Early Afterglows of Gamma-Ray Bursts in a Stratified Medium with a Power-Law Density Distribution

A long-duration gamma-ray burst (GRB) has been widely thought to arise from the collapse of a massive star, and it has been suggested that its ambient medium is a homogenous interstellar medium (ISM) or a stellar wind. There are two shocks when an ultra-relativistic fireball that has been ejected during the prompt gamma-ray emission phase sweeps up the circumburst medium: a reverse shock that propagates into the fireball, and a forward shock that propagates into the ambient medium. In this paper, we investigate the temporal evolution of the dynamics and emission of these two shocks in an environment with a general density distribution of $n\propto R^{-k}$ (where $R$ is the radius) by considering thick-shell and thin-shell cases. A GRB afterglow with one smooth onset peak at early times is understood to result from such external shocks. Thus, we can determine the medium density distribution by fitting the onset peak appearing in the light curve of an early optical afterglow. We apply our model to 19 GRBs, and find that their $k$ values are in the range of 0.4 - 1.4, with a typical value of $k\sim1$, implying that this environment is neither a homogenous interstellar medium with $k=0$ nor a typical stellar wind with $k=2$. This shows that the progenitors of these GRBs might have undergone a new mass-loss evolution.Comment: 32 pages, 5 figures, 1 table, published in Ap

Primordial Black Holes from Sound Speed Resonance during Inflation

We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe. For a general inflaton field, it can seed primordial density fluctuations and their propagation is governed by a parameter of sound speed square. Once if this parameter achieves an oscillatory feature for a while during inflation, a significant non-perturbative resonance effect on the inflaton field fluctuations takes place around a critical length scale, which results in significant peaks in the primordial power spectrum. By virtue of this robust mechanism, primordial black holes with specific mass function can be produced with a sufficient abundance for dark matter in sizable parameter ranges.Comment: 6 pages, 4 figures; v2: figures replotted with corrections, analysis extended, version accepted by Phys.Rev.Let

N′-[1-(2-Pyrid­yl)ethyl­idene]nicotino­hydrazide

In the the title compound, C13H12N4O, the dihedral angle between the aromatic ring planes is 21.7 (3)°. In the crystal structure, interm­olecular N—H⋯O hydrogen bonds lead to C(4) chains

Bis(2-amino­pyrimidine-κN 1)diaqua­dinitrato-κO;κ2 O,O′-cadmium(II) monohydrate

In the title compound, [Cd(NO3)2(C4H5N3)2(H2O)2]·H2O, the Cd atom is seven-coordinated by two 2-amino­pyrimidine mol­ecules, two water mol­ecules, one bidentate nitrate anion and one monodentate nitrate anion. A network of N—H⋯O, N—H⋯N and O—H⋯O hydrogen bonds helps to consolidate the crystal structure

Penta­aqua­bis[4-(2-hydroxy­benzyl­idene­amino)benzene­sulfonato]lead(II)

In the structure of the title compound, [Pb(C13H10NO4S)2(H2O)5], two S—O bonds and one C—N bond have lengths of 1.421 (9), 1.425 (8) and 1.268 (11) Å, respectively, which suggests they are double bonds. Mol­ecules form a two-dimensional layered structure via O—H⋯O and O—H⋯N inter­actions. The Pb atom adopts distorted cubo-octahedral coordination

1-Hydroxymethyl-3,12-dioxa-14-aza­tetracyclo[9.2.1.04,14.05,10]tetradecane

In the title fused-ring compound, C12H13NO3, the two five-membered C3NO rings both approximate to envelope conformations with C atoms in the flap positions. The OH group of the pendant CH2OH unit is disordered over two positions in a 0.528 (5):0.472 (5) ratio. One of the OH groups participates in an O—H⋯N hydrogen bond, generating centrosymmetric dimers in the crystal structure