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This article deals with the most recent developments in the field of exoplanetary science connecting the interior of the planets with their habitability. In this issue, I have specified the importance of interior dynamics and briefly reviewed some of the main factors by which interior of a planet can effect the habitability of extra-solar planets., Comment: Published, 6 pages

The magma ocean period was a critical phase determining how Earth atmosphere developed into habitability. However there are major uncertainties in the role of key processes such as outgassing from the planetary interior and escape of species to space that play a major role in determining the atmosphere of early Earth. We investigate the influence of outgassing of various species and escape of H$_2$ for different mantle redox states upon the composition and evolution of the atmosphere for the magma ocean period. We include an important new atmosphere-interior coupling mechanism namely the redox evolution of the mantle which strongly affects the outgassing of species. We simulate the volatile outgassing and chemical speciation at the surface for various redox states of the mantle by employing a C-H-O based chemical speciation model combined with an interior outgassing model. We then apply a line-by-line radiative transfer model to study the remote appearance of the planet in terms of the infrared emission and transmission. Finally, we use a parameterized diffusion-limited and XUV energy-driven atmospheric escape model to calculate the loss of H$_2$ to space. We have simulated the thermal emission and transmission spectra for reduced or oxidized atmospheres present during the magma ocean period of Earth. Reduced or thin atmospheres consisting of H$_2$ in abundance emit more radiation to space and have larger effective height as compared to oxidized or thick atmospheres which are abundant in H$_2$O and CO$_2$. We obtain the outgassing rates of H2 from the mantle into the atmosphere to be a factor of ten times larger than the rates of diffusion-limited escape to space. Our work presents useful insight into the development of Earth atmosphere during the magma ocean period as well as input to guide future studies discussing exoplanetary interior compositions., Comment: 26 pages, 15 figures, accepted for publication

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_{\rho}(t) \sim t^{\theta_\rho}$ (with $\theta_\rho \simeq 0.25$), while the velocity length scale grows much faster, $viz.$, $L_{v}(t) \sim t^{\theta_v}$ (with $\theta_v \simeq 0.83$). The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave-vector, the scaled structure factors for the density and velocity fields decay with powers $-2.6$ and $-1.52$, respectively., Comment: 15 pages, 4 figures

The magma ocean (MO) is a crucial stage in the build-up of terrestrial planets. Its solidification and the accompanying outgassing of volatiles set the conditions for important processes occurring later or even simultaneously, such as solid-state mantle convection and atmospheric escape. To constrain the duration of a global-scale Earth MO we have built and applied a 1D interior model coupled alternatively with a grey H2O/CO2 atmosphere or with a pure H2O atmosphere treated with a line-by-line model described in a companion paper by Katyal et al. (2019). We study in detail the effects of several factors affecting the MO lifetime, such as the initial abundance of H2O and CO2, the convection regime, the viscosity, the mantle melting temperature, and the longwave radiation absorption from the atmosphere. In this specifically multi-variable system we assess the impact of each factor with respect to a reference setting commonly assumed in the literature. We find that the MO stage can last from a few thousand to several million years. By coupling the interior model with the line-by-line atmosphere model, we identify the conditions that determine whether the planet experiences a transient magma ocean or it ceases to cool and maintains a continuous magma ocean. We find a dependence of this distinction simultaneously on the mass of the outgassed H2O atmosphere and on the MO surface melting temperature. We discuss their combined impact on the MO's lifetime in addition to the known dependence on albedo, orbital distance and stellar luminosity and we note observational degeneracies that arise thereby for target exoplanets.

The evolution of Earth's early atmosphere and the emergence of habitable conditions on our planet are intricately coupled with the development and duration of the magma ocean phase during the early Hadean period (4 to 4.5 Ga). In this paper, we deal with the evolution of the steam atmosphere during the magma ocean period. We obtain the outgoing longwave radiation using a line-by-line radiative transfer code GARLIC. Our study suggests that an atmosphere consisting of pure H$_{2}$O, built as a result of outgassing extends the magma ocean lifetime to several million years. The thermal emission as a function of solidification timescale of magma ocean is shown. We study the effect of thermal dissociation of H$_{2}$O at higher temperatures by applying atmospheric chemical equilibrium which results in the formation of H$_{2}$ and O$_{2}$ during the early phase of the magma ocean. A 1-6\% reduction in the OLR is seen. We also obtain the effective height of the atmosphere by calculating the transmission spectra for the whole duration of the magma ocean. An atmosphere of depth ~100 km is seen for pure water atmospheres. The effect of thermal dissociation on the effective height of the atmosphere is also shown. Due to the difference in the absorption behavior at different altitudes, the spectral features of H$_{2}$ and O$_{2}$ are seen at different altitudes of the atmosphere. Therefore, these species along with H$_{2}$O have a significant contribution to the transmission spectra and could be useful for placing observational constraints upon magma ocean exoplanets., Comment: 22 pages, 17 Figures, accepted for publication in ApJ on March 4

