Recipe: Spitzer Synthetic Photometry

Welcome to the Spitzer Synthetic Photometry page.

If you have a template source spectrum, you may wish to predict the calibrated flux densities that would be reported in the various Spitzer bands (e.g. IRAC 3.6, 4.5, 5.8, 8.0 micron; IRS Peakup Imaging 16, 22 micron; MIPS 24, 70, 160 micron). This can be useful, for instance, in deriving photometric redshifts. After introducing the relevant basic concepts, this page provides step-by-step instructions for determining synthetic, calibrated IRAC, IRS, and MIPS photometry from such a template.

Requirements:

spitzer_synthphot_28Oct2008.tar.gz

gunzip spitzer_synthphot_28Oct2008.tar.gz

tar xvf spitzer_synthphot_28Oct2008.tar

Outline:

1. The Basics
2. Procedure for computing synthetic IRAC photometry (3.6, 4.5, 5.8, and 8 micron)
3. Procedure for computing synthetic IRS Peakup photometry (16, 22 micron)
4. Procedure for computing synthetic MIPS photometry (24, 70, 160 micron)

I. The Basics

Useful Definitions

1. : This is the effective wavelength of the filter. These are defined and tabulated for each Spitzer instrument in the step-by-step guides below.
   
   
2. : This is the monochromatic (measured at the effective wavelength of the filter) flux density of the template spectrum.
   
   
3. : This is the calibrated Spitzer flux density that would be reported (by e.g. MOPEX/APEX) if the template spectrum were observed by one of Spitzer's imagers. It corresponds to the monochromatic (measured at the effective wavelength of the filter) flux density of a source that
   
   
   1. has a standard spectral shape (defined independently for each filter; see the step-by-step guides below); and
      
      
   2. results in the same observed counts as the template source.
      
      
   Thus, = if the template spectrum has the standard spectral shape. However, significant deviations can occur if the template, or source, spectrum is very different than the standard, or reference, spectrum.
   
   
4. K: This is the color correction, which relates the above quantities according to: . The color correction is computed in a different way for each of Spitzer's imagers (see the step-by-step guides below). It requires knowledge of 1) the source spectrum, 2) the reference spectrum, and 3) the filter response.

Differences between IRAC, IRS, and MIPS photometry

1. The filter response curves are given in units of electrons per unit energy for MIPS and in units of electrons per photon for IRAC and IRS. Therefore, the equation used to calculate the color correction from the provided response function is different for MIPS than for IRAC and IRS. These differences are outlined in the step-by-step procedures provided below for each instrument.
   
   
2. The reference spectrum has the shape of a 10,000K blackbody for MIPS and that of a flat spectrum for IRAC and IRS.

Converting from Spitzer photometry to other systems

II. Procedure for computing synthetic IRAC photometry (Also see Section 5.2 of the IRAC Data Handbook)

1. Determine your input spectrum.

   If you are going to calculate the correction using the IDL code, this should be in Janskys (i.e. energy flux per unit frequency) as a function of wavelength . The input spectrum should cover the width of the IRAC filter profile, so long as it has flux there. It should not be zero at the effective wavelength, and thus should generally not be a pure emission-line spectrum.
   
   For example, you could use IDL to generate a power-law spectrum sampled at the same wavelengths as the IRAC channel 1 filter response function (you will need the IDL Astro Library):
   
   

   IDL>readcol, 'irac_tr1_2004-08-09.dat', filter_w, filter_t, format = '(d, d)', /silent IDL>alpha = 2. ; define the exponent of the power-law IDL>c = 2.9979d8 * 1d6 ; speed of light in micron/s IDL>wave = filter_w ;sample the power-law at the same wavelengths as the filter IDL>nu = c / wave IDL>spec_fnu = nu^alpha / 1e28 IDL>plot, wave, spec_fnu, xtit = 'Wavelength (microns)', $ ytit = 'Flux Density (Jy)', charsize = 1.5, /ylog, $ yrange = [0.5, 1.], /ystyle ;plot the power-law spectrum IDL>oplot, filter_w, filter_t / max(filter_t), linestyle = 1 ;overplot the normalized response curve

