2001PASP..113..362C PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, *113:* 362-365, 2001 March ? 2001. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. ------------------------------------------------------------------------ *Offset^ Pointing^ Calibrators^ for^ Large^ Radio^ Telescopes*^ J. J. CONDON^ AND^ Q. F. YIN National^ Radio^ Astronomy^ Observatory,^1 <#fn1>^ 520^ Edgemont^ Road,^ Charlottesville,^ VA^ 22903;^ jcondon@nrao.edu ,^ qyin@nrao.edu ^ /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. ^ ^1 <#cfn1> 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 ------------------------------------------------------------------------