RX J1856.5-3754

   
5 Spectrum and spectral energy distribution

The reduced, flux-calibrated spectrum is shown in Fig. 3. We limit ourselves to the wavelength range of 3800-7000 Å, since at shorter wavelengths the flux calibration becomes unreliable, while at longer wavelengths second-order light starts to contribute significantly for objects as blue as star X (it is negligible shortward of $6500 \,{\rm\AA}$ and rises approximately linearly to 10% at 7000 Å). We also removed 20 Å-wide regions around H$\alpha$, H$\beta$, and H$\gamma$, which are (or might be in case of H$\gamma$) contaminated by nebular emission.

The spectrum does not contain any significant features. The best limits to the equivalent width of any feature are obtained shortward of $\sim$ $5400 \,{\rm\AA}$: about 16 Åfor features with 50% depth beneath the continuum, and about 60 Åfor features with 25% depth.

Figure 3: Optical spectrum of RX J1856.5-3754. For the histogram, the data were averaged in 3-pixel wide bins ($\sim$ $7.5 \,{\rm \AA}$ or $\sim$$60\%$ of a resolution element). The points with (Poisson) error bars reflect averages over 25-pixel ($\sim$ $63 \,{\rm \AA}$) wide bins. These are offset vertically; their zero level is indicated by the dashed line. The dotted line indicates the absorbed Rayleigh-Jeans spectrum that best fits the photometry. The observed spectrum is consistent with this and has no significant features.

The spectrum is shown together with the photometry in Fig. 4. One sees that the spectrum is consistent with both the VLT and HST photometry. Indeed, integrating the spectrum over the B and F450W bandpasses, we infer B=25.22 and m₄₅₀=25.25, which compares well with our photometry (Table 5), giving additional confidence in the calibration of all three data sets.

Both spectrum and photometry indicate a spectral energy distribution close to that of a Rayleigh-Jeans tail, as would be expected for this very hot source. Assuming an intrinsic Rayleigh-Jeans spectrum, we determine the reddening to the source by fitting a reddened $\lambda^{-4}$ spectral distribution to the photometry. We do not include the spectrum in the fit, because we consider its absolute flux calibration somewhat less reliable and also because we wish to use it to verify the result from the photometry. We use the following relation between Vega magnitude $m_{\rm Vega}$ and input spectrum $f_\lambda$,

$$m_{\rm Vega} = -2.5\log \left(\frac{\int f_\lambda\frac{\la... ...hc}R_\lambda\,{\rm d}\lambda} \right)-21.100-\Delta_{\rm ST},$$ (1)

where $R_\lambda$ is the response at wavelength $\lambda$, and $\Delta_{\rm ST}$ is the magnitude difference between the Vega and ST systems (see Table 5). In the latter system, a flat spectrum has the same magnitude in all filters; it matches the Johnson system at V. The integrations are done over photon rates, since what we measure with CCDs is the rate of photons in a particular band. The response curves we used for the WFPC2 filters are the system response curves for the planetary camera, taken from the Space Telescope Science Institute web site. For the B and R filters, we used the Landolt filter curves from Bessell (1990). For the input spectrum, we take

$$f_\lambda=f_{\lambda_0}\left(\frac{\lambda}{\lambda_0}\right)^{-4} 10^{-0.4(A_\lambda-A_{\lambda_0})},$$ (2)

where $f_{\lambda_0}$ is the observed flux at reference wavelength $\lambda_0$ and $A_\lambda$ is the reddening. We use the reddening curve of Cardelli et al. (1989) for R=3.1; we include corrections for the optical as described by O'Donnell (1994). To minimise the covariance between $f_{\lambda_0}$ and A_V, we chose $\lambda_0=5000 \,{\rm\AA}$.

Figure 4: Optical/ultraviolet spectral energy distribution of RX J1856.5-3754. The thick-set points indicate fluxes derived from VLT and HST photometry. The vertical lines indicate the $1\sigma$ errors while the horizontal ones are measures of the filter widths. Overdrawn are the best-fit absorbed (drawn curve) and unabsorbed (dotted curve) Rayleigh-Jeans spectra, as well as the spectrum observed with the VLT, averaged in 25-pixel wide bins ($\sim$ $63 \,{\rm \AA}$).

From the fit to the photometry, we find $f_{5000}=(2.96\pm0.06)\times10^{-19}~ \,{\rm erg} \,{\rm s^{-1}} \,{\rm cm^{-2}} \,{\rm\AA^{-1}}$ and $A_V=0.12\pm0.05$; the fit is acceptable, with $\chi^2_{\rm red}=3.5$ for four degrees of freedom (six bands and two parameters; note that for the uncertainties we used the measurement errors with the zero-point uncertainties added in quadrature; see Table 5). For the reddening curve used, A₅₀₀₀/A_V=1.138, and thus the unabsorbed flux is $f_{\lambda_0,0}=(3.36\pm0.17)\times10^{-19} \,{\rm erg} \,{\rm s^{-1}}~{\, cm^{-2}} \,{\rm\AA^{-1}}$, where the error is dominated by the uncertainty in A_V. The fit is shown in Fig. 4; it can be seen that it also is a good fit to the optical spectrum (see also Fig. 3), with $\chi^2=37$ for 49 degrees of freedom (no free parameters; also for other choices of binning, one finds $\chi^2_{\rm red}\simeq1$).

The inferred reddening is consistent with the range $A_V\simeq0.05\ldots~0.12$ expected from the range in X-ray column density $N_{\rm H}=(1.0\ldots~2.2)\times10^{20} \,{\rm cm^{-2}}$ found from different model fits to the X-ray and EUVE spectrum (Pons et al. 2001; Burwitz et al. 2001). It is also consistent with the limit set by the total amount of reddening along this line of sight, which we can infer from stars L, C, and F. From the difference between the observed colours and the intrinsic colours for these stars (inferred from their spectral types; see Table <3), we infer $E_{B-R}=0.10\,\pm\,0.03$, which corresponds to $A_V=0.20\pm0.06$. Using this reddening, and assuming L, C, and F are main-sequence stars with absolute magnitudes $M_V\simeq5.0$, 5.4, and 5.8 (Cox 2000), respectively, their distances are 2.7, 2.8, and 1.6 kpc, respectively. Thus, they are well in the background relative to star X, as well as relative to the CrA cloud complex, which, apparently, contributes very little extinction in this line of sight, unlike what was suggested previously (Walter et al. 1996).

RX J1856.5-3754