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Register a new userModel X-ray Spectra of Magnetic Neutron Stars with Hydrogen Atmospheres
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Wynn C.G. Ho
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We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with fixed surface fields between B=10^12 and 2x10^13 G and effective temperatures logT_eff=5.5-6.8, as well as with surface B and T_eff distributions around these values. The models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas. The atmospheres directly determine the characteristics of thermal emission from the surface of neutron stars. We also incorporate these model spectra into XSPEC, under the model name NSMAX, thus allowing them to be used by the community to fit X-ray observations of neutron stars.
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The hydrogen and helium accreted by X-ray bursting neutron stars is periodically consumed in runaway thermonuclear reactions that cause the entire surface to glow brightly in X-rays for a few seconds. With models of the emission, the mass and radius of the neutron star can be inferred from the observations. By simultaneously probing neutron star masses and radii, X-ray bursts are one of the strongest diagnostics of the nature of matter at extremely high densities. Accurate determinations of these parameters are difficult, however, due to the highly non-ideal nature of the atmospheres where X-ray bursts occur. Observations from X-ray telescopes such as RXTE and NuStar can potentially place strong constraints on nuclear matter once uncertainties in atmosphere models have been reduced. Here we discuss current progress on modeling atmospheres of X-ray bursting neutron stars and some of the challenges still to be overcome.
The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K_perp of its generalized momentum. In particular, the photoionization process is modified substantially: (i) threshold energies are decreased as compared with those for an atom at rest, (ii) cross section values are changed significantly, and (iii) selection rules valid for atoms at rest are violated by the motion so that new photoionization channels become allowed. To calculate the photoionization cross sections, we, for the first time, employ exact numerical treatment of both initial and final atomic states. This enables us to take into account the quasi-bound (autoionizing) atomic states as well as coupling of different ionization channels. We extend the previous consideration, restricted to the so-called centered states corresponding to relatively small values of K_perp, to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over K. For typical temperatures of neutron star atmospheres, the averaged cross sections differ substantially from those of atoms at rest. In particular, the photoionization edges are strongly broadened by the thermal motion of atoms; this magnetic broadening exceeds the usual Doppler broadening by orders of magnitude. The decentered states of the atoms give rise to the low-energy component of the photoionization cross section. This new component grows significantly with increasing temperature above 10^{5.5} K and decreasing density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.
Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well described by the atmosphere model of a passively cooling neutron star when the burst luminosity is high enough. The observed spectral evolution deviates from the model predictions when the burst luminosity drops below a critical value of 20-70% of the maximum luminosity. We suggest that these deviations are induced by the additional heating of the accreted particles. We present a method for computation of the neutron star atmosphere models heated by accreted particles assuming that their energy is released via Coulomb interactions with electrons. We compute the temperature structures and the emergent spectra of the atmospheres of various chemical compositions and investigate the dependence of the results on the other model parameters. We show that the heated atmosphere develops the hot (20--100 keV) corona-like surface layer cooled by Compton scattering, and the deeper, almost isothermal optically thick region with a temperature of a few keV. The emergent spectra deviate strongly from those of undisturbed neutron star atmospheres, with the main differences being the presence of a high-energy tail and a strong excess in the low-energy part of the spectrum. They also lack the iron absorption edge, which is visible in the spectra of undisturbed low-luminosity atmospheres with solar chemical composition. Using the computed spectra, we obtained the dependences of the dilution and color-correction factors as functions of relative luminosities for pure helium and solar abundance atmospheres. We show that the helium model atmosphere heated by accretion corresponding to 5% of the Eddington luminosity describes well the late stages of the X-ray bursts in 4U 1820-30.
The discovery of photospheric absorption lines in XMM-Newton spectra of the X-ray bursting neutron star in EXO0748-676 by Cottam and collaborators allows us to constrain the neutron star mass-radius ratio from the measured gravitational redshift. A radius of R=9-12km for a plausible mass range of M=1.4-1.8Msun was derived by these authors. It has been claimed that the absorption features stem from gravitationally redshifted (z=0.35) n=2-3 lines of H- and He-like iron. We investigate this identification and search for alternatives. We compute LTE and non-LTE neutron-star model atmospheres and detailed synthetic spectra for a wide range of effective temperatures (effective temperatures of 1 - 20MK) and different chemical compositions. We are unable to confirm the identification of the absorption features in the X-ray spectrum of EXO0748-676 as n=2-3 lines of H- and He-like iron (Fe XXVI and Fe XXV). These are subordinate lines that are predicted by our models to be too weak at any effective temperature. It is more likely that the strongest feature is from the n=2-3 resonance transition in Fe XXIV with a redshift of z=0.24. Adopting this value yields a larger neutron star radius, namely R=12-15km for the mass range M=1.4-1.8Msun, favoring a stiff equation-of-state and excluding mass-radius relations based on exotic matter. Combined with an estimate of the stellar radius R>12.5km from the work of Oezel and collaborators, the z=0.24 value provides a minimum neutron-star mass of M>1.48Msun, instead of M>1.9Msun, when assuming z=0.35.
Structures of X-ray emitting magnetic polar regions on neutron stars in X-ray pulsars are studied in a range of the accretion rate, 10$^{17}$ g s$^{-1} sim 10^{18}$ g s$^{-1}$. It is shown that a thin but tall, radiation energy dominated, X-ray emitting polar cone appears at each of the polar regions. The height of the polar cone is several times as large as the neutron star radius. The energy gain due to the gravity of the neutron star in the polar cone exceeds the energy loss due to photon diffusion in the azimuthal direction of the cone, and a significant amount of energy is advected to the neutron star surface. Then, the radiation energy carried with the flow should become so large for the radiation pressure to overcome the magnetic pressure at the bottom of the cone. As a result, the matter should expand in the tangential direction along the neutron star surface, dragging the magnetic lines of force, and form a mound-like structure. The advected energy to the bottom of the cone should finally be radiated away from the surface of the polar mound and the matter should be settled on the neutron star surface there. From such configurations, we can expect an X-ray spectrum composed of a multi-color blackbody spectrum from the polar cone region and a quasi-single blackbody spectrum from the polar mound region. These spectral properties agree with observations. A combination of a fairly sharp pencil beam and a broad fan beam is expected from the polar cone region, while a broad pencil beam is expected from the polar mound region. With these X-ray beam properties, basic patterns of pulse profiles of X-ray pulsars can be explained too.
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