/Received 2000 November 8; accepted 2000 November 28/
*ABSTRACT*
We present a catalog of pointing calibrators suitable
for offset pointing and for determining the pointing constants of
large radio telescopes. It contains 3399 strong, compact, and
unconfused radio sources with accurate (?_? cos ? ≈ ?_? ≈
0&farcs;5) positions from the NRAO Very Large Array Sky Survey (NVSS)
uniformly covering the sky north of J2000 ? = -40&j0; . The NVSS
images, restored with a &thetas; = 45?? FWHM Gaussian beam, were
also convolved to larger beam sizes &thetas; = 90?? , 180&arcsec;,
360&arcsec;, 540&arcsec;, and 720&arcsec;. The catalog lists the
maximum beam size &thetas;_/m/ for which each calibration source
remains unconfused and a single Gaussian fit yields an rms position
error ? ? &thetas;_/m/ /100. For all ? > -40&j0; , the average
angular distance to the nearest calibrator is only
&angl0;&phis;&angr0; ≈ 0.03 rad, so offset pointing from these
calibrators may reduce slowly varying pointing errors (caused by
incorrect values for the traditional pointing constants, gravitational
deformations, differential thermal expansion, refraction, etc.) by
factors up to &angl0;&phis;&angr0;-1 ≈ 30.
The National Radio Astronomy Observatory is a facility
of the National Science Foundation, operated under cooperative
agreement by Associated Universities, Inc.
*1. INTRODUCTION*
Pointing errors are often more important than surface
deformations in limiting the high-frequency performance of large
radio telescopes. Typically the rms pointing errors in the sky
coordinates (?, ?) are required to satisfy [(?_? cos ?)2 + (?_? )2
]1/2 ? &thetas;/10, where &thetas; is the full width between
half-maximum points of the telescope beam. For a large radio
telescope like the 100 m diameter Green Bank Telescope (GBT) operating
at ? ≈ 3 mm, the beamwidth is only about 7&arcsec; and the
desired pointing errors are less than 1&arcsec;. If the combined
errors in telescope geometry (errors in altitude /a/ and azimuth /A/)
and atmospheric refraction corrections are larger, they may be reduced
by offset pointing relative to nearby calibration sources. The GBT is
unique in that its geometry will ultimately be measured by laser
ranging stations and corrected continuously, but offset pointing will
remain the only way to measure the beam position on the sky and back
up the ranging system during unfavorable weather or equipment downtime.
Pointing constants determined from observations of a few
calibration sources can correct for repeatable pointing errors such as
setting errors. The nonrepeatable pointing errors of large telescopes
are frequently dominated by thermal strains (see Condon, Broderick, &
Seielstad 1989 <#rf3>), which vary slowly with both time (tens of
minutes) and angle (radians). Thus, simple pointing offsets ?/a/ and
?/A/ cos /a/ measured from cross scans on a nearby pointing
calibrator can reduce these and other slowly varying errors (e.g.,
beam shifts caused by changing atmospheric refraction or
gravitational deformations). Calibrators suitable for offset pointing
must be compact (source diameter &thetas;_/s/ < &thetas;),
unconfused, strong enough that their positions can be measured
quickly, and numerous enough that the mean angular distance to the
nearest calibrator is &angl0;&phis;&angr0; ≪ 1 rad. This last
requirement strongly favors the use of offset pointing calibrators on
telescopes with large diameter /D/. Since the number ? of sources per
steradian stronger than some minimum usable flux density /S/_/m/ is
roughly ? ? /S/ and noise sets /S/_/m/ ? /D/-2 , the sky density of
usable calibrators is proportional to /D/3 . We note that phase
calibrator catalogs for high-resolution interferometers like the Very
Large Array (VLA) are not optimum for large single-dish telescopes
for two reasons: (1) Some phase calibrators are contaminated by
extended emission that is resolved away by the interferometer but
visible with a filled aperture. If this extended emission is offset
from the compact radio core, the single-dish position will not agree
with the interferometer position. For example, the quasar 3C 273 is a
VLA phase calibrator whose one-sided jet disqualifies it as a
single-dish pointing calibrator. (2) Many sources suitable for large
single-dish telescopes do not appear in the phase calibrator catalogs
because they are confused by companions in the relatively large
interferometer primary beam or because they are partially resolved on
interferometer baselines longer than /D/.
