Radial Beam Profile Model

Datasets to construct the radial beam profile model are available below. These allow to take into account the color dependent FWHM of the true beam profiles.

The radial beam profile model for SPIRE was developed and described by North, Griffin, Amaral-Rogers 2011 (v2.6). The peak normalized monochromatic flux, depending on the distance from the peak (Theta) can be described as:

A value of -0.85 should be adopted for gamma, which controls the dependence of the FWHM of the variable part of the beam on wavelength. The reference frequency nu_eff is the isophotal frequency for the product of the spectrum of Neptune and the respective SPIRE spectral filter profile.

SPIRE Photometer Beam Profiles

SPIRE Photometer Solid Angles

Normalized Beam Profile Products to Download

Radialized Beam Profile Model

Analysis Details

THIS PAGE IS UNDER CONSTRUCTION

Photometer Beam Profie Data and Analysis

Beam profile Data

SPIRE Photometer Solid Angles

The values in the first line were measured from a very finely sampled observation of Neptune as outlined below. Note that these are only accurate for a source of the same spectral shape. Since SPIRE flux densities for point sources are conventionally quoted for the reference wavelengths 250, 350, and 500 microns, assuming a source spectrum rising proportionally to wavelength (nu*F_nu=const.), we can adopt the same convention for (infinitely) extended sources. In this case the values in the second line apply. For sources of other colors a correction will have to be applied. The radial model beam profile described in a technical document by North, Griffin, Amaral-Rogers 2011 (v2.6) with the data files given below can be used to calculate such.

Normalized Beam Profile Products

The beam profile maps are available with all backgrounds subtracted and in a normalized form to the peak.

Array	All data after background removal	PSF filtered and limited to 700" radius
PSW
PMW
PLW

Datasets to construct a radial beam profile model are available too. These allow to take into account the color dependent FWHM of the true beam profiles.

Solid angles derived from integrating the radial beam profile model over area and frequency were consistent with the numbers above within 1.5%.

Analysis Details

!!Initial Beam Profile The beam profile was reconstructed from four fine scan maps with obsids: 1342186522, 1342186523, 1342186524, 1342186525 Pointing for Neptune proper motion was corrected. HIPE 9.0.1782 and SPIA 1.8 were used. The map reconstruction was performed after median subtraction excluding a radius of 4 arcmin around the source. The maps have 1 arcsec sky bin size.

The resulting original files are:

Array	Image	FITS
PSW	0x5000241aL_PSW_pmcorr_1arcsec.fits
PSW	0x5000241aL_PMW_pmcorr_1arcsec.fits
PSW	0x5000241aL_PLW_pmcorr_1arcsec.fits

Complications that arise when using these maps directly for derivation of beam profiles and solid angles were discussed in a https://nhscsci.ipac.caltech.edu/spire/docs/beam_profiles/omegaCheck.pptx.pdf|presentation and led to a few corrections as follows.

Background fit and removal

0x5000241aL_PSW_pmcorr_1arcsec_bgfit.fits

0x5000241aL_PMW_pmcorr_1arcsec_bgfit.fits

0x5000241aL_PLW_pmcorr_1arcsec_bgfit.fits

%width=500% Ovarlaying the ecliptic coordinate system over the background fit (contours) shows that a an interpretation by a Zodiacal light gradient is at least qualitatively consistent.

Using IRSKY to obtain a rough estimate through extrapolation of its Zodiacal model to SPIRE wavelengths at the position of the observation and one degree towards the ecliptic pole, the following gradients were obtained.

Background source removal

Array	Before Removal	After Removal	Source Positions
PSW

PMW

PLW

Solid Angles

neptune_omega_PSW4.pdf

neptune_omega_PMW4.pdf

neptune_omega_PLW4.pdf

%width=500px% This map shows green rings at 600, 650, and 1000 arcsec radius. The maps become less reliable outside of about 700 arcsec due to decreasing coverage and S/N. The background seems to rise again in the plots of average annular signal vs. radius, which is likely to be due to the lower coverage.

Results

The diagrams showing solid angle vs. radius show a plateau around 600 arcsec which may signal the end of significant contribution from the beam profile. At different integration radii, the following values in arcsec^2 result:

These data are between 3.6 and 6.7% different from the North&Griffin numbers for 1000 arcsec integration radius and between 2.0 and 3.9% for 600 arcsec integration radius.

SPIRE plans to conduct shadow observations of the same region on the sky without Neptune in it in the fall of 2012. These will be used to determine whether the apparent rise outside 700 arcsec is real and they will improve the accuracy of the background level determination substantially, especially for the longer wavelength observations.

A presentation of this data was given to the HCalSG, the Hfi/Spire Cross Calibration Group and the SDAG.

Errors

Another presentation was given at the SDAG, which discussed various sources of uncertainties and concluded that an error of +/- 4% is a conservative estimate at this time.

Correction between Isophotal and Reference Wavelength

It is important to point out that solid angles are color dependent. The FWHM of the beam varies with frequency proportional to nu^gamma. The most recent estimate from Griffin (priv. comm) for gamma is 0.78, 0.85, 0.85, respectively for PSW, PMW and PLW.

As the beam profiles and the solid angles were derived from a map of Neptune, there is a discrepancy to the n*Fnu = const. spectrum that all photometry is color corrected for.

To determine the magnitude of this variation, a radial beam profile model was derived from the final background subtracted 2D beam profiles, following the idea in North, Griffin, Amaral-Rogers 2011 (v2.6). The radial beam profiles are split up into a constant and a variable core part whose radial scale varies with nu^gamma as mentioned above. The solid angle can be found by integrating the product of beam profile, relative spectral response function (RSRF) and source spectrum over radius and wavelength and dividing by the integral over RSRF and source spectrum. The source spectrum for Neptune was approximated by a power law with exponent -1.39. The ratio of the solid angles found for the Neptune power law and a power law with exponent -1 was used to correct the Neptune solid angles to the standard SPIRE reference spectrum.

%width=600px%

This diagram shows the frequency dependency of the solid angles of PSW, PMW, and PLW in comparison to conveniently scaled power law curves with different exponents.

-- BernhardSchulz - 11 Oct 2012