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The magnetic field through the magnetic reconnection process affects the dynamics and structure of astrophysical systems. Numerical simulations are the tools to study the evolution of these systems. However, the resolution, dimensions, resistivity, and turbulence of the system are some important parameters to take into account in the simulations. In this paper, we investigate the evolution of magnetic energy in astrophysical simulations by performing a standard test problem for MHD codes, Orszag-Tang. We estimate the numerical dissipation in the simulations using state-of-the-art numerical simulation code in astrophysics, PLUTO. The estimated numerical resistivity in 2D simulations corresponds to the Lundquist number $\approx 10^{4}$ in the resolution of $512\times512$ grid cells. It is also shown that the plasmoid unstable reconnection layer can be resolved with sufficient resolutions. Our analysis demonstrates that in non-relativistic magnetohydrodynamics simulations, magnetic and kinetic energies undergo conversion into internal energy, resulting in plasma heating., Comment: 8 pages, 3 figures, Accepted in Proceedings of RAGtime 23-25

During substructure formation in magnetized astrophysical plasma, dissipation of magnetic energy facilitated by magnetic reconnection affects the system dynamics by heating and accelerating the ejected plasmoids. Numerical simulations are a crucial tool for investigating such systems. In astrophysical simulations, the energy dissipation, reconnection rate and substructure formation critically depend on the onset of reconnection of numerical or physical origin. In this paper, we hope to assess the reliability of the state-of-the-art numerical codes, PLUTO and KORAL by quantifying and discussing the impact of dimensionality, resolution, and code accuracy on magnetic energy dissipation, reconnection rate, and substructure formation. We quantitatively compare results obtained with relativistic and non-relativistic, resistive and non-resistive, as well as two- and three-dimensional setups performing the Orszag-Tang test problem. We find the sufficient resolution in each model, for which numerical error is negligible and the resolution does not significantly affect the magnetic energy dissipation and reconnection rate. The non-relativistic simulations show that at sufficient resolution, magnetic and kinetic energies convert to internal energy and heat up the plasma. The results show that in the relativistic system, energy components undergo mutual conversion during the simulation time, which leads to a substantial increase in magnetic energy at 20\% and 90\% of the total simulation time of $10$ light-crossing times -- the magnetic field is amplified by a factor of five due to relativistic shocks. We also show that the reconnection rate in all our simulations is higher than $0.1$, indicating plasmoid-mediated regime. It is shown that in KORAL simulations magnetic energy is slightly larger and more substructures are captured than in PLUTO simulations., Comment: 17 pages, 20 Figures

We study the structure and total energy of a strange quark star (SQS) endowed with a strong magnetic field with different rotational frequencies. The MIT bag model is used, with the density-dependent bag constant for the equation of state (EOS). The EOS is computed considering the Landau quantization effect regarding the strong magnetic fields (up to $5\times10^{17}$ G) in the interior of the strange quark star. Using the LORENE library, we calculate the structural parameters of SQS for different setups of magnetic field strengths and rotational frequencies. In each setup, we perform calculations for $51$ stellar configurations, with specified central enthalpy values. We investigate the configurations with the maximum gravitational mass of SQS in each setup. Our models of SQSs are compared in the maximum gravitational mass, binding energy, compactness, and deformation of the star. We show that the gravitational mass might exceed $2.3 M_\odot$ in some models, which is comparable with the mass of the recently detected ``black widow'' pulsar \emph{PSR J0952-0607} and the mass of \emph{GW190814} detected by the LIGO/Virgo collaboration. The deformation and maximum gravitational mass of SQS can be characterized by simple functions that have been fitted to account for variations in both magnetic field strength and frequency. Rapidly rotating strange stars have a minimum gravitational mass given by the equatorial mass-shedding limit., Comment: 18 pages, 10 Figures, 2 tables, submitted to PhysRevD

In this paper, we investigate the newborn strange quark stars with constant entropy. We also use the MIT bag model to calculate the thermodynamic properties in two cases; the density-dependent bag constant and the fixed bag constant (B = 90 MeV). We show that the equation of state becomes stiffer by using the density dependent bag constant and by increasing the entropy. Furthermore, we show that the adiabatic index of the system reaches to 4/3 at high densities. Later, we calculate the structure of a strange quark star using the equation of state and the general relativistic equations of hydrostatic equilibrium, the Tolman-Oppenheimer-Volkoff (TOV) equations. We show that the gravitational mass of the star decreases by increasing the entropy and the maximum gravitational mass is larger when we use the density-dependent bag constant at fixed central energy density. It is shown that the mass-radius relation for this system obeys M R^ 3 for different cases of the calculations. Finally, we show that for a given stellar mass considering the fixed bag constant, the maximum gravitational red shift of a strange quark star occurs at larger values of entropy., Comment: 7 pages, 10 figures, Ind J. Phys. (2020) accepted for publication

We investigate the thermodynamic properties of strange quark matter under the strong magnetic field in the framework of the MIT bag model in two cases of bag constants. We consider two cases of the magnetic field, the uniform magnetic field and the density-dependent magnetic field to calculate the equation of state of strange quark matter. For the case of density-dependent magnetic field, we use a Gaussian equation with two free parameters $\beta$ and $\theta$ and use two different sets of the parameters for the magnetic field changes (a slow and a fast decrease of the magnetic field from the center to the surface). Our results show that the energy conditions based on the limitation of the energy-momentum tensor, are satisfied in the corresponding conditions. We also show that the equation of state of strange quark matter becomes stiffer by increasing the magnetic field. In this paper, we also calculate the structure parameters of a pure strange quark star using the equation of state. We investigate the compactification factor ($2M/R$) and the surface redshift of star in different conditions. The results show that the strange quark star is denser than the neutron star and it is more compact in the presence of the stronger magnetic field. As another result, the compactification factor increases when we use a slow increase of the magnetic field from the surface to the center. Eventually, we compare our results with the observational results for some strange star candidates, and we find that the structure of the strange star candidates is comparable to that of the star in our model., Comment: 20 pages, 12 figures, 3 tables, European Physical Journal A (2019) accepted for publication

In this article we have calculated the structure properties of a strange quark star in static model in the presence of a strong magnetic field using MIT bag model with a density dependent bag constant. To parameterize the density dependence of bag constant, we have used our results for the lowest order constrained variational calculation of the asymmetric nuclear matter. By calculating the equation of state of strange quark matter, we have shown that the pressure of this system increases by increasing both density and magnetic field. Finally, we have investigated the effect of density dependence of bag constant on the structure properties of strange quark star., Comment: 23 pages, 9 figures, Res. in Astron. Astrophys. (2012) accepted