RX J1856.5-3754

   
4 Reduction

The data were reduced using the Munich Image Data Analysis System (MIDAS) and procedures running in the MIDAS environment. From bias frames taken before and after a given night, the bias level appeared somewhat variable, both in time and in position on the detector. However, relative to the levels found from the overscan pixels (determined separately for the four amplifiers), it remained constant. For bias subtraction, therefore, we subtracted both the levels from the overscan regions in individual frames and an average of the overscan-corrected bias frames (for the appropriate gain setting). The averages were determined separately for 1999 and 2000.

4.1 Photometry

All images were corrected for sensitivity variations using flat fields constructed from images of the sky taken at dusk and dawn (for the observations in 2000, only the dawn frames were used, since this produced much cleaner results). Averages were formed of the various series after filtering out cosmic-ray hits, verifying that even for the best-seeing images no stars were mistakenly affected.

Photometry was done by first determining the offset of instrumental magnitudes derived from the average frames from those derived from the images of the first sequence in the night of 2000 May 2, and then applying a calibration determined from the three standard fields observed during that night. We measured instrumental magnitudes using the DAOphot package (Stetson 1987). We used an iterative procedure, in which relatively isolated stars were selected and used to define a point-spread function (PSF), next the PSF was used to fit all stars and to subtract all but the PSF stars, and then the cleaned frame was used to determined an improved PSF, etc. We found that to model the variations in the PSF over the frame, a second-order dependence on position was required. Aperture corrections were determined from the difference between the fitted magnitudes and magnitudes measured in 20-pixel (4 $^{\prime \prime }$) radius apertures on the PSF stars in the final frame in which all non-PSF stars had been removed.

The standard fields were analysed in two separate ways. For deriving the calibration using the Landolt (1992) photometry, we simply determined appropriate aperture magnitudes on the reduced frames (if not overexposed; in practice, we could only use the short frames). We inferred extinction coefficients of 0.126 and 0.076 in B and R, respectively, which are smaller than the typical values of 0.21 and 0.13 listed by ESO. We did not have sufficient data to measure the colour terms accurately, although we could confirm that the colour term for the B band is significant ( -0.025(B-R), i.e., the ESO B band is bluer than Landolt B), while the colour term for the R band is negligible. We estimate that the final uncertainty in the zero points is about 0.02 mag.

We also tried to calibrate our fields using fainter stars, since for many faint stars in Landolt fields, Stetson (2000) has obtained calibrated magnitudes from archive observations. For this purpose, we analysed the frames using point-spread function fitting as described above. Unfortunately, however, while for the field of PG 1657+078, there are 32 stars with B-band magnitudes and 44 with R, for the field of PG 0942-029 there is only one star. As a result, we cannot derive an accurate solution including extinction terms, but only confirm the solution found using the Landolt photometry.

In Table 5, we list photometry for all point-like objects which are present in the HST Planetary Camera images taken through the F606W filter (Walter et al. 1996; Walter 2001), and which are detected in both B and R. One word of caution about the brightest stars, with , which are overexposed in many of the R-band images. The magnitudes of these stars have been determined by PSF fitting to those pixels which were not overexposed, and are therefore somewhat more uncertain. We compared the magnitudes for these stars with magnitudes inferred from the first series of images, in which overexposure is less of an issue because of the relatively bad seeing. We found that the photometry in Table 5 may slightly underestimate the true brightness of the stars, by $\sim$ $0.01 \,{\rm mag}$.

4.2 Spectroscopy

For the spectroscopy, the flat fielding turned out to be problematic, because the spectroscopic flats, taken with the internal flat-field lamp illuminating the instrument cover, had an illumination pattern so different from that of the actual observations on sky that they were useless. Since the observations of the flux standards indicated that fringing was not a problem and that pixel-to-pixel sensitivity variations were much smaller than the sky-subtraction uncertainties for our very faint source, we decided to forego flat-fielding altogether. In order to equalise the four quadrants of the chip, which are read out through amplifiers with slightly different gain, we multiplied with the gains for the different amplifiers as measured by the instrument team. This provided very satisfactory results.

For the sky subtraction, clean regions along the slit within about 100 pixels of the sources of interest were selected, and these were fitted using a polynomial function. The order of the polynomial was mostly zero, but could be increased up to quadratic at any given column as long as further terms increased the goodness of the fit to the sky regions significantly. For each set of observations, the sky-subtracted images were registered and added together.

