Estimation and prediction of credit risk based on rating transition systems

Risk management is an important practice in the banking industry. In this paper we develop a new methodology to estimate and predict the probability of default (PD) based on the rating transition matrices, which relates the rating transition matrices to the macroeconomic variables. Our method can overcome the shortcomings of the framework of Belkin et al. (1998), and is especially useful in predicting the PD and doing stress testing. Simulation is conducted at the end, which shows that our method can provide more accurate estimate than that obtained by the method of Belkin et al. (1998).Comment: 15 page

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

Microscopic explanation for black hole phase transitions via Ruppeiner geometry: two competing factors-the temperature and repulsive interaction among BH molecules

Charged dilatonic black hole (BH) has rather rich phase diagrams which may contain zeroth-order, first-order as well as reentrant phase transitions (RPTs) depending on the value of the coupling constant $\alpha$ between the electromagnetic field and the dilaton. We try to give a microscopic explanation for these phase transitions by adopting Ruppeiner's approach. By studying the behaviors of the Ruppeiner invariant $R$ along the co-existing lines, we find that the various phase transitions may be qualitatively well explained as a result of two competing factors: the first one is the low-temperature effect which tends to shrink the BH and the second one is the repulsive interaction between the BH molecules which, on the contrary, tends to expand the BH. In the standard phase transition without RPT, as temperature is lowered, the first kind of factor dominates over the second one, so that large black hole (LBH) tends to shrink and thus transits to small black hole (SBH); While in the RPT, after the LBH-SBH transition, as temperature is further decreased, the strength of the second factor increases quickly and finally becomes strong enough to dominate over the first factor, so that SBH tends to expand to release the high repulsion and thus transits back to LBH. Moreover, by comparing the behavior of $R$ versus the temperature $T$ with fixed pressure to that of ordinary two-dimensional thermodynamical systems but with fixed specific volume, it is interesting to see that SBH behaves like a Fermionic gas system in cases with RPT, while it behaves oppositely to an anyon system in cases without RPT. And in all cases, LBH behaves like a nearly ideal gas system.Comment: 16 pages, 7 figures;v2:minor modifications, refs added;v3:minor modifications, more refs added; v4:minor modifications to match published versio

Population Synthesis of Black Hole X-Ray Binaries

We present a systematic study of the X-ray binaries (XRBs) containing a black hole (BH) and a non-degenerate companion, in which mass transfer takes place via either capturing the companion's wind or Roche lobe overflow (RLO). As shown in our previous work that focusing on the formation and evolution of detached BH binaries, our assumed models relevant to BH's progenitors predicted significantly different binary properties \citep{sl19}. In this paper, we further follow the evolutionary paths of the BH systems that appearing as XRBs. By use of both binary population synthesis and detailed binary evolution calculations, we can obtain the potential population of BH XRBs. Distributions at the current epoch of various binary parameters have been computed. The observed sample of wind-fed XRBs can be well reproduced under assumption of all our models. The wind-fed XRBs are expected to be so rare ($\lesssim 100$) that only a couple of such systems have been detected. Comparison of known RLO XRBs with the calculated distributions of various binary parameters indicates that only the models assuming relatively small masses for BH progenitors can roughly match the observations. Accordingly we estimate that there are hundreds of RLO XRBs in the Milky Way, of which the majority are low-mass XRBs. The RLO systems may become ultraluminous X-ray sources (ULXs) if the BH accretes at a very high rate, we expect that about a dozen ULXs with a BH accretor may exist in a Milky Way$-$like galaxy.Comment: 17 pages, 15 figures, 2 tables, accepted by Ap

Population Synthesis of Galactic Be-star Binaries with A Helium-star Companion

LB-1 was originally suggested to harbour a very massive ($\sim 70 M_\odot$) black hole, but was recently suggested to be a post-mass transfer binary containing a Be star and a helium (He) star. In this paper, we use the binary population synthesis method to simulate the potential population of the Be$-$He binaries in the Milky Way. Mass transfer process during the progenitor binary evolution plays a vital role in determining the possible properties of the Be$-$He binary population. By constructing a range of physical models with significantly different mass-transfer efficiencies, we obtain the predicted distributions at the current epoch of the component masses and the orbital periods for the Be$-$He binaries. In particular, we show that, LB-1 very likely has evolved through non-conservative mass transfer if it is indeed a Be$-$He system. We estimate that there are more than $10^{3}$ Be$-$He binaries with V-band apparent magnitudes brighter than LB-1.Comment: 8 pages, 5 figures, accepted by Ap