N. V. Erkaev

Anomalous magnetosheath properties during Earth passage of an interplanetary magnetic cloud

The aim of this paper is to model for the first time the variation of field and flow parameters in the magnetosheath during Earth passage of an interplanetary magnetic cloud. Under typical Solar wind conditions, magnetohydrodynamic (MHD) effects on the flow of plasma in the terrestrial magnetosheath are important only in a layer adjacent to the magnetopause which is a few thousand kilometers thick (“depletion layer” or “magnetic barrier”). During the passage of an interplanetary magnetic cloud, however, conditions upstream of the bow shock depart strongly from the norm. In this case, interplanetary parameters vary slowly over a wide range of values. Values of the upstream Alfven Mach number are much lower than those otherwise sampled (∼3 versus 8–10). Together with the magnetic shear across the magnetopause, this parameter plays a central role in determining the structure of the magnetosheath close to the magnetopause. As a consequence of sustained low values of the upstream Alfven Mach number, the magnetic field exerts a strong influence on the flow over a very substantial fraction of the magnetosheath throughout the duration of cloud passage, i.e., for a time period of the order of 1–2 days. We apply an algorithm to integrate the ideal MHD equations, using a boundary layer technique, and compute the variations of field and flow parameters along the stagnation streamline. We choose as our example the magnetic cloud which passed Earth on January 14–15, 1988. The interaction of this cloud with the magnetosphere, as regards the resulting ionospheric flow patterns and the substorm activity, has been the subject of various investigations. Using information from these studies, we obtain results on the magnetosheath when the magnetopause is modeled, first as a tangential discontinuity and then as a rotational discontinuity. Our results are in good general agreement with recent observations on the behavior of field and flow quantities in the magnetosheath region adjacent to the magnetopause. In addition, we predict the existence of a magnetic barrier when the upstream Alfven Mach number is low, irrespective of the magnetic shear across the magnetopause.

Three‐dimensional, one‐fluid, ideal MHD model of magnetosheath flow with anisotropic pressure

We present a three-dimensional, one-fluid, steady state magnetohydrodynamic (MHD) model of magnetosheath flow near the subsolar line with unequal plasma pressures perpendicular (P⊥) and parallel (P‖) to the magnetic field (P⊥ > P‖). Aside from an assumption on the total pressure normal to the magnetopause, our analytical-numerical method is completely general and is an extension of our isotropic, “magnetic string” MHD model, which we describe in detail here. The MHD equations are closed by a relation between P⊥ and P‖ as in the Bounded Anisotropy Model [Denton et al. 1994] corresponding to the threshold of the electromagnetic proton cyclotron wave instability. We take an IMF oriented perpendicular to the solar wind velocity. As boundary conditions, we have Rankine-Hugoniot relations at the bow shock and a no-flow condition at the magnetopause. We obtain steady state profiles of the magnetic field and plasma parameters for upstream sonic and Alfven Mach numbers equal to 10, and compare them with the isotropic case (P‖ = P⊥). Anisotropy slightly thickens the magnetosheath. In the anisotropic model, the density, the parallel and perpendicular temperatures, plasma pressures, and betas all decrease toward the magnetopause. Isotropic profiles lie between those of quantities perpendicular and parallel to the field. Anisotropy has considerable effect on the density profile, which lies below that in the isotropic limit throughout the magnetosheath. Density depletion results from stretching of magnetic field lines, which is caused by field-aligned plasma flow. Approaching the magnetopause, the tangential component of velocity parallel to the magnetic field decreases, while the tangential component perpendicular to the magnetic field increases. These are features characterizing a stagnation line flow at the magnetopause. The acceleration along the magnetic field is produced by the gradient of P‖ and the mirror force, which depends on anisotropy. They both make substantial contributions and are responsible for the changes we see from isotropy. The acceleration perpendicular to magnetic field is also larger than in the case of isotropy and is caused by the gradient of total pressure, the magnetic strength, and the mirror force. In addition, acceleration in both directions is affected by the decreasing density.

