611–613. Atreya, S.K., Adams, E.Y., Niemann, H.B., et al., 2006. Titan’s methane cycle. Planet. Space Sci 54, 1177–1187. Erwin, J., Tucker, O.J., R.E. Johnson, R.E., 2013. Hybrid fluid/kinetic modeling of Pluto’s atmosphere. Icarus 226, 375–384. Gilliam, A.E., Lerman, A., 2014. Evolution of Titan’s major atmospheric gases and cooling since accretion. Planet. Space Sci. 93–94, 41–53. Glein, C.R., 2015. Noble gases, nitrogen, and methane from the deep interior to the atmosphere of Titan. Icarus 250, 570–586. Huebner, W., 2015. http://phidrates.space.swri.edu/ Accessed 27.01.15. Johnson, R.E., 2004. The magnetospheric plasma-driven evolution of satellite atmospheres. Astrophys. J. 609, L99–L102. Johnson, R.E., Volkov, A.N., Erwin, J.T., 2013. Molecular-kinetic simulations of escape from the ex-planet and exoplanets: Criterion for transonic flow. ApJ Lett. 768 (L4) 6p. Erratum: ApJ Lett. 774, 90 (1p.). Johnson, R.E., Oza, A., Young, L.A., et al., 2015. Volatile loss and classification of Kuiper Belt objects. Astrophys. J. 809 (43), 9 p. Krasnopolsky, V.A., 2009. A photochemical model of Titan’s atmosphere and ionosphere. Icarus 201, 226–256. Kuramoto, K., Matsui, T., 1994. Formation of a hot proto-atmosphere onthe accreting giant icy satellites: implications for the origin and evolution of Titan, Ganymede, and Callisto. J. Geophys. Res. 99, 21183–21200. Lammer, H., Kasting, J.F., Chassefière, E., et al., 2008. Atmospheric escape and evolution of terrestrial planets and satellites. Space Sci. Rev. 139, 399–436. Lammer, H., Odert, P., Leitzinger, M., et al., 2009. Determining the mass loss limit for close-in exoplanets: What can we learn from transit obervations? Astron. Astrophys. 506 (1), 399–410. Ledvina, S.A., Brecht, S.H., Cravens, T.E., 2012. The orientation of Titan’s dayside ionosphere and its effects on Titan’s plasma interaction. Earth Planets Space 64, 207–230. Mandt, K.E., Mousis, O., Lunine, J., et al., 2014. Protosolar ammonia as the unique source of Titan’s nitrogen. ApJ Lett. 788 (L24), 5p. Mandt, K., Mousis, O., Chassefière, E., 2015. Comparative planetology of the history of nitrogen isotopes in the atmospheres of Titan and Mars. Icarus 254, 259–261. Penz, T., Lammer, H., Kulikov, Y.N., et al., 2005. The influence of the solar particle and radiation environment on Titan’s atmosphere evolution. Adv. Space Res. 36, 241–250. Ribas, I., Guinan, E.F., Güdel, M., et al., 2005. Evolution of the solar activity over time ˚ Asand effects on planetary atmospheres. I. High-energy irradiances (1–1700 A). trophys. J. 622, 680–694. Schaller, E.L., Brown, M.E., 2007. Volatile loss and retention on Kuiper Belt objects. Astrophys. J. 659, L61–L64. Sillanpaa, I., Johnson, R.E., 2015. The role of ion-neutral collisions in Titan’s magnetospheric interaction. Planet. Space Sci. 108, 73–86. Snowden, D., Yelle, R.V., 2014. The thermal structure of Titan’s upper atmosphere, II: Energetics. Icarus 228, 64–77 http://dx.doi.org/10.1016/j.icarus.2013.08.027. Strobel, D.F., 1982. Chemistry and evolution of Titan’s atmosphere. Planet. Space Sci. 30, 839–848. Tucker, O.J., Johnson, R.E., 2009. Thermally driven atmospheric escape: Monte Carlo simulations for Titan’s atmosphere. Planet. Space Sci. 57, 1889–1894. Tucker, O.J., Erwin, J.T., Deighan, J.I., et al., 2012. Thermally driven escape from Pluto’s atmosphere: A combined fluid/kinetic model. Icarus 217, 408–415.
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