The vertical composition of neutrino-dominated accretion disks in gamma-ray bursts

We investigate the vertical structure and elements distribution of neutrino-dominated accretion flows around black holes in spherical coordinates with the reasonable nuclear statistical equilibrium. According our calculations, heavy nuclei tend to be produced in a thin region near the disk surface, whose mass fractions are primarily determined by the accretion rate and the vertical distribution of temperature and density. In this thin region, we find that $^{56}\rm Ni$ is dominant for the flow with low accretion rate (e.g., $0.05$$M_{\odot}$ $\rm s^{-1}$) but $^{56}\rm Fe$ is dominant for the high counterpart (e.g., $1 M_{\odot}$ $\rm s^{-1}$). The dominant $^{56}\rm Ni$ in the special region may provide a clue to understand the bumps in the optical light curve of core-collapse supernovae.Comment: 15 pages, 2 figures, accepted for publication in Ap

Maxima of the QQ-index of non-bipartite C3C_{3}-free graphs

A classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite graph of order $n$ with size $m>\lfloor \frac{n^{2}}{4}\rfloor$ contains a triangle. Lin, Ning and Wu [Comb. Probab. Comput. 30 (2021) 258-270] proved a spectral version of Mantel's theorem for given order $n.$ Zhai and Shu [Discrete Math. 345 (2022) 112630] investigated a spectral version for fixed size $m.$ In this paper, we prove $Q$-spectral versions of Mantel's theorem.Comment: 14 pages, 4 figure

Millicharged Atomic Dark Matter

We present a simplified version of the atomic dark matter scenario, in which charged dark constituents are bound into atoms analogous to hydrogen by a massless hidden sector U(1) gauge interaction. Previous studies have assumed that interactions between the dark sector and the standard model are mediated by a second, massive Z' gauge boson, but here we consider the case where only a massless gamma' kinetically mixes with the standard model hypercharge and thereby mediates direct detection. This is therefore the simplest atomic dark matter model that has direct interactions with the standard model, arising from the small electric charge for the dark constituents induced by the kinetic mixing. We map out the parameter space that is consistent with cosmological constraints and direct searches, assuming that some unspecified mechanism creates the asymmetry that gives the right abundance, since the dark matter cannot be a thermal relic in this scenario. In the special case where the dark "electron" and "proton" are degenerate in mass, inelastic hyperfine transitions can explain the CoGeNT excess events. In the more general case, elastic transitions dominate, and can be close to current direct detection limits over a wide range of masses.Comment: 5 pages, 2 figures; v2: added references, and formula for dark ionization fraction; published versio