Density Scale Height Research Articles

Numerical study of granulation in anelastic thermal convection in spherical shells

The present work investigates granulation or convective flow patterns in density-stratified (or anelastic) convection in spherical shells. The density-stratified thermal convection is typically present in astrophysical systems (such as solar convection); motivated by this, we performed a series of three-dimensional anelastic convection simulations in a spherical shell geometry using an in-house developed hybrid solver. We explored the effect of Rayleigh number and density scale height on the convective flow patterns. The granulation (or cell-like structures) are more prominent at higher density scale height and Rayleigh number. The granulation is further characterized by kinetic energy and helicity spectra. Our results support the argument that the convective flow patterns (or granulation) emerge due to inverse cascade owing to the presence of density stratification. Convective patterns (or granulation) are identified based on length scales, time scales, and flow velocity. The length scale of granules is further verified using a solar granulation model. Our analysis suggests the existence of inverse cascade and supergranulation on the spherical surface due to density-stratified thermal convection in spherical shells.

“Cold capture” of micrometeorites in Archean and Quaternary atmospheres: Effects of dilute exospheres

Micrometeorites (MM) that undergo low heating could have provided a source of organic material to the Earth during the Archean (4-2.5 Ga ago) before life emerged, given that the density of interplanetary dust and larger grains were much higher than today. Amino acids are destroyed on atmospheric entry if the temperature rises above the pyrolysis temperature of few hundred degrees Celsius, depending on type of amino acid. A numerical study was carried out to obtain temperature statistics along relatively rare grazing angle trajectories in the Quaternary (modern) and Archean atmospheres to determine the probability of “cold capture” below pyrolysis temperatures. Effects of the thermospheric temperature and density was considered for the Quaternary atmosphere, and an extended hydrogen/helium envelope remnant from the protosolar nebula was considered for the Archean atmosphere.An important result for the Archean is an elevated “cold capture” probability (twice the capture probability of the modern atmosphere, up to 7%–8%) for low heating below 500 °C of small asteroidal grains around 20μm in diameter, and geocentric velocities in the range 3–5 km/s, provided that there was a remnant envelope. Cometary 20μm grains of higher geocentric velocities did not have such an elevated capture probability. If the Archean atmosphere did not have an envelope, it was found that these capture probabilities were lower than for the modern atmosphere for both cometary and asteroidal grains, due to smaller density scale height of the lower Archean atmosphere leading to faster heating rate. Radiative degradation of amino acids in these relatively small grains should be considered more closely since the X-ray and XUV-flux from the Sun was larger by a factor of about 5–10 in the Archean.Very low maximum temperatures were found for 20μm asteroidal and cometary grains in the Quternary atmosphere, with temperatures in the range 150–200 °C, but with a very small capture probability in this range of typically less than 0.3%. All 300μm asteroidal grains were heated to temperatures above 500 °C for all atmosphere models. The probability of heating to temperatures < 500 °C of 100μm asteroidal grains, was estimated to 0.3% or less for all models. Most 100μm cometary grains were heated to temperatures > 500 °C for all models.

The acoustic size of the Sun

ABSTRACT Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that radius is more-or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ non-homologously from those of the standard solar model.

Equatorially trapped Rossby waves in radiative stars

AbstractObservations by recent space missions reported the detection of Rossby waves (r‐modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This article aims to study the theoretical dynamics of Rossby‐type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near‐surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby‐gravity, and inertia‐gravity waves was obtained. The solutions were found to be confined around the equator, leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes.

