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tl;dr¶
The discovery of the Fermi Bubbles has led to a lot of interesting speculation about high energy phenomena originating at the center of the Milky Way. The analysis tools applied both in the original discovery and for testing subsequent physical hypotheses leave room for improvement, particularly in terms of moving from qualitative to quantitative assessment of the results. Here we describe one potential approach leveraging Haar wavelets to capture the expected multi-scale nature of structure in all-sky gamma-ray maps, coupled with statistics to quantify the tradeoffs between detection of detail and "false detections" resulting from photon counting noise.
Some example results are shown below. Or you can just jump in to the reading.
The following "movies" show results across a range of parameters. You can drag the slider manually or play via the controls.
The first result shows the "statistically significant difference" between a model of expected emission and the data for the 1-2 GeV energy range as a function of the false detection rate. Read the rest of the article to understand how "statistically significant difference" is evaluated. The take away here is that the Fermi bubbles, including some substructure, are robustly recovered even for a false detection rate as low as 1e-8 (which you can interpret as meaning we'd expect one out of every 100 billion wavelet coefficients as being accidentally detected due to noise). This also shows the tradeoff between noise and detail which can be controlled via the false detection rate.
This shows the reconstructed image as a function of wavelet scale given a false detection rate of 1e-6. Note how this detects the bubble "edges" at small scales, and broader excess at larger scales.
© 2023 Dave Dixon