Super-Eddington winds from Type I X-ray bursts

We present hydrodynamic simulations of spherically symmetric super-Eddington winds from radius-expansion type I X-ray bursts. Previous studies assumed a steady-state wind and treated the mass-loss rate as a free parameter. Using MESA, we follow the multi-zone time-dependent burning, the convective and radiative heating of the atmosphere during the burst rise, and the launch and evolution of the optically thick radiation-driven wind as the photosphere expands outward to radii $r_{\rm ph} \gtrsim 100\text{ km}$. We focus on neutron stars (NSs) accreting pure helium and study bursts over a range of ignition depths. We find that the wind ejects $\approx 0.2\%$ of the accreted layer, nearly independent of ignition depth. This implies that $\approx 30\%$ of the nuclear energy release is used to unbind matter from the NS surface. We show that ashes of nuclear burning are ejected in the wind and dominate the wind composition for bursts that ignite at column depths $\gtrsim 10^9\text{ g cm}^{-2}$. The ejecta are composed primarily of elements with mass numbers $A> 40$, which we find should imprint photoionization edges on the burst spectra. Evidence of heavy-element edges has been reported in the spectra of strong, radius-expansion bursts. We find that after $\approx 1\text{ s}$ the wind composition transitions from mostly light elements ($^4$He and $^{12}$C), which sit at the top of the atmosphere, to mostly heavy elements ($A>40$), which sit deeper down. This may explain why the photospheric radii of all superexpansion bursts show a transition after $\approx 1\text{ s}$ from a superexpansion ($r_{\rm ph}>10^3\text{ km}$) to a moderate expansion ($r_{\rm ph}\sim 50\text{ km}$).Comment: 13 pages, 13 figures. Matches the version published in Ap

Dynamic hedging of portfolio credit derivatives

We compare the performance of various hedging strategies for index collateralized debt obligation (CDO) tranches across a variety of models and hedging methods during the recent credit crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic models do not necessarily perform better than static models, nor do high-dimensional bottom-up models perform better than simpler top-down models. When it comes to hedging, top-down and regression-based hedging with the index provide significantly better results during the credit crisis than bottom-up hedging with single-name credit default swap (CDS) contracts. Our empirical study also reveals that while significantly large moves—“jumps”—do occur in CDS, index, and tranche spreads, these jumps do not necessarily occur on the default dates of index constituents, an observation which shows the insufficiency of some recently proposed portfolio credit risk models.hedging, credit default swaps, portfolio credit derivatives, index default swaps, collateralized debt obligations, portfolio credit risk models, default contagion, spread risk, sensitivity-based hedging, variance minimization

Nonlinear dynamical tides in white dwarf binaries

Compact white dwarf (WD) binaries are important sources for space-based gravitational-wave (GW) observatories, and an increasing number of them are being identified by surveys like ZTF. We study the effects of nonlinear dynamical tides in such binaries. We focus on the global three-mode parametric instability and show that it has a much lower threshold energy than the local wave-breaking condition studied previously. By integrating networks of coupled modes, we calculate the tidal dissipation rate as a function of orbital period. We construct phenomenological models that match these numerical results and use them to evaluate the spin and luminosity evolution of a WD binary. While in linear theory the WD's spin frequency can lock to the orbital frequency, we find that such a lock cannot be maintained when nonlinear effects are taken into account. Instead, as the orbit decays, the spin and orbit go in and out of synchronization. Each time they go out of synchronization, there is a brief but significant dip in the tidal heating rate. While most WDs in compact binaries should have luminosities that are similar to previous traveling-wave estimates, a few percent should be about ten times dimmer because they reside in heating rate dips. This offers a potential explanation for the low luminosity of the CO WD in J0651. Lastly, we consider the impact of tides on the GW signal and show that LISA and TianGO can constrain the WD's moment of inertia to better than 1% for deci-Hz systems.Comment: 21 pages, 18 figures. Submitted to MNRA

Prediction of Atomization Energy Using Graph Kernel and Active Learning

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effect of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 +- 0.01 kcal/mol using as few as 2000 training samples on the QM7 data set