2 Observations and data reduction

 

The field of PSR J0030+0451 was observed in service mode on July 26 and August 13, 2001, with the FOcal Reducer/low dispersion Spectrograph (FORS2) on the ESO/VLT/UT2 telescope, with a pixel scale of 0 $.\!\!^{\prime\prime}$2. We used Bessel filters for B and V, and an ESO special filter for R ( $R_{\rm special}$, henceforth called $R_{\rm s}$). Unfortunately, some of the V images were corrupted by bad CCD columns near the expected position of the pulsar and were not used in the analysis. The images we used are listed in Table 2.

Bias subtraction and flatfielding were performed in a standard way, and the reduced individual images were aligned using a set of bright, non-saturated field stars. Standard utilities from the NOAO IRAF package were then used to combine the images applying the averaged sigma clipping algorithm avsigclip with the scale parameter equal to none. The pulsar vicinity is shown for B, V and $R_{\rm s}$ bands in Fig. 1.

 

 

Table 2: Log of VLT observations of PSR J0030+0451 in the $BVR_{\rm s}$ bands. Exposure time is 720 s for all frames.

No.	Date	Band	Time	Airmass	Seeing
	UT		UT		arcsec
1	26.07.01	B	09:40	1.172	0.6
2			09:53	1.188	0.5
3	13.08.01	B	04:55	1.579	1.1
4			05:09	1.495	1.1
5			06:34	1.208	0.8
6			07:56	1.150	0.7
7			08:09	1.155	0.9
8		V	05:38	1.358	0.7
9			05:52	1.311	0.8
10			06:06	1.269	0.8
11			07:14	1.159	0.7
12			07:28	1.151	0.6
13			07:42	1.149	0.7
14		$R_{\rm s}$	06:47	1.187	0.7
15			08:24	1.167	0.7
16			08:37	1.181	0.7
17			08:53	1.205	0.7
18			09:07	1.230	0.7

Figure 1: Left panel: $1\hbox {$^\prime $ }\times 1\hbox {$^\prime $ }$ overview of the PSR J0030+0451 field extracted from the $6\farcm8\times6\farcm8$ frame of the VLT/FORS2 image in the $R_{\rm s}$ band. The central box is blown-up in the smaller panels. A nearby bright USNO star (object 1) and two other stellar objects (2 and 5 from Table 3) are marked. Smaller panels: $8\hbox {$^{\prime \prime }$ }\times 8\hbox {$^{\prime \prime }$ }$ pulsar vicinity in the $BVR_{\rm s}$ bands. $3\sigma$ uncertainty ellipses of the expected pulsar position at the epoch of the VLT observations are marked. No pulsar is detected in these frames. Two objects are marked "5'' (referring to Table 3) and "6'' in the $R_{\rm s}$ image, and are discussed in the text.

 

 

Table 3: Magnitudes of several stars in the PSR J0030+0451 field with coordinates and offsets from the pulsar position shown in the table. Stars 1, 2 and 5 are marked within the left frame in Fig. 1, while 3 and 4 are outside this frame.

No.	$\alpha_{2000}$	$\delta_{2000}$	Offset	B	V	$R_{\rm s}$
1	00:30:27.83	+04:51:35.2	$\ \ \ \$7 $.\!\!^{\prime\prime}$5	19.20$\pm$0.01	-	-
2	00:30:29.25	+04:51:18.3	$\ \ ~$34 $.\!\!^{\prime\prime}$6	22.32$\pm$0.02	20.92$\pm$0.01	20.27$\pm$0.01
3	00:30:39.33	+04:53:15.4	3$^\prime$21 $.\!\!^{\prime\prime}$9	23.77$\pm$0.06	22.08$\pm$0.01	21.29$\pm$0.01
4	00:30:25.39	+04:53:14.2	1$^\prime$39 $.\!\!^{\prime\prime}$3	24.15$\pm$0.07	22.40$\pm$0.02	21.78$\pm$0.01
5	00:30:27.32	+04:51:36.9	$\ \ \ \;$3 $.\!\!^{\prime\prime}$2	23.82$\pm$0.05	23.69$\pm$0.06	23.63$\pm$0.06
PSR	00:30:27.43	+04:51:39.67	$\ \ \ \ \ \ ~-$	$\ge$27.3	$\ge$27.0	$\ge$27.0

