adabin

Adaptive binning algorithm for 2D maps (please cite Li et al. 2023).

The core function is adap_bin() function in adabin.py. For display, simply run recon_plot() in map_plot.py.

In order to recover as many spatial pixels as possible, we use an adaptive binning scheme. For independent, identically distributed data we expect the S/N of binned data to increase in proportion to the square root of the number of binned pixels. This increase is paid for by a corresponding decrease in spatial resolution, and thus we only want to bin pixels where we are required to do so for S/N reasons. We therefore carry out the following steps:

(1) First we create a series of maps which cover the same area as our data, which we denote map_1, map_2, map_4, map_8, and so forth, where map_N is a map where we have binned each group of N^2 adjacent pixels in our data together. Therefore map_1 is our original data, while in map_2 we have averaged together every 2 times 2 set of pixels into a single pixel; thus map_2 has half the resolution and 4 times fewer pixels than map_1, but each pixel has 2 times the S/N of the original data. Similarly, in map_4 we bin together every set of 4 times 4 pixels from the original map to create a map with 16 times fewer pixels but 4 times the S/N, and so forth.

(2)We then generate an output map with the same size as map_1. For each pixel in the output map, we first locate the corresponding pixel in map_1, and ask if its S/N ratio is above some specified threshold. If so, we set the value of the pixel in the output map to the value of the pixel in map_1. If the S/N does not reach our threshold, we then examine the pixel in map_2 that covers the same area, and use its value instead if the S/N ratio is high enough. If not, we proceed to map_4, and so forth. We fill in every pixel in the output map in this manner.

We illustrate this process in the figure below, taking the [SII]6731 map of NGC7674 (also named as SN2011hb) in AMUSING++ as an example. The left panel shows the original data, with pixels below a S/N ratio of 3 masked. The middle panel shows the value N of the map_N for which the S/N reaches the target S/N of 3. As is clear from the figure, the algorithm uses high-resolution data in high S/N regions, and degrades smoothly to more and more binned data in regions of weak signal. The right panel then shows the final output, adaptively binned map. Again, we see that high-resolution information has been preserved where possible, but now none of the map area is masked.

If applying the code to an original datacube instead of a reduced line map, one needs a fitted continuum. In this case take a small window (typically $\pm5$ angstrom) centered at an emission line in a spectrum, then the signal is the sum of all the residuals after removing the continuum in the window.

signal = $\Sigma_{i} (s_i - c_i)$,

where $s$ is the original spectrum while $c$ is the fitted continuum, and $i$ represents each wavelength. The noise is written as

niose = $\sqrt{\Sigma_{i} (n_{s, i}^2 + n_{c, i}^2)}$,

where $n_s$ and $n_c$ are the noises of the original spectrum and the continuum, respectively. Note that this has to be done pixel-by-pixel because in one datacube the emission line will be shifted due to galaxy rotation. Once having a signal map and a noise map as above, put them into ADABIN.