From both the individual and the summed sky-subtracted images, spectra were extracted using an optimal weighting scheme similar to that of Horne (1986). For this purpose, the spatial profile of the bright star (either F or L) was determined, and this was used to extract optimally weighted spectra at the position of the bright star itself, as well as at the position of star X. Furthermore, for verification, spectra were extracted at a number of empty positions. These were all consistent with zero flux.

The dispersion relation was found using an exposure of helium, argon and mercury lamps. Line positions were determined for positions along the whole slit. At a single position, a fourth order fit was sufficient, giving root-mean-square residuals of 0.5 Å; to obtain the same residuals for a two-dimensional relation required terms up to fifth order along the dispersion direction and second order along the spatial direction (for a total of 18 terms). The latter solution was used to calculate the wavelengths for all extracted spectra.

4.3 Spectral Images

In the extracted spectra of RX J1856.5-3754, emission lines of H$\alpha$ and H$\beta$ appeared. Inspection of the sky-subtracted frames showed that these lines were extended, especially along the slit over star F. In fact, it extended into the regions used to define the sky emission, and hence it had been partly removed in the sky-subtraction stage. In order to provide a cleaner picture, we rebinned the raw images to spectral images, in which every column is at a constant wavelength, removed cosmic rays, and formed averages for the two slit positions (excluding the first spectrum, which had a cosmic-ray hit at H$\beta$near the target). Next, we determined the sky emission as a function of wavelength in regions far away from the neutron star, and subtracted this from all columns. The parts of the images around H$\alpha$ and H$\beta$ are shown in Fig. 1. From these spectral images, it is already clear that the neutron star has a nebula which is extended along the path it has travelled. This is confirmed by our H$\alpha$ imaging. The H$\alpha$ images and a discussion of the nature of this nebula will be presented elsewhere (van Kerkwijk & Kulkarni 2001).

  
4.4 Flux calibration of the spectra

For the flux calibration, the spectra were first corrected for atmospheric extinction using the average La Silla extinction curve. While this will be only approximately correct, it facilitates the next step, the determination of the slit losses. For this purpose, the ratio with the wide-slit spectra was formed for each of the bright star spectra taken through the 1 $^{\prime \prime }$ slit. These ratio spectra were approximated with second-degree polynomials, which were used to correct all spectra.

Finally, the spectra were corrected for the response of the spectrograph derived from the observation of the spectrophotometric standard EG 274 (Hamuy et al. 1992, 1994). The spectra of this standard were extracted in the same manner as described above, but in addition a correction was made for the blue second-order light that overlaps the part of the spectrum at $6500 \,{\rm\AA}$ (the correction was determined with the help of the spectrum taken through the GG 435 filter). We observed the DA white dwarf BPM 16274 as an additional calibrator. Unfortunately, we realised later that this star is only calibrated in the ultraviolet. We still used it to verify our response curve using a model spectrum kindly provided by D. Koester (for $T_{\rm eff}=18\,750 \,{\rm K}$ and $\log{}g=7.83$, as inferred by Bragaglia et al. 1995, and normalised to V=14.20, as measured by Eggen 1969). For wavelengths longer than $\sim$ $3700 \,{\rm\AA}$, the comparison was very satisfactory, as was a similar comparison using a DA white-dwarf model provided by D. Koester for EG 274 ( $T_{\rm eff}=24\,250 \,{\rm K}$, $\log{}g=8.05$; Vauclair et al. 1997).

The above gives us confidence that the relative calibration over the spectral range is accurate. The accuracy of the absolute calibration, however, is less clear, since the spectra of EG 274 were taken in the beginning of the night, when some patchy cirrus was still present. In order to assess the influence of the cirrus, we compared fluxes from all B-band (acquisition) images and all wide-slit spectra. We found that there were variations before about 1UT, but that after that time the measured count rates indicate the sky was clear. To see whether our flux calibration was influenced by the cirrus, we used the B, V, and R filter curves of Bessell (1990) to determine synthetic B, V, and R-band magnitudes for all brighter objects in our wide-slit spectra. For BPM 16274, we find V=14.20, B-V=-0.04, quite consistent with the observed V=14.20, B-V=-0.015 (Eggen 1969). Also for stars F (twice), L, and C (in the slit for the star L position; see Fig. 1), the synthetic magnitudes are in good agreement with our B and R-band photometry, as can be seen in Table 3. We conclude that the absolute calibration of our spectra is accurate to 0.02 mag.

