Basal heating in the atmospheres of cool stars

Summary This paper reviews observational evidence concerning the existence of so-calledbasal heating that occurs in the outer atmospheres of all stars with convective envelopes. Effects of basal heating depend primarily on the effective temperature, with little sensitivity to surface gravity or elemental abundances. Basal heating occurs predominantly in the chromosphere, possibly in the (lower) transition region, but not at an observable level in coronae (except perhaps in early F-type and in M-type dwarf stars). Basal fluxes are observed in the slowest rotators where it shows no significant modulation. The basal flux level is observed directly on the Sun only over regions void of intrinsically strong photospheric fields. There is substantial quantitative observational and theoretical evidence that the basal emission from stellar outer atmospheres is caused by the dissipation of acoustic waves generated by turbulent convection. The magnetic canopy turns out to be of little consequence, but effects of intrinsically weak fields on the basal mechanism cannot be entirely ruled out. Solar observations constrain the spatio-temporal character of the basal atmosphere and the acoustic flux levels as a function of height, resulting in a model in which intermittent wave dissipation causes emission characteristic of both cool and warm atmospheric areas, in which — at least in the solar case — a time-averaged chromospheric temperature rise may not even exist.     

The 10 October 1999 HIP 9369 occultation by the northern polar region of Jupiter: ingress and egress lightcurves analysis

The occultation of bright star HIP9369 by the northern polar region of Jupiter was observed from four locations in North and South America, providing four data sets for ingress and egress. The inversion of the eight occultation lightcurves provides temperature profiles at different latitudes ranging from 55°N to 73.2°N. We estimate the errors on the profiles due to the uncertainties of the inversion method and compare the value of the temperature at the deepest level probed (∼ 50 μbar) with previous observations. The shape of the temperature gradient profile is found similar to previous investigations of planetary atmospheres with propagating and breaking gravity waves. We analyze the small scale structures in both lightcurves and temperature profiles using the continuous wavelet transform. The calculated power spectra of localized fluctuations in the temperature profiles show slopes close to −3 for all eight profiles. We also isolate and reconstruct the three-dimensional geometry of a single wave mode with vertical and horizontal wavelengths of respectively 3 and 70 km. The identified wave is consistent with the gravity wave regime, with a horizontal phase speed nearly parallel to the planetary meridian. Nevertheless, the dissipation of the corresponding wave in Jupiter’s stratosphere should preclude its detection at the observed levels and an acoustic wave cannot be ruled out.     

The excitation, propagation and dissipation of waves in accretion discs: the non-linear axisymmetric case

We analyse the non-linear propagation and dissipation of axisymmetric waves in accretion discs using the ZEUS-2D hydrodynamics code. The waves are numerically resolved in the vertical and radial directions. Both vertically isothermal and thermally stratified accretion discs are considered. The waves are generated by means of resonant forcing, and several forms of forcing are considered. Compressional motions are taken to be locally adiabatic  ( γ =5/3)  . Prior to non-linear dissipation, the numerical results are in excellent agreement with the linear theory of wave channelling in predicting the types of modes that are excited, the energy flux by carried by each mode, and the vertical wave energy distribution as a function of radius. In all cases, waves are excited that propagate on both sides of the resonance (inwards and outwards). For vertically isothermal discs, non-linear dissipation occurs primarily through shocks that result from the classical steepening of acoustic waves. For discs that are substantially thermally stratified, wave channelling is the primary mechanism for shock generation. Wave channelling boosts the Mach number of the wave by vertically confining the wave to a small cool region at the base of the disc atmosphere. In general, outwardly propagating waves with Mach numbers near resonance  ℳ_r≳0.01  undergo shocks within a distance of order the resonance radius.     

Propagation of tropospheric gravity waves into the upper atmosphere of Mars

We study the propagation of gravity waves in the martian atmosphere using a linearized one-dimensional full-wave model. Calculations are carried out for atmospheric parameters characteristic of Mars Orbiter Laser Altimeter (on Mars Global Surveyor MGS) observations of apparent gravity waves in high latitude clouds and MGS radio occultation measurements of temperature variations with height suggestive of gravity wave activity. Waves that reach the thermosphere produce fluctuations in density comparable in amplitude with the density variations detected in Mars Odyssey aerobraking data. Gravity waves of modest amplitude are found to deposit momentum and generate significant heating and cooling in the martian atmosphere. The largest heating and cooling effects occur in the thermosphere, at altitudes between about 130 and 150 km, with heating occurring at the lower altitudes and cooling taking place above.     