Ideal MHD flow behind interplanetary shocks driven by magnetic clouds

We present an ideal MHD theory to describe for the first time the “magnetic barrier” (or “depletion layer”) of that class of interplanetary ejecta called magnetic clouds. By “magnetic barrier” we mean that region of the sheath where the magnetic pressure is comparable to, or larger than, the gas pressure and where, therefore, the effects of the magnetic field on the flow are substantial. We model magnetic clouds as cylindrical flux ropes. We consider three cases: one steady state and two nonsteady situations. The two nonsteady situations correspond to (1) a self-similarly expanding magnetic cloud, and (2) to a nonexpanding magnetic cloud which has a net bulk motion with respect to the medium at infinity. In all cases the cloud drives an interplanetary shock ahead of it. We describe an algorithm to integrate the MHD equations in which the behavior of the sum of the magnetic and plasma pressure is prescribed. We assume here that the sum of the magnetic and plasma pressure is constant along any line normal to the magnetic cloud boundary. We find that in steady state the cloud boundary cannot be a tangential discontinuity, that is, a finite magnetic barrier thickness can only be obtained with a reconnecting cloud boundary. In general, the magnetic barriers of magnetic clouds are thick, that is, they are a substantial fraction of the clouds sheath. In steady state and the nonsteady case (situation 2, above), their width depends inversely on the Alfven Mach number. The non-steady state (situation 1) has similarities with the problem of solar wind flow around the terrestrial magnetosphere. In particular, the barrier thickness in this case is proportional to the inverse square of the Alfven Mach number. This work should be useful in the interpretation of data from the sheath region ahead of magnetic clouds driving interplanetary shocks.

Aspects of MHD flow about Venus

We describe the “magnetic string” approach to integrating the dissipationless magnetohydrodynamic (MHD) equations for flow around planetary obstacles and apply it to some aspects of the flow in the magnetosheath of Venus. Our method has both analytical and numerical components and is particularly suited to study the structure of the magnetic barrier (depletion layer). We do not include ion pickup processes and thus discuss only the contribution to the structure of the Venus magnetosheath made by the flow of the shocked solar wind. We work with an interplanetary magnetic field which is directed orthogonal to the solar wind bulk velocity. Magnetic forces on the flow are strongly dependent on the Alfven Mach number upstream of the bow shock, and one aim of this work is to study the dependence of field and flow quantities in the Venus magnetosheath on this parameter, thus allowing further future comparisons with data under a variety of interplanetary conditions. A second aim is to compare our MHD model results to a synopsis of observations made by the Pioneer Venus Orbiter. As one main conclusion, we show that this method leads, in principle, to a standoff bow shock position in good agreement with observations. We find, namely, that for a low but reasonable Alfven Mach number, our MHD-modeled magnetosheath is only ∼ 3.6% thinner in the Sun-Venus direction than that given by observations. Our method is complementary to three-dimensional, global MHD simulations of the solar wind-Venus interaction and offers versatility to modeling other aspects of the complicated interaction of the solar wind with Venus.

Atmosphere expansion and mass loss of close-orbit giant exoplanets heated by stellar XUV: I. Modeling of hydrodynamic escape of upper atmospheric material

In the present series of papers we propose a consistent description of the mass loss process. To study the effects of intrinsic magnetic field of a close-orbit giant exoplanet (so-called Hot Jupiter) on the atmospheric material escape and formation of planetary inner magnetosphere in a comprehensive way, we start with a hydrodynamic model of an upper atmosphere expansion presented in this paper. While considering a simple hydrogen atmosphere model, we focus on selfconsistent inclusion of the effects of radiative heating and ionization of the atmospheric gas with its consequent expansion in the outer space. Primary attention is paid to investigation of the role of specific conditions at the inner and outer boundaries of the simulation domain, under which different regimes of material escape (free- and restricted- flow) are formed. Comparative study of different processes, such as XUV heating, material ionization and recombination, H3+ cooling, adiabatic and Lyman-alpha cooling, Lyman-alpha reabsorption is performed. We confirm basic consistence of the outcomes of our modeling with the results of other hydrodynamic models of expanding planetary atmospheres. In particular, we obtain that under the typical conditions of an orbital distance 0.05 AU around a Sun-type star a Hot Jupiter plasma envelope may reach maximum temperatures up to ~9000K with a hydrodynamic escape speed ~9 km/s resulting in the mass loss rates ~(4-7)*10^10 g*s . In the range of considered stellar-planetary parameters and XUV fluxes that is close to mass loss in the energy limited case. The inclusion of planetary intrinsic magnetic fields in the model is a subject of the following up paper (Paper II).

Dust kinetic Alfvén and acoustic waves in a Lorentzian plasma

Dust kinetic Alfven waves (DKAWs) with finite Larmor radius effects have been examined rigorously in a uniform dusty plasma in the presence of an external magnetic field. A dispersion relation of low-frequency DKAW on the dust acoustic velocity branch is obtained in a low-β Lorentzian plasma. It is found that the influence of the Lorentzian distribution function is more effective for perpendicular component of group velocity as compared with parallel one. Lorentzian-type charging currents are obtained with the aid of Vlasov theory. Damping/instability due to dust charge fluctuation is found to be insensitive with the form of distribution function for DKAW. The possible applications to dusty space plasmas are pointed out.

