3 Astrometrical referencing and photometry

3.1 Astrometry

The radio position of PSR B0950+08 at the epoch of the observations (see Table 1) was determined using the VLA observations by Fomalont et al. (1992) and the most recent measurements of the pulsar proper motion by Brisken et al. (2002).

Astrometric referencing of our image was made using positions of five of nine reference stars from the USNO A-2.0 catalogue visible within the $\sim$ $6\hbox{$^\prime$ }\times13\hbox{$^\prime$ }$ frame of the CCD chip containing the pulsar. The PSFs of these stars are not corrupted by the CCD oversaturation effects. We used IRAF tasks ccmap/cctran for the astrometric transformation of the image. RMS errors of the astrometric fit are $0\hbox{$.\!\!^{\prime\prime}$ }086$ and $0\hbox{$.\!\!^{\prime\prime}$ }090$ for RA and Dec, respectively, whereas the residuals for all stars are < $0\hbox{$.\!\!^{\prime\prime}$ }13$. All of them are less than the nominal USNO catalogue accuracy 0 $.\!\!^{\prime\prime}$24. Combining the RMS errors of the fit, the USNO catalogue accuracy and the radio position errors (see Table 1) we estimate total uncertainties of the pulsar position, as well as the astrometric referencing accuracy for the whole Subaru image, as 0 $.\!\!^{\prime\prime}$26 in both RA and Dec.

3.2 Identification and morphology of the candidate to the pulsar counterpart

As seen from Fig. 1, the optical counterpart of PSR B0950+08 can only be identified with a faint, ${S/N \simeq 7}$, isolated object clearly visible near the center of the $24\hbox{$^{\prime\prime}$ }\times24\hbox{$^{\prime\prime}$ }$ fragment of the Subaru image (Fig. 1a). The object overlaps with the error circle of the pulsar radio position with radius 0 $.\!\!^{\prime\prime}$26, corresponding to $1\sigma$ uncertainty of our astrometrical referencing (Fig. 1c). The source profile of the object is elongated E-W, with $FWHMs \sim 1\hbox{$.\!\!^{\prime\prime}$ }0$ and $\sim$ $0\hbox{$.\!\!^{\prime\prime}$ }7$ along E-W and S-N directions, respectively. Owing to the low S/N ratio, we do not resolve any point-like structure within the source profile. Formal Gaussian fitting of the whole object profile yields the coordinates $\alpha_{2000} = 9^{\rm h}53^{\rm m}09\hbox{$.\!\!^{\rm s}$ }288(17)$, $\delta_{2000} = 7^\circ$55$^\prime$35 $.\!\!^{\prime\prime}$89(26). The offset from the radio position is 0 $.\!\!^{\prime\prime}$43 W-S. It is within $1.75\sigma$ of the astrometrical accuracy and can be considered as negligible given our seeing and S/N values.

To compare our image with the previous optical-UV observations of the pulsar field by Pavlov et al. (1996) we reanalyzed astrometrical referencing of the HST/FOC image retrieved from the HST archive. The rotated box in Fig. 1a borders the FOV of the HST/FOC observations. Pavlov et al. (1996) found in this field the only point-like object with the offset $\simeq$1 $^{\prime \prime }$  (Pavlov 2000) from the pulsar radio position. Such a large offset at the relatively high spatial resolution of the HST/FOC observations, $\simeq$0 $.\!\!^{\prime\prime}$014, makes identification of the FOC object with the pulsar and with the Subaru pulsar counterpart doubtful. We revised the FOC astrometry making use of the FOC position angle and the only reference point visible at the north corner of the FOC image, an extended object o1 (see Fig. 1b). We assumed that o1 is a distant background object and its proper motion is negligible. Gaussian center coordinates of o1 were determined in the Subaru image ( $\alpha_{2000}=9^{\rm h}53^{\rm m}09\hbox{$.\!\!^{\rm s}$ }489(2)$, $\delta_{2000} = 7^\circ$55$^\prime$42 $.\!\!^{\prime\prime}$2(1)) and in the FOC image (with the accuracy $\la$ $0\hbox{$.\!\!^{\prime\prime}$ }02$), and were used to correct reference frame of the FOC image. The coordinates of the FOC pulsar candidate in the corrected system at the epoch of the FOC observations are $\alpha_{2000}=9^{\rm h}53^{\rm m}09\hbox{$.\!\!^{\rm s}$ }298$, $\delta_{2000}=7^\circ55\hbox{$^\prime$ }35\hbox{$.\!\!^{\prime\prime}$ }76$. Given that, the discrepancy between the FOC counterpart position and the radio position at the epoch of the HST observations, $\alpha_{2000}=9^{\rm h}53^{\rm m}09\hbox{$.\!\!^{\rm s}$ }314(3)$, $\delta_{2000}=7^\circ55\hbox{$^\prime$ }35\hbox{$.\!\!^{\prime\prime}$ }88(4)$, marked by "+" in the inset in Fig. 1b, is decreased to 0 $.\!\!^{\prime\prime}$27. This is comparable to the astrometrical referencing accuracy of the Subaru image.