Discovery of an extended G giant chromosphere in the 2019 eclipse of γ Per

The November 2019 eclipse of γ Per was a rare opportunity to seek evidence for a chromosphere of the G8 giant, hitherto suspected but not detected. Twenty-nine years after the only other observed eclipse, we aim to find chromospheric absorption in the strong Ca II H&amp;K lines, and to determine its column densities and scale height. Using the Telescopio Internacional de Guanajuato Robótico-Espectroscópico (TIGRE) in Guanajuato (central Mexico) before, during and after the 8 days of total eclipse, we obtained good S/N spectra of the G8 giant alone and composite spectra of the partial phases, near eclipse and far from eclipse. In the near UV of the Ca II H&amp;K and Hϵ lines, the G giant spectrum that was adequately scaled was subtracted from the composite spectra in partial phases, near and far from eclipse, to obtain the A3 companion spectra with and without traces of chromospheric absorption. In addition, we used PHOENIX full non-local thermodynamic equilibrium model atmospheres on the blue A star spectrum, iSpec spectral analysis of the red G giant spectrum, and evolution tracks to study both components of γ Per. For the first time, we present evidence for this rare type of a not very extended G giant chromosphere, reaching out about half of an A-star radius (~1.5 Gm) with a scale height of only 0.17 Gm. By its location in the Hertzsprung-Russell diagram, the γ Per G8 giant is very close to the onset of more extended chromospheres. Furthermore, we show that this giant has a rather inactive chromosphere, and a recent 5 ksec XMM pointing reveals only a very faint, low-energy corona. While the γ Per primary has a mass of ~3.6 M⊙, and its A3 companion has one of ~2.4 M⊙, the latter is too cool (8400 ± 300 K), which is too evolved on the main sequence to be the same age as the primary. The high eccentricity of the 5329.08 days long-period orbit may therefore be reminiscent of a rare capture event. Using the eclipse method, we resolve a pivotal case of a G giant chromosphere, which seems to represent a low-gravity analogue of the inactive Sun. A systematic change of giant chromospheric extent by Hertzsprung-Russell diagram position is confirmed. Compared to the solar chromosphere, the density scale height increases with gravity by ∝ ɡ−1.5.

Visible Emission Line Spectroscopy of the Solar Corona During the 2019 Total Solar Eclipse

Spectroscopic measurements of the low solar corona are crucial to understanding the mechanisms that heat the corona and accelerate the solar wind, yet the lowest solar radii (R_{odot }) of the corona are difficult to observe. Our expedition collected narrow wavelengths of visible light at 530.3, 637.4, and 789.2 nm emitted by Fe xiv, x, and xi ions, respectively, from the total solar eclipse on 2019 July 2 at 20:40 UTC in Rodeo, Argentina with a bespoke 3-channel spectrometer. This paper describes the instrument and data calibration method that enables diagnostics out to {approx},1.0~R_{odot } above the solar limb within a bright helmet streamer. We find that Fe x and xi lines are dominant through 0.3~R_{odot }, with Fe xiv maintaining a stronger signal at higher elevations. Thermal line width broadening is consistent with 1.5 MK for the cooler Fe x, 2 MK for Fe xi, and 3 MK for the hotter Fe xiv line, which can be interpreted as differing density scale heights within isolated, isothermal flux tubes. The Doppler measurements correspond to bulk plasma motion ranging from −12 to +2.5 km s−1, with Fe xiv moving at nearly an assumed solid body rotation rate throughout 1.0~R_{odot }. After considering coronal rotation, these measurements are likely associated with plasma motion along the dominant longitudinal orientation of the magnetic field at the streamer base within 0.4~R_{odot }. These results show that high-resolution spectroscopy of visible light offers valuable diagnostics of the low corona, and lend insight into the interconnected loop complexity within helmet streamers.

Rossby waves on stellar equatorial β planes: Uniformly rotating radiative stars

Context. Rossby waves arise due to the conservation of total vorticity in rotating fluids and may govern the large-scale dynamics of stellar interiors. Recent space missions have collected a lot of information about the light curves and activity of many stars, which triggered observations of Rossby waves in the stellar surface and interiors. Aims. We aim to study the theoretical properties of Rossby waves in stratified interiors of uniformly rotating radiative stars with a sub-adiabatic vertical temperature gradient. Methods. We used the equatorial β plane approximation and linear vertical gradient of temperature to study the linear dynamics of equatorially trapped Rossby and inertia-gravity waves in interiors of radiative stars. The governing equation was solved by the method of separation of variables in the vertical and latitudinal directions. Results. Vertical and latitudinal solutions of the waves are found to be governed by Bessel functions and Hermite polynomials, respectively. Appropriate boundary conditions at the stellar surface and poles define analytical dispersion relations for Rossby, Rossby-gravity, and inertia-gravity waves. The waves are confined in surface layers of 30–50 H0, where H0 is the surface density scale height, and they are trapped between the latitudes of ±600. Observable frequencies (normalised by the angular frequency of the stellar rotation) of Rossby waves with m = 1 (m = 2), where m is the toroidal wavenumber, are in the interval of 0.65–1 (1.4–2), depending on the stellar rotation, radius, and surface temperature. Conclusions. Rossby-type waves can be systematically observed using light curves of Kepler and TESS (Transiting Exoplanet Survey Satellite) stars. Observations and theory then can be used for the sounding of stellar interiors.

