Icarus 141, 299–306 (1999) Article ID icar.1999.6169, available online at http://www.idealibrary.com on Emissivity and the Fate of Pluto’s Atmosphere J. A. Stansberry1 Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, Arizona 86001 E-mail: [email protected] and R. V. Yelle2 Center for Space Physics, Boston University, Boston, Massachusetts 02215 Received July 30, 1998; revised February 19, 1999 out that the vapor pressure of such an atmosphere would un- We present a simplified model for seasonal changes in Pluto’s dergo large pressure changes as the temperature of the ice on surface–atmosphere system. The model demonstrates the potential the surface changed in response to eccentricity-driven changes importance of the solid-state phase transition between -N2 and in insolation. The subsequent discovery that N2 ice is much -N2, and the accompanying change in emissivity, for predicting more abundant on Pluto than CH4 ice (Owen et al. 1993) means the seasonal bulk of Pluto’s (and Triton’s) atmosphere. Specifically, that Pluto’s atmosphere is dominated by N2 (its vapor pressure is the model shows that under simplified but not unreasonable as- 4 '10 times larger than that of CH4 at Pluto temperatures (Brown sumptions Pluto may have nearly the same atmospheric pressure and Ziegler 1979)), but does not change the expectation of sea- at aphelion as it does now, near perihelion. The emissivity change sonally induced pressure oscillations, because N will also form which accompanies the – phase change should be included in 2 the next generation of Pluto and Triton seasonal models for the a vapor-pressure atmosphere. purposes of understanding the evolution of their atmospheres over Observations pertaining to the pressure of Pluto’s atmosphere seasonal and climatic timescales. c 1999 Academic Press and the temperature of its N2 ice are consistent with vapor- Key Words: Pluto; Pluto, atmosphere; Pluto, surface; Triton; pressure equilibrium. A stellar occultation by Pluto in 1988 atmospheres, evolution. set a lower limit on the perihelion surface pressure of 3 bar (Elliot et al. 1989, Hubbard et al. 1989, Elliot and Young 1992, Millis et al. 1993). Stansberry et al. (1994) argued that INTRODUCTION the occultation may not have reached Pluto’s surface, and that Pluto posesses a deep (50 km) troposphere. This hypothe- Pluto’s orbital eccentricity (0.25) means that it recieves 2.8 sis, strengthened by recent results indicating that Triton’s at- times as much sunlight at perihelion (which occurred in 1989) mosphere may now posess a troposphere approximately 50 km as it does at aphelion. The idea that this extreme insolation varia- deep (Elliot et al. 1999) implies that the true surface pressure of tion might lead to extreme changes in the bulk of the atmosphere N2 on Pluto is nearer 19 bar. Tryka et al. (1993) also argued followed close on the heels of the realization that Pluto posesses for a higher surface pressure, near 60 bar, on the basis of the an atmosphere. Cruikshank et al. (1976) discovered absorption observed shape of the N2 ice absorption feature. These pressures features in Pluto’s near-IR spectrum which were eventually at- correspond to the vapor pressure of N2 over a temperature range tributed to the presence of CH4 ice (Cruikshank and Apt 1984). of 35–40 K (Brown and Ziegler 1979). This is in excellent agree- Although the observed spectrum was due solely to absorption ment with temperatures calculated on the basis of surface en- by ice, it meant that Pluto had at least a tenuous CH4 atmo- ergy balance (Stansberry et al. 1994), and is not inconsistent with sphere because CH4 has a significant (0.1–100 bar) vapor pres- temperatures derived from far-IR observations of emission from sure at temperatures then predicted for Pluto (Cruikshank and Pluto (Altenhoff et al. 1988, Jewitt 1994, Stern et al. 1993, Tryka Silvaggio 1979, Trafton 1980). Stern and Trafton (1984) pointed et al. 1994, Spencer et al. 1997). Phase equilibrium is usually encountered in systems consid- 1 erably smaller than the entire surface–atmosphere interface of Current address: Steward Observatory, University of Arizona, 933 N. a planet (although Triton is another example of such a situ- Cherry Avenue, Tucson, AZ 85721. 2 Current address: Department of Physics and Astronomy, Northern Arizona ation). Despite the large scale of this system, the conditions University, Flagstaff, AZ 86011. of vapor–solid phase equilibrium, namely a single pressure and 299 0019-1035/99 $30.00 Copyright c 1999 by Academic Press All rights of reproduction in any form reserved. 