Five observations of the hard X-ray spectrum of Her X-1 from RXTE show that
the similar to 41 keV energy of the cyclotron scattering line is constant
within statistics of a few percent per observation. The overall spectral sh
ape, on the other hand, varies somewhat, with an rms of 2%. If the 41 keV f
eature truly originates as cyclotron resonance scattering in an unchanging
3 x 10(12) G dipole field not far above the neutron star surface, these obs
ervations constrain the average height of scattering to within a range of 1
80 m. This is consistent with models that put the radiating structure withi
n meters of the surface of the neutron star. In other pulsars, observed lin
e centroid changes have been correlated with luminosity changes, and if int
erpreted as variations of the height at which scattering takes place, many
hundreds of meters are required. These RXTE data, which sample nearly a fac
tor of 2 in unabsorbed luminosity, are in conflict with a particular model
for such an extended radiating structure. Comparison with other observation
s over many years indicates strongly that the centroid energy of this absor
ption line has increased some time between 1991 and 1993 by 23%, from 34 to
41 keV. Moreover, the cutoff energy of the spectral continuum increased at
the same time from 16 to 20 keV, which is, within the statistical error of
5%, in direct proportion to the centroid. This may be a sign that both the
se characteristics of the spectrum are controlled in the same way by the ma
gnetic field strength in the region of scattering.