Historical Summary of Flux Calibration Sources

TIP Last Update: JeffMangum - 03 April 2013


Contents


TIP The information on this page dates from pre-2010 when we were trying to figure out which potential flux calibration sources would be worth investigating. Some of this information is a bit dated, but kept for historical context.

Planets

Many planets are resolved in interferometer measurements. Most measured planetary fluxes are derived by referencing to flux measurements of Mars, whose flux can be model-predicted to about the 10% level. Some effects which limit the reliability of a Mars-determined flux calibration, and which are not taken account of in models which predict the Martian flux, are dust storms, illumination phase effects, and the influence of the polar caps.

The prospects for using planets as flux calibration standards has improved recently with the publication of the seven-year absolute calibration analysis of the WMAP observations of Jupiter, Saturn, Mars, Uranus, and Neptune by Weiland et. al. (2010). By absolutely calibrating against the CMB monopole, the WMAP team has derived the following results:
  • Jupiter:
    • Disk-integrated brightness temperature uncertainties < 1%.
    • Variability about mean temperature of < 0.4+-0.2 %.
    • No detected polarized emission at any band.
    • Note that synchrotron emission might be measurable (at a small level) up to 40 GHz. Literature estimates of synchrotron component at 23 GHz are about 1% of total flux at that frequency.
  • Mars:
    • Disk-integrated brightness temperature uncertainties <= 3%.
    • Compare results to Wright (1976) model, as WMAP measurements represent average over many weeks of measurements.
    • Find that they needed to scale Wright model predictions by 0.936 to match overall WMAP measurements at W-band.
    • Note 5+-2 % decrease in surface emissivity as a function of frequency over the 20 to 100 GHz WMAP observing range. Wright model does not predict such a change in emissivity with frequency.
    • Compared to DIRBE measurements with reasonable agreement.
    • Wright model, scaled, can reproduce W- through K-band WMAP observations by 0.5% to 2%.
  • Saturn:
    • Disk-integrated brightness temperature uncertainties <= 3%.
    • Fit disk plus rings model to measurements.
    • Model reproduces observed brightness temperatures to about 3%.
  • Uranus:
    • Disk-integrated brightness temperature uncertainties are 3% at W-band and 7% at K- and Ka-band.
    • Long-term (over 66 years of observations) changes in the whole-disk temperature have already been noted in the literature.
    • Long-term changes correlate with changing viewing aspect angle of the south pole.
    • No variability with time noted in the WMAP measurements.
    • Note that there is a "dip" in the WMAP Ka-band measurements compared to neighboring frequencies (not previously noted). No explanation for this dip is given, though atmospheric absorption is ventured as a guess.
    • Find good agreement with past measurements.
  • Neptune:
    • Due to signal-to-noise limitations disk-integrated brightness temperature uncertainties are > 5%
    • Past measurements suggest that whole-disk temperature is stable to within 8% over the past 20 years.
    • No variability with time noted in the WMAP measurements.
    • Find good agreement with past measurements.
  • Celestial Sources:
    • Measured a list of 5 celestial sources of various types:
      • Cas A
      • Cyg A
      • Tau A (Crab Nebula)
      • 3C58
      • 3C274 (Virgo A)
    • Typical Stokes I fluxes are good to 1-3%.
    • Measure frequency-dependent decrease in Cas A and Tau A (both SNRs) fluxes of 0.53% and 0.22% per year, respectively. This measured decrease is consistent with previous determinations.
    • For 3C274 there is a measured year-to-year variation of about 2% in K, Ka, and Q-bands.

