Abstract. The grid of the models of radiative shock waves propagating through partially ionized hydrogen gas with temperature 3000 K ≤ T1 ≤ 8000 K and density 10 −12 gm cm −3 ≤ ρ1 ≤ 10 −9 gm cm −3 is computed for shock velocities 20 km s −1 ≤ U1 ≤ 90 km s −1 . The fraction of the total energy of the shock wave irreversibly lost due to radiation flux ranges from 0.3 to 0.8 for 20 km s −1 ≤ U1 ≤ 70 km s −1 . The postshock gas is compressed mostly due to radiative cooling in the hydrogen recombination zone and final compression ratios are within 1 < ρN /ρ1 < ∼ 10 2 , depending mostly on the shock velocity U1. The preshock gas temperature affects the shock wave structure due to the equilibrium ionization of the unperturbed hydrogen gas, since the rates of postshock relaxation processes are very sensitive to the number density of hydrogen ions ahead the discontinuous jump. Both the increase of the preshock gas temperature and the decrease of the preshock gas density lead to lower postshock compression ratios. The width of the shock wave decreases with increasing upstream velocity while the postshock gas is still partially ionized and increases as soon as the hydrogen is fully ionized. All shock wave models exhibit stronger upstream radiation flux emerging from the preshock outer boundary in comparison with downstream radiation flux emerging in the opposite direction from the postshock outer boundary. The difference between these fluxes depends on the shock velocity and ranges from 1% to 16% for 20 km s −1 ≤ U1 ≤ 60 km s −1 . The monochromatic radiation flux transported in hydrogen lines significantly exceeds the flux of the background continuum and all shock wave models demonstrate the hydrogen lines in emission.

Abstract. We considered the structure of steady-state plane-parallel radiative shock waves propagating through the partially ionized hydrogen gas of temperature T 1 = 3000 K and density 10 −12 g cm −3 ≤ ρ 1 ≤ 10 −9 g cm −3 . The upstream Mach numbers range within 6 ≤ M 1 ≤ 14. In frequency intervals of hydrogen lines the radiation field was treated using the transfer equation in the frame of the observer for the moving medium, whereas the continuum radiation was calculated for the static medium. Doppler shifts in Balmer emission lines of the radiation flux emerging from the upstream boundary of the shock wave model were found to be roughly one-third of the shock wave velocity: −δV ≈ 1 3 U 1 . The gas emitting the Balmer line radiation is located at the rear of the shock wave in the hydrogen recombination zone where the gas flow velocity in the frame of the observer is approximately one-half of the shock wave velocity: −V * ≈ 1 2 U 1 . The ratio of the Doppler shift to the gas flow velocity of δV/V * ≈ 0.7 results both from the small optical thickness of the shock wave in line frequencies and the anisotropy of the radiation field typical for the slab geometry. In the ambient gas with density of ρ 1 > ∼ 10 −11 g cm −3 the flux in the Hα frequency interval reveals the double structure of the profile. A weaker Hβ profile doubling was found for ρ 1 10 −10 g cm −3 and U 1 < ∼ 50 km s −1 . The unshifted redward component of the double profile is due to photodeexcitation accompanying the rapid growth of collisional ionization in the narrow layer in front of the discontinuous jump.

Hydrodynamic models of short-period Cepheids were computed to determine the pulsation period as a function of evolutionary time during the first and third crossings of the instability strip. The equations of radiation hydrodynamics and turbulent convection for radial stellar pulsations were solved with the initial conditions obtained from the evolutionary models of population I stars (X = 0.7, Z = 0.02) with masses from 5.2M ⊙ to 6.5M ⊙ and the convective core overshooting parameter 0.1 α ov 0.3. In Cepheids with period of 4 d the rate of pulsation period change during the first crossing of the instability strip is over fifty times larger than that during the third crossing. Polaris is shown to cross the instability strip for the first time and to be the fundamental mode pulsator. The best agreement between the predicted and observed rates of period change was obtained for the model with mass of 5.4M ⊙ and the overshooting parameter α ov = 0.25. The bolometric luminosity and radius are L = 1.26 · 10 3 L ⊙ and R = 37.5R ⊙ , respectively. In the HR diagram Polaris is located at the red edge of the instability strip.

Theoretical estimates of the rates of radial pulsation period change in Galactic Cepheids with initial masses 5.5M_\odot <= Mzams <= 13M_\odot, chemical composition X=0.7, Z=0.02 and periods 1.5 day <= P <= 100 day are obtained from consistent stellar evolution and nonlinear stellar pulsation computations. Pulsational instability was investigated for three crossings of the instability strip by the evolutionary track in the HR diagram. The first crossing occurs at the post-main sequence helium core gravitational contraction stage which proceeds in the Kelvin--Helmholtz timescale whereas the second and the third crossings take place at the evolutionary stage of thermonuclear core helium burning. During each crossing of the instability strip the period of radial pulsations is a quadratic function of the stellar evolution time. Theoretical rates of the pulsation period change agree with observations but the scatter of observational estimates of dP/dt noticeably exceeds the width of the band (\delta\log |dP/dt| <= 0.6) confining evolutionary tracks in the period - period change rate diagram. One of the causes of the large scatter with very high values of dP/dt in Cepheids with increasing periods might be the stars that cross the instability strip for the first time. Their fraction ranges from 2% for Mzams=5.5M_\odot to 9% for Mzams=13M_\odot. Variable stars \alpha UMi and IX Cas seem to belong to such objects.Comment: 16 pages, 4 figures. Accepted for publication in Astronomy Letter

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