The FOC image is presented in Fig. 1b in the corrected coordinates. The overlaid contour map of the Subaru image shows that the Subaru and HST detected the same object near the pulsar position. In the blown up image of the object in Fig. 1c the FOC contour map is additionally shifted with respect to the Subaru image by -0 $.\!\!^{\prime\prime}$014 in RA and 0 $.\!\!^{\prime\prime}$199 in Dec to compensate for the pulsar proper motion during the 6.75 yr interval between the HST and Subaru observations. Isophotes on the contour maps in Figs. 1b,c correspond to the levels (in counts) above the background $l_n=S+n\sigma$, where S is the mean sky value near the pulsar, $\sigma$ is the sky standard deviation related to one pixel, $n=1,2,3,\ldots,8$ and $1,3,5,\ldots,15$ for the Subaru and HST maps, respectively. The better agreement of the Subaru and HST source positions after the correction for the pulsar proper motion in Fig. 1c favours the object as the optical counterpart of PSR B0950+08.

We also note that, although the HST/FOC pulsar counterpart profile is point-like, the edges of its wings are slightly elongated E-W (Fig. 1c). The elongation directions in both the FOC and Subaru images coincide and are approximately orthogonal to the vector of the proper motion of the pulsar marked by the arrow in Fig. 1c. Such an orientation may suggest the association of the elongation with a faint torus-like structure of a possible compact pulsar nebula as detected around young Crab-like pulsars (e.g., Weisskopf et al. 2000). However, it may be also a projection of a faint extended background object at the pulsar position.

To summarize, our analysis shows that the HST and Subaru detected the same object. With the allowance for the pulsar proper motion, the offsets from the PSR B0950+08 radio positions at the HST and Subaru observational epochs are in the range (0 $.\!\!^{\prime\prime}$3-0 $.\!\!^{\prime\prime}$4), which are within $1.7\sigma$ error of the Subaru astrometrical referencing and negligible compared to our seeing of 0 $.\!\!^{\prime\prime}$7.

3.3 Photometry

Weather conditions were stable during our observations. We derived the atmospheric extinction coefficient in the B band k_B= 0 $.\!\!^{\rm m}$ $18 \pm 0.02$ from the variation of the count rates of four stars in the pulsar field with airmass during our observations (see Table 2). Insignificant decrease of the extinction, within 1-$\sigma$ level, was noticed from the beginning to the end of observations.

Photometric referencing was carried out using three defocused standard stars from the field PG1047 (Landolt 1992) with $V\sim13$, along with five fainter, $V\sim 21$, unsaturated secondary standard stars from the PSR B0656+14 field (Kurt et al. 1998) observed in the BRI bands the same night. The derived photometric zeropoint in the B band was $28.28\pm0.02$. The instrumental magnitudes of the detected optical source were measured for a range of aperture radii of (1-3) CCD pixels centered at the "+" in Fig. 1c. They were corrected for the PSF of bright stars (some details on the method we used can be found in Koptsevich et al. 2001). Within the measurement errors, the results for different apertures coincided and a 2 pixel radius was adopted as optimal. The magnitude of the detected optical source, $B=27.07\pm0.16$, corresponds to the absolute flux $F_{B}=(5.97\pm0.88)\times 10^{-31}$ erg cm^-2 s^-1 Hz^-1 or $0.0597 \pm 0.0088~\mu$Jy. The error includes statistical error of the instrumental magnitude measurements, the error of the zeropoint, and an allowance for possible atmospheric extinction variations.

Figure 2: Optical and X-ray observations of PSR B0950+08. Solid cross in the X-ray range corresponds to the mean flux in the E=(0.08-2.4) keV band derived from the BB spectral fit of the ROSAT data (Manning & Willmore 1994). Square-filled belt shows unabsorbed spectrum resulted from this fit. Dot-dashes outline the results of the PL fit of the same data with $\pm 1\sigma$ uncertainties. Stripe-filled belt shows unabsorbed BB fit of the HST/FOC data, and dashed cross shows corresponding mean flux as one would expect in the ROSAT band. The fits are extrapolated toward the X-ray and optical ranges, respectively, and their parameters are shown in the plot. The widths of the belts correspond to $\pm 1\sigma$ uncertainties of the fits. As seen, the optical emission is likely to be of nonthermal origin and apparently follows the extrapolation of the X-ray PL fit of the ROSAT data with a spectral index $\alpha _{\nu } \simeq 0.32$ close to the low boundary of $1\sigma$ uncertainty of the fit (see Sect. 4 for details).