Simultaneous constraints on the mass and radius of Aql X-1 from quiescence and X-ray burst observations

The measurement of neutron star mass and radius is one of the most direct way to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type-I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X-1, as a reliable distance estimation, high signal-to-noise ratio quiescent spectra from Chandra and XMM-Newton, and photospheric radius expansion bursts from RXTE are available. This is also used to verify the consistency between the two methods, and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X-1 should be in the range of $4.0-5.75$ kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X-1 are compatible with strange star equations of state and conventional neutron star models.Comment: 16 pages, 9 figures, accepted by Ap

An Ultra Low Mass and Small Radius Compact Object in 4U 1746-37?

Photospheric radius expansion (PRE) bursts have already been used to constrain the masses and radii of neutron stars. RXTE observed three PRE bursts in 4U 1746-37, all with low touchdown fluxes. We discuss here the possibility of low mass neutron star in 4U 1746-37 because the Eddington luminosity depends on stellar mass. With typical values of hydrogen mass fraction and color correction factor, a Monte-Carlo simulation was applied to constrain the mass and radius of neutron star in 4U 1746-37. 4U 1746-37 has a high inclination angle. Two geometric effects, the reflection of the far side accretion disc and the obscuration of the near side accretion disc have also been included in the mass and radius constraints of 4U 1746-37. If the reflection of the far side accretion disc is accounted, a low mass compact object (mass of $0.41\pm0.14~M_{\odot}$ and radius of $8.73\pm1.54~\rm km$ at 68% confidence) exists in 4U 1746-37. If another effect operated, 4U 1746-37 may contain an ultra low mass and small radius object ($M=0.21\pm0.06~M_{\odot},~R=6.26\pm0.99~\rm km$ at 68% confidence). Combined all possibilities, the mass of 4U 1746-37 is $0.41^{+0.70}_{-0.30}~M_\odot$ at 99.7% confidence. For such low mass NS, it could be reproduced by a self-bound compact star, i.e., quark star or quark-cluster star.Comment: accepted by Ap

The accretion rate independence of horizontal branch oscillation in XTE J1701-462

We study the temporal and energy spectral properties of the unique neutron star low-mass X-ray binary XTE J1701-462. After assuming the HB/NB vertex as a reference position of accretion rate, the horizontal branch oscillation (HBO) of the HB/NB vertex is roughly 50 Hz. It indicates that the HBO is independent with the accretion rate or the source intensity. The spectral analysis shows $R_{\rm{in}}\propto\dot{M}_{\rm{Disk}}^{2.9\pm0.09}$ in the HB/NB vertex and $R_{\rm{in}}\propto\dot{M}_{\rm{Disk}}^{1.7\pm0.06}$ in the NB/FB vertex, which implies that different accretion rate may be produced in the HB/NB vertex and the NB/FB vertex. The Comptonization component could be fitted by constrained broken power law (CBPL) or nthComp. Different with GX 17+2, the frequencies of HBO positively correlate with the inner disk radius, which contradict with the prediction of Lense-Thirring precession model. XTE J1701-462, both in the Cyg-like phase and in the Sco-like phase, follows a positive correlation between the break frequency of broad band noise and the characteristic frequency of HBO, which is called the W-K relation. An anticorrelation between the frequency of HBO and photon energy is observed. Moreover, the rms of HBO increases with photon energy till ~10 keV. We discuss the possible origin of HBO from corona in XTE J1701-462.Comment: 45 pages, 18 figures, accepted by Ap

Normalized solutions for Sobolev critical Schr\"odinger-Bopp-Podolsky systems

We study the Sobolev critical Schr\"odinger-Bopp-Podolsky system \begin{gather*} -\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3, -\Delta\phi+\Delta^2\phi=4\pi u^2\quad \text{in } \mathbb{R}^3, \end{gather*} under the mass constraint $$\int_{\mathbb{R}^3}u^2\,dx=c$$ for some prescribed $c>0$, where $2<p<8/3$, $\mu>0$ is a parameter, and $\lambda\in\mathbb{R}$ is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions.Comment: 19 page

Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder\u27s fixed point theorem, we show that there exists a positive constant c∗ such that the system possesses a traveling wave solution for any given c\u3ec∗. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for c=c∗ is established by means of Corduneanu\u27s theorem. The nonexistence of traveling wave solution in the case of