-- JeffMangum - 2010-08-09

Asteroids and TNOs

Asteroids are also compact and bright blackbody emitters that may be used as primary flux calibrators. The bolometer observations at 250 GHz of 15 nearby asteroids (heliocentric distance r = 2.0-3.5 au, geocentric distances \Delta = 1-5 AU) by Altenhoff et al. (1994) found strong continuum emission (50-1200 mJy; TB = 150-200 K), which agrees with the blackbody model within the uncertainty of calibration on Mars. They are compact, \theta_D (arcsec)=0.28~[D/(200km)][ r (pc)]^{-1} -- an order of magnitude smaller than Uranus or Neptune. Their flux density changes significantly due to thier and Earth's orbital motion around the Sun, but the changes are highly predictable. Because they are not perfectly round, small oscillation in observed flux is also expected from rotation, which is about 4% peak to peak over 9 hour period in the case of the largest asteroid Ceres (Altenhoff et al. 1996).

Sizes and Albedos of TNOs

(The following is from Cruikshank etal. (2006) PPIV, "Physical Properties of TNOs")

Measurements of thermal emission can also be used to also constrain the sizes, and thereby albedos, of unresolved targets. Tedesco et al. (2002) used Infrared Astronomical Satellite (IRAS) thermal detections of asteroids to build a catalog of albedos and diameters. IRAS also detected thermal emission from the Centaur object Chiron and the Pluto-Charon system, and those data were used to determine albedos and sizes for those objects (Sykes et al., 1987, 1991, 1999). Advances in the sensitivity of far-IR and sub-mm observatories have recently allowed the detection of thermal emission from a small sample of TNOs, providing the first meaningful constraints on their sizes and albedos (e.g., Jewitt etLellouch et al., 2002; Altenhoff et al., 2004).

The Radiometric Method

The radiometric method for determining albedos and sizes typically utilizes measurements of both the visible and thermal-IR brightness of an object. The visible brightness is proportional to the product of an object’s visible geometric albedo, pV, and cross-sectional area, pi*r2, while the thermal brightness depends on the bolometric albedo, A (which determines the temperature), and the cross-sectional area. Given knowledge or an assumption for the phase integral, q, (A = q pV), measurements of the visible and thermal brightness can in principle be combined to solve directly for both the size of the object and its albedo.

Radiometric detections of TNOs have been made using the Infrared Space Observatory (ISO), the James Clerk Maxwell Telescope (JCMT) in Hawaii, the 30-m IRAM sub-mm telescope in Spain, and the Spitzer Space Telescope. Thomas et al. (2000) reported the first thermal detection of a TNO (excepting Pluto/Charon) based on ISO observations at a wavelength of 90 micron. Altenhoff et al. (2004) report sub-millimeter measurements or limits for six TNOs, and review the observations of Varuna (Jewitt et al., 2001; Lellouch et al., 2002) and 2002 AW197 (Margot et al., 2004). The IRAM sub-mm data were all taken at a wavelength of 1.2 mm. Grundy et al. (2005) also reanalyzed the sub-millimeter data from all four of those studies using a consistent thermal-modeling approach. Cruikshank et al. (2005b) and Stansberry et al. (2005, 2006) have reported Spitzer observations of six TNOs at wavelengths of 24 and 70 micron.

The Thermal Method

Just as direct radiometric observations yield information on the sizes and albedos of outer Solar System bodies, spectra in the thermal region (described in section 4) can be similarly used. The emissivity spectra shown in section 4 were created by dividing the measured spectral energy distribution (SED) by a model of the thermal continuum. An estimate of the size and albedo of a body can be obtained by allowing the radius and albedo to vary in the model in order to find the best thermal continuum fit to the SED, just as was done with the Spitzer MIPS radiometry, but with a different data set. The absolute calibration of IRS has an uncertainty of ~20%, which propagates to uncertainties of ~5% in the size estimate (see Emery et al., 2006 for further discussion). The derived effective radii and albedos using the Standard Thermal Model (STM) are listed in Table 4; close agreement with the MIPS radiometry is found in most cases.

Ultracompact HII Regions

Ultracompact HII regions may also be useful at low frequencies, but extended dust distribution is a serious problem at high frequencies.

