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23.3 Working with Two Dimensional Extracted Spectra

Sensitivity Units and Conversions

Your two dimensional extracted spectrum (_sx2, or _x2d file) has units of erg cm-2 sec-1 Å-1 arcsec-2. The conversion from counts to surface brightness (I) is calculated by the pipeline as:

C is the wavelength-dependent count rate, which is the ratio of the total counts to the exposure time. The exposure time is given in the EXPTIME header keyword.
G is the detector gain, which is unity for MAMA observations. For the CCD, this is the conversion from counts to electrons, the value for which is given in the header keyword ATODGAIN.
h is Planck's constant.
c is the speed of light.
T^sys is the wavelength-dependent integrated system throughput divided by the area of the unobstructed HST mirror, which is given in the PHOTTAB reference file table.
A_HST is the area of the unobstructed HST mirror.
d is the dispersion in Å/pixel, derived from the CD1_1 header keyword.
m_s is the plate scale in arcseconds/pixel in the cross-dispersion direction, which is the product of the CD2_2 header keyword value and (3600 -arcsec/degree).
W is the slit width in arcseconds.
is the wavelength in Angstroms. The flux from a fully extended continuum source as transmitted by the science slit, over an arbitrary number of pixels in the spatial direction (Npix_s) and taken over an arbitrary number of pixels in the wavelength direction (Npix)¹, is given by:
in units of ergs/cm²/sec/Å, where:
µ(I) is the average value of the surface brightness, I, over the Npix_s ¥Npixpixels in the rectangle being integrated. For an emission line source, the situation is somewhat different. There, the line surface brightness, I_line, from an emission line feature, in ergs sec^-1 cm^-2 arcsec^-2is given as:
where:
I is as given above (i.e., the values in the _x2d or _sx2 image).
m is the plate scale (in arcsec/pixel) in the dispersion direction as given in the SCALE_A1 header keyword.
All other parameters are as above. Having performed this conversion, one can take an average or sum of the value of I_line over the extent of a feature to get the mean, µ(I_line), or to get the total flux from the line:
over a Npix ¥mby Npix_s ¥m_sregion on the sky_,where Npix ¥mequals the width of the emission feature in the spectral direction.
The factor W ¥d / m converts between diffuse continuum source surface brightness and diffuse emission line surface brightness and is given in the CONT2EML header keyword; it is simply the slit width expressed in Angstroms. The solid angle of a pixel in arcsec² (m_s ¥m)is given in the header keyword OMEGAPIX.
Finally, the DIFF2PT keyword in the data header gives the conversion factor to flux units in erg cm-2 sec-1 Å-1 for a point source. The DIFF2PT keyword is calculated as:
where W and m_s are as above, T^ap is the wavelength-averaged point-source aperture throughput for the science aperture (which is determined from the reference table specified by the keyword APERTAB), and H(h) is the wavelength-dependent correction for the extraction slit of height h to a slit of infinite height, which is obtained from the reference table specified by the keyword PCTAB. That is, to derive the flux from a point source, integrate the _x2d or _sx2 file over the default extraction slit height (from the PCTAB) and multiply the result by DIFF2PT. The default extraction slit height for first-order modes is at present 11 pixels for the MAMAs and 7 pixels for the CCD. If the desired extraction slit height differs from the default, the PCTAB has a set of wavelength-dependent corrections for selected alternative apertures that must also be applied. See STIS ISR 98-01 for further details. Of course, point source observers are better advised to use the x1d task to extract a one-dimensional spectrum from their long-slit first-order data, which will then apply the wavelength-dependent aperture throughput, the defined point source extraction aperture and calibration, as well as perform background subtraction.
In general we note that the cross dispersion profiles can be quite extended (particularly in the far-UV and in the near-infrared); fluxes derived for extended sources from the _x2d files as above assume that the sources are extended on scales which contain the bulk of the cross dispersion flux from a point source. As we make further progress analyzing the cross dispersion profiles and their effect on the accuracies of point source and diffuse source fluxes we will provide updates on the WWW and through the STANs.
See also Chapter 6 of the STIS Instrument Handbook for a more detailed discussion of units and conversions for different source types.

23.3.1 Wavelength and Spatial Information

Two-dimensionally extracted spectra have been wavelength calibrated and rectified to a linear wavelength scale. Tasks such as splot can work directly on the _sx2.fits and _x2d files and can read the wavelength header information which is stored in the standard FITS CD-matrix keywords. Alternatively you can use these keywords directly to determine the wavelength or distance along the slit at any pixel as:

where (x) is the wavelength at any given x pixel, and s(y) is the distance along the slit from slit center for any given y pixel, in units of degrees.

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¹ To keep from degrading the spectral purity Npix ¥m must be less than W.

stevens@stsci.edu

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