Spitzer-IRS aperture corrections

The width of the LL slit (14-36µm) is bigger than the width of the SL slit (5-7.5µm): 10.2 versus 3.6 arcseconds. This means that for (semi-)extended sources, such as galaxies, a larger fraction of the source will fall within the LL slit than within the SL slit.
To give an example: At z=0.09 the SL slit will record light from the inner r=3 kpc, and the LL slit from the inner r=8.6 kpc around the nucleus. At z=0.30 these numbers are r=8 kpc (SL) and r=23 kpc, respectively.

The SL and LL slits are also almost orthogonal to each other. In the dispersion direction the SL slit thus covers a different part of a galaxy than the LL slit does.

Because of the different aperture sizes, stringing together a SL and LL spectrum of an extended source will result in a jump in flux at the stitching wavelength (14.0-14.2µm observed wavelength), with the higher flux occuring in the LL spectral segment.

For the purpose of spectral decomposition or spectral fitting an aperture correction is needed to remove the jump. In IDEOS we chose to scale up the SL spectral orders to match the LL ones, resulting in median correction factors of 1.16.

How do we stitch? As explained in our Paper I, Hernán-Caballero et al. (2016), MNRAS, 445, 1796, we use the small overlap between orders (SL1 and SL2; LL1 and LL2) and between modules (SL1 and LL2) to match the continua in both spectral segments. At some redshifts the order or module overlap occurs in a spectral feature. For instance a PAH feature: e.g. the PAH127 feature at redshifts z=0.10 to z=0.14. For these sources we have no choice but to match the continuum+PAH emission in both segments.

The implicit assumption in applying the aperture correction is that the source properties as probed in the bigger LL slit are the same as in the smaller SL slit. While this may be true for some diffuse extended galactic objects, this will not be true for galaxies. The LL spectrum will have a larger contribution from the galaxy disk than the SL spectrum does. Only above z=0.3 this problem will go away, as even the SL will probe a radius of r=8 kpc around the nucleus. At z>0.3, a SL scaling factor above unity thus implies an issue with the centering of the source in the SL slit.
Note that galaxies in an advanced stage of merging are far more compact than normal (starburst) galaxies. Some appear as point sources for Spitzer-IRS. Galaxies like these will not require aperture corrections as large as other galaxies at the same redshift.

What are the practical implications of an aperture correction? It depends. Remember the implicit assumption in the scaling of SL to LL: the source properties as probed in the bigger LL slit are the same as in the smaller SL slit. For a coronal line originating from the AGN point source it is hard to argue that this line would be similarly distributed within the SL slit as within the LL slit. Luckily, the main mid-infrared AGN tracers 14.32 & 24.32µm [NeV] and 25.89µm [O IV] all fall in the LL spectral range even at z=0 and hence do not require any scaling.
For lower excitation lines like 12.81µm [NeII] it is easier to argue that they also contribute outside the SL slit within the LL slit width, as HII regions are found along spiral arms and bars. On the other hand, even for these lines the flux is likely concentrated where most of the star formation occurs: towards the nucleus.
The reality thus may be that spectral scaling distorts a diagnostic line ratio that is composed of a line in SL and a line in LL by 2-20% and even higher for nearby galaxies. This distortion should always be kept in mind when interpreting subtle differences among galaxies, or between an observed and a model ratio.
Only for higher redshift sources the spectral features residing in the 5 to 14µm range will shift into the LL module one by one: at z>0.1 both lines in the [NeV]/[NeII] and in the [NeIII]/[NeII] ratio will be observed in the LL orders. And at z>0.35 also both lines of the [S IV]/[S III] ratio. The plots below are intended to give an indication of what redshift ranges are sweetspots and what wavelength ranges require attention for the correct interpretation of a line ratio.

The scaling factors applied to the spectral segments of a spectrum are listed in the header of each IDEOS spectrum, and can also be found in the 'SED' tab of a single source results page in the IDEOS portal.

Each scaling comes with an uncertainty, which propagates to shorter wavelengths. If, for instance, the SL1-LL2 scaling cannot be pinned down to better than a factor 1.03 to 1.08, this uncertainty propagates to the rest of the SL spectrum. If on top of that the SL2 scaling relative to SL1 falls between 1.01 and 1.03, the uncertainty in the absolute flux in the SL2 spectral segment ranges between 1.03x1.01 on the low end and 1.08x1.03 on the high end. This means that the integrated flux of a feature in SL2 will have a systematic uncertainty of 4% to 11% in addition to the uncertainty computed in the fit. Equivalent widths, optical depths and crystalline silicate strengths are not affected by this.