Astron. Astrophys. 338, 200-208 (1998)

2. Observations and reduction

2.1. The observations

The HI synthesis measurements were obtained with the Westerbork Synthesis Radio Telescope (WSRT); this instrument consists of 10 fixed and 4 movable parabolic dishes of 25 metres diameter, together spanning a baseline of 2.8 km. A integration produces a map of a field as large as the primary beam (FWHM of ). In such a map each source produces grating responses in form of ellipses, with diameters of in right ascension and in declination, and multiples thereof. Doubling the integration time, with the movable telescopes moved to different positions, results in doubling of the diameters of the grating responses. We used integrations; therefore the smallest grating responses had radii of and in and , respectively. This can cause confusion problems for extended objects; see Sect. 3.2.

Another shortcoming of synthesis observations in general is the lack of short-spacing information; the shortest spacing available to us was 36 meters. As a result, very large structures (e.g. a constant background across the primary beam) are not detectable.

The parameters of our observations are summarized in Table 1.

Table 1. Observational parameters of WSRT HI obervations of HVC 100-7+100 and HVC 347+35-112

2.2. Calibration of the data

The data were calibrated by observing standard point sources, before and after each integration, for 30 minutes on each of two frequencies, shifted 2 MHz (i.e., 422 km s^-1) on either side from the central frequency used on the HVC field. The shift is necessary to avoid Galactic absorption effects in the calibrator observations.

From the observations of the calibrators we derived gain and phase corrections, making use of "redundancy" (Wieringa 1992), and moreover using the self-cal method (Noordam & de Bruyn 1982). The averages of gains and phase corrections from all four calibration observations were applied to the data, for each velocity.

2.3. Additional smoothing

Since the signals were very weak, we used only baselines up to 1440 meters, giving basic angular resolutions of by . In order to improve the signal/noise ratio, we performed additional smoothing in right ascension and declination, resulting in synthesized beams as given in Table 1. Also, we performed box smoothing in velocity over seven channels, resulting in a velocity resolution of 7.6 km s^-1.

2.4. Cleaning of the maps

The grating responses at distance (Sect. 2.1) can result in confusion problems for extended structures. The first object, HVC 100-7+100, turned out to be so small that the grating responses cause no problems, although the missing short spacings can still distort our observations. However, for HVC 347+35-112 the grating responses give serious problems. Moreover, since this object is at negative declination, only part of the required hour-angle coverage could be obtained. This results in a synthesized antenna beam (or point spread function) with strong (positive or negative) side-lobes, as shown in the first panel of Fig. 4. Striking are the butterfly-like near side-lobes and the x-shaped "spokes" at greater angular distance.

The method CLEAN (Högbom 1974, Schwarz 1978) was used to remove side-lobe effects as much as possible. For HVC 100-7+100 cleaning is straightforward; but for HVC 347+35-112, where the u v plane is not fully sampled, cleaning can give ambiguous results. In order to set additional constraints, we chose two regions (see Fig. 1) where cleaning was allowed to put -functions.

Fig. 1. Example of cleaning. The grating ring responses at a distance indicated by the horizontal arrow can give ambiguities. CLEAN can further have problems with the strong negative sidelobes (30%); in order to avoid such problems, two boxes around the strongest two positive features were defined, in which searching by CLEAN was allowed.

The cleaned channel maps for the appropriate velocities are displayed in Figs. 2 and  4 for the two objects. The first two panels give the synthesized antenna-pattern and the continuum map, respectively; the third panel shows the distribution of HI column density in the HVC (Sect. 2.5).

Fig. 2. Maps of HVC 100-7+100. The top-left panel shows the synthesized beam, with maximum 1. The top-middle panel shows the continuum; the two background sources have fluxes of 155 and 100 mJy, respectively. The top-right panel gives the HI column densities (or "total hydrogen"); contour values, in units of  atoms cm-2, are -0.66, -0.33, (dashed), , , , , . The remaining panels show monochromatic brightness distributions, at velocities spaced by 4.13 km s-1 from to  km s-1, as given in the top-left corner of each panel; brightness temperatures are shown in gray-scale, identified by scale-bar at top-right, and by contours, with values 0.038 K (dashed), 0.051 K, 0.077 K, 0.102 K, 0.128 K and 0.140 K (dashed). Velocity resolution: 7.6 km s-1; angular resolution: (FWHM), shown by hatched ellipse in continuum panel. The position of the star 4 Lac is marked by an asterisk.

