Can the massive neutron star PSR J0348+0432 be a hyperon star?

Whether the massive neutron star PSR J0348+0432 can change into a hyperon star is studied in the framework of the relative mean field theory by choosing the suitable hyperon coupling constants. We find that whether the mesons $\sigma^{*}$ and $\phi$ being considered or not, the neutron star PSR J0348+0432 all can change into a hyperon star and the hyperon star transition density are the same for the two cases. We also find that the canonical mass neutron star also can change into a hyperon star in a minor hyperon star transition density as the mesons $\sigma^{*}$ and $\phi$ are not considered. Our results confirms some of recent conclusions.Comment: 11 pages,7 figures, This paper was published in Acta Physica Polonica B, 2017, 48(2): 171-18

The moment of inertia of the neutron star PSR J0348+0432 and its proto neutron star

The difference of the moment of inertia of the neutron star PSR J0348 + 0432 and that of its proto neutron star is studied in the framework of the relativistic mean field theory considering baryon octet. The temperature of the proto neutron star PSR J0348+0432 is chosen as T=5 MeV. The calculations show that the central baryon number density of the proto neutron star PSR J0348+0432 is in the range 0.623$\sim$0.813 fm$^{-3}$, decreased by 2$\sim$7\% compared to that of the neutron star PSR J0348+0432. The radius of the proto neutron star PSR J0348+0432 is in the range 13.101$\sim$12.419 km, increased by 1$\sim$2\% compared to that of the neutron star PSR J0348+0432. The moment of inertia of the proto neutron star PSR J0348+0432 is in the range 1.939$\times$10$^{45}$$\sim$1.638$\times$10$^{45}$ g.cm$^{2}$, increased by about 2$\sim$7\% compared to that of the neutron star PSR J0348+0432.Comment: 5 pages,5 figures, published by Astrophys Space Sci,2017,362(5):9

The hyperons in the massive neutron star PSR J0348+0432

Whether the massive neutron star PSR J0348+0432 can become a hyperon star is examined in the framework of the relativistic mean field theory by adjusting the hyperon coupling constants. It is found that at the central baryon number density of the massive neutron star PSR J0348+0432, the relative particle number density of hyperons is smaller than those of neutrons and so it can not change into a hyperon star. In its center, it is mainly composed of $\Lambda$, $\Xi^{-}$ and a few $\Xi^{0}$. We also found that for the neutron star with a maximum mass of 1.4 M$_{\odot}$, it can change into a hyperon star and the hyperon star transition density is 0.668 fm$^{-3}$, at which the hyperons are only composed of $\Lambda$. At its center, the hyperons are also only composed of $\Lambda$ and the ratio of the hyperons is a little larger than that of the neutrons. This illustrates that the NS1.4M$_{\odot}$ has just changed into a hyperon star.Comment: 14 pages,8 figures, This paper was published in Chinese Journal of Physics, 2015, 53(6): 1-1

On the moment of inertia of PSR J0348+0432

The moment of inertia of the massive neutron star PSR J0348+0432 is studied in the framework of the relativistic mean field theory by choosing suitable hyperon coupling constants. By this method, we find that the suggested radius of the massive neutron star PSR J0348+0432 is in the range $R=12.957\sim12.246$ km by the observation $M$=1.97$\sim$2.05 M$_\odot$. We also find that the suggested moment of inertia $I$ of the massive neutron star PSR J0348+0432 is in the range $I$=1.9073$\times$10$^{45}\sim$1.5940$\times10^{45}$ g.cm$^{2}$ by the observation $M$=1.97$\sim$2.05 M$_\odot$. Massive pulsars hint that the interaction inside them should be very "strong". Though hyperons considered will reduce the maximum mass, but in principle we may have models predicting maximum masses higher than 2 M${_\odot}$ by choosing suitable parameters, in a degree of freedom of hadron. Our calculations have proved the above and perfectly agree with the results both of Aaron W et al and P\'etri J et al.Comment: 9 pages,3 figures, This paper was published in Chinese Journal of Physics, 2016, 54(5): 839-84

The property difference between the neutron star PSR J0348+0432 and its proto neutron star

The property difference between the neutron star PSR J0348+0432 and its proto neutron star is studied in the framework of the relativistic mean field theory considering neutrino trapping. We see that the central baryon number density of the proto neutron star PSR J0348+0432 is in the range $\rho_{c, PNS}=0.539\sim0.698$ fm$^{-3}$, which is smaller than that of the neutron star PSR J0348+0432 $\rho_{c, NS}=0.634\sim0.859$ fm$^{-3}$. Inside the neutron star PSR J0348+0432, only the neutrons, protons, $\Lambda$ and $\Xi^{-}$ produce, whereas the hyperons $\Sigma^{-}, \Sigma^{0}, \Sigma^{+}$ and $\Xi^{0}$ all do not appear. But in the proto neutron star PSR J0348+0432, hyperons $\Sigma^{-}$, $\Sigma^{0}$, $\Sigma^{+}$ and $\Xi^{0}$ all will produce, though their relative particle number density are still very small, no more than 2\%. This shows that higher temperature will be advantageous to the hyperon production

Examination of the influence of the f0_{0}(975) and ϕ\phi(1020) mesons on the surface gravitional redshift of the neutron star PSR J0348+0432