This paper describes the construction of a catalog of single-dish
pointing calibrators (ý 2 <#sc2>) and presents the catalog itself in ý
3 <#sc3> and Table 1 <#tb1>.
<201051.tb1.html> TABLE 1 POINTING CALIBRATION SOURCES
*2. CATALOG CONSTRUCTION*
Offset pointing calibrators should be strong, compact, and
unconfused yet numerous enough that the nearest lies within &phis;
≪ 1 rad of any position on the sky covered by the catalog. To
quantify these requirements, we estimate the errors in positions
measured by orthogonal scans across a source made with a telescope
whose beam is Gaussian with FWHM &thetas;. Then
is the normalized beam pattern (Fig. 1 <#fg1>). The statistical weight
contributed by each part of the scan to the fitted position is
If the scan is truncated at offsets ?/x/, then the variance of the
fitted position is increased by the factor
Equations (2) <#df2> and (3) <#df3> are also plotted in Figure 1
<#fg1>. Offsets near /x/ = &thetas;/2 are most important for the fit,
and fits to scans truncated at /x/ = ?3&thetas;/4 yield position
errors only slightly larger than those from arbitrarily long scans,
where ? is the signal-to-noise ratio of the fit (Condon 1997 <#rf1>).
In practice, single-dish scans should extend as far as /x/ ≈
?3&thetas;/2 to allow for baseline gradients caused by spillover
radiation, receiver drift, and atmospheric emission. For large
telescopes like the GBT operating at short wavelengths, the rms noise
will be ≈1 mJy, small even for short (? ≈ 1 s) integration
times, and many thousands of extragalactic sources are strong enough
to act as calibrators at short wavelengths. At wavelengths longer
than ? ≈ 6 cm, confusion by background sources dominates receiver
noise, and only the strongest sources can be used. Fortunately,
offset pointing is rarely required when the beamwidth is large enough
that confusion is important.
<201051.fg1.html>
FIG. 1.?If a Gaussian beam (/dotted line/) of FWHM width &thetas; is
scanned across a point source, the contribution (/solid line/) to the
statistical weight of the position fit is greatest for offsets /x/
≈ &thetas;/2. If the scan is truncated only /x//&thetas;
beamwidths on either side of the source, the variance in the measured
position is multiplied by ?2 (/x//&thetas;)/?2 (?) (/dashed line/).
The primary mechanical errors in an altitude-azimuth telescope
(e.g., azimuth zero offset, gravitational bending error, vertical
collimation error) are sinusoidal functions of /a/ and /A/ (Stumpff
1972 <#rf7>), so an exact pointing correction at the position of a
calibration source offset by some angle &phis; will reduce their
contributions to the program-source pointing error by a factor
≈&phis;-1 , where &phis; is measured in radians. The probability
distribution of the angular distance &phis; to the nearest calibration
source from a random position north of ? = -40&j0; is
???
where ? = /N//? is the mean sky density in a catalog of /N/ sources
covering ? sr (Condon, Balonek, & Jauncey 1975 <#rf2>). The mean
angular distance is
Thus, ? ≫ 1 is essential for a catalog of offset pointing
calibrators.
Potential calibration sources were selected from the 1.4 GHz NRAO
VLA Sky Survey (NVSS; Condon et al. 1998 <#rf4>) catalog by the
criteria /S/ > 500 mJy, deconvolved source major axis &thetas;_/s/ <
20?? (98% confidence upper limit), and rms position uncertainties
[(?_? cos ?)2 + (?_? )2 ]1/2 < 1?? . Nearly all of the
candidates have ?_? cos ? = 0&farcs;45, ?_? = 0&farcs;56. Postage
stamp subimages centered on the candidate positions were extracted
from the 4&j0; ? 4&j0; NVSS images, all of which have &thetas; =
45?? FWHM resolution and are sensitive to smooth emission extended
up to several arcminutes.