Acoustic-gravity waves in the thermosphere of Venus

Properties of acoustic-gravity waves in the upper atmosphere of Venus are studied using a two-fluid model which includes the effects of wave-induced diffusion in a diffusively separated atmosphere. In conjunction with neutral mass spectrometer data from the Pioneer Venus orbiter, the theory should provide information on the distribution of wave sources in the Venus upper atmosphere. Observed wave structure in species density measurements should generally have periods ?30–35 min, small N₂, CO, and O amplitudes, and highly variable phase shifts relative to CO₂. A near resonance may exist between downward phase-propagating internal gravity and diffusion waves near the 165-km level at periods near 29 min. As a result, if very large He wave amplitudes are observed near this level, it will indicate that the wave source is below the 150- to 175-km level and that the exospheric temperature is close to 350°K. Wave energy dissipation may be an important mechanism for heating of the nightside Venus thermosphere. Large-density oscillations in stratospheric cloud layer constituents are also possible and may be detectable by the Pioneer Venus large probe neutral mass spectrometer.     

Wave heating of the solar chromosphere

The nonmagnetic interior of supergranulation cells has been thought since the 1940s to be heated by the dissipation of acoustic waves. But all attempts to measure the acoustic flux have failed to show sufficient energy for chromospheric heating. Recent space observations with TRACE, for example, have found 10% or less of the necessary flux. To explain the missing energy it has been speculated that the nonmagnetic chromosphere is heated mainly by waves related to the magnetic field. If that were correct, the whole chromosphere, magnetic as well as nonmagnetic, would be heated mainly by waves related to the magnetic field. But contrary to expectation, the radiation emerging from the nonmagnetic chromosphere shows none of the signatures of magnetic waves, only those of acoustic waves. Nearly all the heating of the nonmagnetic chromosphere must therefore be due to acoustic waves. In the magnetic network on the boundary of supergranulation cells, on the other hand, the small filling factor of the magnetic field in the photosphere implies that only a small fraction of the wave flux that travels upward to heat the chromosphere can be channeled by the magnetic field. Hence, while some of the energy that is dissipated in the magnetic network is in the form of magnetic waves, most of it must be in the form of acoustic waves. Thus, the quiet solar chromosphere, instead of being heated mainly by magnetic waves throughout, must be heated mainly by acoustic waves throughout. The full wave flux heating the quiet chromosphere must travel through the photosphere. In the nonmagnetic medium, this flux is essentially all in the form of acoustic waves; TRACE registers at most 10% of it, perhaps because of limited spatial resolution.     

Buoyancy waves in Pluto’s high atmosphere: Implications for stellar occultations

We apply scintillation theory to stellar signal fluctuations in the high-resolution, high signal/noise, dual-wavelength data from the MMT observation of the 2007 March 18 occultation of P445.3 by Pluto. A well-defined high wavenumber cutoff in the fluctuations is consistent with viscous-thermal dissipation of buoyancy waves (internal gravity waves) in Pluto’s high atmosphere, and provides strong evidence that the underlying density fluctuations are governed by the gravity-wave dispersion relation.     

Solar atmospheric heating

The solar atmosphere is heated by a flux of mechanical waves propagating in one or more of the modes: acoustic, Alfvén and gravitational.The acoustic theory is compared with observational data and found inadequate. First, the theory is based quantitatively on the Böhm-Vitense convection zone model, and large-scale convective motions (supergranulation) and magnetic fields (unipolar regions) show that convection has another form. On the other hand, when granular motions are invoked the energy flux is too small. Second, atmospheric heating is localized in faculae, and enhanced acoustic flux beneath these regions is no longer explicable. Finally, the short periods of 10–30 s invoked recently appear inexplicable. Objections to the gravitational wave heating process are given briefly.Previous objections to Alfvén waves as an energy source followed from the belief that fields were generally uniform and of strength 50 G, now known to be incorrect. Models of Alfvén wave generation are based on (i) granule eddy motions, (ii) overstable oscillations in subsurface flux tubes and sunspot flux ropes, and (iii) supergranule motions, both horizontal and vertical.The first provides waves which propagate along thin flux tubes oscillating as taut wires in a compressible fluid; they may explain mottles, fibrils and other small emission features. The second may explain the enormous dissipation in spot groups, including flares. The third has been invoked earlier to explain spicules, and may have effects in the solar wind.     

