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A residual for SBF work

This tutorial prepares the input an SBF analysis starts from: a smooth galaxy model and the residual image. It uses UGC 12517 and stops where ELLIPROF's role ends; the later steps of an SBF distance (point-source corrections, the PSF, the power-spectrum fit and a calibration) are described in Workflow. The numbers below are checks of the galaxy model.

1. Fit and write the products

elliprof u12517j.fits \
    --mask u12517j.dmask --sky 3246 \
    X0=567 Y0=562 R0=9 R1=347 NR=23 NITER=10 RMSTAR \
    -o u12517.dat \
    -m u12517.prf --residual u12517_residual.fits
  • The model keeps the default 3rd- and 4th-order harmonic terms (see Harmonic analysis).
  • The residual is mask × (science − sky − model): 0 on masked pixels, float32, with the science image's WCS.

2. Look at it

The central region of the UGC 12517 residual in red and blue, and the same region divided by the square root of the model, in grey, with masked pixels grey.
The real residual (left) and residual / √model (right; a downstream step, shown for illustration).

Look for:

  • rings or 4-fold patterns: the model does not follow the galaxy. Try more isophotes (NR), more iterations (NITER), or check the model harmonics.
  • a large-scale gradient or offset: the sky is wrong, or the galaxy has structure (dust, disk) that the model cannot describe.
  • point sources: globular clusters and background galaxies that the mask did not remove. The downstream analysis must detect them.

3. Check the residual in annuli

In elliptical annuli that follow the galaxy, the median residual should be a very small fraction of the model. (This table is made by docs/scripts/residual_checks.py.)

annulus (a, pixels) good pixels median residual median residual / median model robust rms of residual/√model
20–40 2,986 −8.1 −0.0001 2.11
40–80 11,935 −16.5 −0.0004 2.11
80–160 47,785 7.8 +0.0006 2.13
160–320 180,849 5.0 +0.0015 2.47
  • The median residual is below 0.2% of the model in every annulus. The model removes the galaxy's smooth light well.
  • The scatter of residual/√model (a robust, MAD-based estimate that ignores most unmasked sources) combines photon noise, detector noise, any remaining sources and the stellar fluctuations. Separating these is exactly what the power-spectrum analysis does; the scatter alone is not an SBF measurement.

4. Normalise (downstream, for illustration)

The first downstream step is usually to divide by √model. In Python:

import numpy as np
from astropy.io import fits
from elliprof import load_mask

res = fits.getdata("u12517_residual.fits").astype(float)
model = fits.getdata("u12517.prf").astype(float)
good = load_mask("u12517j.dmask") != 0   # the same mask as the fit

norm = np.full(res.shape, np.nan)
ok = good & (model > 0)
norm[ok] = res[ok] / np.sqrt(model[ok])

hdr = fits.getheader("u12517_residual.fits")   # keeps the WCS
fits.writeto("u12517j_norm.fits", norm.astype(np.float32), hdr, overwrite=True)

Why not just use res != 0?

elliprof sets masked pixels to exactly 0, so res != 0 is nearly the mask, but not quite. A good pixel can also be exactly 0. In the UGC 12517 residual, 2 good pixels are exactly 0 (103,404 zeros for 103,402 masked pixels). Use the original mask.

5. Hand over

For the downstream analysis you now have:

File Use
u12517.prf normalisation (√model), and the galaxy brightness for colours
u12517_residual.fits the fluctuation image, before large-scale cleaning and point-source masking
u12517.dat the isophote geometry, e.g. to define elliptical annuli
the mask the same pixels to exclude

Record the elliprof version, the sky, the mask and every fit parameter with your SBF result (see What a result should report).

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