arXiv subjects

Z. F. Gao

Publications and source records attributed to Z. F. Gao.

11 recordsLinked to original sources

arXiv2023

A measure of cosmological distance using the \civ\ Baldwin effect in quasars

We use the anticorrelation between the equivalent width (EW) of the C\,\textsc{iv} 1549 Å emission line and the continuum luminosity in the quasars rest frame (Baldwin effect) to measure their luminosity distance as well as estimate cosmological parameters. We obtain a sample of 471 Type I quasars with the UV/optical spectra and EW (C\,\textsc{iv}) measurements in the redshift range of $2.3< z< 7.1$ including 25 objects at $5 < z < 7.1$, which can be used to investigate the C\,\textsc{iv} Baldwin effect and determine cosmological luminosity distance. The relation $EW(C\,\textsc{iv}) \propto {(λ{L_λ})^γ}$ can be applied to check the inverse correlation between the C\,\textsc{iv} EW and ${L_λ}$ of quasars and give their distance, and the data suggest that the EW of C\,\textsc{iv} is inversely correlated with continuum monochromatic luminosities. On the other hand, we also consider dividing the Type I quasars sample into various redshift bins, which can be used to check if the C\,\textsc{iv} EW-luminosity relation depends on the redshift. Finally, we apply a combination of Type I quasars and SNIa Pantheon to test the property of dark energy concerning whether or not its density deviates from the constant, and give the statistical results.

astro-ph.CO↗

arXiv2016

Modified Fermi Energy of Electrons in a Superhigh Magnetic Field

In this paper, we investigate the electron Landau-level stability and its influence on the electron Fermi energy, $E_{\rm F}(e)$, in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity $g_{n}$, the electron Landau-level stability coefficient is introduced. According to the requirement that $g_{n}$ decreases with increasing the magnetic field intensity $B$, the magnetic-field index $β$ in the expression of $E_{\rm F}(e)$ must be positive. By introducing the Dirac$-δ$ function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to $E_{\rm F}(e)$ in a superhigh magnetic field (SMF). This solution has a low magnetic-field index of $β=1/6$, compared with the previous one, and works when $ρ\geq 10^{7}$~g cm$^{-3}$ and $B_{\rm cr}\ll B\leq 10^{17}$~Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density $n_e$, and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As $B$ increases, more and more electrons will occupy higher Landau levels, though $g_{n}$ decreases with the Landau level number $n$. The enhanced $n_{e}$ in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for megnetars.

astro-ph.HE↗

arXiv2015

The Effects of Superhigh Magnetic Fields on Equations of States of Neutron Stars

By introducing Dirac ?-function in superhigh magnetic field, we deduce a general formula for pressure of degenerate and relativistic electrons, Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynamic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows: the stronger the magnetic field strength, the higher the electron pressure becomes; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star. Since this is an original work in which some uncertainties could exist, to further modify and perfect our theory model should be considered in our future studies.

hep-ph↗

arXiv2015

Constraining the Braking Indices of Magnetars

Due to the lack of long term pulsed emission in quiescence and the strong timing noise, it is impossible to directly measure the braking index $n$ of a magnetar. Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of the mean braking indices of eight magnetars with SNRs, and find that they cluster in a range of $1\sim$42. Five magnetars have smaller mean braking indices of $1 3$ for other three magnetars are attributed to the decay of external braking torque, which might be caused by magnetic field decay. We estimate the possible wind luminosities for the magnetars with $1 3$ within the updated magneto-thermal evolution models. Although the constrained range of the magnetars' braking indices is tentative, due to the uncertainties in the SNR ages, which come from distance uncertainties and the unknown conditions of the expanding shells, our method provides an effective way to constrain the magnetars' braking indices if the measurements of the SNRs' ages are reliable, which can be improved by future observations.

astro-ph.HE↗

arXiv2013

Numerical simulation of the electron capture process in a magnetar interior

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy $E$ ($E > Q$, $Q$ is the threshold energy of inverse $β-$decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient $q$ and the effective electron capture rate $Γ_{\rm eff}$. By using $Γ_{\rm eff}$, the values of $L_{\rm X}$ and $L_{\rm ν}$ are calculated, where and $L_{\rm ν}$, $L_{\rm X}$ are the average neutrino luminosity of Anomalous X-ray Pulsars (AXPs) and the average X-ray luminosity of AXPs, respectively. The complete process of electron capture inside a magnetar is simulated numerically.

astro-ph.HE↗

arXiv2013

Evolution of superhigh magnetic fields of magnetars

In this paper, we consider the effect of Landau levels on the decay of superhigh magnetic fields of magnetars. Applying ${}^3P_2$ anisotropic neutron superfluid theory yield a second-order differential equation for a superhigh magnetic field $B$ and its evolutionary timescale $t$. The superhigh magnetic fields may evolve on timescales $\sim (10^{6}-10^{7})$ yrs for common magnetars. According to our model, the activity of a magnetar may originate from instability caused by the high electron Fermi energy.