On mode conversion and wave reflection in magnetic Ap stars

We investigate the effect of a strong large-scale magnetic field on the reflection of high-frequency acoustic modes in rapidly oscillating Ap stars. To that end, we consider a toy model composed of an isothermal atmosphere matched on to a polytropic interior and determine the numerical solution to the set of ideal magnetohydrodynamic equations in a local plane-parallel approximation with constant gravity. Using the numerical solution in combination with approximate analytical solutions that are valid in the limits where the magnetic and acoustic components are decoupled, we calculate the relative fraction of energy flux that is carried away in each oscillation cycle by running acoustic waves in the atmosphere and running magnetic waves in the interior. For oscillation frequencies above the acoustic cut-off, we show that most energy losses associated with the presence of running waves occur in regions where the magnetic field is close to vertical. Moreover, by considering the depth dependence of the energy associated with the magnetic component of the wave in the atmosphere we show that a fraction of the wave energy is kept in the oscillation every cycle. For frequencies above the acoustic cut-off frequency, such energy is concentrated in regions where the magnetic field is significantly inclined in relation to the local vertical. Even though our calculations were aimed at studying oscillations with frequencies above the acoustic cut-off frequency, based on our results we discuss what results may be expected for oscillations of lower frequency.     

Reconnection sites in Jupiter’s magnetotail and relation to Jovian auroras

The Galileo spacecraft explored Jupiter’s magnetotail in a low-inclination orbit, where it detected the signatures of tail reconnection. In this paper, we examine and classify the tail reconnection signatures into four types: dipolarizations, strong northward B_θ excursions, tailward-moving plasmoids and planetward-moving plasmoids. The distribution of these four types of events is used to infer the most probable location of the Jovian tail reconnection site to be near 0200 LT at a planetocentric distance of 80 Jovian radii. Dipolarizations are mainly observed planetward of this point, and strong northward B_θ excursions and plasmoids are found mostly tailward. The observations also suggest that the Jovian tail reconnection starts at a point (neutral point), a localized region in the tail, instead of along an extended azimuthal line (X-line). Using the updated Khurana’s Jupiter’s magnetospheric model, which includes the external field and the effects of the swept-back configuration of tail field lines, we map the signatures of Jovian tail reconnection into the Jupiter’s ionosphere. We confirm that the dawn auroral storms or the polar dawn spots observed by the Hubble Space Telescope (HST) are located close to the extrapolated footpoints of tail dipolarizations and could be the auroral signatures of tail reconnection.     

Scale-dependent infrared radiative damping rates on Mars and their role in the deposition of gravity-wave momentum flux

Using a Curtis-matrix model of 15 μm CO₂ radiative cooling rates for the martian atmosphere, we have computed vertical scale-dependent IR radiative damping rates from 0 to 200 km altitude over a broad band of vertical wavenumbers ∣m∣ = 2π(1-500 km)⁻¹ for representative meteorological conditions at 40°N and average levels of solar activity and dust loading. In the middle atmosphere, infrared (IR) radiative damping rates increase with decreasing vertical scale and peak in excess of 30 days⁻¹ at ∼50-80 km altitude, before gradually transitioning to scale-independent rates above ∼100 km due to breakdown of local thermodynamic equilibrium. We incorporate these computed IR radiative damping rates into a linear anelastic gravity-wave model to assess the impact of IR radiative damping, relative to wave breaking and molecular viscosity, in the dissipation of gravity-wave momentum flux. The model results indicate that IR radiative damping is the dominant process in dissipating gravity-wave momentum fluxes at ∼0-50 km altitude, and is the dominant process at all altitudes for gravity waves with vertical wavelengths ?10-15 km. Wave breaking becomes dominant at higher altitudes only for “fast” waves of short horizontal and long vertical wavelengths. Molecular viscosity plays a negligible role in overall momentum flux deposition. Our results provide compelling evidence that IR radiative damping is a major, and often dominant physical process controlling the dissipation of gravity-wave momentum fluxes on Mars, and therefore should be incorporated into future parameterizations of gravity-wave drag within Mars GCMs. Lookup tables for doing so, based on the current computations, are provided.     

