Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron stars

There is observational evidence that central compact objects (CCOs) in supernova remnants have moderately strong magnetic fields $B\sim10^{11}$ G. Meanwhile, available models of partially ionized hydrogen atmospheres of neutron stars with strong magnetic fields are restricted to $B\gtrsim10^{12}$ G. We extend the equation of state and radiative opacities, presented in previous papers for $10^{12}\mbox{ G}\lesssim B \lesssim 10^{15}$ G, to weaker fields. An equation of state and radiative opacities for a partially ionized hydrogen plasma are obtained at magnetic fields $B$, temperatures $T$, and densities $\rho$ typical for atmospheres of CCOs and other isolated neutron stars with moderately strong magnetic fields. The first- and second-order thermodynamic functions, monochromatic radiative opacities, and Rosseland mean opacities are calculated and tabulated, taking account of partial ionization, for $3\times10^{10}\mbox{ G}\lesssim B\lesssim 10^{12}$ G, $10^5$ K $\lesssim T\lesssim 10^7$ K, and a wide range of densities. Atmosphere models and spectra are calculated to verify the applicability of the results and to determine the range of magnetic fields and effective temperatures where the incomplete ionization of the hydrogen plasma is important.