We inspected the contour plot (see Fig. 2 <#fg2>) of each
subimage and rejected candidates having confusing sources nearer than
3&thetas; and stronger than 1% of the candidate peak flux density.
This requirement on confusion flux may seem overly conservative, but
it allows for the possibility that the confusing source has a much
flatter spectrum than the calibrator and may be relatively stronger
at frequencies much higher than 1.4 GHz. For example, the /D/ = 100
m GBT has a 45&arcsec; beamwidth at ? ≈ 17 GHz, and a 1%
flat-spectrum confusing source at 1.4 GHz might become a 10%
confusing source at 17 GHz.
<201051.fg2.html>
FIG. 2.? Sample contour plots of calibrator candidates. The left
column of three plots shows an accepted calibration source for
beamwidths as large as &thetas;_/m/ = 180?? . The candidate in the
top right plot is acceptable only at &thetas;_/m/ = 45?? because
the confusing source is offset by more than 3&thetas;_/m/ but is too
close at &thetas; = 90?? resolution (/middle right plot/). The bottom
right plot shows a rare case of an unresolved candidate embedded in
an extended source. It was rejected only because of the extended
emission, which shifts the fit for a single Gaussian to the west; the
eastern confusing source is fainter than 1% of its peak flux density.
Contours are at ?1 mJy beam-1 ? 1, 2, 4, 8, &ldots;.
A single elliptical Gaussian was fitted to each unconfused
candidate over a square always extending ?2&thetas; from the source
position. Fitting such long baselines is unnecessary on VLA images but
conservatively simulates the linear baselines, which must be
subtracted to remove gradients from single-dish scans. We required
that the fitted major axis and minor axis be within the range 45?? ?
1?? , corresponding to a deconvolved source size &thetas;_/s/ ? 10??
. Thus, the calibrators should be nearly unresolved by beams as small
as &thetas; ≈ 20?? . For beams significantly smaller than that,
the calibrator may be resolved, particularly if it does not have a
flat radio spectrum between 1.4 and 5 GHz. Also, at frequencies much
higher than 1.4 GHz, the centroid position of a source like 3C 273,
with a flat-spectrum core and a one-sided steep-spectrum jet, may
shift by a fraction of its angular size. Finally, if the angular
separation between the fitted position and the NVSS catalog position
exceeded 0&farcs;5, the candidate was rejected. This ensures that
both confusion and extended emission from the candidate do not shift
the position determined by fitting a single Gaussian to the source. A
few candidates appeared in the VLA calibrator list at positions
offset by more than 2&arcsec; from their NVSS positions; they were
eliminated. The 3399 candidates passing all of these tests were
deemed to be suitable calibrators for single-dish observations with
beamwidths up to 45&arcsec;.
Next, the subimages containing the surviving calibration sources
were convolved to &thetas; = 90?? resolution and subjected to the
confusion test above. Also the fitted Gaussian sizes had to be 90??
? 2?? and the fitted positions less than 0&farcs;7 from the NVSS
positions. Since the NVSS is sensitive to sources up to several
arcminutes in size, this ensures that any possible extended emission
does not displace the position measured with the larger beam by more
than &thetas;/100. Like our requirement on confusion flux, the
&thetas;/100 requirement may seem overly conservative, but it allows
for the possibility that the centroid position of a slightly extended
source may vary with observing frequency. The 2514 calibrators
passing these tests were classified as acceptable for beams up to
90&arcsec;, and their postage stamp images were convolved to &thetas;
= 180?? resolution. The relative flux criterion for confusing sources
was relaxed to 2%, but the 3&thetas; separation requirement was kept.
The size and offset criteria were 180?? ? 4?? and less than
1&farcs;5, respectively, leaving 1918 sources. Only those with /S/ >
1 Jy were tested at &thetas; = 360?? resolution. The criteria were
less than 4% confusion flux, 360?? ? 8?? sizes, and less than
3&farcs;4 offsets; 523 remained. At &thetas; = 540?? , the size
range was 540?? ? 12?? and the allowed offsets were less than
5&farcs;3; 222 sources passed. Finally, there are 68 calibration
sources at &thetas; = 720?? resolution with sizes 740?? ? 16?? and
offsets less than 7&farcs;1.