The effect of the mesons $f_{0}(975)$ and $\phi(1020)$ on the surface gravitional redshift of the neutron star PSR J0348+0432 is examined in the framework of the relativistic mean field theory by choosing the suitable hyperon coupling constants. We find that compared with that without considering the mesons $f_{0}(975)$ and $\phi(1020)$, the value range of the radius $R$ of the neutron star PSR J0348+0432 would be changed from a narrow range 12.964 km $\sim$ 12.364 km to a wider range 12.941 km $\sim$ 11.907 km corresponding to the observation mass M=1.97 M$_{\odot}$$\sim$2.05 M$_{\odot}$. We also find that the value range of the surface gravitational redshift $z$ of the neutron star PSR J0348+0432 changes from 0.3469 $\sim$ 0.3997 to 0.3480 $\sim$ 0.4263 corresponding to the observation mass M=1.97 M$_{\odot}$$\sim$2.05 M$_{\odot}$ as the mesons $f_{0}(975)$ and $\phi(1020)$ being considered. These mean the radius $R$ and the surface gravitational redshift $z$ all will be constrained in a wider scope as the mesons $f_{0}(975)$ and $\phi(1020)$ being considered. We also can see that the difference of the radius and the surface gravitational redshift is not so large whether the mesons $f_{0}(975)$ and $\phi(1020)$ being considered or not. This indicates that the mesons $f_{0}(975)$ and $\phi(1020)$ do not play a major role in the massive neutron star PSR J0348+0432.Comment: 5 pages,3 figures, This paper was published in Physical Review C, 2015, 92(5): 05580

The properties of the neutron star PSR J0348+0432

The properties of the massive neutron star PSR J0348+0432 is calculated in the framework of the relativistic mean field theory by choosing the suitable hyperon coupling constants. It is found that the central energy density $\epsilon_{c}$ and the central pressure $p_{c}$ of the massive neutron star PSR J0348+0432 respectively are 1.5 times larger and 3.6 times larger than those of the canonical mass neutron star. It is also found that in the neutron star PSR J0348+0432 there are five kinds of baryons appearing: n, p, $\Lambda$, $\Xi^{-}$ and $\Xi^{0}$ but in the canonical mass neutron star there are only three kinds of particles appearing: n, p and $\Lambda$. In our models, the positive well depth $U_{\Sigma}^{(N)}$ will restrict the production of the hyperons $\Sigma^{-}$, $\Sigma^{0}$ and $\Sigma^{+}$ and therefore either in the neutron star PSR J0348+0432 or in the canonical mass neutron star the hyperons $\Sigma^{-}$, $\Sigma^{0}$ and $\Sigma^{+}$ all do not appear. In addition, our results also show that the radius $R$ of the massive neutron star PSR J0348+0432 is less than that of the canonical mass neutron star while the gravitational redshift of the former is larger than that of the latter.Comment: 11 pages, 7 figures, This paper was published in International Journal of Modern Physics D, 2015, 24(8): 155005

On a Lower Bound for the Time Constant of First-Passage Percolation

We consider the Bernoulli first-passage percolation on $\mathbb Z^d (d\ge 2)$. That is, the edge passage time is taken independently to be 1 with probability $1-p$ and 0 otherwise. Let ${\mu(p)}$ be the time constant. We prove in this paper that $$\mu(p_1)-\mu({p_2})\ge \frac{\mu(p_2)}{1-p_2}(p_2-p_1)$$ for all $0\leq p_1<p_2< 1$ by using Russo's formula.Comment: 7 page

On The Waiting Time for A M/M/1 Queue with Impatience

This paper focuses on the problem of modeling the correspondence pattern for ordinary people. Suppose that letters arrive at a rate $\lambda$ and are answered at a rate $\mu$. Furthermore, we assume that, for a constant $T$, a letter is disregarded when its waiting time exceeds $T$, and the remains are answered in {\it last in first out} order. Let $W_n$ be the waiting time of the $n$-th {\it answered} letter. It is proved that $W_n$ converges weekly to $W_T$, a non-negative random variable which possesses a density with {\it power-law} tail when $\lambda=\mu$ and with exponential tail otherwise. Note that this may provide a reasonable explanation to the phenomenons reported by Oliveira and Barab\'asi in \cite{OB}.Comment: 10 page

Study of Bc→ψ(2S)KB_{c} \rightarrow \psi(2S) K, ηc(2S)K\eta_{c}(2S)K, ψ(3770)K\psi(3770)K decays with perturbative QCD approach

We study the $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays with perturbative QCD approach (pQCD) based on $k_T$ factorization. The new orbitally excited charmonium distribution amplitudes $\psi(1^{3}D_{1})$ based on the Schr\"{o}dinger wave function of the $n=1$, $l=2$ state for the harmonic-oscillator potential are employed. By using the corresponding distribution amplitudes, we calculate the branching ratio of $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays and the form factors $A_{0,1,2}$ and $V$ for the transition $B_{c}$$\rightarrow$$\psi(1^{3}D_{1})$. We obtain the branching ratio of both $B_{c}$$\rightarrow$$\psi(2S)$K and $B_{c}$$\rightarrow$$\eta_{c}(2S)$K are at the order of $10^{-5}$. The effects of two sets of the S-D mixing angle $\theta=-12^{\circ}$ and $\theta=27^{\circ}$ for the decay $B_{c}$$\rightarrow$$\psi(3770)$K are studied firstly in this paper. Our calculations show that the branching ratio of the decay $B_{c}$$\rightarrow$$\psi(3770)$K can be raised from the order of $10^{-6}$ to the order of $10^{-5}$ at the mixing angle $\theta=-12^{\circ}$, which can be tested by the running LHC-b experiments.Comment: 12pages, 2 figure