Formation of the Double Neutron Star System PSR J1930−-1852

The spin period (185 ms) and period derivative ($1.8\times10^{-17}\,\rm s\,s^{-1}$) of the double neutron star (DNS) system PSR J1930$-$1852 recently discovered indicate that the pulsar was mildly recycled through the process of Roche-lobe overflow. This system has the longest orbital period (45 days) of the known DNS systems, and can be formed from a helium star-NS binary if the initial mass of the helium star was $\lesssim 4.0M_{\odot}$; otherwise the helium star would never fill its Roche-lobe \citep{t15}. At the moment of the supernova explosion, the mass of the helium star was $\lesssim3.0M_{\odot}$. We find that the probability distribution of the velocity kick imparted to the new-born neutron star has a maximum at about $30 \,\rm km\,s^{-1}$ (and a tail up to $260 \,\rm km\,s^{-1}$), indicating that this NS most probably received a low kick velocity at birth.Comment: 9 pages, 4 figures, accepted for publication in Ap

On the formation of Be stars through binary interaction

Be stars are rapidly rotating B type stars. The origin of their rapid rotation is not certain, but binary interaction remains to be a possibility. In this work we investigate the formation of Be stars resulting from mass transfer in binaries in the Galaxy. We calculate the binary evolution with both stars evolving simultaneously and consider different possible mass accretion histories for the accretor. From the calculated results we obtain the critical mass ratios $q_{\rm cr}$ that determine the stability of mass transfer. We also numerically calculate the parameter $\lambda$ in common envelope evolution, and then incorporate both $q_{\rm cr}$ and $\lambda$ into the population synthesis calculations. We present the predicted numbers and characteristics of Be stars in binary systems with different types of companions, including helium stars, white dwarfs, neutron stars, and black holes. We find that in Be/neutron star binaries the Be stars can have a lower limit of mass $\sim 8 M_{\odot}$ if they are formed by stable (i.e., without the occurrence of common envelope evolution) and nonconservative mass transfer. We demonstrate that isolated Be stars may originate from both mergers of two main-sequence stars and disrupted Be binaries during the supernova explosions of the primary stars, but mergers seem to play a much more important role. Finally the fraction of Be stars which have involved binary interactions in all B type stars can be as high as $\sim 13$, implying that most of Be stars may result from binary interaction.Comment: 38 pages, 14 figures, 1 table, accepted for publication in Ap

A Population of Ultraluminous X-ray Sources with An Accreting Neutron Star

Most ultraluminous X-ray sources (ULXs) are believed to be X-ray binary systems, but previous observational and theoretical studies tend to prefer a black hole rather than a neutron star accretor. The recent discovery of 1.37 s pulsations from the ULX M82 X-2 has established its nature as a magnetized neutron star. In this work we model the formation history of neutron star ULXs in an M82- or Milky Way-like galaxy, by use of both binary population synthesis and detailed binary evolution calculations. We find that the birthrate is around $10^{-4}\, \rm yr^{-1}$ for the incipient X-ray binaries in both cases. We demonstrate the distribution of the ULX population in the donor mass - orbital period plane. Our results suggest that, compared with black hole X-ray binaries, neutron star X-ray binaries may significantly contribute to the ULX population, and high-mass and intermediate-mass X-ray binaries dominate the neutron star ULX population in M82- and Milky Way-like galaxies, respectively.Comment: 13 pages, 5 figures, accepted for publication in Ap

Formation and Evolution of Galactic Intermediate/Low-Mass X-ray Binaries

We investigate the formation and evolutionary sequences of Galactic intermediate- and low-mass X-ray binaries (I/LMXBs) by combining binary population synthesis (BPS) and detailed stellar evolutionary calculations. Using an updated BPS code we compute the evolution of massive binaries that leads to the formation of incipient I/LMXBs, and present their distribution in the initial donor mass vs. initial orbital period diagram. We then follow the evolution of I/LMXBs until the formation of binary millisecond pulsars (BMSPs). We find that the birthrate of the I/LMXB population is in the range of $9\times10^{-6} - 3.4\times10^{-5} \, {\rm yr^{-1}}$, compatible with that of BMSPs which are thought to descend from I/LMXBs. We show that during the evolution of I/LMXBs they are likely to be observed as relatively compact binaries with orbital periods $\lesssim$ 1 day and donor masses $\lesssim 0.3 M_{\odot}$. The resultant BMSPs have orbital periods ranging from less than 1 day to a few hundred days. These features are consistent with observations of LMXBs and BMSPs. We also confirm the discrepancies between theoretical predications and observations mentioned in the literature, that is, the theoretical average mass transfer rates ($\sim 10^{-10} M_{\odot}$\,yr$^{-1}$) of LMXBs are considerably lower than observed, and the number of BMSPs with orbital periods $\sim 0.1-10$ day is severely underestimated. These discrepancies imply that something is missing in the modeling of LMXBs, which is likely to be related to the mechanisms of the orbital angular momentum loss.Comment: 30 pages, 13 figure

On the role of supernova kicks in the formation of Galactic double neutron star systems