Anisotropic magnetosheath: Comparison of theory with wind observations near the stagnation streamline

We carry out a first comparison with spacecraft measurements of our recent three-dimensional, one-fluid magnetohydrodynamic (MHD) model for the anisotropic magnetosheath [Erkaev et al., 1999], using data acquired by the Wind spacecraft on an inbound magnetosheath pass on December 24, 1994. The spacecraft trajectory was very close to the stagnation streamline, being displaced by less than 1/2 hour from noon and passing at low southern magnetic latitudes (∼4.5°). All quantities downstream of the bow shock are obtained by solving the Rankine-Hugoniot equations taking the pressure anisotropy into account. In this application of our model we close the MHD equations by a “bounded anisotropy” ansatz using for this purpose the inverse correlation between the proton temperature anisotropy, Ap (≡ Tp⊥/Tp‖− 1), and the proton plasma beta parallel to the magnetic field βp‖ observed on this pass when conditions are steady. In the model the total perpendicular pressure is prescribed and not obtained self-consistently. For all quantities studied we find very good agreement between the predicted and the observed profiles, indicating that the bounded anisotropy method of closing the magnetosheath equations, first suggested by Denton et al. [1994], is valid and reflects the physics of the magnetosheath well. We assess how sensitive our model results are to different parameters in the Ap = α0βp‖−a1 (a1 > 0) relation, taking for a1 the two limiting values (0.4, 0.5) resulting from the two-dimensional hybrid simulations of Gary et al. [1997], and varying a0 in the range 0.6 – 0.8. Input solar wind conditions are as measured on this pass. In general, the model profiles depend more strongly on a0 than on a1. In particular, decreasing a0 narrows the width of the plasma depletion layer (PDL) and widens the mirror stable region. For the lowest value of a0, the mirror stable region extends sunward of the outer edge of the PDL. For the other two values of a0, and regardless of the value of a1, it is contained within the PDL. Finally, we also study phenomenological double-poly tropic laws and find poly tropic indices γ⊥ ≈ 1 and γ‖ ≈ 1.5. These results agree well with those of Hau et al. [1993] inferred from Active Magnetospheric Particle Tracer Explorers/Ion Release Module data on a crossing of the near-subsolar magnetosheath.

Effects on the Jovian magnetosheath arising from solar wind flow around nonaxisymmetric bodies

We investigate the MHD structure of the Jovian magnetosheath along the Sun-Jupiter line and, particularly, the region where the interplanetary magnetic field (IMF) exerts a large influence on the magnetosheath flow (the “magnetic barrier”). We do this by integrating numerically the dissipationless MHD equations in their “magnetic string” formulation. The lack of axisymmetry of the magnetospheric obstacle introduces corresponding asymmetries in the Jovian magnetosheath. The dominant effect on the flow is produced by the IMF component orthogonal to Jupiters rotational equator. The thicknesses of the magnetosheath and magnetic barrier depend sensitively on the orientation of the IMF, decreasing monotonically as the inclination of the IMF to the rotational equator decreases. The magnetic barrier practically disappears when the IMF vector lies in the equator. For an arbitrary orientation of the IMF the magnetosheath magnetic field along the stagnation streamline is not only compressed as the magnetopause is approached but also rotates smoothly toward the direction of the Jovian rotation axis. This effect is absent in the case of flow around axisymmetric obstacles, such as the terrestrial magnetosphere.

EUV-driven mass-loss of protoplanetary cores with hydrogen-dominated atmospheres: the influences of ionization and orbital distance

We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results to those obtained by the energy-limited escape formula which is widely used for mass loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over- or underestimate the hydrogen mass loss rates by amounts that depend on the stellar EUV flux and planetary parameters such as mass, size, effective temperature, and EUV absorption radius.

Identifying the “true” radius of the hot sub-Neptune CoRoT-24b by mass loss modelling

For the hot exoplanets CoRoT-24b and CoRoT-24c, observations have provided transit radii R-T of 3.7 +/- 0.4R(circle plus) and 4.9 +/- 0.5R(circle plus), and masses of = 5.7M(circle plus) and 28 +/- 11M(circle plus), respectively. We study their upper atmosphere structure and escape applying an hydrodynamic model. Assuming R-T +/- R-PL, where R-PL is the planetary radius at the pressure of 100 mbar, we obtained for CoRoT-24b unrealistically high thermally driven hydrodynamic escape rates. This is due to the planets high temperature and low gravity, independent of the stellar EUV flux. Such high escape rates could last only for< 100 Myr, while R-PL shrinks till the escape rate becomes less than or equal to the maximum possible EUV-driven escape rate. For CoRoT-24b, R-PL must be therefore located at approximate to 1.9-2.2R(circle plus) and high altitude hazes/clouds possibly extinct the light at R-T. Our analysis constraints also the planets mass to be 5-5.7M(circle plus). For CoRoT-24c, R-PL and R-T lie too close together to be distinguished in the same way. Similar differences between R-PL and R-T may be present also for other hot, low-density sub-Neptunes.