1. SPIRE Flux Calibration: Implementation
George J. Bendo
and the SPIRE-ICC

2. Basic Equations
Derivative of flux calibration curves (from empirical analysis):
Flux calibration curve (integral of above equation):
V0 is a zero-point voltage that is selected to match the background in dark sky.
K1, K2, and K3 are unique parameters for each bolometer that are derived using the techniques discussed here.
An additional K4 term is used to scale the RSRF-weighted flux density to produce monochromatic flux densities (assuming υFυ is constant).

3. Calibration Strategy
PCal flash observations taken against backgrounds with different surface brightnesses give the relation between V and 1/ΔV. These data can then be used with the derivative of the flux calibration curve to give unscaled versions of K1 and K2 and a scaled value of K3.
Fine scan observations in which each bolometer scans over Neptune are used to scale the K1 and K2 parameters.

4. PCal Flash Observations
Instrument was pointed at a series of locations near Sgr A* during PCal flash observations to get 1/ΔV vs V measurements. Each bolometer falls within a region that should be ~75% of the peak surface brightness.
Additional PCal flash measurements against dark sky were used to constrain the part of the curve near V0.

5. Results: Unscaled Derivatives of Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

6. Results: Unscaled Derivatives of Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

7. Results: Unscaled Derivatives of Calibration Curves
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

8. Neptune Fine Scan Observations
In these observations, each bolometer in SPIRE passed across Neptune in a very fine pattern. This gave measurements of the peak and background voltages that could be used to scale the calibration curves.
To derive the peak and background voltages, we fit the timeline data (not the map data) with two dimensional Gaussian functions. An example is shown below.

9. Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration

10. Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration

11. Results: Scaled Calibration Curves
Solid line: V3-0 flux calibration
Dotted line: V2-3 flux calibration

12. Problematic Bolometers
Some of the dead, noisy, and slow bolometers could not be calibrated because of difficulties with performing analysis on the sample. The following number of bolometers were not calibrated:
PSW 7
PMW 1
PLW 1
16 bolometers in PSW and 7 bolometers in PMW saturated on Neptune. To calibrated these bolometers, we used fine scan observations of 3C We calibrated the signal from 3C 273 for the “good” bolometers, and then used the signal from 3C 273 to scale the bolometers that saturated on Neptune.

13. Sources of Uncertainty (Individual Bolometers)
Uncertainty from fits to PCal flash data.
Uncertainty in scaling terms.
Uncertainty in model flux densities of calibration source.

14. Uncertainty from PCal Fits
Because of degeneracy problems with the nonlinear equation fit to the PCal flash data, we cannot derive simple uncertainties in the K parameters from the fit. Instead, we used a Monte Carlo approach to create plots that show the uncertainty in the calibration curves as a function of voltage. The typical fractional uncertainties from the PCal flash fits derived this way are ~ The maximum uncertainties do not supercede

15. Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

16. Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

17. Uncertainty from PCal Fits
Dotted lines: Voltages for V0 and V0-VPeak (Neptune)

18. Uncertainty from Scaling Terms
The table below lists the uncertainties for the scaling of the calibration curves for individual bolometers based on the uncertainty in the peak voltage measurements of Neptune or 3C 273. The maximum fractional uncertainties in the PSW and PMW arrays are for bolometers that saturated on Neptune. Most other bolometers have uncertainties much closer to the mean.
Array
Mean Fractional Uncertainty
Maximum Fractional Uncertainty
PSW
0.0098
0.11
PMW
0.010
0.12
PLW
0.0016
0.040

19. Tests of Flux Calibration
The new Flux Calibration Product was used to process standard large and small scan map data for two sources:
Neptune (primary calibrator)
Gamma Dra (secondary calibrator)
The results can be used to gauge the random uncertainty in the flux calibration as well as variations in the flux calibration over time.
Measurements of the flux densities were performed on the timeline data. Mapping the data increases the dispersion in the flux density measurements, as binning the data into map pixels will effectively blur the data. The source extraction tools currently included in HIPE (DAOPHOT and Sussextractor) both systematically undermeasure flux densities, and Sussextractor also functions very poorly for >100 mJy sources.

20. Neptune Measured/Model Flux Densities
Triangles: Small scan map
Squares: Large scan map

21. Neptune Measured/Model Flux Densities
Triangles: Small scan map
Squares: Large scan map

22. Neptune Measured/Model Flux Densities
Triangles: Small scan map
Squares: Large scan map

23. Neptune Measured/Model Flux Densities
Array
Measured/Model Flux Density Ratios
All
Large Map
Small Map
PSW / / /
PMW / / /
PLW / / /

24. Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map

25. Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map

26. Gamma Dra Measured Flux Densities
Triangles: Small scan map
Squares: Large scan map

27. Gamma Dra Measured Flux Densities
Array
Model Flux Density (Jy)
Measured Flux Densities (mJy)
All
Large Map
Small Map
PSW
251
258 +/- 3
260 +/- 2
258 +/- 4
PMW
127
139 +/- 4
140 +/- 5
138 +/- 4
PLW 61
74 +/- 5
75 +/- 5
73 +/- 5
These are monochromatic flux densities without color corrections (and without a u in color).

28. Conclusions
Although a few individual bolometers have calibration uncertainties of >5%, each array as a whole can measure flux densities with the following accuracies:
PSW 1.5%
PMW 1.7%
PLW 0.5%
The accuracy of the flux calibration for >100 mJy sources will primarily be limited by the Neptune models.