# NOTE: This model is now in the Xspec release and this page is superceded by the Xspec manual

The NSAGRAV model is an extended version of the NSA code previously implemented in the XSPEC package. In comparison with NSA, this code provides the spectra emitted from a nonmagnetic hydrogen atmosphere of a neutron star with surface gravitational acceleration g ranging from 1e13 to 1e15 cm/s^2, allowed by equations of state for the neutron star matter (the NSA model uses the spectra calculated for g=2.43e14 cm/s^2). The uniform surface (effective) temperature is in the range of Log T_eff(K) = 5.5 - 6.5. The atmosphere is in radiative and hydrostatic equilibrium; sources of heat are well below the atmosphere. The radiative force and electron heat conduction are included in the models, but they are of no importance in the specified ranges of T_eff and g. The model spectra are provided as seen by a distant observer, with allowance for the GR effects.

The neutron star mass M and radius R determine the redshift parameter,

g_r=[1-2.952*M/R]^0.5,
and the gravitational acceleration at the surface,
g=1.33e16*M/R^2/g_r cm/s^2,
where M is in units of solar mass, and R is in km. The allowed domain in the M-R plane corresponds to g_r^2 > 1/3 and 1e13 < g < 1e15 cm/s^2. (This domain is restricted by the solid curves in the figure). If chosen M and R values correspond to g_r or/and g values outside the allowed domain, then the code sets the latters to be the closest limiting values (e.g., if one chooses M=2, R=8, then the code will use g_r=3^{-1/2}=0.578 instead of g_r=0.512 corresponding to the M and R chosen), which would lead to unphysical results.

The values of the effective temperature and radius as measured by a distant observer ("values at infinity") are:

T^\infty = g_r*T_eff, R^\infty = R/g_r.
The NSAGRAV model may be useful for putting constraints on M and R from spectral fits to thermal emission detected from neutron stars, provided the quality of the observational data are good enough to warrant a detailed analysis. The parameters M and R can be fixed at specific values or allowed to vary within a reasonable range (see the note above). For example, one can run spectral fits on a M-R grid (using the "steppar" command of XSPEC) within the allowed parameter domain (see above).

The normalization parameter (added automatically by XSPEC) is K=1/D^2, where D is distance to the neutron star (in pc). It can be fixed in spectral fits if the distance is known.

Please send your comments/questions (if any) to Slava Zavlin (vyacheslav.zavlin@msfc.nasa.gov) and/or George Pavlov (pavlov@astro.psu.edu). If you publish results obtained using this model please reference Zavlin et al. (1996, A&A 315, 141).

The model parameters are :

 par1 = logTeff, (unredshifted) effective temperature par2 = Mns, neutron star gravitational mass (in units of solar mass) par3 = Rns, "true" neutron star radius (in km) K = 1/D2, where D is the distance to the object in pc

The source code, lmodel.dat entries and nsa_gm0.0, nsa_gm0.5, nsa_gm1.0, nsa_gp0.5, nsa_gp1.0, model data files are available. The model data files should either be placed in the $XANADU/spectral/xspec/manager (V11),$XANADU/spectral/modelIonData (V12) directory or the XSPEC command xset NSAGRAV_DIR directory-path used to define the directory containing the model data files.

Keith Arnaud, Lab. for High Energy Astrophysics, NASA/Goddard Space Flight Center
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