In this work we focus on a group of Galactic double neutron star (DNS) systems with long orbital periods of $\gtrsim 1$ day and low eccentricities of $\lesssim 0.4$. The feature of these orbital parameters is used to constrain the evolutionary processes of progenitor binaries and the supernova (SN) kicks of the second born NSs. Adopting that the mass transfer during primordial binary evolution is highly non-conservative (rotation-dependent), the formation of DNS systems involves a double helium star binary phase, the common envelope (CE) evolution initiates before the first NS formation. During the CE evolution the binary orbital energy is obviously larger when using a helium star rather than a NS to expel the donor envelope, this can help explain the formation of DNS systems with long periods. SN kicks at NS birth can lead to eccentric orbits and even the disruption of binary systems, the low eccentricities require that the DNSs receive a small natal kick at the second collapse. Compared with the overall distribution of orbital parameters for observed DNS binaries, we propose that the second born NSs in most DNS systems are subject to small natal kicks with the Maxwellian dispersion velocity of less than $80 \,\rm km\,s^{-1}$, which can provide some constraints on the SN explosion processes. The mass distribution of DNS binaries is also briefly discussed. We suggest that the rotation-dependent mass transfer mode and our results about SN kicks should be applied to massive binary evolution and population synthesis studies.Comment: 7 figures, 2 tables, accepted by Ap

Can the Subsonic Accretion Model Explain the Spin Period Distribution of Wind-fed X-ray Pulsars?

Neutron stars in high-mass X-ray binaries (HMXBs) generally accrete from the wind matter of their massive companion stars. Recently Shakura et al. (2012) suggested a subsonic accretion model for low-luminosity ($<4\times 10^{36}$ ergs$^{-1}$), wind-fed X-ray pulsars. To test the feasibility of this model, we investigate the spin period distribution of wind-fed X-ray pulsars with a supergiant companion star, using a population synthesis method. We find that the modeled distribution of supergiant HMXBs in the spin period - orbital period diagram is consistent with observations provided that the winds from the donor stars have relatively low terminal velocities ($\lesssim 1000$ kms$^{-1}$). The measured wind velocities in several supergiant HMXBs seem to favor this viewpoint. The predicted number ratio of wind-fed X-ray pulsars with persistent X-ray luminosities higher and lower than $4\times 10^{36}$ ergs$^{-1}$ is about $1:10$.Comment: 17 pages, 3 figures, accepted for publication in Ap

Generalized Dyson Brownian motion, McKean-Vlasov equation and eigenvalues of random matrices

Using It\^o's calculus and the mass optimal transportation theory, we study the generalized Dyson Brownian motion (GDBM) and the associated McKean-Vlasov evolution equation with an external potential $V$. Under suitable condition on $V$, we prove the existence and uniqueness of strong solution to SDE for GDBM. Standard argument shows that the family of the process of empirical measures $L_N(t)$ of GDBM is tight and every accumulative point of $L_N(t)$ in the weak convergence topology is a weak solution of the associated McKean-Vlasov evolution equation, which can be realized as the gradient flow of the Voiculescu free entropy on the Wasserstein space over $\mathbb{R}$. Under the condition $V''\geq -K$ for some constant $K\geq 0$, we prove that the McKean-Vlasov equation has a unique solution $\mu(t)$ and $L_N(t)$ converges weakly to $\mu(t)$ as $N\rightarrow \infty$. For $C^2$ convex potentials, we prove that $\mu(t)$ converges to the equilibrium measure $\mu_V$ with respect to the $W_2$-Wasserstein distance on $\mathscr{P}_2(\mathbb{R})$ as $t\rightarrow \infty$. Under the uniform convexity or a modified uniform convexity condition on $V$, we prove that $\mu(t)$ converges to $\mu_V$ with respect to the $W_2$-Wasserstein distance on $\mathscr{P}_2(\mathbb{R})$ with an exponential rate as $t\rightarrow \infty$. Finally, we discuss the double-well potentials and raise some conjectures

On the Law of Large Numbers for the empirical measure process of Generalized Dyson Brownian motion

We study the generalized Dyson Brownian motion (GDBM) of an interacting $N$-particle system with logarithmic Coulomb interaction and general potential $V$. Under reasonable condition on $V$, we prove the existence and uniqueness of strong solution to SDE for GDBM. We then prove that the family of the empirical measures of GDBM is tight on $\mathcal {C}([0,T],\mathscr{P}(\mathbb{R}))$ and all the large $N$ limits satisfy a nonlinear McKean-Vlasov equation. Inspired by previous works due to Biane and Speicher, Carrillo, McCann and Villani, we prove that the McKean-Vlasov equation is indeed the gradient flow of the Voiculescu free entropy on the Wasserstein space of probability measures over $\mathbb{R}$. Using the optimal transportation theory, we prove that if $V"\geq K$ for some constant $K\in \mathbb{R}$, the McKean-Vlasov equation has a unique weak solution. This proves the Law of Large Numbers and the propagation of chaos for the empirical measures of GDBM. Finally, we prove the longtime convergence of the McKean-Vlasov equation for $C^2$-convex potentials $V$.Comment: Update revised version of the previous version. arXiv admin note: text overlap with arXiv:1303.124

Interference of quantum channels in single photon interferometer

We experimently demonstrate the interference of dephasing quantum channel using single photon Mach-Zender interferometer. We extract the information inaccessible to the technology of quantum tomography. Further, We introduce the application of our results in quantum key distribution.Comment: 3 pages, 5 figure

The Classification of Quantum Symmetric-Key Encryption Protocols

The classification of quantum symmetric-key encryption protocol is presented. According to five elements of a quantum symmetric-key encryption protocol: plaintext, ciphertext, key, encryption algorithm and decryption algorithm, there are 32 different kinds of them. Among them, 5 kinds of protocols have already been constructed and studied, and 21 kinds of them are proved to be impossible to construct, the last 6 kinds of them are not yet presented effectively. That means the research on quantum symmetric-key encryption protocol only needs to consider with 5 kinds of them nowadays.Comment: 12pages, no figure