RX J1856.5-3754

  
6 Deviations from a Rayleigh-Jeans tail?

Above, we assumed a $\lambda^{-4}$ spectral energy distribution for star X. Indeed, from the observations, we cannot determine the slope of the spectrum independently: spectra with $f_\lambda=f_{\lambda_0}(\lambda/\lambda_0)^{-\alpha}$ reproduce the photometry equally well as long as $A_V=0.12\pm0.06+0.89(\alpha-4)$. However, stars L, C, and F pose an upper limit of 0.20 mag on the reddening to star X. Using 0<A_V<0.20, one infers that , i.e., the spectrum has to have a slope very close to that of a Rayleigh-Jeans tail.

6.1 Limits to a non-thermal component

Our data place stringent constraints on any contribution from non-thermal emission. For instance, fitting a sum of a Rayleigh-Jeans tail and a non-thermal spectrum with $f_\nu\propto\nu^{0.1}$ (i.e., $f_\lambda\propto\lambda^{-2.1}$), such as observed for the Crab pulsar (Sollerman et al. 2000; Carramiñana et al. 2000), the best-fit has zero contribution from non-thermal emission and the same reddening as inferred above. Even for zero reddening, the best-fit contribution is only 11% at 6000 Å(for this fit, $\chi^2=5$). The 95% confidence upper limit to a non-thermal contribution for a Crab-like spectrum is 20% at 6000 Å(for a non-thermal spectrum with $f_\nu\propto\nu^{-0.8}$, as observed for Geminga Martin et al. 1998, this reduces to 8%).

6.2 Limits to emission from an accretion disk

We also considered whether an accretion disk might be present, from which RX J1856.5-3754 is accreting. Accretion from "debris disks'' has been invoked in models of anomalous X-ray pulsars (e.g., Van Paradijs et al. 1995; Chatterjee et al. 2000). Furthermore, Perna et al. (2000) suggested that the deviation from a Rayleigh-Jeans spectrum found from optical observations of PSR B0656+14 (Koptsevich et al. 2001 and references therein) could be due to the presence of such a disk. For RX J1856.5-3754, we considered two cases. For the first, we assumed the source is powered by accretion from a disk, in which case both viscous heating (Shakura & Sunyaev 1973) and irradiation by the neutron star (Vrtilek et al. 1990) lead to optical emission. We used routines described by Hulleman et al. (2000a,b) to calculate the emission from both processes, integrating between an inner radius $r_{\rm in}$ and an outer radius of $10^{14} \,{\rm cm}$. For the neutron star spectrum, we take the black-body fit of Pons et al. (2001) that best fits the observed X-ray to optical spectral energy distribution ( $kT=48 \,{\rm eV}$, $R/d=0.11 \,{\rm km}/{\rm pc}$) and a distance of 60 pc as inferred from the parallax (Walter 2001). We found that for a disk extending all the way in to the neutron star ( $r_{\rm {}in}=10^6 \,{\rm cm}$), the optical emission predicted far exceeds that observed, by three orders of magnitude in R. In order for the emission to remain below 10% of the R-band flux (i.e., ), the inner radius had to be $2\times10^9 \,{\rm cm}$. This could be the radius where the disk is disrupted by a magnetic field; if so, and if the neutron star were rotating at equilibrium, its period would have to be $40 \,{\rm s}$. If such a disk were present, its spectrum would be very red. At the limit, one would predict J=22 and $K=19 \,{\rm mag}$.

In principle, the neutron star could have a disk even if the X-ray emission is not due to accretion, in which case the mass accretion rate could be lower and hence the viscous heating of the disk much reduced. In the second case we considered, therefore, we ignored the contribution of viscous heating. Also for this case, the disk cannot extend all the way in to the neutron star (it would still exceed the observed R-band flux by an order of magnitude); we find ( ; at the limit, the predicted infrared magnitudes are J=23 and K=20).

We conclude that all measurements are consistent with a slightly reddened Rayleigh-Jeans spectrum, with no evidence for features or for a contribution from non-thermal emission or an accretion disk.

Acknowledgements

We thank the ESO staff, in particular Thomas Szeifert and Hermann Böhnhardt, for their expert help with both observing runs. This research made use of the SIMBAD data base. The Munich Image Data Analysis System is developed and maintained by the European Southern Observatory. M.H.vK. acknowledges support of a fellowship from the Royal Netherlands Academy of Science, and S.R.K. support from NASA and NSF.

RX J1856.5-3754