SHARC II Calibrators (Advanced)

You probably don't need to worry about this material. It is provided as a convenience.

Secondary Calibrators

The following reported fluxes are at 350 microns. Mars, Uranus, and Neptune were used as primary calibrators. The quoted systematic uncertainties of 10-30% depend on the number of observations and elevation coverage.

Solar System Objects

These sources have fluxes dependent on the distance from the Earth to the object and the distance from the Sun to the object. To calculate the flux of a source, use the following formula:

T_B = T_1AU / sqrt(r)
Flux = (solid angle) * B_nu(T_B)

where:

T_B = brightness temperature (K)
T_1AU = brightness temperature if the source were at r = 1 AU
r = heliocentric range (AU)
B_nu = Planck function, evaluated at 350 microns

The solid angle (angular diameter) and heliocentric range can be obtained from the JPL Horizons System. IMPORTANT NOTES:

The tabulation below does NOT give the brightness temperature, since the objects are not 1 AU from the Sun.
For planets, which have relatively large angular diameter, the flux per 9" beam is significantly less than the total flux.

The observed values of T_1AU are derived from measurements with SHARC II since 2003.

Source      # Obs. Runs  T_1AU (K)
----------  -----------  ---------
CALLISTO         9       281 +- 28
CERES           11       274 +- 27
DAVIDA           2       319 +- 57
EGERIA           2       272 +- 27
GANYMEDE         8       240 +- 24
JUNO             5       328 +- 33
Mars         (primary)   271
Mercury          2       379 +-127
Neptune      (primary)   336
PALLAS           6       311 +- 31
TITAN            4       213 +- 21
Uranus       (primary)   287
VESTA            9       258 +- 26

Evolved Stars

Some of these sources have 10-20% long-period variability (Sandell 1994; Jenness et al. 2002), but are otherwise excellent calibration sources. Observed (mean) fluxes are derived from measurements with SHARC II since 2003.

Source    # Obs. Runs  Peak Flux(Jy/9" beam)
--------  -----------  ---------------------
CIT6          10          2.42+- 0.24
CRL618        10         19.4 +- 1.9
CRL2688        7         41.6 +- 4.2
IRC10216      13         24.4 +- 2.4
O_CET          7          2.33+- 0.23
OH231.8       13         17.6 +- 1.8
VYCMA          2         15.6 +- 1.8

Blazars

These sources are compact, but highly variable.

Source    Obs. Run  # Meas.  Peak Flux(Jy/9" beam)
--------  --------  -------  ---------------------
0420-014  2003 Jan    35          5.2+-1.6
0420-014  2004 Sep     1          0.9+-0.3

3C273     2003 Jan    10          2.2+-0.7
3C273     2003 Feb     2          2.4+-0.7
3C273     2004 Jan     6          1.3+-0.4
3C273     2004 Apr     2          0.8+-0.3
3C273     2004 Jun     2          0.8+-0.2

3C345     2003 Jan     4          1.0+-0.3
3C345     2003 Feb     1          0.9+-0.3
3C345     2003 Mar     7          0.8+-0.2
3C345     2004 Jan     3          1.2+-0.4
3C345     2004 Apr     3          1.1+-0.3
3C345     2004 Jun     3          0.7+-0.2

3C84      2003 Jan     5          0.8+-0.2
3C84      2003 Oct     1          1.4+-0.4

OJ287     2003 Jan     6          0.9+-0.2

Other Galactic and Extragalactic Sources

These sources range from compact (ARP220) to multiple/extended (NGC 2071).

Source     # Obs. Runs  Peak Flux(Jy/9" beam)
---------  -----------  ---------------------
ARP220         17         10.2 +-  1.0
G34.3           6        434   +- 43
GL490           4         32.2 +-  3.2
HLTAU           7         15.9 +-  1.6
IRAS16293       9        127   +- 13
K-350           4        129   +- 14
L1551           3         45.2 +-  4.5
NGC2071         7         60.5 +-  6.1
NGC6334I        1        420   +-126
TWHYA           4          6.13+-  0.68
W3OH            3        160   +- 24
W75N            5        267   +- 27

Calibration Relations -- 350 microns

THE REMAINING DISCUSSION APPLIES TO sharcsolve DATA REDUCTION ONLY.

The following equation is appropriate for calibration of SHARC II data:

tau(SHARC II) = A [tau(radiometer) - B]. Note negative sign.
Definition of flux conversion factor: flux = (raw signal) * exp(tau(SHARC II)*airmass) * (conversion factor) / f(elevation)].
f(elevation) = telescope response function, which depends on elevation

To determine A, B, the conversion factor, and the telescope response function, I analyzed the images of the candidate calibration sources in many of the observing runs so far. For the signal, I used the amplitude of the best-fit gaussian ("fitgauss") to the reduced image; this is then a "peak" voltage and not an integrated voltage. I used "sharcsolve", which outputs signals in mV, referred to output. I only used scans in high gain mode, which is used almost exclusively.

Note: The dependence of detector responsivity on atmospheric emissivity is absorbed into the tau relation. THIS IS TRUE FOR sharcsolve, BUT NOT FOR crush REDUCTION.

observing run	A(225 GHz)	B(225 GHz)	A(350 micron)	B(350 micron)	conv. factor, Jy/mV	response function f
2002 Nov, DSOS off
2003 Jan. 3-13, DSOS off	27.20	0.011			1.90	f, Jan. 2003
2003 Feb. 18-28, DSOS off			1.208	0.39	2.27	f, Feb. 2003
2003 Mar. 1-5, DSOS on			1.226	0.40	1.75	f, Mar. 2003
2003 Apr., DSOS on			0.994	0.12	2.70	f, Apr. 2003
2003 May, DSOS on
2003 August, DSOS on
2003 Sept. 24-Oct. 17, DSOS mostly on	31.29	0.010			1.41	uniform (1.0)
2004 Jan, DSOS on	32.04	0.015			1.61	uniform (1.0)
2004 Jan, DSOS on			1.212	0.33	1.55	uniform (1.0)

Note: For the period February-May 2003, values tau(350 micron)/23 were stored in the data files in place of the tau(225 GHz), which was not functional.

To see a graphic demonstration of how the telescope efficiency got worse at high elevation during January 2003 (prior to DSOS implementation), take a look at these beam maps. (Contour levels are 5%, 10%, 20%, and 50% of the peak.)

Calibration Solution Details

The following equation is the basis for the calibration solution:

F = S * G * exp[A(tau225 - B) * airmass] / f(elevation)
F = flux in Jy
S = measured signal
G = flux conversion factor (units Jy/mV), a fit parameter
A, B = fit parameters
tau225 = JCMT polynomial fit to 225 GHz opacity from CSO radiometer
airmass = 1.0/sin(elevation)
f(elevation) = telescope response function, not a fit parameter

The technique is least-squares minimization using the logarithm of the basic equation:

ln(F) = ln(S) + ln(G) + A(tau225 - B)*airmass - ln(f)

The telescope response function was adjusted "by eye" to flatten the residuals vs. elevation. The fit residuals for January 2003 are shown below:

The gray curve shows the applied telescope response function.

Other residual plots for January 2003 are also available:
residual vs. tau
residual vs. tau*airmass
residual vs. date
residual vs. UT

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