Estimates of gravity wave drag on Mars: Indication of a possible lower thermospheric wind reversal

Spectral gravity wave parameterization suitable for planetary thermospheres applied to wind and temperature from Mars Climate Database reveals enormously strong drag incompatible with the wind distribution. It points out to a possible wind reversal in the 110-140 km layer similar to the one in the Earth’s lower thermosphere.     

Radiative instability of a cloudy planetary atmosphere

A cloudy planetary atmosphere at rest is shown to be unstable to disturbances of large horizontal scale. The energy source for the instability is the change in radiative heat flux associated with vertical displacement near the emitting level. A simple model is described in which Q∞ δz, where Q is the net heating rate in the cloud and δz is vertical displacement. The constant of proportionality may be either positive or negative. Disturbances may take the form of either quasi-steady geostrophic motions or amplified inertia-gravity waves. The model is applied to Jupiter's zonal winds and to motions near the Venus cloud tops, and provides a possible explanation for many important features of these two flows.     

Trapped gravity waves and the five-minute oscillations of the solar atmosphere

The various modes of hydrodynamic waves are considered for a model of the solar atmosphere which is based on the Bilderberg model and includes the effects of ionization. The atmosphere forms a potential well for internal gravity waves, since the stability is low at the base (near the convection) and low again in the region of partial ionization in the chromosphere. Calculations show that there are two resonant (trapped) modes of internal gravity waves for horizontal wavelengths based on the scale of the granulation. The properties of these modes are in close agreement with the two modes of oscillation observed by Frazier (1968). Trapped acoustic modes are found to have periods too short to account for the observations.Presently Visiting Fellow, Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, Colo.     

Jupiter’s moment of inertia: A possible determination by Juno

The moment of inertia of a giant planet reveals important information about the planet’s internal density structure and this information is not identical to that contained in the gravitational moments. The forthcoming Juno mission to Jupiter might determine Jupiter’s normalized moment of inertia NMoI = C/MR² by measuring Jupiter’s pole precession and the Lense–Thirring acceleration of the spacecraft (C is the axial moment of inertia, and M and R are Jupiter’s mass and mean radius, respectively). We investigate the possible range of NMoI values for Jupiter based on its measured gravitational field using a simple core/envelope model of the planet assuming that J₂ and J₄ are perfectly known and are equal to their measured values. The model suggests that for fixed values of J₂ and J₄ a range of NMoI values between 0.2629 and 0.2645 can be found. The Radau–Darwin relation gives a NMoI value that is larger than the model values by less than 1%. A low NMoI of ∼0.236, inferred from a dynamical model (Ward, W.R., Canup, R.M. [2006]. Astrophys. J. 640, L91–L94) is inconsistent with this range, but the range is model dependent. Although we conclude that the NMoI is tightly constrained by the gravity coefficients, a measurement of Jupiter’s NMoI to a few tenths of percent by Juno could provide an important constraint on Jupiter’s internal structure. We carry out a simplified assessment of the error involved in Juno’s possible determination of Jupiter’s NMoI.     

Bifurcations of ion acoustic solitary waves and periodic waves in an unmagnetized plasma with kappa distributed multi-temperature electrons

Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa distributed) cool and hot electrons have been investigated using non-perturbative approach. We have transformed basic model equations to an ordinary differential equation involving electrostatic potential. Then we have applied the bifurcation theory of planar dynamical systems to the obtained equation and we have proved the existence of solitary wave solutions and periodic wave solutions. We have derived two exact solutions of solitary and periodic waves depending on the parameters. From the solitary wave solution and periodic wave solution, we have shown the effects of density ratio p of cool electrons and ions, spectral index κ, and temperature ratio σ of cool electrons and hot electrons on characteristics of ion acoustic solitary and periodic waves.     