Main Sequence Stars

An alternate primary flux calibrator for ALMA might be main sequence stars. The photospheric emission from many nearby main sequence stars should be detectable in the continuum at millimeter and submillimeter wavelengths. For example, the Sun at a distance of 10 pc is about 1 mas in diameter and will have about 1.3 mJy of flux at 650 GHz. Active regions on the Sun will cause some flux variations, perhaps at the few percent level or less. The zodiacal dust in the solar system may be at the level of ~1 percent or more, depending on how much cool dust resides in the outer parts of the solar system. Predicting the precise flux (likely to be somewhat higher because of the higher effective temperature at mm wavelengths) will require fairly detailed models of stellar atmospheres.

By searching the HIPPARCOS data set, Richard Simon has found that there are ~250 stars which will be brighter than 2 mJy at 650 GHz. Of these, he finds that the number of non-variable, non-binary, unresolved on a 3 km baseline main-sequence stars visible from Chajnantor is much smaller -- ~22 stars, listed in Table 1. There are probably other suitable stars which are not listed as main sequence. The integration times needed to achieve SNR=20 are computed assuming an rms noise of 0.50 X t(min)^{-1/2} mJy, which is the sensitivity for a 40 X 10-m array (corrected for the collecting area from the sensitivity calculation for a 40 X 8-m array by Holdaway 1997a).

Table 1: Candidate main sequence stars for primary flux calibration
Catalog No. Name RA(1950) Dec(1950) Parallax V Spec Type Teff Diam. S(650) tintSorted ascending
(arcsec) (mag) (K) (mas) (mJy) (min)
113368 24Alp PsA 343.73 -29.89 0.130 1.17 A3 8720 2.24 11.8 0.8
7588 Alp Eri 23.97 -57.49 0.023 0.45 B3 18700 1.53 7.9 1.6
8102 52Tau Cet 25.42 -16.19 0.274 3.49 G8 5570 2.09 5.1 3.8
49669 32Alp Leo 151.43 12.21 0.042 1.36 B7 13000 1.36 5.0 4.0
108870 Epslnd 329.97 -57.02 0.276 4.69 K5 4350 2.29 4.9 4.2
66459   203.81 35.97 0.092 9.06 M9 2500 5.28 4.3 5.4
22449 1Pi 30ri 71. 79 6.88 0.125 3.19 F6 6360 1.64 4.2 5.7
9236 Alp Hyi 29.31 -61.81 0.046 2.86 FO 7200 1.45 4.0 6.3
54872 68Del Leo 167.87 20.80 0.057 2.56 A4 8460 1.25 3.5 8.2
8903 6Bet Ari 27.97 20.56 0.055 2.64 A5 8200 1.27 3.5 8.2
57757 5Bet Vir 177.03 2.05 0.092 3.59 F8 6200 1.45 3.2 9.8
71908 Alp Cir 219.60 -64.76 0.061 3.18 F1 7045 1.32 3.1 10.4
84143 Eta Sea 257.14 -43.18 0.046 3.32 F3 6740 1.36 3.1 10.4
19849 400mi2Eri 63.22 -7.77 0.198 4.43 K1 5080 1.61 3.1 10.4
27072 13Gam Lep 85.59 -22.47 0.111 3.59 F7 6280 1.40 3.0 11.1
65109 lot Cen 199.44 -36.45 0.056 2.75 A2 8970 1.04 2.6 14.8
15510 49.53 -43.25 0.165 4.26 G8 5570 1.47 2.5 16.0
109176 24lot Peg 331.18 25.10 0.085 3.77 F5 6440 1.22 2.4 17.4
78072 41Gam Ser 238.54 15.81 0.090 3.85 F6 6360 1.21 2.3 18.9
69701 99lot Vir 213.35 -5.77 0.047 4.07 F7 6280 1.13 2.0 25.0
64394 43Bet Com 197.38 28.14 0.109 4.23 GO 6030 1.15 1.9 27.7
28103 16Eta Lep 88.53 -14.17 0.066 3.71 F1 7045 1.03 1.9 27.7


Giant and Supergiant Stars

Main sequence stars are small in angular size, but may be too weak (the brightest are of order a few mJy at 650 GHz) to be considered as viable primary or secondary calibrators. Giant and supergiant stars, however, although cooler, are much larger and hence brighter. The brighter ones have flux density on the order of 10s of mJy at 650 GHz (and scale as \lambda^{-2}). Their sizes are typically a few masec.

