Observables of spheroidal magnetized strange stars

We study stable spheroidal configurations of magnetized strange stars using an axially symmetric metric in spherical coordinates that uses a gamma parameter to link the anisotropy in the equation of state due to the magnetic field with the deformation of the star. The stars are composed by magnetized strange quark matter described within the framework of the MIT bag model. Their masses, radii, eccentricity, redshift and mass quadrupole moment are computed. Results are compared with spherical strange star solutions obtained with Tolman-Oppenheimer-Volkoff equations and observational data of strange star candidates. In the spheroidal model the observables depend directly on the deformation of the star, and, even though it is small, the observables strongly deviate from the corresponding spherical configurations. Thus, the highest values of the mass quadrupole moment correspond to the intermediate mass regime. These differences might allow us to discriminate between models with and without magnetic field when compared with observations.

Figure 1

(a) Stability window for magnetized SQM in the plane $\mathbf{B}$ vs ${\mathtt{B}}_{\mathtt{Bag}}$ for fixed values of baryon density $n_B/n_0$, taking $n_0=0.16{\mathrm{fm}}^{-3}$. (b) Energy per baryon ($E/n_B$) as a function of the perpendicular pressure ($P_{\perp }$) at $B=[0,5\times {10}^{17},{10}^{18}]$ G and for fixed values of the ${\mathtt{B}}_{\mathtt{Bag}}=[65,75]\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 2

EoS for magnetized SSs at $B=[0,5\times {10}^{17},{10}^{18}]$ G. (a) ${\mathtt{B}}_{\mathtt{Bag}}=65\mathrm{MeV}/{\mathrm{fm}}^3$. (b) ${\mathtt{B}}_{\mathtt{Bag}}=75\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 3

Solutions for spheroidal configurations in comparison with TOV solutions and the nonmagnetized configuration at $B=5\times {10}^{17}$ G and $B={10}^{18}$ G, where $r$ represents both radii $R$ and $Z$. (a) ${\mathtt{B}}_{\mathtt{bag}}=65\mathrm{MeV}/{\mathrm{fm}}^3$. (b) ${\mathtt{B}}_{\mathtt{bag}}=75\mathrm{MeV}/{\mathrm{fm}}^3$ [34].

Figure 4

Equatorial radius (a) $R$ and (b) $\gamma$ as a function of the central energy density for ${\mathtt{B}}_{\mathtt{bag}}=65\mathrm{MeV}/{\mathrm{fm}}^3$. The gray lines correspond to different values of the magnetic field between $B={10}^{17}$ G and $B={10}^{18}$ G, taking steps of $1\times {10}^{17}$ G.

Figure 5

Elipticity $\epsilon$ as a function of (a) mass $M$ and (b) energy density $E$ at $B=[0,5\times {10}^{17},{10}^{18}]$ G and for fixed values of ${\mathtt{B}}_{\mathtt{Bag}}=[65\mathrm{MeV}/{\mathrm{fm}}^3$, 75 $\mathrm{MeV}/{\mathrm{fm}}^3]$.

Figure 6

Mass $M$ as function of (a) energy density $E$ and (b) ratio between $M$ and the baryon mass $M_B$ at $B=[0,5\times {10}^{17},{10}^{18}]$ G and for fixed values of ${\mathtt{B}}_{\mathtt{Bag}}=[65\mathrm{MeV}/{\mathrm{fm}}^3$, 75 $\mathrm{MeV}/{\mathrm{fm}}^3]$.

Figure 7

Comparison of observational data for candidates of SSs with the stars obtained from Eqs. (10) and (13). The shaded regions correspond to theoretical constraints: Gravitational collapse (I); requirement of finite pressure inside the star (II); causality (III); rotational stability (IV) [25].

Figure 8

Gravitational redshift $z_{rs}$ as a function of mass $M$ at $B=[0,5\times {10}^{17},{10}^{18}]$ G for TOV and the $\gamma$ equations. (a) ${\mathtt{B}}_{\mathtt{Bag}}=65\mathrm{MeV}/{\mathrm{fm}}^3$. (b) ${\mathtt{B}}_{\mathtt{Bag}}=75\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 9

Mass quadrupole moment $Q$ as a function of mass $M$ at $B=5\times {10}^{17}$ G for ${\mathtt{B}}_{\mathtt{Bag}}=65\mathrm{MeV}/{\mathrm{fm}}^3$ and ${\mathtt{B}}_{\mathtt{Bag}}=75\mathrm{MeV}/{\mathrm{fm}}^3$.