1. Introduction

2. Data reduction and results

3. Products to download

4. Usage

5. Bugs and caveats

6. References

For IRS observations in which the source is not well centered in the slit, part of the stellar PSF falls outside of the slit, leading to flux loss. In extreme cases, not only the absolute flux level is wrong, but also the shape of the spectrum is highly distorted, especially close to the edge of the orders. When there are indications that the observation was misspointed and the precise absolute flux level and shape of the spectrum is important, one should correct for these effects. Such kind of correction is not implemented in the Spitzer data reduction pipeline. For point sources, flux loss in off-centered sources can be efficiently corrected if we know the beam profiles of the different IRS slits.

In order to construct the beam profiles for all four IRS slits, we reduced and analyzed dedicated IRS calibration measurements taken in spectral mapping mode in a regular grid. Table 1 shows a log of these calibration observations. The colored x signs in Figs. 1-8 show the grid points where the star was positioned with respect to the slit; the plus sign marks the center of the slit; the short line points towards north.

We used the pipeline processed post-BCD files (coa2d.fits, pipeline version S15.3.0). No sky subtraction was done. At each spatial position, we divided the measured spectrum with a synthetic MARCS model spectrum appropriate for the measured star (Decin et al. 2004). We stored the result in a data cube with two spatial dimensions and one wavelength dimension. We resampled these data cubes to finer spatial grid, smoothed them in wavelength, and interpolated over a few grid points with very noisy measurements.

Figure 1. Map of the data grid for Short Low 1.	Figure 2. Map of the data grid for Short Low 2.
Figure 3. Map of the data grid for Short Low 1.	Figure 4. Map of the data grid for Short Low 2.
Figure 5. Map of the data grid for Short High.	Figure 6. Map of the data grid for Long Low 1.
Figure 7. Map of the data grid for Long Low 2.	Figure 8. Map of the data grid for Long High.

Figure 9 below shows an example how the data cubes were calculated. In the top panel, black dots show the measured spectrum of HR 6688, obtained with the Short High channel. The red line shows the model spectrum for the same star. The bottom panel displays the data grid: the + sign marks the slit center, red dots show the position of the star relative to the slit center, the rectangle indicates the slit itself, while the x sign marks the position where the spectrum plotted in the top panel was taken. The data cube at a certain (x,y) position contains the ratio of the measured and the model spectrum.

Figure 9. Spectrum of HR 6688 taken with the Short High channel at an offset of (0.45",1.70").

The data cubes can be visualized in many ways. You can plot e.g. the correction factors at a certain wavelength as a function of x or y offset (i.e. distance from the slit center along the slit or perpendicular to the slit). Some examples are plotted in Figs. 10-13.

We checked whether the measured beam profiles are consistent with the PSFs provided by Spitzer's Tiny Tim (J. Krist). In Figs. 10-13 we plotted the correction factors (i.e. the ratio between the observed and the model spectrum) at different distances from the slit center at a certain wavelength. We found slight differences: the measured profiles were in general narrower than the model PSFs, and in some cases they were not centered at zero. We examined several effects that can cause such kind of differences between the measured and model profiles. We found that the differences can be attributed to pixelization effects (pixel sizes are 1.8" for SL, 2.3 arcsec for SH, 5.1 arcsec for LL and 4.5 arcsec for LH), and to small (few tenths of arcsec) uncertainties in the exact position of the calibration star with respect to the slit. Based on our analysis, we suggest to use the measured profiles to correct off-center science measurements if the distance of the science target perpendicular to the slit is larger than 0.5".

Figure 10. Beam profile of the Short Low 1 channel through the slit center, perperdicular to the slit. Filled dots: measured; open dots: pixelized model.	Figure 11. Beam profile of the Long Low 1 channel through the slit center, perpendicular to the slit. Filled dots: measured; open dots: pixelized model.
Figure 12. Beam profile of the Short High channel through the slit center, perperdicular to the slit. Filled dots: measured; open dots: pixelized model.	Figure 13. Beam profile of the Long High channel through the slit center, perperdicular to the slit. Filled dots: measured; open dots: pixelized model.

