Planetary and Space Science 48 (2000) 51±58 Dynamics of Titan's thermosphere H. Rishbeth a, b,*, R.V. Yelle a, M. Mendillo a aCenter for Space Physics, Boston University, Boston, MA02215, USA bDepartment of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK Received 11 January 1999; received in revised form 28 May 1999; accepted 23 June 1999 Abstract We estimate the wind speeds in Titan's thermosphere by considering the various terms of the wind equation, without actually solving it, with a view to anticipating what might be observed by the Cassini spacecraft in 2004. The winds, which are driven by horizontal pressure gradients produced by solar heating, are controlled in the Earth's thermosphere by ion-drag and coriolis force, but in Titan's thermosphere they are mainly controlled by the nonlinear advection and curvature forces. Assuming a day± night temperature dierence of 20 K, we ®nd that Titan's thermospheric wind speed is typically 60 m s1. In contrast, the Earth's thermospheric winds, of order 50 m s1, do not equalize day and night temperatures. We speculate on other factors, such as the electrodynamics of Titan's thermosphere and the tides due to Saturn. # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction by listing some features of the Earth's thermosphere above about 150 km: Titan's atmosphere is comparable in density to the Earth's, though much colder. Both atmospheres have 1. large day±night temperature dierences exist, of an upper region called the thermosphere, situated at order 300 K, mainly due to the absorption of solar heights above about 600 km in Titan's atmosphere and XUV; 1 80 km in the Earth's, in which the temperature 2. winds blow, with speeds of order 50 m s (i.e., increases upwards because of the absorption of solar nearly 1 Earth radius per day), both meridionally extreme ultraviolet and X-rays (XUV). The XUV radi- (summer±winter) and zonally (day±night); ation, possibly augmented in Titan's case by ¯uxes of 3. the winds do not equalize day and night tempera- energetic electrons and neutral atoms from Saturn, tures; heats the neutral air and sets up gradients of tempera- 4. the wind speeds are largely controlled by ion-drag ture and pressure that drive global wind systems. because of the high concentration of ions, which are Energy inputs from the mesosphere and the magneto- constrained in their motion by the geomagnetic sphere may also play a part in the dynamics. Titan ®eld; also experiences strong gravitational tides because of 5. vertical wind shears are limited by molecular vis- the proximity of Saturn. In this paper we apply current cosity, so that wind speeds are almost height-inde- ideas about the Earth's thermosphere and ionosphere pendent. to discuss the thermospheric dynamics of Titan, a None of these apply to the Earth's middle and lower topic not treated in detail by current models. We start atmosphere, where the day±night temperature dier- ences are very much smaller, ion-drag does not exist, and the wind patterns are coriolis-controlled. We shall * Corresponding author. University of Southampton, Department show that conditions are dierent again in Titan's of Physics and Astronomy, Southampton, SO17 1BJ, UK. Tel.: +44-2380-592073; fax: +44-2380-593910. thermosphere, mainly because of the slow rotation and E-mail address: [email protected] (H. Rishbeth). the much weaker solar radiation. 0032-0633/00/$20.00 # 1999 Elsevier Science Ltd. All rights reserved. PII: S0032-0633(99)00076-8 52 H. Rishbeth et al. / Planetary and Space Science 48 (2000) 51±58 Titan is 10 AU from the Sun. Its radius (r )is thermospheric winds without actually solving the full 2575 km and its rotational and orbital period is about equation. First we have to estimate the horizontal 16 Earth days. The acceleration due to gravity ( g )is pressure dierences that drive the winds (Section 3). In 1.35 m s2 at the surface, but falls o to 0.63 m s2 at Sections 4±6 we estimate the relative strengths of the the height (h ) of 1100 km for which our calculations processes that control and limit the wind speeds, are made. The atmosphere has a surface pressure namely curvature, coriolis force, ion-drag and vis- p = 1.4 Â 105 Pa=1.4 bar=1.4 Earth atmospheres, cosity, and discuss the form the wind system might and is mostly composed of molecular nitrogen N2 with take. This ``scaling analysis'' requires some knowledge minor constituents such as CH4. The mesopause is at of the results, and we cannot comment on whether the about 600 km, with temperature T = 135 