Examination of the multitude of signals from the phase transition of a neutron star to a quark star

The diverse nature of the signal resulting from the phase transition of a neutron star to a quark star and the corresponding astrophysical observations are studied in the present work. The phase transition process is initiated by a density change at the star's center that deconfines matter, followed by weak combustion to attain absolutely stable strange quark matter. The weak combustion results in the generation of huge neutrino-antineutrino pairs, which annihilate and deposit energy on the star's surface. Structural changes due to the energy loss result in the star's misalignment angle evolution and generate gravitational waves. The energy budget and time signature for the neutrino-antineutrino annihilation are compared with the observed isotropic energy for a short $\gamma$-ray burst. The misalignment angle evolves to align with the star's symmetry axis, which leads to the sudden increase or decrease of radio intensity from the pulsar. The corresponding gravitational wave emission, both continuous and burst, also has a unique signature pointing towards astrophysical phase transition.

Figure 1

The figure shows the spin down of a $1.6M_{\odot }$ star from 860 to 557 Hz as the central pressure of the star increase. The horizontal line of pressure $6\times {10}^{34} \mathrm{dyn}/{\mathrm{cm}}^2$ indicates the point from where QM becomes more stable than hadronic matter.

Figure 2

Energy deposition rate on the surface of the QS plotted as a function of time. The $y$ axis of the top section shows the total amount of energy deposited on the star's surface at that instant in time. The bottom section shows the spectrum of the pulse emitted in ergs as a function of time. The total energy has been normalized by ${10}^{50}\mathrm{ergs}$. At $t=29.7$ and 55.9, the value of $E\left(t\right)$ gives the total energy that has been emitted throughout the process for $1.6M_{\odot }$ and $2.0M_{\odot }$ stars, respectively. $E_{iso}$ and $t_{90}$ for a few GRBs are shown as references for the energy and time scale of typical millisecond bursts. The vertical columns indicate the error in the measurement of the observed $t_{90}$.

Figure 3

Snapshot of simulation of the dynamic evolution of neutrino and antineutrino escape and annihilation. At each snapshot, the neutrino and antineutrino can be seen to be produced due to PT and get annihilated. The corresponding energy deposited on the surface at each radius is shown as a heat map. The simulation only shows deposition along $\theta =\pi /2$ (equatorial region); however, the total energy is emitted from the entire volume of the star. The dark sphere is the opaque region for neutrinos.

Figure 4

Misalignment angle evolution due to energy emitted from the star for two different masses. The misaligned angle is seen to be decreasing and going towards alignment. The more massive star has a higher probability of attaining alignment than the lower mass star. Here the initial angle is taken to be $\pi /5\left({36}^{\circ }\right)$.

Figure 5

Top: The GW signal template emitted from rotating NSs due to PT. The $y$ axis shows the $h_{+}$ polarization of the GW normalized with the amplitude $h_0$. The distance from the Earth's surface is taken to be 2 kpc, and the line of sight angle is taken to be ${30}^{\circ }$. The first, second, and third GW plots are for a $2.0M_{\odot }$ star where the amplitude is shown for regions before, during, and after PT with no PT amplitude in the background for reference. Bottom: The spectral decomposition of the continuous emission of GW, indicating peaks in the different frequency regions as the PT evolves as compared to no PT.

Figure 6

Normalized intensity of radio emission from a $2.0M_{\odot }$ radio pulsar plotted with respect to the evolution of the misalignment angle of the pulsar. The $P$ for the pulsar evolves from 20.0 to 17.69 ms in 55.9 ms of PT time. The intensity drops sharply as the misalignment angle passes through the line of sight [here from $\chi =\pi /5$ (${36}^{\circ }$) to $\chi =10\pi /51$ (${35}^{\circ }$)] and then the intensity is seen to be increasing due to gain in rotational velocity [for $\chi =10\pi /51$ (${35}^{\circ }$) to $\chi =10\pi /95$ (${19}^{\circ }$)]. This can cause the pulsar signal to disappear or appear depending on the line of sight.