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Register a new userExtended Self-similar Solution for Circumstellar Material-Supernova Ejecta Interaction
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In this note, we present a detailed self-similar solution to the interaction of a uniformly expanding gas and a stationary ambient medium, with an application to supernovae interacting with preexisting circumstellar media (Type IIn SNe). We implement the generalized solution into the Modular Open Source Fitter for Transients (MOSFiT), an open-source Python package for fitting extragalactic transient light curves.
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The interaction of a SN ejecta with a pre-existing circumstellar material (CSM) is one of the most promising energy sources for a variety of optical transients. Recently, a semi-analytic method developed by Chatzopoulos et al. (2012, hereafter CWV12) has been commonly used to describe the optical light curve behaviors under such a scenario. We find that the expressions for many key results in CWV12 are too complicated for readers to make order of magnitude estimation or parameter dependency judgement. Based on the same physical picture, here we independently re-derive all the formulae and re-establish a set of reader friendly formula expressions. Nevertheless, we point out and correct some minor errors or typos existing in CWV12.
Supernova (SN) 2014C is a unique explosion where a seemingly typical hydrogen-poor stripped envelope SN started to interact with a dense, hydrogen-rich circumstellar medium (CSM) a few months after the explosion. The delayed interaction suggests a detached CSM shell, unlike in a typical SN IIn where the CSM is much closer and the interaction commences earlier post-explosion; indicating a different mass loss history. We present near- to mid-infrared observations of SN 2014C from 1-5 years after the explosion, including uncommon 9.7 $mu$m imaging with COMICS on the Subaru telescope. Spectroscopy shows that the interaction is still ongoing, with the intermediate-width He I 1.083 $mu$m emission present out to our latest epoch 1639 days post-explosion. The last Spitzer/IRAC photometry at 1920 days post-explosion further confirms ongoing CSM interaction. The 1-10 $mu$m spectral energy distributions (SEDs) can be explained by a dust model with a mixture of 69% carbonaceous and 31% silicate dust, pointing to a chemically inhomogeneous CSM. The inference of silicate dust is the first among interacting SNe. An SED model with purely carbonaceous CSM dust is possible, but would require more than 0.22 $M_{odot}$ of dust, which is an order of magnitude larger than what observed in any other SNe, measured in the same way, at this epoch. The light curve beyond 500 days is well fit by an interaction model with a wind-driven CSM and a mass loss rate of $sim 10^{-3} , M_{odot},rm yr^{-1}$, which presents an additional CSM density component exterior to the constant density shell reported previously in the literature. SN 2014C could originate in a binary system, similar to RY Scuti, which would explain the observed chemical and density profile inhomogeneity in the CSM.
The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical $E^{-2}$ spectrum predicted by the standard Diffusive Shock Acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The $gamma$-ray probes of the acceleration spectra of CRs on-the-spot, inside of the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the $combination$ of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two ``polar caps of a spherical shock where the local magnetic field is within $simeq45^{circ}$ to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at expanding shock surface with an arbitrary energy dependence of particle diffusivity $kappa$. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where $kappa$ cancels out.
We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, thermally driven wind originating from a disc in which the density is a power law function of radius. Our scale-free solution is strictly only valid in the absence of gravity or centrifugal support; comparison with 2D hydrodynamic simulations of winds from Keplerian discs however demonstrates that the scale-free solution is a good approximation also in the outer regions of such discs, and can provide a reasonable description even for launch radii well within the gravitational radius of the flow. Although other authors have considered the flow properties along streamlines whose geometry has been specified in advance, this is the first isothermal calculation in which the flow geometry and variation of flow variables along streamlines is determined self-consistently. It is found that the flow trajectory is very sensitive to the power-law index of radial density variation in the disc: the steeper the density gradient, the stronger is the curvature of streamlines close to the flow base that is required in order to maintain momentum balance perpendicular to the flow. Steeper disc density profiles are also associated with more rapid acceleration, and a faster fall-off of density, with height above the disc plane. The derivation of a set of simple governing equations for the flow structure of thermal winds from the outer regions of power law discs offers the possibility of deriving flow observables without having to resort to hydrodynamical simulation.
In hierarchical evolution, voids exhibit two different behaviors related with their surroundings and environments, they can merge or collapse. These two different types of void processes can be described by the two-barrier excursion set formalism based on Brownian random walks. In this study, the analytical approximate description of the growing void merging algorithm is extended by taking into account the contributions of voids that are embedded into overdense region(s) which are destined to vanish due to gravitational collapse. Following this, to construct a realistic void merging model that consists of both collapse and merging processes, the two-barrier excursion set formalism of the void population is used. Assuming spherical voids in the Einstein de Sitter Universe, the void merging algorithm which allows us to consider the two main processes of void hierarchy in one formalism is constructed. In addition to this, the merger rates, void survival probabilities, void size distributions in terms of the collapse barrier and finally, the void merging tree algorithm in the self-similar models are defined and derived.
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