   
4.5 Previous photometry of stars L, C, and F

While our spectrophotometry of stars L, C, and F agrees well with our own photometry, it disagrees with measurements in the literature: the synthetic V-band magnitudes are 0.4 mag brighter than both the V-band magnitudes of Neuhäuser et al. (1997) and the V-band magnitudes inferred from Gunn g and r measurements of Campana et al. (1997). (The magnitudes of Walter et al. 1996 differ even more, by $\sim$ $1 \,{\rm mag}$, but Neuhäuser et al. have already noted that Walter et al. used an incorrect zero point.)

Comparing colours, we find that our synthetic B-V and V-R colours are systematically redder and bluer, respectively, than those of Neuhäuser et al. (1997). The inferred B-R values, however, are consistent. This suggests there may be a problem with the V-band only. Indeed, the V, B-V, and V-R values listed by Neuhäuser et al. imply Band R-band magnitudes that are in reasonable agreement with our values for bright stars like stars L, C, and F. If our synthetic B and R are correct, however, our synthetic V should be correct too, since the three bands are tied to each other by relative calibration on wide-slit spectra, which proved very reliable on BPM 16274.

In order to settle the issue, we classified the spectra (see Fig. 2), using the spectral atlases of Silva & Cornell (1992) and Torres-Dodgen & Weaver (1993). All three stars appear to be of spectral type G; see Table 3. For all three, our colours are consistent with the spectral types (for a small amount of reddening; see Sect. 5), while the B-V and V-R (but not B-R) colours of Neuhäuser et al. (1997) and the g-r colour of Campana et al. (1997) are inconsistent with the spectral types (independent of reddening). We thus conclude that, despite the inconsistencies with earlier work, our calibration is reliable.

 

 

Table 3: Spectral types, colours and magnitudes for stars L, C, and F. For each star, the first line lists the spectral type inferred from the spectra and the corresponding intrinsic colours (for a main-sequence star; Cox 2000). The following lines list synthetic magnitudes and colours derived from the wide-slit spectra (two for star F), and magnitudes derived from our images. All magnitudes and colours have $\sim 0.02 \,{\rm mag}$uncertainty.

Star	Spectral type	B	(B-V)	V	(V-R)	R
L	G3-6 V-III		0.64-0.66		0.36-0.37
		18.07	0.74	17.33	0.41	16.92
		18.06				16.93
C	G6-8 V-III		0.66-0.76		0.37-0.44
		18.56	0.78	17.78	0.43	17.35
		18.53				17.34
F	G9-K0 V-III		0.79-0.82		0.45-0.47
		17.94	0.88	17.06	0.46	16.60
		17.93	0.86	17.07	0.46	16.61
		17.91				16.58

  
4.6 Archival HST imaging

RX J1856.5-3754 has been a regular target for WFPC2 observations with HST, both to measure broad-band photometry (Walter & Matthews 1997; Pons et al. 2001) and to determine the proper motion and parallax (Walter 2001). We reanalysed all images (see Table 4), both to provide a final verification of our flux calibration, and to extend the optical spectral energy distribution for RX J1856.5-3754 to shorter wavelengths. In our analysis, we take into account that during the last years updated zero points have become available (Baggett et al. 1997), and that new prescriptions have been published for correcting for changes in the amount of contaminants on the CCD windows (Baggett & Gonzaga 1998), for the so-called "long-versus-short anomaly'' (Casertano & Mutchler 1998), and for the slowly degrading charge-transfer efficiency (CTE; Whitmore et al. 1999); the latter two are particularly important for faint objects. Furthermore, recently a package specifically written for WFPC2 photometry, HSTPHOT, has been made available by Dolphin (2000a), which includes many of the above corrections (Dolphin 2000b).

Figure 2: Spectra of stars L, C, and F. These are used for classification and verification of the flux calibration in Sect. 4.5; see also Table 3.

Our analysis started with the pipe-line reduced WFPC2 images. We measured photometry using HSTPHOT, as well as, for comparison, our own procedures. For the HSTPHOT reduction, we followed the prescription of Dolphin (2000a): (i) mask bad pixels; (ii) combine images taken at the same position and remove cosmic ray hits; (iii) determine sky levels; (iv) remove hot pixels; and (v) measure photometry by point-spread function fitting on the combined image(s). In the last step, we disabled the determination of point-spread function residuals and aperture corrections for the F170W image exposures, since these lack a sufficient number of well-exposed stars. For the F170W exposures, we also had to make a change to the source code for the sky determination, viz., to remove the constraint that the fitted sky level had to be positive. While this constraint is physically reasonable, slight inadequacies in the pipe-line subtraction of the bias and dark current can lead to negative count rates, which, if not corrected for, lead one to underestimate a source's brightness; this is indeed the case for the F170W images. Another change we made to the source code was that we forced the use of the published (Dolphin 2000b) charge-transfer efficiency corrections for all bands (the MULTIPHOT routine in the HSTPHOT distribution uses more recent corrections for the optical filters, but not for the ultraviolet ones; the difference is rather small).