Extrapolation of the infrared emission from the photosphere of K-M giants that are already established as mid-infrared (MIR) absolute calibration stars is the most promising set of potential standards to investigate. As the millimeter fluxes from these giant stars cannot be below the Rayleigh-Jeans (RJ) extrapolation of their MIR emission, a simple test places a giant star in either the flux calibration standard category or in the science target category:
  • If a cool giant is observed to have the expected RJ emission at 3mm and beyond then it becomes a millimeter/submillimeter standard.
  • If a cool giant‘s 3mm and longer flux significantly exceeds the RJ prediction then it becomes a science target, potentially with a submillimeter- or millimeter-active chromosphere.

K-M Giants as Mid-Infrared Flux Standards

Martin Cohen (UCB) and collaborators have developed an all-sky network of over 615 of these MIR absolute standards. Each is represented by a complete, continuous spectrum between 1 and 35 microns. The procedure for creating these spectra has been absolutely validated by the MSX mission (Midcourse Space eXperiment). MSX made direct, on-orbit comparisons of the fluxes of the bright archetypes of these stars with absolutely characterized "emission reference spheres”. MSX validated the brightness of tens of fainter cool giants selected from the catalog of 615 K-M giants. Every MIR calibrator also has a known radiometric diameter so that a requirement by ALMA for standards with diameters smaller than some specified size can be applied. The entire network of K-M giants has also recently been observed photometrically by AKARI‘s Far Infrared Surveyor (FIS) from 60-160 µm. A pre-culling of this list of K-M giants can be made by eliminating candidates whose FIR emission exceeds the RJ predictions.

Background Information on Infrared Flux Calibration Using K-M Giants

Over the past twenty years Martin Cohen and collaborators have carried out a major effort to rationalize and unify absolute calibration from optical to infrared (IR) by providing absolute spectra, complete from 1−35 µm, of K and M giants (e.g., Cohen et al. 1999, AJ, 117, 1864. Currently these constitute an all-sky network of 615 stars offering about one star every 70 square degrees. These calibrators are widely used and have supported many IR satellites, instruments on large ground-based telescopes, airborne and space-based sensors. Stellar spectra for all the 422 stars of the published network (version 2.1) are available online. Price et al. 2004, AJ, 128, 889, of US Air Force Phillips Laboratory, published their 3-year independent appraisal of these MIR calibrators using the Midcourse Space eXperiment (MSX) precision radiometric measurements. This appraisal validated the radiometric basis from 8−21 micron at the 1.1% absolute level, within quoted 1-sigma errors. Every star in the network has a computed angular diameter. The radiometric diameters of 374 of the first network of 422 published stars have been adopted for use as long-baseline stellar interferometric calibrators (Bord´e et al. 2002, A&A, 393, 183). Consequently, the network of cool giants has been peer-reviewed, carries an independent absolute validation from the USAF, and has been accepted by a community quite different from that for which it was originally intended.

Several bright cool giants were used in the absolute calibration of the European Space Agency’s Infrared Space Observatory (ISO) for its long wavelength photometer. These stars were extrapolated to 300 micron on the basis of purely radiative photospheres and merged well with planet and asteroid flux calibrators (Schulz et al. 2002, A&A, 381, 1110). The same role was recently fulfilled by the same giants for the calibration of Japan’s FIR all-sky surveyor (FIS: 65-160µm) (Shirahata et al. 2009, PASJ, 61, 737).