Wave constraints for Titan’s Jingpo Lacus and Kraken Mare from VIMS specular reflection lightcurves

Stephan et al. (Stephan, K. et al. [2010]. Geophys. Res. Lett. 37, 7104-+.) first saw the glint of sunlight specularly reflected off of Titan’s lakes. We develop a quantitative model for analyzing the photometric lightcurve generated during a flyby in which the specularly reflected light flux depends on the fraction of the solar specular footprint that is covered by liquid. We allow for surface waves that spread out the geographic specular intensity distribution. Applying the model to the VIMS T58 observations shows that the waves on Jingpo Lacus must have slopes of no greater than 0.15°, two orders of magnitude flatter than waves on Earth’s oceans. Combining the model with theoretical estimates of the intensity of the specular reflection allows a tighter constraint on the waves: ?0.05°. Residual specular signal while the specular point lies on land implies that either the land is wetted, the wave slope distribution is non-Gaussian, or that 5% of the land off the southwest edge of Jingpo Lacus is covered in puddles. Another specular sequence off of Kraken Mare acquired during Cassini’s T59 flyby shows rapid flux changes that the static model cannot reproduce. Points just 1 min apart vary in flux by more than a factor of two. The present dataset does not uniquely determine the mechanism causing these rapid changes. We suggest that changing wind conditions, kilometer-wavelength waves, or moving clouds could account for the variability. Future specular observations should be designed with a fast cadence, at least 6 points per minute, in order to differentiate between these hypotheses. Such new data will further constrain the nature of Titan’s lakes and their interactions with Titan’s atmosphere.     

VLA observations of Jupiter’s synchrotron radiation at 15 and 22 GHz

We observed Jupiter’s synchrotron radiation at frequencies of 15 and 22 GHz using the VLA (Very Large Array) in its most compact configuration (D-array) in March 1991. The spatial brightness distribution of the emission at these high frequencies appears to be very similar to that seen at lower frequencies (5 GHz down to 330 MHz). We measured a total nonthermal flux density at 15 and 22 GHz of 1.5 ± 0.15 Jy and 1.5 ± 0.4 Jy, respectively (both normalized to a geocentric distance of 4.04 AU). These numbers agree well with model spectra of Jupiter’s synchrotron radiation that were obtained by fitting the planet’s nonthermal radio emission between 74 MHz and 8 GHz and suggest a maximum cutoff in electron energies at ∼100 MeV. The degree of linear polarization observed with the VLA is 21.5 ± 1.9% at 15 GHz.     

Power spectral analysis of Jupiter’s clouds and kinetic energy from Cassini

We present suggestive evidence for an inverse energy cascade within Jupiter’s atmosphere through a calculation of the power spectrum of its kinetic energy and its cloud patterns. Using Cassini observations, we composed full-longitudinal mosaics of Jupiter’s atmosphere at several wavelengths. We also utilized image pairs derived from these observations to generate full-longitudinal maps of wind vectors and atmospheric kinetic energy within Jupiter’s troposphere. We computed power spectra of the image mosaics and kinetic energy maps using spherical harmonic analysis. Power spectra of Jupiter’s cloud patterns imaged at certain wavelengths resemble theoretical spectra of two-dimensional turbulence, with power-law slopes near −5/3 and −3 at low and high wavenumbers, respectively. The slopes of the kinetic energy power spectrum are also near −5/3 at low wavenumbers. At high wavenumbers, however, the spectral slopes are relatively flatter than the theoretical prediction of −3. In addition, the image mosaic and kinetic energy power spectra differ with respect to the location of the transition in slopes. The transition in slope is near planetary wavenumber 70 for the kinetic energy spectra, but is typically above 200 for the image mosaic spectra. Our results also show the importance of calculating spectral slopes from full 2D velocity maps rather than 1D zonal mean velocity profiles, since at large wavenumbers the spectra differ significantly, though at low wavenumbers, the 1D zonal and full 2D kinetic energy spectra are practically indistinguishable. Furthermore, the difference between the image and kinetic energy spectra suggests some caution in the interpretation of power spectrum results solely from image mosaics and its significance for the underlying dynamics. Finally, we also report prominent variations in kinetic energy within the equatorial jet stream that appear to be associated with the 5 μm hotspots. Other eddies are present within the flow collar of the Great Red Spot, suggesting caution when interpreting snapshots of the flow inside these features as representative of a time-averaged state.