Rimmed and rippled accretion disc models to explain AGN continuum lags

ABSTRACT We propose a solution to the problem of accretion disc sizes in active galactic nuclei being larger when measured by reverberation mapping than predicted by theory. Considering the disc’s exposed-surface thickness profile H(r), our solution invokes a steep rim or rippled structures irradiated by the central lamp-post. We model the continuum lags and the faint and bright disc spectral energy distribution (SED) in the best-studied case NGC 5548 (black hole mass $M_\bullet =7\times 10^7\, \mathrm{M}_\odot$, disc inclination i = 45°). With the lamp-post off, the faint-disc SED fixes a low accretion rate $\dot{M}\simeq 0.0014~\mathrm{M}_\odot \, {\rm yr}^{-1}$ and high prograde black hole spin a• ≃ 0.93, for which $r_{\rm in}=2\, G\, M_\bullet /c^2$ and $L_{\rm disc}=0.25\, \dot{M}\, c^2$. The bright-disc SED then requires a lamp-post luminosity ${L_{\rm LP}}\simeq 5\, \dot{M}\, c^2/(1-A)$ for disc albedo A. Reprocessing on the thin disc with T ∝ r−3/4 gives time lags τ ∝ λ4/3 but three times smaller than observed. Introducing a steep H(r) rim, or multiple crests, near r ∼ 5 light days, reprocessing on the steep centre-facing slope increases temperatures from ∼1500 to ∼6000 K, and this increases optical lags to match the lag data. Most of the disc surface maintains the cooler T ∝ r−3/4 profile that matches the SED. The bright lamp-post may be powered by magnetic links tapping the black hole spin. The steep rim occurs near the disc’s dust sublimation radius as in the ‘failed disc wind model for broad-line clouds’. Lens–Thirring torques aligning the disc and black hole spin may also raise a warp and associated waves. In both scenarios, the small density scale height implied by the inferred value of H(r) suggests possible marginal gravitational instability in the disc.

Using Anisotropies as a Forensic Tool for Decoding Supernova Remnants

We present a method for analyzing supernova remnants (SNRs) by diagnosing the drivers responsible for structure at different angular scales. First, we perform a suite of hydrodynamic models of the Rayleigh–Taylor instability (RTI) as a supernova (SN) collides with its surrounding medium. Using these models we demonstrate how power spectral analysis can be used to attribute which scales in an SNR are driven by RTI and which must be caused by intrinsic asymmetries in the initial explosion. We predict the power spectrum of turbulence driven by RTI and identify a dominant angular mode that represents the largest scale that efficiently grows via RTI. We find that this dominant mode relates to the density scale height in the ejecta, and therefore reveals the density profile of the SN ejecta. If there is significant structure in an SNR on angular scales larger than this mode, then it is likely caused by anisotropies in the explosion. Structure on angular scales smaller than the dominant mode exhibits a steep scaling with wavenumber, possibly too steep to be consistent with a turbulent cascade, and therefore might be determined by the saturation of RTI at different length scales (although systematic 3D studies are needed to investigate this). We also demonstrate, consistent with previous studies, that this power spectrum is independent of the magnitude and length scales of perturbations in the surrounding medium and therefore this diagnostic is unaffected by “clumpiness” in the circumstellar medium.

Multi-Fluid MHD Simulations of Europa's Plasma Interaction: Effects of Variation in Europa's Atmosphere.

Europa's plasma interaction is inextricably coupled to its O2 atmosphere by the chemical processes that generate plasma from the atmosphere and the sputtering of magnetospheric plasma against Europa's ice to generate O2. Observations of Europa's atmosphere admit a range of possible densities and spatial distributions (Hall et al., 1998, https://doi.org/10.1086/305604). To better understand this system, we must characterize how different possible configurations of the atmosphere affect the 3D magnetic fields and bulk plasma properties near Europa. To accomplish this, we conducted a parameter study using a multi‐fluid magnetohydrodynamic model for Europa's plasma interaction (Harris et al., 2021, https://doi.org/10.1029/2020ja028888). We varied parameters of Europa's atmosphere, as well as the conditions of Jupiter's magnetosphere, over 18 simulations. As the scale height and density of Europa's atmosphere increase, the extent and density of the ionosphere increase as well, generating strong magnetic fields that shield Europa's surface from impinging plasma on the trailing hemisphere. We also calculate the precipitation rate of magnetospheric plasma onto Europa's surface. As the O2 column density increased from (1–2.5) × 1014 cm−2, the precipitation rate decreased sharply then leveled off at 2 × 1024 ions/s for simulations with low magnetospheric plasma density and 6.4 × 1024 ions/s for simulations with high magnetospheric plasma density. These results indicate that the coupling between Europa's plasma populations and its atmosphere leads to feedback that limits increases in the ionosphere density.