2. Estimate the flux density of the input spectrum at the effective wavelength.

   Given that the IRAC photometry is referenced to a spectrum with , the effective wavelength is defined as:
   
   
   
   This is equation 5.11 in the IRAC Handbook. For reference, the effective wavelengths of the IRAC filters are:
   
   3.550 micron for channel 1
   4.493 micron for channel 2
   5.731 micron for channel 3
   7.872 micron for channel 4
   
   For the example, we could draw the effective wavelength on the plot:
   
   

   IDL>lambda_eff = 3.550 IDL>oplot, [lambda_eff, lambda_eff], 10.^(!y.crange), linestyle = 2

   
   We can also estimate , the flux density of the input spectrum at :
   
   

   IDL>linterp, wave, spec_fnu, lambda_eff, fnu_lambda_eff IDL>plotsym, 0, 1, /fill IDL>plots, lambda_eff, fnu_lambda_eff, psym = 8

   
   

3. Determine the color correction, which for IRAC is defined by the following equation.

   
   
   Here, is the reference spectrum evaluated at the effective wavelength; is the template spectrum evaluated at the effective wavelength; and is the filter response function as a function of frequency in units of electrons per photon.
   
   Note that this expression is equivalent to equation 5.8 in the IRAC Data Handbook.
   
   You can evaluate the expression above on your own by first ensuring that the response curve and the template spectrum (and reference spectrum) are on the same grid. You can choose an arbitrary normalization for the flat IRAC reference spectrum . However, two more convenient options are available:
   
   

   1. If your input spectrum is tabulated in Section 5.2 of the IRAC Handbook, you can use the color correction from the tables. Then the expected Spitzer flux density is just given by:
      
      
      
      
   2. You can calculate the color correction using the IDL code as follows.
      
      
      1. Obtain the IRAC response curves, . Current versions have been provided in the download directory with names irac*.dat. For updates check:
         
         http://ssc.spitzer.caltech.edu/irac/spectral_response.html.
         
         Note that the IRAC response curves are provided in units of electrons per photon! The subscript is supposed to remind you of this.
         
         
      2. Load the spectral response into IDL variables, e.g. filter_w (microns) and filter_t, like the 1st IDL line in Step 1 above. Load the template spectrum into, e.g. wave (microns) and spec_fnu (Jy).
         
         
      3. Calculate the color correction.

         IDL>K = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'IRAC', /colorcorr)

         
         Note that the downloadable IDL code provides good agreement with the values tabulated in Section 5.2 of the IRAC Handbook for various types of science spectra. The results are consistent to within half a percent. The fact that the values are not exactly the same is likely due to differences in the interpolation and integration methods.
         
         

4. Calculate the calibrated Spitzer flux density using the following equation.

   
   
   For the example, you could plot the Spitzer flux density:
   
   

   IDL>fnu_Spitzer = fnu_lambda_eff * K IDL>plots, lambda_eff, fnu_Spitzer, psym = 8

   
   Alternatively, the IDL code will also directly output the calibrated Spitzer flux density if the colorcorr keyword is not set. For example:
   
   

   IDL>fnu_Spitzer = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'IRAC')

III. Procedure for computing synthetic IRS Peakup photometry (Also see Section 6.3 of the IRS Data Handbook)

1. Determine your input spectrum.

   If you are going to calculate the correction using the IDL code, this should be in Janskys (i.e. energy flux per unit frequency) as a function of wavelength . The input spectrum should cover the width of the IRS Peakup filter profile, so long as it has flux there. It should not be zero at the effective wavelength, and thus should generally not be a pure emission-line spectrum.
   