 

 

Table 4: Log of archival HST/WFPC2 imaging. The F606W and F450W images are taken at two dither positions, different by 5.5 pixels in both X and Y, while the F300W and F170W images are all taken at the same position.

Identifier	UT	Filter	$t_{\rm int}$
u3im010[1-4]	1996 Oct. 6	F606W	$3\times1000+1400$
u3im010[5-6]		F300W	$2\times1200$
u51g010[1-8]	1999 Mar. 30	F606W	$8\times900^{\rm a}$
u51g030[1-4]	May 24	F170W	$2\times2800+2\times2600$
u51g040[1-8]	26	F450W	$8\times900$
u51g020[1-2]	Sep. 16	F300W	$2\times1300$
u51g020[3-6]		F606W	$3\times1300+1290.5$

$^{\rm a}$ u51g0106 has a high background and a large number of cosmic-ray hits. It has not been used in the analysis.

In Table 5, we list the results. For the F300W and F606W filters, the averages of the individual measurements are listed (no significant variability was found for any star). Comparing the HST photometry with our ground-based results, we find that the two are consistent.

To verify our technique, we also measured aperture photometry on averaged images, produced in the manner described by van Kerkwijk et al. (2000). We measured count rates in apertures with a range of radii, derived aperture corrections to the standard 0 $.\!\!^{\prime\prime}$5 radius aperture, calculated the corrections discussed above (following the above references and the HST data and WFPC2 instrument handbooks), and converted to calibrated magnitudes by applying a 0.1 mag aperture correction from the 0 $.\!\!^{\prime\prime}$5 aperture to infinity and using the zero points of Baggett et al. (1997). We note that, as alluded to above, some corrections are large, especially for faint objects. For star X, the "long-vs-short'' corrections are -0.17, -0.3, -0.3, and $-0.4 \,{\rm mag}$ in F606W, F450W, F300W, and F170W, respectively (but see below); the 1996 CTE corrections are -0.07 and $-0.13 \,{\rm mag}$in F606W and F300W, respectively; and the 1999 CTE corrections are -0.11, -0.14, -0.30, and $-0.23 \,{\rm mag}$ in F606W, F450W, F300W, and F170W, respectively.

  

Table 5: Photometry of RX J1856.5-3754 and stars in the field. All magnitudes are in the Vega system. For star X, the uncertainties are as listed. For all other stars, an indication of the uncertainty is given by the presence of no ( $\sigma <0.035 \,{\rm mag}$), one ( $0.035<\sigma <0.075$) and two colons ( $0.075<\sigma <0.125$). The zero point uncertainty is about 0.05 mag for the F170W band, and 0.02 mag for all others.

Comparing the results with those derived using HSTPHOT, we found good consistency for the brighter stars. For the fainter stars like star X, however, this was only the case if we did not apply the "long-versus-short'' correction. Indeed, no such correction is applied in HSTPHOT, since Dolphin (2000b) has not found any evidence for it; he argues that its appearance likely reflects inaccurate sky subtraction in the procedures used by Casertano & Mutchler (1998). We do not have strong independent evidence either way, but note that if we do apply the correction, our VLT photometry for faint objects like star X becomes inconsistent with the HST results (while the results remain consistent for the brighter stars, since these are not affected).

Comparing to the magnitudes listed by Walter & Matthews (1997) and Walter (2001), we find that our results are roughly consistent for the brighter stars, but that they differ for the fainter stars; in particular, for star X, while the F606W magnitude is virtually identical, our F300W magnitude is 0.4 mag brighter than that of Walter & Matthews (note that these authors list magnitudes on the ST system). We suspect that the differences largely reflect our use of up-to-date corrections. This suspicion is strengthened by the fact that Pons et al. (2001), after making similar corrections, also find fluxes that differ from those of Walter & Matthews (1997). Indeed, their results are very similar to ours (their fluxes are fainter by $0.04\ldots~0.10$ mag and their uncertainties slightly larger, since they use aperture photometry rather than point-spread function fitting).

RX J1856.5-3754