The sky distribution of the calibrators is shown in Figure 3
<#fg3>; it is essentially uniform north of ? = -40&j0; . For our
catalog of /N/ = 3399 calibrators covering ? = 10.3 sr,
&angl0;&phis;&angr0; ≈ 0.028 rad ≈ 1&fdg;6. Thus, offset
pointing errors for observations made with &thetas; ? 45?? may be up
to 30 times smaller than absolute pointing errors. For &thetas;_/m/ =
90?? , 180&arcsec;, 360&arcsec;, 540&arcsec;, and 720&arcsec;, only
/N/ = 2514, 1918, 523, 222, and 68 calibrators, respectively, are
available. The corresponding mean offsets are &angl0;&phis;&angr0;
≈ 0.032, 0.037, 0.07, 0.11, and 0.19 rad.
<201051.fg3.html>
FIG. 3.?Sky distribution of single-dish pointing calibrators. Different
symbols indicate the largest beamwidth &thetas; for which each
calibrator is appropriate.
*3. THE CATALOG*
The catalog (see Table 1 <#tb1>) contains /N/ = 3399 pointing
calibrators which have rms position uncertainties ?_? cos ? ≈ ?_?
≈ 0&farcs;5 and should not be significantly resolved by beams as
narrow as &thetas; = 20?? . Subsets of the catalog should yield
?&thetas;/100 errors on cross scans made with beams &thetas; > 45?? .
A portion is shown here for guidance regarding its form and content.
For each source, the catalog gives the J2000 right ascension and
declination from the NVSS, the largest FWHM beam &thetas;_/m/ (in
arcseconds) for which the calibrator is suitable, the 1.4 GHz NVSS
flux density (in janskys), and the ? ≈ 5 GHz flux density (in
janskys), usually from the S5 (K?hr et al. 1981 <#rf6>), GB6 (Gregory
et al. 1996 <#rf5>), or Parkes-MIT-NRAO (Wright et al. 1996 <#rf8>
and references therein) catalogs. These 5 GHz flux densities are
already ≈10 yr old, so the listed values are no longer accurate
for variable sources. Nonetheless, those sources with apparent
spectral indices ?(1.4, 5) ? -? log /S//? log ? < 0.5 are probably
quite compact, being either variable or synchrotron self-absorbed, and
they should be good offset pointing calibrators even for observations
made with beamwidths &thetas; < 20?? . The steep-spectrum sources
may be extended up to 10&arcsec; FWHM, and their positions at
frequencies much higher than 1.4 GHz may be displaced slightly if
they contain flat-spectrum cores and one-sided steep-spectrum jets.
*REFERENCES*
* Condon, J. J. 1997, PASP, 109, 166 First citation in article
<#crf1> | NASA ADS
* Condon, J. J., Balonek, T. J., & Jauncey, D. L. 1975, AJ, 80, 887
First citation in article <#crf2> | NASA ADS
* Condon, J. J., Broderick, J. J., & Seielstad, G. A. 1989, AJ, 97,
1064 First citation in article <#crf3> | NASA ADS
* Condon, J. J., Cotton, W. D., Greisen, E. W., Yin, Q. F., Perley,
R. A., Taylor, G. B., & Broderick, J. J. 1998, AJ, 115, 1693 First
citation in article <#crf4> | Full Text
| NASA ADS
* Gregory, P. C., Scott, W. K., Douglas, K., & Condon, J. J. 1996,
ApJS, 103, 427 First citation in article <#crf5> | NASA ADS
* K?hr, H., Witzel, A., Pauliny-Toth, I. I. K., & Nauber, U. 1981,
A&AS, 45, 367 First citation in article <#crf6> | NASA ADS
* Stumpff, P. 1972, Kleinheubacher Berichte, 15, 431 First citation
in article <#crf7>
* Wright, A. E., Griffith, M. R., Hunt, A. J., Troup, E., Burke, B.
F., & Ekers, R. D. 1996, ApJS, 103, 145 First citation in article
<#crf8> | NASA ADS