Vol 42, No 6 (2016)

We show that density spikes begin to form from dark matter particles around primordial black holes immediately after their formation at the radiation-dominated cosmological stage. This stems from the fact that in the thermal velocity distribution of particles there are particles with low velocities that remain in finite orbits around black holes and are not involved in the cosmological expansion. The accumulation of such particles near black holes gives rise to density spikes. These spikes are considerably denser than those that are formed later by the mechanism of secondary accretion. The density spikes must be bright gamma-ray sources. Comparison of the calculated signal from particle annihilation with the Fermi-LAT data constrains the present-day cosmological density parameter for primordial black holes with masses M_BH ≥ 10⁻⁸M_⊙ from above by values from Ω_BH ≤ 1 to Ω_BH ≤ 10−8, depending on MBH. These constraints are several orders of magnitude more stringent than other known constraints.

We have performed calculations by abandoning the assumption of local thermodynamic equilibrium (within the so-called non-LTE approach) for Al I and Si I with model atmospheres corresponding to stars of spectral types F–G–Kwith differentmetal abundances. To take into account inelastic collisions with hydrogen atoms, for the first time we have applied the cross sections calculated by Belyaev et al. using model approaches within the formalism of the Born–Oppenheimer quantum theory. We show that for Al I non-LTE leads to higher ionization (overionization) than in LTE in the spectral line formation region and to a weakening of spectral lines, which is consistent with earlier non-LTE studies. However, our results, especially for the subordinate lines, differ quantitatively from the results of predecessors. Owing to their large cross sections, the ion-pair production and mutual neutralization processes Al I(nl) + HI(1s) ↔ Al II(3s²) + H⁻ provide a close coupling of highly excited Al I levels with the Al II ground state, which causes the deviations from the equilibrium level population to decrease compared to the calculations where the collisions only with electrons are taken into account. For three moderately metal-deficient dwarf stars, the aluminum abundance has been determined from seven Al I lines in different models of their formation. Under the assumption of LTE and in non-LTE calculations including the collisions only with electrons, the Al I 3961 ˚A resonance line gives a systematically lower abundance than the mean abundance from the subordinate lines, by 0.25–0.45 dex. The difference for each star is removed by taking into account the collisions with hydrogen atoms, and the rms error of the abundance derived from all seven Al I lines decreases by a factor of 1.5–3 compared to the LTE analysis. We have calculated the non- LTE corrections to the abundance for six subordinate Al I lines as a function of the effective temperature (4500 K ≤ T_eff ≤ 6500 K), surface gravity (3.0 ≤ log g ≤ 4.5), and metal abundance ([M/H] = 0, −1, −2, and −3). For Si I including the collisions with HI leads to the establishment of equilibrium populations in the spectral line formation region even in hot metal-deficient models and to vanishingly small departures from LTE in spectral lines.

Based on five high-resolution spectra in the range 5625–7525 ˚A taken in 1995 and covering the ascending branch of the light curve from minimum to maximum, we have performed spectroscopic studies of the classical Cepheid ζ Gem. The atmospheric parameters and chemical composition of the Cepheid have been refined. The abundances of the key elements of the evolution of yellow supergiants are typical for an object that has passed the first dredge-up: a C underabundance, N, Na, and Al overabundances, and nearly solar O and Mg abundances. We have estimated [Fe/H] = +0.01 dex; the abundances of the remaining elements are also nearly solar. The metal absorption lines in all spectra show a clear asymmetry and the formation of secondary blue (B1 and B2) and red (R1 and R2) components, just as for the Cepheid X Sgr. The Hα absorption line is also split into blue (B) and red (R) components with different depths changing with pulsation phase. To analyze the velocity field in the atmosphere of ζ Gem, we have estimated the radial velocities from specially selected (with clear signatures of the B1, B2, R1, and R2 components) absorption lines (neutral atoms and ions) of metals (38 lines) and the B and R components of the Hα line. Analysis of these estimates has shown that their scatter is from −22 to 36 km s⁻¹ for all pulsation phases but does not exceed 35–40 km s⁻¹ for each individual phase, while it does not exceed 22 km s⁻¹ for the Hα line components. The radial velocity estimates for the metal lines and their B1 and B2 components have been found to depend on the depths, suggesting the presence of a velocity gradient in the atmosphere. No significant difference in velocities between the atoms and ions of the metal lines is observed, i.e., there is no significant inhomogeneity in the upper atmospheric layers of the Cepheid. Since the averaged radial velocity estimates for the cores of the metal lines and their B1 and B2 components change with pulsation phase and coincide with those for the B component of the Hα line, they are all formed in the Cepheid’s atmosphere. The formation and passage of a shock wave due to the κ-mechanism at work can be responsible for the stronger scatter of the B1 and B2 components in their velocities at phases after the Cepheid’s minimum radius. The averaged velocities of the R1 components also change with pulsation phase and differ only slightly from the remaining ones. On the other hand, the mean velocity estimate for the R component of the Hα line at all phases is +32.72 ± 2.50 km s⁻¹ and differs significantly from the bulk of the velocities, suggesting the formation of this component in the envelope around the Cepheid. The unusual behavior of the mean velocities for the R2 components of the metal absorption lines can also point to their formation in the envelope and can be yet another indicator of its presence around ζ Gem.