Anisotropy of magnetized quark matter

Strong transient magnetic fields are generated in noncentral relativistic heavy-ion collisions. These fields induce anisotropy within the strongly interacting medium that, in principle, can affect the thermodynamic properties of the medium. We use the Polyakov loop extended Nambu Jona-Lasinio model to study the quark matter subjected to an external magnetic field at vanishing baryon chemical potential (${\mathit{\mu }}_{\mathit{B}}$). We have estimated the degree of anisotropy in the speed of sound and isothermal compressibility within the magnetized quark matter as a function of temperature (T) and magnetic field (eB). This study helps us to understand the extent of directionality generated in the initial stages of noncentral collisions while giving us useful information about the system.

Figure 1

Squared speed of sound’s longitudinal ($c_s^{2\parallel }$) (left) and transverse ($c_s^{2\perp }$) (right) components against temperature ($T$).

Figure 2

Squared speed of sound ($c_s^{2\parallel }$ and $c_s^{2\perp }$) against the magnetic field ($eB$) for different temperatures: $T=0.12\mathrm{GeV}$ (left), $T=0.155\mathrm{GeV}$ (middle), and $T=0.3\mathrm{GeV}$ (right).

Figure 3

Anisotropy in squared speed of sound ($\mathrm{\Delta }{c}_s^2/c_s^{2\parallel }$) against $T$ (left) and $eB$ (right). Here, $\mathrm{\Delta }{c}_s^2=c_s^{2\parallel }-c_s^{2\perp }$.

Figure 4

Isothermal compressibility (${\kappa }_T$) against temperature ($T$) at zero magnetic field. A comparison of this work (PNJL) with different models (HRG, EV-HRG [26], and CSPM [25]) and experimental results from ALICE [111].

Figure 5

Isothermal compressibility: longitudinal component (${\kappa }_T^{\parallel }$) (left) and transverse component (${\kappa }_T^{\perp }$) (right) against temperature ($T$) for different value of magnetic field ($eB$).

Figure 6

${\kappa }_T^{\parallel }$ and ${\kappa }_T^{\perp }$ against $eB$ at $T=0.12\mathrm{GeV}$ (left), $T=0.155\mathrm{GeV}$ (middle), and $T=0.3\mathrm{GeV}$ (right).

Figure 7

Anisotropy in isothermal compressibility $(\mathrm{\Delta }{\kappa }_T/{\kappa }_T^{\parallel })$ as a function of temperature ($T$) (left) and magnetic field ($eB$) (right), $\mathrm{\Delta }{\kappa }_T={\kappa }_T^{\parallel }-{\kappa }_T^{\perp }$.