   For example, you could use IDL to generate a power-law spectrum sampled at the same wavelengths as the IRS Blue Peakup filter response function (you will need the IDL Astro Library):
   
   

   IDL>readcol, 'bluePUtrans.txt', filter_w, filter_t, format = '(d, d)', /silent IDL>alpha = -2. ; define the exponent of the power-law IDL>c = 2.9979d8 * 1d6 ; speed of light in micron/s IDL>wave = filter_w ;sample the power-law at the same wavelengths as the filter IDL>nu = c / wave IDL>spec_fnu = 1e28 * nu^alpha IDL>plot, wave, spec_fnu, xtit = 'Wavelength (microns)', $ ytit = 'Flux Density (Jy)', charsize = 1.5, /ylog, $ yrange = [10, 200], /ystyle ;plot the power-law spectrum IDL>oplot, filter_w, filter_t * 50. / max(filter_t), linestyle = 1 ;overplot the normalized response curve

2. Estimate the flux density of the input spectrum at the effective wavelength.

   Given that the IRS peak-up imagers are referenced to a spectrum with , the effective wavelength is defined as:
   
   
   
   This is identical to equation 6.1 in the IRS Data Handbook. For reference, the effective wavelengths of the IRS filters are:
   
   15.8 micron for the Blue peakup filter
   22.3 micron for the Red peakup filter
   
   For the example with the Blue Peakup camera, you could draw the effective wavelength on the plot:
   
   

   IDL>lambda_eff = 15.8 IDL>oplot, [lambda_eff, lambda_eff], 10.^(!y.crange), linestyle = 2

   
   We can also estimate , the flux density of the input spectrum at .
   
   

   IDL>linterp, filter_w, spec_fnu, lambda_eff, fnu_lambda_eff IDL>plotsym, 0, 1, /fill IDL>plots, lambda_eff, fnu_lambda_eff, psym = 8

   
   

3. Determine the color correction, which for the IRS is defined by the following equation.

   
   
   Here, is the reference spectrum evaluated at the effective wavelength; is the template spectrum evaluated at the effective wavelength; and is the filter response function as a function of frequency in units of electrons per photon.
   
   You can evaluate the expression above on your own by first ensuring that the response curve and the template spectrum (and reference spectrum) are on the same grid. You can choose an arbitrary normalization for the flat IRS reference spectrum . However, two more convenient options are available:
   
   

   1. If your input spectrum is well-described by a blackbody or power-law over the IRS filter of interest, you can estimate the color correction from these tables.
      
      
   2. You can calculate the color correction using the IDL code as follows.
      
      
      1. Obtain the IRS Peakup response curves, . Current versions have been provided in the download directory with names *PUtrans.txt. For updates check:
         
         http://ssc.spitzer.caltech.edu/irs/spectral_response.html
         
         Note that the IRS response curves are provided in units of electrons per photon! The subscript is supposed to remind you of this.
         
         
      2. Load the spectral response into IDL variables, e.g. filter_w (microns) and filter_t, like the 1st IDL line in Step 1 above. Load the template spectrum into, e.g. wave (microns) and spec_fnu (Jy).
         
         
      3. Calculate the color correction.
         
         

         IDL>K = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'IRS', /colorcorr)

         
         Note that the downloadable IDL code provides good agreement with the values tabulated in the color correction section of the IRS webpage for various types of science spectra. The results are consistent to within half a percent. The fact that the values are not exactly the same is likely due to differences in the interpolation and integration methods. Note that this IDL code computes color corrections for the IRS peak-up filters as calibrated in pipeline versions S17 and greater. It is not to be used for data reduced with older versions of the pipeline.
         
         

4. Calculate the calibrated Spitzer flux density using the following equation.

   
   
   For the example, you could plot the Spitzer flux density:
   
   

   IDL> fnu_Spitzer = fnu_lambda_eff * K IDL>plots, lambda_eff, fnu_Spitzer, psym = 8

   
   Alternatively, the IDL code will also directly output the calibrated Spitzer flux density if the colorcorr keyword is not set. For example:
   
   

   IDL>fnu_Spitzer = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'IRS')

IV. Procedure for computing synthetic MIPS photometry (Also see Section 3.7 of the MIPS Data Handbook)

1. Determine your input spectrum.

   If you are going to calculate the correction using the IDL code, this should be in Janskys (i.e. energy flux per unit frequency) as a function of wavelength . The input spectrum should cover the width of the MIPS filter profile, so long as it has flux there. It should not be zero at the effective wavelength, and thus should generally not be a pure emission-line spectrum.
   
