20
M. C. Miller
In addition, there are several puzzling aspects to the quiescent emission. For stars
that have undergone several outbursts we have a decent estimate of their overall
accretion rate. We can thus estimate the luminosity produced in the crust by electron
capture reactions (e.g., [46]), which should be the minimum emergent luminosity.
We also expect that the flux we see from the star should decline smoothly after
cessation of accretion, and thus not have short timescale increases and decreases. In
addition, if cooling is the only process, the spectrum should be purely thermal. All
these expectations are violated in several stars. The quiescent thermal luminosity
of 1H 1905+00 is L < 2 × 10 30 erg s −1 , which is significantly below standard
predictions [111]. Several stars vary in intensity by a factor of a few on timescales
of days to years during their decline (for a discussion see [217]). In addition, many
of the field low-luminosity stars have significant, even dominant, nonthermal tails
(e.g., Cen X-4; [54, 195]).
It is possible that these discrepancies can be understood within the basic picture.
For example, enhanced neutrino emission in the crust would not be observed, so this
could explain the underluminous stars. Short timescale variability might be caused
by the motion of obscuring matter in these binaries. Nonthermal spectral tails could
be caused by coronal emission from the companion star [32, 51], magnetospheric
activity, or some small residual accretion. Thus although the simple model is
contradicted, plausible additions could rescue it. This nonetheless contributes an
additional note of caution to radius inferences from these stars, and means that
although the small radii reported from current qLMXB fits are similar to the small
radii reported from some fits to X-ray bursts, both methods are dominated by
systematic errors.
The second category of sources for spectral modeling and radius inferences is
isolated neutron stars. We will encounter these again in Sect. 1.5 when we discuss
cooling processes, but here we focus on what can be learned about radii. Exactly the
same principles apply as for the qLMXBs, except that these stars do not accrete (the
accretion rate from the interstellar medium is negligible; see [33] for a discussion).
The same questions apply for these stars as they do for qLMXBs. For example, the
spectra of young isolated neutron stars (such as the Crab pulsar) have significant
nonthermal components probably caused by magnetospheric emission. Distances
are also often difficult to establish, and the spectra can be fit using various spectra
that give significantly different answers for the radius.
A case in point is RX J1856.5–3754, which is the brightest of the eight
thermally emitting isolated neutron stars discovered using ROSAT. Its spectrum is
featureless and can be fitted using a Planck spectrum, a heavy element spectrum, or a
spectrum appropriate for condensed matter with a thin hydrogen envelope [206]. An
interesting puzzle that constrains the atmospheric model is that the best-fit Planck
spectrum to the X-ray data underpredicts the optical flux by a factor of ∼6 [48]. The
distance has been estimated to be 117 ± 12 pc [228] or 161 ± 12 pc [222], although
the data for the latter were re-analyzed to find a distance of 123
+11
−15 pc [229]. It has
been argued that this star has a radius of >14 km, which if true would make a strong
case for hard equations of state. However, better atmospheric modeling suggests a
M. C. Miller
In addition, there are several puzzling aspects to the quiescent emission. For stars
that have undergone several outbursts we have a decent estimate of their overall
accretion rate. We can thus estimate the luminosity produced in the crust by electron
capture reactions (e.g., [46]), which should be the minimum emergent luminosity.
We also expect that the flux we see from the star should decline smoothly after
cessation of accretion, and thus not have short timescale increases and decreases. In
addition, if cooling is the only process, the spectrum should be purely thermal. All
these expectations are violated in several stars. The quiescent thermal luminosity
of 1H 1905+00 is L < 2 × 10 30 erg s −1 , which is significantly below standard
predictions [111]. Several stars vary in intensity by a factor of a few on timescales
of days to years during their decline (for a discussion see [217]). In addition, many
of the field low-luminosity stars have significant, even dominant, nonthermal tails
(e.g., Cen X-4; [54, 195]).
It is possible that these discrepancies can be understood within the basic picture.
For example, enhanced neutrino emission in the crust would not be observed, so this
could explain the underluminous stars. Short timescale variability might be caused
by the motion of obscuring matter in these binaries. Nonthermal spectral tails could
be caused by coronal emission from the companion star [32, 51], magnetospheric
activity, or some small residual accretion. Thus although the simple model is
contradicted, plausible additions could rescue it. This nonetheless contributes an
additional note of caution to radius inferences from these stars, and means that
although the small radii reported from current qLMXB fits are similar to the small
radii reported from some fits to X-ray bursts, both methods are dominated by
systematic errors.
The second category of sources for spectral modeling and radius inferences is
isolated neutron stars. We will encounter these again in Sect. 1.5 when we discuss
cooling processes, but here we focus on what can be learned about radii. Exactly the
same principles apply as for the qLMXBs, except that these stars do not accrete (the
accretion rate from the interstellar medium is negligible; see [33] for a discussion).
The same questions apply for these stars as they do for qLMXBs. For example, the
spectra of young isolated neutron stars (such as the Crab pulsar) have significant
nonthermal components probably caused by magnetospheric emission. Distances
are also often difficult to establish, and the spectra can be fit using various spectra
that give significantly different answers for the radius.
A case in point is RX J1856.5–3754, which is the brightest of the eight
thermally emitting isolated neutron stars discovered using ROSAT. Its spectrum is
featureless and can be fitted using a Planck spectrum, a heavy element spectrum, or a
spectrum appropriate for condensed matter with a thin hydrogen envelope [206]. An
interesting puzzle that constrains the atmospheric model is that the best-fit Planck
spectrum to the X-ray data underpredicts the optical flux by a factor of ∼6 [48]. The
distance has been estimated to be 117 ± 12 pc [228] or 161 ± 12 pc [222], although
the data for the latter were re-analyzed to find a distance of 123
+11
−15 pc [229]. It has
been argued that this star has a radius of >14 km, which if true would make a strong
case for hard equations of state. However, better atmospheric modeling suggests a