TOI-3757 b: A Low-density Gas Giant Orbiting a Solar-metallicity M Dwarf

We present the discovery of a new Jovian-sized planet, TOI-3757 b, the lowest-density transiting planet known to orbit an M dwarf (M0V). This planet was discovered around a solar-metallicity M dwarf, using Transiting Exoplanet Survey Satellite photometry and confirmed with precise radial velocities from the Habitable-zone Planet Finder (HPF) and NEID. With a planetary radius of 12.0 R ⊕ and mass of 85.3 M ⊕, not only does this object add to the small sample of gas giants (∼10) around M dwarfs, but also its low density ( g cm−3) provides an opportunity to test theories of planet formation. We present two hypotheses to explain its low density; first, we posit that the low metallicity of its stellar host (∼0.3 dex lower than the median metallicity of M dwarfs hosting gas giants) could have played a role in the delayed formation of a solid core massive enough to initiate runaway accretion. Second, using the eccentricity estimate of 0.14 ± 0.06, we determine it is also plausible for tidal heating to at least partially be responsible for inflating the radius of TOI-3757b b. The low density and large scale height of TOI-3757 b makes it an excellent target for transmission spectroscopy studies of atmospheric escape and composition (transmission spectroscopy measurement of ∼ 190). We use HPF to perform transmission spectroscopy of TOI-3757 b using the helium 10830 Å line. Doing this, we place an upper limit of 6.9% (with 90% confidence) on the maximum depth of the absorption from the metastable transition of He at ∼10830 Å, which can help constraint the atmospheric mass-loss rate in this energy-limited regime.

Numerical Convergence of 2D Solar Convection in Implicit Large-eddy Simulations

Abstract Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations of turbulent flows at high Reynolds (Re) numbers. However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here, we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between 642 and 20482 grid points, along with the estimation of their effective viscosities, resulting in effective Reynolds numbers between 1 and ∼104. The thermodynamic structure of our model resembles the solar interior, including a fraction of the radiative zone and the convection zone. In the convective layer, the ILES solutions converge for the simulations with ≥5122 grid points, as evidenced by the integral properties of the flow and its power spectra. Most importantly, we found that even a resolution of 1282 grid points, Re ∼ 10 , is sufficient to capture the dynamics of the large scales accurately. This is a consequence of the ILES method allowing the energy contained in these scales to be the same in simulations with low and high resolution. Special attention is needed in regions with a small density scale height driving the formation of fine structures unresolved by the numerical grid. In the stable layer, we found the excitation of internal gravity waves, yet high resolution is needed to capture their development and interaction.

The Coronal Veil

Abstract Coronal loops, seen in solar coronal images, are believed to represent emission from magnetic flux tubes with compact cross sections. We examine the 3D structure of plasma above an active region in a radiative magnetohydrodynamic simulation to locate volume counterparts for coronal loops. In many cases, a loop cannot be linked to an individual thin strand in the volume. While many thin loops are present in the synthetic images, the bright structures in the volume are fewer and of complex shape. We demonstrate that this complexity can form impressions of thin bright loops, even in the absence of thin bright plasma strands. We demonstrate the difficulty of discerning from observations whether a particular loop corresponds to a strand in the volume, or a projection artifact. We demonstrate how apparently isolated loops could deceive observers, even when observations from multiple viewing angles are available. While we base our analysis on a simulation, the main findings are independent from a particular simulation setup and illustrate the intrinsic complexity involved in interpreting observations resulting from line-of-sight integration in an optically thin plasma. We propose alternative interpretation for strands seen in Extreme Ultraviolet images of the corona. The “coronal veil” hypothesis is mathematically more generic, and naturally explains properties of loops that are difficult to address otherwise—such as their constant cross section and anomalously high density scale height. We challenge the paradigm of coronal loops as thin magnetic flux tubes, offering new understanding of solar corona, and by extension, of other magnetically confined bright hot plasmas.