In the single-scattering theory of electromagnetic radiation, the {\it fractal regime} is a definite range in the photon momentum-transfer $q$, which is characterized by the scaling-law behavior of the structure factor: $S(q) \propto 1/q^{d_f}$. This allows a straightforward estimation of the fractal dimension $d_f$ of aggregates in {\it Small-Angle X-ray Scattering} (SAXS) experiments. However, this behavior is not commonly studied in optical scattering experiments because of the lack of information on its domain of validity. In the present work, we propose a definition of the multiple-scattering structure factor, which naturally generalizes the single-scattering function $S(q)$. We show that the mean-field theory of electromagnetic scattering provides an explicit condition to interpret the significance of multiple scattering. In this paper, we investigate and discuss electromagnetic scattering by three classes of fractal aggregates. The results obtained from the TMatrix method show that the fractal scaling range is divided into two domains: 1) a genuine fractal regime, which is robust; 2) a possible anomalous scaling regime, $S(q) \propto 1/q^{\delta}$, with exponent $\delta$ independent of $d_f$, and related to the way the scattering mechanism uses the local morphology of the scatterer. The recognition, and an analysis, of the latter domain is of importance because it may result in significant reduction of the fractal regime, and brings into question the proper mechanism in the build-up of multiple-scattering., Comment: 9 pages, 4 figures, accepted for publication in Journal of Quantitative Spectroscopy and Radiative Transfer (JQSRT)

Interplanetary dust particles (IDPs) are an important constituent of the earth's stratosphere, interstellar and interplanetary medium, cometary comae and tails, etc. Their physical and optical characteristics are significantly influenced by the morphology of silicate aggregates which form the core in IDPs. In this paper we reinterpret scattering data from laboratory analogs of cosmic silicate aggregates created by Volten et al. \cite{volten2007}, to extract their morphological features. By evaluating the structure factor, we find that the aggregates are mass fractals with a mass fractal dimension $d_{m} \simeq 1.75$. The same fractal dimension also characterizes clusters obtained from {\it diffusion limited aggregation} (DLA). This suggests that the analogs are formed by an irreversible aggregation of stochastically-transported silicate particles, Comment: 11 pages, 7 figures, accepted for publication in JQSRT. JQSRT, 2014

We study the extinction properties of the composite dust grains, consisting of host silicate spheroids and graphite as inclusions, using discrete dipole approximation (DDA). We calculate the extinction cross sections of the composite grains in the ultraviolet spectral region, 1200\AA -3200\AA and study the variation in extinction as a function of the volume fraction of the inclusions. We compare the model extinction curves with the observed interstellar extinction curves obtained from the data given by the International Ultraviolet Explorer (IUE) satellite. Our results for the composite grains show a distinct variation in the extinction efficiencies with the variation in the volume fraction of the inclusions. In particular, it is found that the wavelength of peak absorption at `2175\AA' shifts towards the longer wavelength with the variation in the volume fraction of inclusions. We find that the composite grain models with the axial ratios viz. 1.33 and 2.0 fit the observed extinction reasonably well with a grain size distribution, a = 0.005-0.250$\mu m$. Moreover, our results of the composite grains clearly indicate that the inhomogeneity in the grain structure, composition and the surrounding media modifies the extinction properties of the grains., Comment: 11 pages, 8 figures, accepted for publication in PASP

A composite dust grain model which simultaneously explains the observed interstellar extinction, polarization, IR emission and the abundance constraints, is required. We present a composite grain model, which is made up of a host silicate oblate spheroid and graphite inclusions. The interstellar extinction curve is evaluated in the spectral region 3.4-0.1$\mu m$ using the extinction efficiencies of the composite spheroidal grains for three axial ratios. Extinction curves are computed using the discrete dipole approximation (DDA). The model curves are subsequently compared with the average observed interstellar extinction curve and with an extinction curve derived from the IUE catalogue data., Comment: 10 pages, 3 figures