The radio position of PSR J0030+0451 at the epoch of the VLT observations (for which 13.08.01 was adopted, see Table 1) was determined using recent radio ephemerides (A. Lommen 2001, private communication for additional Arecibo observations). Astrometrical referencing of our images was made with IRAF tasks ccmap/cctran using the positions of several dozens of reference stars from the USNO A-2.0 catalogue seen in the images and optimizing the astrometrical fit by removing step by step the reference stars with the largest residuals. For the 5 most suitable stars we finally got 1$\sigma$ rms-errors of 0 $.\!\!^{\prime\prime}$05 and 0 $.\!\!^{\prime\prime}$11, and maximum residuals of 0 $.\!\!^{\prime\prime}$20 and 0 $.\!\!^{\prime\prime}$24, in RA and Dec, respectively. Combining the rms-errors with the nominal USNO accuracy of 0 $.\!\!^{\prime\prime}$24 and radio ephemeris uncertainties, we obtained the 3$\sigma$ pulsar VLT/FORS position uncertainties 0 $.\!\!^{\prime\prime}$79 and 0 $.\!\!^{\prime\prime}$88 in RA and Dec, respectively. The resulting 3$\sigma$ error ellipse is marked in the smaller images in Fig. 1. No reliable counterpart candidate was detected within, or close to the error ellipse of the expected pulsar position. We also double-checked the astrometry with 5 stars from the GSC-II catalog. The obtained rms errors were 0 $.\!\!^{\prime\prime}$05 and 0 $.\!\!^{\prime\prime}$11 in RA and Dec, respectively, and the expected pulsar position was moved 0 $.\!\!^{\prime\prime}$06 west and 0 $.\!\!^{\prime\prime}$14 north in respect to the USNO position. However, since the main source of errors is the catalog uncertainty, we accept the USNO results as more conservative estimate.

For the photometric calibrations we used the photometric standards from the PG1323-085 and SA109 fields (Landolt 1992), observed at the second night of our observations, and average Paranal extinction coefficients. We then derived $3\sigma$ detection limits as $m=-2.5\log\left(3\sigma\sqrt{A}/T_{\rm exp}\right)+m_0$, where $\sigma$ is the standard deviation of the flux in counts per pixel, $T_{\rm exp}$ is the exposure time, A is the area of an aperture (in pix²) with a radius of 1 $\hbox{$^{\prime\prime}$ }$ (corresponding to $\sim$83% of the flux in a PSF of our images), and m₀ is the photometric zeropoint, including corrections for atmospheric extinction. The limits are: B = 27.3, V = 27.0, and $R_{\rm s} = 27.0$.

In Table 3 we list $BVR_{\rm s}$ magnitudes for several of the objects in the PSR J0030+0451 field. Object 1 is the USNO star U0900_00118426 marked in the left panel of Fig. 1. It is oversaturated in our V and $R_{\rm s}$ images. Object 5 is the source seen at the bottom right of the blown-up images in Fig. 1. This is the closest object to the radio position of the pulsar clearly detected in all our images. Although it is too blue to be a normal star, it cannot be considered a pulsar counterpart candidate because of the large offset (3 $.\!\!^{\prime\prime}$4) from the radio position, provided the radio astrometry is as accurate as claimed by Lommen et al. (2000). Like most other blue objects in the field at this magnitude level (we found at least five objects roughly of the same color), it is most likely extragalactic, and similar to blue objects found in the HDF images. The object marked "6'' in the upper right of the $R_{\rm s}$ image in Fig. 1, is only marginally detected at $R_{\rm s}=27.45\pm 0.61$. It is not detected in the other bands and may well be an artefact of the reductions. It is also too far (3 $.\!\!^{\prime\prime}$1) from the radio pulsar position to be an optical counterpart candidate.