Eruption characteristics of lunar localized pyroclastic deposits as evidenced by remotely sensed water, mineralogy, and regolith

Explosive volcanic eruptions are responsible for producing localized pyroclatic deposits found across the lunar surface. These small localized pyroclastic deposits are thought to have erupted through transient, vulcanian-like eruptions. We used several remote data products, including a water abundance map, to understand the compositional and physical properties of these pyroclastic deposits. Within these deposits, we found strong relationships between water abundance and pyroxene abundance, glass abundance, regolith density scale height, and longitude. These relationships suggest that water abundance can be used to estimate the gas content of an eruption, cooling rate of erupted pyroclasts, optical density of the eruption plume, degree of fragmentation of an eruption, and infer on the distribution of water in the lunar interior. Further, we deduce that the excess water abundance within these pyroclastic deposits represents interior water content, which we tied to other remote measurements that represent important petrological and volcanological parameters to understand eruption dynamics and behavior.

On the relationship between energy input to the ionosphere and the ion outflow flux under different solar zenith angles

The ionosphere is one of the important sources for magnetospheric plasma, particularly for heavy ions with low charge states. We investigate the effect of solar illumination on the number flux of ion outflow using data obtained by the Fast Auroral SnapshoT (FAST) satellite at 3000–4150 km altitude from 7 January 1998 to 5 February 1999. We derive empirical formulas between energy inputs and outflowing ion number fluxes for various solar zenith angle ranges. We found that the outflowing ion number flux under sunlit conditions increases more steeply with increasing electron density in the loss cone or with increasing precipitating electron density (> 50 eV), compared to the ion flux under dark conditions. Under ionospheric dark conditions, weak electron precipitation can drive ion outflow with small averaged fluxes (~ 107 cm−2 s−1). The slopes of relations between the Poynting fluxes and outflowing ion number fluxes show no clear dependence on the solar zenith angle. Intense ion outflow events (> 108 cm−2 s−1) occur mostly under sunlit conditions (solar zenith angle < 90°). Thus, it is presumably difficult to drive intense ion outflows under dark conditions, because of a lack of the solar illumination (low ionospheric density and/or small scale height owing to low plasma temperature).Graphical abstract

Radius ratio dependency of the instability of fully compressible convection in rapidly rotating spherical shells

Based on the fully compressible Navier–Stokes equations, the linear stability of thermal convection in rapidly rotating spherical shells of various radius ratios $\eta$ is studied for a wide range of Taylor number $Ta$, Prandtl number $Pr$ and the number of density scale height $N_\rho$. Besides the classical inertial mode and columnar mode, which are widely studied by the Boussinesq approximation and anelastic approximation, the quasi-geostrophic compressible mode is also identified in a wide range of $N_\rho$ and $Pr$ for all $\eta$ considered, and this mode mainly occurs in the convection with relatively small $Pr$ and large $N_\rho$. The instability processes are classified into five categories. In general, for the specified wavenumber $m$, the parameter space ($Pr, N_\rho$) of the fifth category, in which the base state loses stability via the quasi-geostrophic compressible mode and remains unstable, shrinks as $\eta$ increases. The asymptotic scaling behaviours of the critical Rayleigh numbers $Ra_c$ and corresponding wavenumbers $m_c$ to $Ta$ are found at different $\eta$ for the same instability mode. As $\eta$ increases, the flow stability is strengthened. Furthermore, the linearized perturbation equations and Reynolds–Orr equation are employed to quantitatively analyse the mechanical mechanisms and flow instability mechanisms of different modes. In the quasi-geostrophic compressible mode, the time-derivative term of disturbance density in the continuity equation and the diffusion term of disturbance temperature in the energy equation are found to be critical, while in the columnar and inertial modes, they can generally be ignored. Because the time-derivative term of the disturbance density in the continuity equation cannot be ignored, the anelastic approximation fails to capture the instability mode in the small-$Pr$ and large-$N_\rho$ system, where convection onset is dominated by the quasi-geostrophic compressible mode. However, all the modes are primarily governed by the balance between the Coriolis force and the pressure gradient, based on the momentum equation. Physically, the most important difference between the quasi-geostrophic compressible mode and the columnar mode is the role played by the disturbance pressure. The disturbance pressure performs negative work for the former mode, which appears to stabilize the flow, while it destabilizes the flow for the latter mode. As $\eta$ increases, in the former mode the relative work performed by the disturbance pressure increases and in the latter mode decreases.