Millimeter Emission Studies of K-M Giants

Cohen etal. 2005, AJ, 129, 2836 imaged two normal, non-coronal, MIR-bright, K-giant standards: Alpha Tau and Alpha Boo, in the 1.4 and 2.8 mm continuum using BIMA. If a star radiates as predicted for a photosphere then its flux can be used as a fiducial at that wavelength. If the flux rises above the expected photospheric level, regardless of the physics, this renders it invalid for amplitude calibration. Cohen etal. found that Alpha Tau's flux rose above the RJ extrapolation beyond 200 micron. The combination of observations from FIR and mm regimes, together with theoretical modeling of both radiative equilibrium model atmospheres (Carbon etal. 1982, ApJS, 49,207) and a NLTE chromospheric model (McMurry 1999, MNRAS, 302, 37), indicates that the RJ approximation fails in this star due to chromospheric emission. Alpha Boo is likewise not useful as a sub/mm flux calibrator.

Despite the millimeter results for Alpha Tau and Alpha Boo, not every cool giant has a millimeter-chromosphere. In May 2010 Martin Cohen and collaborators undertook an initial test of their concept by observing the MIR southern standard, Gamma Cru, with the ATCA equipped with the Compact Array Broadband BackEnd. FIR data show this star to be a RJ emitter from 65 to 160 micron. Its predicted RJ flux at 94 GHz is 8.6mJy and it was strongly detected at 8.0±0.6mJy.

K-M Giant Star Millimeter and Submillimeter Emission Studies

Given that the predicted millimeter and submillimeter emission from many K-M giant stars is in the milli-Jansky range, K-M giant stars are definitely viable absolute flux calibration sources. Issues that need to be studied to characterize these objects as millimeter/submillimeter flux standards are:

  • Characterize RJ extrapolation of MIR emission to look for excess emission (due to an active chromosphere)
  • Monitor flux for time variability
  • Measure flux at 90 GHz and higher frequencies to extend MIR extrapolation and develop set of submillimeter flux standards

-- JeffMangum - 2010-11-30

Long-Period Variable Stars

Recently, Mark Gurwell, Mark Reid, and Karl Menten have extended an early study of the applicability of Mira variables as absolute standards (Reid and Menten 1997, ApJ, 476, 327, Radio Photospheres of Long-Period Variable Stars ), using some 230, 345 and 690 GHz SMA observations. The results so far are encouraging in the sense that an accurate estimate of flux densities at high frequencies can be derived from (supposedly) more accurate flux density measurements at lower frequencies (perhaps set through very accurate flux calibration using standard feed horns as Jack Welch has been working on).

Here is a synopsis of the Reid and Menten (1997) work on this subject:
  • Measured flux density variations of less than +-15% at centimeter wavelengths (8-24 GHz).
  • Measured flux densities ~ 0.8-3 mJy at 22.4 GHz.
  • Note that cm emission is relatively insensitive to circumstellar dust emission.
  • In the stellar photosphere model developed as a result of these measurements, the cm emission comes from the "radio photosphere" (see Reid and Menten Figure 12). Millimeter emission will likely originate from a "molecular photosphere", located just inside the radio photosphere.
  • Based on model developed for the radio/millimeter emission from these stars, the strongest stars in the Reid and Menten sample (oCet and WHya) should have flux densities of about (0.04, 0.3, 2.4) Jy at (3, 1, and 0.3) mm, respectively. Plenty strong enough to be primary flux calibration sources.


Quasars

At radio wavelengths, the primary flux density calibrators are mostly external radio galaxies, e.g., at the VLA, the standard is 3C295, which is used to monitor 3C286, 3C48, etc... every 16 months. 3C286 and 3C48 are secondary flux density calibrators (but are effectively used as if they are primaries). Their variations are small and slow, on physical grounds; the emission is dominated by the radio lobes. By the time you get to the mm/submm, the emission is generally weaker, and dominated by the core (lobes go like \lambda^{0.7} while the core is closer to flat spectrum), which is variable. So, while they might be good secondary calibrators, these sources are probably not useful as primary calibrators.

-- JeffMangum - 06 Sep 2006
Topic revision: r1 - 2013-04-03, JeffMangum
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