2.5. Total HI

The HI column density (sometimes called "total HI") in the HVC was derived by adding those parts of the CLEANed data cube which show significant radiation (above 3); for this a 3-D CLEAN was used, with a 3-D Gaussian restoration beam. The intensities given in mJy beam^-1 were scaled into brightness temperatures [K] using:

where c: velocity of light, k: Boltzmann's constant, : frequency of observation, : frequency of 21-cm line, : flux density per synthesized beam, : beam solid angle, and : FWHM of synthesized clean beam (assumed to be Gaussian) in right ascension and declination. The values and are listed in Table 1. The column density is then:

The resulting maps are shown in the top-right panels of Figs 2 and 4. The maps are based on the WSRT observations only, and are not corrected for the missing short spacings, nor for the sensitivity differences in the primary beam. These corrections are applied in the later stages of the reduction: Sects. 2.6and  2.7.

2.6. 21-cm line spectra

From the 3-D cleaned data cube we have determined HI-line spectra for specific areas of sky, by plotting the brightness temperatures averaged over such areas as a function of radial velocity. In Fig. 3a and b we consider the following spectra, all calculated for the position of the star 4 Lac:

1. The spectrum measured at Westerbork, within the synthesized beam resulting from the smoothing operations described above (and corrected for the sensitivity differences within this synthesized beam).

2. The spectrum measured with the 76-meter single dish at Jodrell Bank (beam: FWHM = 12 arcmin) by Bates et al. (1991).

3. The Westerbork spectrum averaged over the Jodrell Bank beam (assumed to be Gaussian, with 12 arcmin FWHM).

4. A combination: Spectrum 1 + Spectrum 2 - Spectrum 3, as discussed in Sect. 2.7.

Since a synthesis telescope is insensitive to extended sources of radiation, an averaged Westerbork spectrum may contain less flux than the corresponding single-dish spectrum (see Sect. 3.1).

Fig. 3a and b. HI spectra of HVC 100-7+100 at the position of the star 4 Lac (see also text of Sect. 2.6and Sect. 2.7). a  Spectrum 3: WSRT data, averaged over Jodrell Bank beam (12 arcmin FWHM). Spectrum 2: Jodrell Bank spectrum (Bates et al., 1991). b  Spectrum 1: WSRT data, smoothed to a resolution of  arcmin. Spectrum 4: Best estimate of spectrum at star position, obtained as Spectrum 1 + Spectrum 2 - Spectrum 3.

2.7. Estimate of the column density at the position of the star

The column densities given by Eq. 2had to be corrected for the primary beam (Sect. 2.6) and for the effects of the missing short spacings. The usual method for the latter correction is to process a series of single-dish maps (obtained from a raster of spectra around the field centre of the synthesis map), in order to extract the missing u v-data (zero spacing and short spacings). This method requires a considerable amount of single-dish data, and moreover has some fundamental drawbacks (Schwarz & Wakker 1991). Since we were interested mainly in at the star's position, , we could use a simpler approach, described by Schwarz et al. (1995). In short this method consists of observing the HI spectrum at the position of the star with a large single-dish telescope (Spectrum 2 in Sect. 2.6); then subtracting from this the spectrum of the fine-structure, found from the synthesis observations and smoothed with the single-dish beam (Spectrum 3); and finally adding the unsmoothed synthesis spectrum (Spectrum 1). The resulting Spectrum 4 ( Sp. 1 + Sp. 2 -Sp. 3) is a good approximation of the true spectrum at the star's position.

2.8. Derived physical parameters

If the distance D is known, the mass of atomic hydrogen in the object can be derived from the column-density (or "total hydrogen") map:

where is the mass of the hydrogen atom, and is the column density at position i in units of .

The density can be derived if we can make an estimate of the line-of-sight dimension of the cloud, L. The usual assumption is made that L is similar to the smallest dimension of the cloud across the sky, ; this assumption holds for spheres and for filamentary objects, but not for "pancakes". Then:

© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998
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