300 STANSBERRY AND YELLE temperature, have been theoretically shown to apply to the entire The term is the ratio of the total area of the N2 ice to its cross- ice–atmosphere interface (Leighton and Murray 1966, Trafton sectional area as viewed from the Sun; i.e., it is the ratio of the 1984, Yelle et al. 1995). Thus, a variety of observations and the- area over which thermal reradiation from the ice occurs to the ory are consistent with the idea that Pluto’s near-perihelion atmo- area receiving sunlight. sphere is in equilibrium with the surface N2 ice. We note that the We wish to use these relations to predict the seasonal vari- dual-volatile seasonal model of Trafton (1990) leads to atmo- ability of the temperature of Pluto’s N2 ice, and thereby the at- spheric pressures of N2 considerably lower than those derived mospheric pressure. In order to do so we must know the values from the single-volatile considerations above, and that the of the albedo, emissivity, and as a function of time. Volatile Trafton model gives results consistent with a 3-bar surface tranport models have been used to predict the distribution of pressure for Pluto (Trafton et al. 1998). That model is also of in- N2 ice, i.e., , as a function of time under the assumption of terest because, like the model we present here, it predicts that un- constant frost albedo and emissivity (Spencer 1990; Stansberry der certain conditions Pluto’s atmosphere may not freeze out at et al. 1990; Hansen and Paige 1992, 1996; Brown and Kirk aphelion. However, the other dual-volatile model for Triton and 1994). In general these models do a poor job of both explain- Pluto (Stansberry et al. 1996b, Trafton et al. 1998) comes to dif- ing the observed albedo patterns on Triton and predicting the ferent conclusions, so for current purposes we will assume that changes in atmospheric pressure which have now been detected single-phase vapor-pressure equilibrium is an adequate para- on Triton (Elliot et al. 1997, 1998). There is no reason to expect digm for exploring the seasonal evolution of Pluto’s atmospheric them to perform better on Pluto. Because our primary interest in pressure. this study is to examine the effect of emissivity on the seasonal frost temperature, and because existing volatile transport mod- THERMAL MODEL els are of limited utility in predicting the time behavior of ,we simply take = 4 in our models, equivalent to assuming that the Nitrogen ice everywhere on the surface of Pluto is at the entire planet is covered by N2 ice. Later we discuss how changes same temperature because sublimation, atmospheric transport, in due to volatile transport would influence our results. We fur- and condensation act to efficiently redistribute energy across the ther assume that N2 ice has a bolometric albedo of 0.8, based globe (e.g., Spencer et al. 1997 and references therein). The usual on Voyager imaging results from Triton (Stansberry et al. 1990) equation for the diurnally averaged equilibrium temperaure of and mutual event albedo maps of Pluto (Stansberry et al. 1994). the surface, as a function of latitude (), The detailed emissivity behavior of the N2 is discussed below. As noted above, Eqs. (1)–(3) are only applicable if the condi- Z 1 T 4 = , tion of frost isothermality is satisfied. The amount of latent heat Teq( ) S0(1 A) d cos (1) T that can be transported around the globe by winds of a given velocity dependens upon the atmospheric density: as the atmo- where is the emissivity of the ice, is the Stefan–Boltzmann spheric pressure falls, winds will grow stronger. When the wind constant, Teq is the radiative equilibrium temperature of the sur- speed begins to approach the sound speed, significant pressure face, S0 is the solar flux at Pluto, A is the bolometric albedo of gradients will be required to drive the flow (Trafton and Stern the ice (which we set to 0.8), is longitude, T is the longi- 1983, Yelle et al. 1995). The presence of significant pressure tude of the terminator at a given latitude, and is the local solar differences in the atmosphere implies temperature differences zenith angle, must be modified to account for the latent heat flux between different regions of N2 ice on the surface with which in the equation of local energy balance. Writing the cossine of the atmosphere is in contact; i.e., the condition of isothermal- the diurnally averaged solar zenith angle (the integral in Eq. (1)) ity is violated. Spencer et al. (1997) show that the condition of as ¯ gives isothermality breaks down when the N2 ice temperature falls below about 31 K, with a corresponding atmospheric pressure S ¯ (1 A) = T 4 + Lm˙ , (2) 0 of 0.1 bar. where L is the latent heat of sublimation per unit mass of N2 9 1 (2.6 10 erg/g ) (Brown and Ziegler 1979), and m˙ is the sub- EMISSIVITY AND THE – PHASE TRANSITION limation mass flux. For current conditions on Pluto the temper- ature of the N2 is the same everywhere to within a small fraction The N2 – solid phase transition occurs at T = 35.6 K, of a Kelvin (Yelle et al.