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

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).

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.

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.

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

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

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

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.

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

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

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

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 273. 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.

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

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 ~0.0002. The maximum uncertainties do not supercede 0.005.

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

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

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

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

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.

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

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

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

Neptune Measured/Model Flux Densities Array Measured/Model Flux Density Ratios All Large Map Small Map PSW 0.995 +/- 0.007 0.996 +/- 0.009 0.994 +/- 0.003 PMW 0.993 +/- 0.010 0.997 +/- 0.013 0.992 +/- 0.004 PLW 1.001 +/- 0.003 1.000 +/- 0.003 1.002 +/- 0.003

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

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

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

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).

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.