K and press- wind pattern is stable against small-scale circulations ure p = 0.01 Pa=1 Â 107 bar. At 1100 km, with (of size<<r ) and instabilities. We can at least hope to T = 185 K, the atmospheric scale height is given by show that our results are appropriate to global-scale H=kT/mg=RT/Mg = 86 km, where k is Boltzmann's circulations and self-consistent within our assumptions. constant and R the universal gas constant, and the Other factors, such as electrodynamic eects and the mean molecular mass is m in kg or M in atomic mass gravitational tides due to Saturn, may well be import- units; we take M = 27 for N2 with a small proportion ant but we cannot at present evaluate their eects of CH4. (Sections 7 and 8). We sum up in Section 9, with a Theoretical steady-state models of Titan's iono- view to anticipating what might be observed by the sphere have been constructed by Yung et al. (1984), Ip Cassini spacecraft in 2004. (1990), Yelle (1991), Keller et al. (1992) and Fox and Yelle (1997). In the upper ionosphere, at heights above about 1500 km, the main source of ionization is the 2. The thermospheric equation of motion impact of electrons (roughly 10±100 eV) from Saturn's magnetosphere. Lower down, the main daytime source For both Earth and Titan, the air is constrained to is photoionization by solar XUV, peaking at the level move on a spherical surface in a rotating coordinate of unit optical depth at 1000±1200 km, corresponding system rotating at angular velocity O (7.3 Â 105 rad to the Earth's daytime E and F1 layers at 100±180 km. s1 for Earth, 4.5 Â 106 rad s1 for Titan). The According to Fox and Yelle (1997), the peak electron equation for the horizontal wind velocity U in the 9 3 density Ne at solar zenith angle 608 is 7.5 Â 10 m at thermosphere takes the form height 1030 km. Ip's (1990) model has a higher peak 2 at around 1300 km, due to electron impact ionization, dU=dt F 2O Â U U Â U Â a=a vni U but other models lack this feature. These models are 2 based on data acquired at the Voyager ¯y-bys in Vi m=rr U rC D 1 1980±1981 and thus represent high solar activity. From ground-based observations of an occultation of where a star by Titan, Hubbard et al. (1993) deduced that at dU=dt @U=@t U ÁrU 2 heights of 250±450 km Titan's atmosphere is oblate, and inferred wind speeds of order 100 m s1, but in- Here F denotes the horizontal component of the force formation on thermospheric winds is lacking. per unit mass due to the pressure gradient, given by Titan has no counterpart to the Earth's ionospheric 1=rrp, m is the coecient of molecular viscosity, F2-peak at 250±350 km, where the relatively abundant and r is the air density. The neutral-ion collision fre- + oxygen atoms give rise to long-lived O ions and the quency vni is given by the product of the neutral-ion electron distribution is controlled both by photochem- collision parameter Kni and the ion concentration Ni, istry and dynamics. Instead, Titan's ionosphere has a summed over all ions present. The ion-drag term is complex photochemical regime, in which the principal only eective if the ion velocity Vi diers from the ions are hydrocarbons CxHy and, in some models, neutral-air wind U, which requires a magnetic ®eld + H2CN . With dissociative recombination coecients (Section 6). C is a tidal potential, which could be a05 Â 1013 m3 s1 for these ions, the mean lifetime absorbed into F though we display it separately, and of the ionization is given by 1= 2aNe0130 s. This D represents the drag due to momentum transferred time is so short that, by day, the ionization must be from the lower atmosphere, for example by gravity close to chemical equilibrium, and by night, the iono- waves. sphere's survival must depend on other sources such as As gravity is omitted, the ``wind equation'', Eq. (1) Saturn's magnetospheric electrons. applies only to the horizontal components of U.If In Section 2 we consider the various terms in the gravity is included, the vertical component of this equation of motion for the neutral air in the thermo- equation is dominated by gravity and the vertical sphere, and see what we can deduce about Titan's pressure gradient force, and eectively reduces to the H. Rishbeth et al. / Planetary and Space Science 48 (2000) 51±58 53 hydrostatic equation @p/@h=g (Rishbeth et al., 1969). We make no attempt to discuss vertical winds in this paper. The coriolis term 2O Â U gives rise to the ``geostrophic wind'' that is dominant in the Earth's lower atmosphere, but is less important in the thermo- sphere.