astro-ph.HE↗

arXiv2013

Landau level-superfluid modified factor and effective X/$γ$-ray coefficient of a magnetar

As soon as the energy of electrons near the Fermi surface are higher than $Q$, the threshold energy of inverse $β-$ decay, the electron capture process will dominate. The resulting high-energy neutrons will destroy anisotropic ${}^3P_2$ neutron superfluid Cooper pairs. By colliding with the neutrons produced in the process $n+ (n\uparrow n\downarrow)\longrightarrow n+ n+ n$, the kinetic energy of the outgoing neutrons will be transformed into thermal energy. The transformed thermal energy would transported from the star interior to the star surface by conduction, then would be transformed into radiation energy as soft X-rays and gamma-rays. After a highly efficient modulation within the pulsar magnetosphere, the surface thermal emission (mainly soft X/$γ$-ray emission) has been shaped into a spectrum with the observed characteristics of magnetars. By introducing two important parameters: Landau level-superfluid modified factor and effective X/$γ$-ray coefficient, we numerically simulate the process of magnetar cooling and magnetic field decay, and then compute magnetars' soft X/$γ$-ray luminosities $L_{X}$. Further, we obtain aschematic diagrams of $L_{X}$ as a function of magnetic field strength $B$. The observations are compared with the calculations.

astro-ph.HE↗

arXiv2013

Magnetic field decay of magnetars in supernova remnants

In this paper, we modify our previous research carefully, and derive a new expression of electron energy density in superhigh magnetic fields. Based on our improved model, we re-compute the electron capture rates and the magnetic fields' evolutionary timescales $t$ of magnetars. According to the calculated results, the superhigh magnetic fields may evolve on timescales $\sim (10^{6}-10^{7})$ yrs for common magnetars, and the maximum timescale of the field decay, $t\approx 2.9507 \times 10^{6}$ yrs, corresponding to an initial internal magnetic field $B_{\rm 0}= 3.0 \times 10^ {15}$ G and an initial inner temperature $T_{\rm 0}= 2.6 \times 10^ {8}$ K. Motivated by the results of the neutron star-supernova remnant(SNR) association of Zhang $\&$ Xie(2011), we calculate the maximum $B_{\rm 0}$ of magnetar progenitors, $B_{\rm max}\sim (2.0\times 10^{14}-2.93 \times 10^{15})$ G when $T_{\rm 0}= 2.6 \times 10^ {8}$ K. When $T_{\rm 0}\sim 2.75 \times 10^ {8}-~1.75 \times 10^ {8}$ K, the maximum $B_{\rm 0}$ will also be in the range of $\sim 10^{14}-10^{15}$ G, not exceeding the upper limit of magnetic field of a magnetar under our magnetar model. We also investigate the relationship between the spin-down ages of magnetars and the ages of their SNRs, and explain why all AXPs associated with SNRs look older than their real ages, whereas all SGRs associated with SNRs appear younger than they are.

astro-ph.HE↗

arXiv2013

The surface and inner temperatures of magnetars

Assuming that the timescale of the magnetic field decay is approximately equal to that of the stellar cooling via neutrino emission, we obtain a one-to-one relationship between the effective surface thermal temperature and the inner temperature. The ratio of the effective neutrino luminosity to the effective X-ray luminosity decreases with decaying magnetic field.

astro-ph.HE↗

arXiv2013

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons ($E_{F}(e)$) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a Neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: $E_{F}(e)$ is related to density $ρ$, the mean electron number per baryon $Y_{e}$ and magnetic field strength $B$.

astro-ph.HE↗

arXiv2010

A very large glitch in PSR B2334+61

Seven years of pulse time-of-arrival measurements have been collected from observations of the young pulsar PSR B2334+61 using the Nanshan radio telescope of Urumqi Observatory. A phase-connected solution has been obtained over the whole data span, 2002 August to 2009 August. This includes a very large glitch that occurred between 2005 August 26 and September 8 (MJDs 53608 and 53621). The relative increase in rotational frequency for this glitch, $Δν_{g}/ν~\sim~20.5\times10^{-6}$, is the largest ever seen. Although accounting for less than 1\% of the glitch, there were two well-defined exponential decay terms with time constants of 21 and 147 days respectively. There was also a large long-term increase in the spindown rate with $Δ\dotν_p/\dotν\sim 0.011$ at the time of the glitch. A highly significant oscillation with a period of close to one year is seen in the post-glitch residuals. It is very unlikely that this can be accounted for by a pulsar position error or proper motion -- it appears to result from effects interior to the neutron star. Implications of these results for pulsar glitch models are discussed.

astro-ph.HE↗