Ring Configurations of Point Vortices in Polar Atmospheres

This paper examines the stability and nonlinear evolution of configurations of equal-strength point vortices equally spaced on a ring of constant radius, with or without a central vortex, in the three-dimensional quasi-geostrophic compressible atmosphere model. While the ring lies at constant height, the central vortex can be at a different height and also have a different strength to the vortices on the ring. All such configurations are relative equilibria, in the sense that they steadily rotate about the \(z\) axis. Here, the domains of stability for two or more vortices on a ring with an additional central vortex are determined. For a compressible atmosphere, the problem also depends on the density scale height \(H\), the vertical scale over which the background density varies by a factor \(e\). Decreasing \(H\) while holding other parameters fixed generally stabilises a configuration. Nonlinear simulations of the dynamics verify the linear analysis and reveal potentially chaotic dynamics for configurations having four or more vortices in total. The simulations also reveal the existence of staggered ring configurations, and oscillations between single and double ring configurations. The results are consistent with the observations of ring configurations of polar vortices seen at both of Jupiter’s poles [1].

Ionosphere of Mars during the consecutive solar minima 23/24 and 24/25 as seen by MARSIS-Mars Express

The Mars' ionospheric behavior during two consecutive solar minima (23/24 and 24/25) is investigated with the same dataset. In particular, we use the Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) on board Mars Express to investigate the total electron content behavior of the whole atmosphere in relation to the solar irradiance (EUV and X-ray fluxes), the solar zenith angle and the heliocentric distance. The topside variability of the electron density profiles is also investigated through variations in the peak density and neutral scale height. Moreover, the equations of the NeMars empirical model of the Martian ionosphere for low solar activity are tested for both minima. We have found that the topside ionosphere of Mars behaved similarly at both solar minima. However, when considering the bottomside, a pronounced reduction in ionization in particular cases is suggested. In addition, larger TEC values are found during the solar minimum 24/25 in the nightside sector that may indicate possible larger plasma transport than during the minimum 23/24. Finally, this study confirms that the ionospheric empirical NeMars model equations derived by Sanchez-Cano et al. (2016) for the low solar activity period during the solar minimum 23/24 are also valid and accurate for the solar minimum 24/25. The long duration of Mars Express is a critical factor for determining the long-term Martian ionospheric variability, which in turn, is essential for understanding the global evolution of the planet's atmosphere.

Relating the Properties of Chromospheric Condensation to Flare Energy Transported by Thermal Conduction

Abstract Chromospheric condensation is a brief episode of downflow often accompanying energy release and evaporation in a solar flare. While this component of a flare reflects the energy release process only indirectly, it can be observed at high spatial and temporal resolution, even from the ground. It appears in spectroscopic observations of cooler lines, formed below ∼105 K, as a redshift that peaks and decays after less than 1 minute. In order to use this signature to infer characteristics of solar flare energy release, it is important to establish quantitative relationships with properties of the condensation. The initial investigation reported here does so after restricting consideration to energy transport via thermal conduction into a simplified, stratified chromosphere. We develop an analytical expression for the decay of a condensation propagating into a stratified atmosphere. This model provides a relationship between shock velocity and preshock density structure. We also use one-dimensional gasdynamic simulations to explore the dynamics of these shocks as they penetrate into the stratified chromosphere. We find that the peak downflow speed primarily reflects the energy flux into the chromosphere, while the product of this velocity and the redshift duration is proportional to the preshock density scale height as H ≃ 0.6u 0 τ.

Magnetoacoustic wave energy dissipation in the atmosphere of solar pores.

The suitability of solar pores as magnetic wave guides has been a key topic of discussion in recent years. Here, we present observational evidence of propagating magnetohydrodynamic wave activity in a group of five photospheric solar pores. Employing data obtained by the Facility Infrared Spectropolarimeter at the Dunn Solar Telescope, oscillations with periods of the order of 5 min were detected at varying atmospheric heights by examining Si ɪ 10827 Å line bisector velocities. Spectropolarimetric inversions, coupled with the spatially resolved root mean square bisector velocities, allowed the wave energy fluxes to be estimated as a function of atmospheric height for each pore. We find propagating magnetoacoustic sausage mode waves with energy fluxes on the order of 30 kW m-2 at an atmospheric height of 100 km, dropping to approximately 2 kW m-2 at an atmospheric height of around 500 km. The cross-sectional structuring of the energy fluxes reveals the presence of both body- and surface-mode sausage waves. Examination of the energy flux decay with atmospheric height provides an estimate of the damping length, found to have an average value across all five pores of Ld ≈ 268 km, similar to the photospheric density scale height. We find the damping lengths are longer for body mode waves, suggesting that surface mode sausage oscillations are able to more readily dissipate their embedded wave energies. This work verifies the suitability of solar pores to act as efficient conduits when guiding magnetoacoustic wave energy upwards into the outer solar atmosphere. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.