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7.4.6.5 Surface brightness measurements ¶

In astronomy, Surface brightness is most commonly measured in units of magnitudes per arcsec\(^2\) (for the formal definition, see Brightness, Flux, Magnitude and Surface brightness). Therefore it involves both the values of the pixels within each input label (or output row) and their position.

--sb

The surface brightness (in units of mag/arcsec\(^2\)) of the labeled region (objects or clumps). For more on the definition of the surface brightness, see Brightness, Flux, Magnitude and Surface brightness.

--sb-error

Error in measuring the surface brightness (the --sb column). This column will use the value given to --spatialresolution in the processing (in pixels). For more on --spatialresolution, see MakeCatalog inputs and basic settings and for the equation used to derive the surface brightness error, see Surface brightness error of each detection.

--upperlimit-sb

The upper-limit surface brightness (in units of mag/arcsec\(^2\)) of this labeled region (object or clump). In other words, this option measures the surface brightness of noise within the footprint of each input label.

This is just a simple wrapper over lower-level columns: setting B and A as the value in the columns --upperlimit and --area-arcsec2, we fill this column by simply use the surface brightness equation of Brightness, Flux, Magnitude and Surface brightness.

--half-sum-sb

Surface brightness (in units of mag/arcsec\(^2\)) within the area that contains half the total sum of the label’s pixels (object or clump). This is useful as a measure of the sharpness of an astronomical object: for example a star will have very few pixels at half the maximum, so its --half-sum-sb will be much brighter than a galaxy at the same magnitude. Also consider --half-max-sb below.

This column just plugs in the values of half the value of the --sum column and the --half-sum-area column, into the surface brightness equation. Therefore please see the description in --half-sum-area to understand the systematics of this column and potential biases (see Morphology measurements (non-parametric)).

--half-max-sb

The surface brightness (in units of mag/arcsec\(^2\)) within the region that contains half the maximum value of the labeled region. Like --half-sum-sb this option this is a good way to identify the “central” surface brightness of an object. To know when this measurement is reasonable, see the description of --fwhm in Morphology measurements (non-parametric).

--sigclip-mean-sb

Surface brightness (over 1 pixel’s area in arcsec\(^2\)) of the sigma-clipped mean value of the pixel values distribution associated to each label (object or clump). This is useful in scenarios where your labels have approximately constant surface brightness values after after removing outliers: for example in a radial profile, see Invoking astscript-radial-profile).

In other scenarios it should be used with extreme care. For example over the full area of a galaxy/star the pixel distribution is not constant (or symmetric after adding noise), their pixel distributions are inherently skewed (with fewer pixels in the center, having a very large value and many pixels in the outer parts having lower values). Therefore, sigma-clipping is not meaningful for such objects! For more on the definition of the surface brightness, see Brightness, Flux, Magnitude and Surface brightness, for more on sigma-clipping, see Sigma clipping.

The error in this magnitude can be retrieved from the --sigclip-mean-sb-delta column described below, and you can use the --sigclip-std-sb column to find when the magnitude has become noise-dominated (signal-to-noise ratio is roughly 1). See the description of these two options for more.

--sigclip-mean-sb-delta

Scatter in the --sigclip-mean-sb without using the standard deviation of each pixel (that is given by --instd in MakeCatalog inputs and basic settings). The scatter here is measured from the values of the label themselves. This measurement is therefore most meaningful when you expect the flux across one label to be constant (as in a radial profile for example).

This is calculated using the equation in Surface brightness error of each detection, where \(\Delta{A}=0\) (since sigma-clip is calculated per pixel and there is no error in a single pixel). Within the equation to derive \(\Delta{M}\) (the error in magnitude, derived in Magnitude measurement error of each detection), the signal-to-noise ratio is defined by dividing the sigma-clipped mean by the sigma-clipped standard deviation.

--sigclip-std-sb

The surface brightness of the sigma-clipped standard deviation of all the pixels with the same label. For labels that are expected to have the same value in all their pixels (for example each annulus of a radial profile) this can be used to find the reliable (\(1\sigma\)) surface brightness for that label. In other words, if --sigclip-mean-sb is fainter than the value of this column, you know that noise is becoming significant. However, as described in --sigclip-mean-sb, the sigma-clipped measurements of MakeCatalog should only be used in certain situations like radial profiles, see the description there for more.