A Mechanical Model for Magnetized Relativistic Blastwaves

The evolution of a relativistic blastwave is usually delineated under the assumption of pressure balance between forward- and reverse-shocked regions. However, such a treatment usually violates the energy conservation law, and is inconsistent with existing MHD numerical simulation results. A mechanical model of non-magnetized blastwaves was proposed in previous work to solve the problem. In this paper, we generalize the mechanical model to the case of a blastwave driven by an ejecta with an arbitrary magnetization parameter $\sigma_{\rm ej}$. We test our modified mechanical model by considering a long-lasting magnetized ejecta and found that it is much better than the pressure-balance treatment in terms of energy conservation. For a constant central engine wind luminosity $L_{\rm ej} = 10^{47}{\rm erg~s^{-1}}$ and $\sigma_{\rm ej} < 10$, the deviation from energy conservation is negligibly small at small radii, but only reaches less than $25\%$ even at $10^{19}{\rm cm}$ from the central engine. For a finite life time of the central engine, the reverse shock crosses the magnetized ejecta earlier for the ejecta with a higher $\sigma_{\rm ej}$, which is consistent with previous analytical and numerical results. In general, the mechanical model is more precise than the traditional analytical models with results closer to those of numerical simulations.Comment: Accepted for publication in MNRAS; 8 pages, 2 figure

Engine-fed Kilonovae (Mergernovae) -- I. Dynamical Evolution and Energy Injection / Heating Efficiencies

A binary neutron star merger is expected to be associated by a kilonova, transient optical emission powered by radioactive decay of the neutron-rich ejecta. If the post-merger remnant is a long-lived neutron star, additional energy injection to the ejecta is possible. In this first paper of a series, we study the dynamical evolution of the engine-fed kilonova (mergernova) ejecta in detail. We perform a semi-analytical study of the problem by adopting a modified mechanical blastwave model that invokes interaction between a Poynting-flux-dominated flow and a non-magnetized massive ejecta. Shortly after the engine is turned on, a pair of shocks would be excited. The reverse shock quickly reaches the wind-acceleration region and disappears (in a few seconds), whereas the forward shock soon breaks out from the ejecta (in $10^2$ - $10^3$ seconds) and continues to propagate in the surrounding interstellar medium. Most of the energy injected into the blastwave from the engine is stored as magnetic energy and kinetic energy. The internal energy fraction is $f_{\rm int} < 0.3$ for an ejecta mass equal to $10^{-3}M_{\odot}$. Overall, the energy injecting efficiency $\xi$ is at most $\sim 0.6$ and can be as small as $\sim 0.04$ at later times. Contrary to the previous assumption, efficient heating only happens before the forward shock breaks out of the ejecta with a heating efficiency $\xi_t \sim (0.006 - 0.3)$, which rapidly drops to $\sim 0$ afterwards. The engine-fed kilonova lightcurves will be carefully studied in Paper II.Comment: 16 pages, 8 figures, accepted for publication on MNRA

A Mechanical Model for Magnetized Relativistic Blastwaves

The evolution of a relativistic blastwave is usually delineated under the assumption of pressure balance between forward- and reverse-shocked regions. However, such a treatment usually violates the energy conservation law, and is inconsistent with existing magnetohydrodynamic numerical simulation results. A mechanical model of non-magnetized blastwaves was proposed in previous work to solve the problem. In this paper, we generalize the mechanical model to the case of a blastwave driven by an ejecta with an arbitrary magnetization parameter $\sigma_{\rm ej}$. We test our modified mechanical model by considering a long-lasting magnetized ejecta and found that it is much better than the pressure-balance treatment in terms of energy conservation. For a constant central engine wind luminosity $L_{ \ rm ej} = 10^{47} { \ rm erg ~ s^{-1}}$ and $\ sigma_{ \ rm ej} \u3c 10$, the deviation from energy conservation is negligibly small at small radii but only reaches less than $25{{\ \rm per\ cent}}$ even at 1019 cm from the central engine. For a finite lifetime of the central engine, the reverse shock crosses the magnetized ejecta earlier for the ejecta with a higher $\sigma_{\rm ej}$, which is consistent with previous analytical and numerical results. In general, the mechanical model is more precise than the traditional analytical models with results closer to those of numerical simulations

Relation Between Gravitational Mass and Baryonic Mass for Non-Rotating and Rapidly Rotating Neutron Stars

With a selected sample of neutron star (NS) equations of state (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass Mg and baryonic mass Mb, and the relations between the maximum NS mass supported through uniform rotation (Mmax) and that of nonrotating NSs (MTOV). We find that for an EOS-independent quadratic, universal transformation formula (Mb=Mg+A×M2g)(Mb=Mg+A×Mg2), the best-fit A value is 0.080 for non-rotating NSs, 0.064 for maximally rotating NSs, and 0.073 when NSs with arbitrary rotation are considered. The residual error of the transformation is ∼ 0.1M⊙ for non-spin or maximum-spin, but is as large as ∼ 0.2M⊙ for all spins. For different EOSs, we find that the parameter A for non-rotating NSs is proportional to R−11.4R1.4−1 (where R1.4 is NS radius for 1.4M⊙ in units of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01M⊙ for the quadratic form and less than 0.01M⊙ for the cubic form ((Mb=Mg+A1×M2g+A2×M3g)(Mb=Mg+A1×Mg2+A2×Mg3)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (Mmax − MTOV)/MTOV and the spin period normalized to the Keplerian period PP, i.e., log10Δm=(−2.74±0.05)log10P+log10(0.20±0.01)log10Δm=(−2.74±0.05)log10P+log10(0.20±0.01), which is independent of EOS models. These empirical relations are helpful to study NS-NS mergers with a long-lived NS merger product using multi-messenger data. The application of our results to GW170817 is discussed