   For example, you could use IDL to generate a 150 K blackbody spectrum sampled at the same wavelengths as the 24 micron filter response function (you will need the IDL Astro Library):
   
   

   IDL>readcol, 'filtresponse24.txt', filter_w, filter_t, /silent IDL>c = 2.9979d8 * 1d6 ; speed of light in micron/s IDL>temp = 150. ; blackbody temperature in Kelvin IDL>wave = filter_w ;sample the blackbody at the wave wavelengths as the filter IDL>nu = c / wave IDL>spec_fnu = 5e9 * blackcgs(temp, nu) IDL>plot, wave, spec_fnu, /ylog, xtit = 'Wavelength (microns)', $ ytit = 'Flux Density (Jy)', charsize = 1.5 ;Plot the blackbody IDL>norm = 5. / max(filter_t) IDL>oplot, filter_w, filter_t * norm, linestyle = 1 ;overplot the normalized filter response curve

2. Estimate the flux density of the input spectrum at the effective wavelength.

   For MIPS, the effective wavelength is defined as:
   
   
   
   This is equation 3.1 in the MIPS Data Handbook. For reference, the effective wavelengths of the MIPS filters are:
   
   23.68 micron
   71.42 micron
   155.9 micron
   
   For the example with the MIPS 24 micron filter, you could draw the effective wavelength on the plot:
   
   

   IDL>lambda_eff = 23.68 IDL>oplot, [lambda_eff, lambda_eff], 10.^(!y.crange), linestyle = 2

   
   Also we can estimate , the flux density of the input spectrum at .
   
   

   IDL>linterp, filter_w, spec_fnu, lambda_eff, fnu_lambda_eff IDL>plotsym, 0, 1, /fill IDL>plots, lambda_eff, fnu_lambda_eff, psym = 8

3. Determine the color correction, which for MIPS is defined by the following equation.

   
   
   Here, is the reference spectrum evaluated at the effective wavelength; is the template spectrum evaluated at the effective wavelength; and is the filter response function as a function of frequency in units of electrons per unit energy.
   
   Since the MIPS response is in different units than the IRAC and IRS response functions, the equation for the color correction is different.
   
   You can evaluate the expression above on your own by first ensuring that the response curve and the template spectrum (and reference spectrum) are on the same grid. You can choose an arbitrary normalization for the 10,000 K MIPS reference spectrum. However, two more convenient options are available:
   
   

   1. If your input spectrum is tabulated in Section 3.7.4 of the MIPS Handbook, you can use the color correction from the tables.
      
      
   2. You can calculate the color correction using the IDL code as follows.
      
      
      1. Obtain the appropriate MIPS response curve, . Current versions have been provided in the download directory with names filt*.txt. For updates check:
         
         http://ssc.spitzer.caltech.edu/mips/spectral_response.html
         
         Note that the MIPS response curves are provided in units of electrons per unit energy!
         
         
      2. Load the spectral response into IDL variables, e.g. filter_w (microns) and filter_t, like the 1st IDL line in Step 1 above. Load the template spectrum into, e.g. wave (microns) and spec_fnu (Jy).
         
         
      3. Calculate the color correction.
         
         

         IDL>K = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'MIPS', /colorcorr)

      
      Note that the downloadable IDL code provides good agreement with the values tabulated in Section 3.7.4 of the MIPS Handbook for various types of science spectra. The results are consistent to within half a percent for 24, 70, and 160 microns. The fact that the values are not exactly the same is likely due to differences in the interpolation and integration methods.
      
      

4. Calculate the calibrated Spitzer flux density using the following equation.

   
   
   For the example, you could plot the Spitzer flux density:
   
   

   IDL>fnu_Spitzer = fnu_lambda_eff * K IDL>plots, lambda_eff, fnu_Spitzer, psym = 8

   
   Alternatively, the IDL code will also directly output the calibrated Spitzer flux density if the colorcorr keyword is not set. For example:
   
   

   IDL>fnu_Spitzer = spitzer_synthphot(wave, spec_fnu, filter_w, filter_t, 'MIPS')

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