INTDATA	FLOAT = Array[41, 29, 1230]
INTX	FLOAT = Array[41]
INTY	FLOAT = Array[29]
O	FLOAT = Array[1230]
RAWDATA	FLOAT = Array[315, 1230]
RAWX	FLOAT = Array[315]
RAWY	FLOAT = Array[315]
W	FLOAT = Array[1230]

The variable 'W' contains the wavelength information, 'O' the orders. 'RAWDATA' contains the raw correction factors (before resampling), 'RAWX' and 'RAWY' the corresponding x and y coordinates (the raw correction factors for some example wavelengths are plotted in Figs 10-13; while the raw x and y coordinates are plotted in the grid maps in Figs. 1-8). 'INTDATA' is already resampled for a somewhat finer, and more importantly, regular grid. 'INTX' and 'INTY' contain the x and y coordinates for this regular grid. In case of other channels, the variable names will be the same, but their lengths will be different.

The regular grid makes interpolation very easy. Here is an example:

; RESTORE THE DATA CUBE
restore, 'sh.sav'
a=size(intdata)
size_w=a[3] ;size of datacube in the wavelength direction
size_y=a[2] ;size of datacube in the y direction
size_x=a[1] ;size of datacube in the x direction
dummy = fltarr(size_y,size_w)
corr = fltarr(size_w)

; ENTER THE POSITION OF YOUR TARGET:
ra_star = 292.25362500
dec_star = 9.645191667

; ENTER THE SLIT POSITION FROM THE IRS OBSERVATION YOU WANT TO CORRECT:
ra_slt=292.253889214286
dec_slt=9.64393041428572
pa_slt=164.470667142857

; DETERMINE HOW OFF-CENTER YOUR TARGET IS:
gcirc, 1, ra_star/15., dec_star, ra_slt/15., dec_slt, dist
posang, 1, ra_star/15., dec_star, ra_slt/15., dec_slt, ang
x=dist*cos((ang-pa_slt)/180*!PI)
y=dist*sin((ang-pa_slt)/180*!PI)
print, 'x= ', x, ' arcsec' &$
print, 'y= ', y, ' arcsec' &$

; INTERPOLATE CORRECTION FACTORS FOR THE POSITION CALCULATED ABOVE:
for ii=0, size_w-1 do begin &$ ;LOOP FOR ALL WAVELENGTHS
for jj=0, size_y-1 do begin &$ ;LOOP FOR ALL ROWS
dummy[jj,ii] = interpol(intdata[*,jj,ii], intx, x) &$
endfor &$
endfor

corr=fltarr(b)
for ii=0, size_w-1 do begin &$ ;LOOP FOR ALL WAVELENGTHS
corr[ii] = interpol(dummy[*,ii], inty, y) &$
endfor

; CORRECT DATA:
flux_corr = flux/corr

Please note that in this example the vector containing the flux values to correct, 'flux', should correspond to the same wavelength scale than the correction vector (i.e. since w[51] = 6.7 micron, flux[51] should be your flux at 6.7 micron). If it is not so at the beginning, you can always do a similar interpolation also in the wavelength direction.

Here is an example how such kind of correction can affect your data:

Figure 14. Short High channel spectrum of Parsamian 21 before and after correction for slit loss.

• These corrections were developed by Ágnes Kóspál, during her time as a Visiting Graduate Student in the Spitzer Science Center (Fall 2006, advisor David R. Ardila).
  
• You can read a shortened version of the above description in the appendix of Kóspál et al. 2008, MNRAS 383, 1015. If you find the tools above useful, we'd appreciate if you could cite this paper.
• You can find the synthetic MARCS stellar model spectra here: IRS templates by L. Decin
• You can find Tiny Tim model PSFs for Spitzer here: Tiny Tim for Spitzer by J. Krist