Sister blog of Physicists of the Caribbean. Shorter, more focused posts specialising in astronomy and data visualisation.

Wednesday 13 April 2022

Not interesting but important

Well... it's probably unfair to say it isn't interesting. But when I read this paper I was expecting some cool scientific findings, of which there are none. Instead, this paper presents a new method for analysing HI spectra in a robust, reliable, objective way, providing quantitative ways to describe things like the shape of the profile and whether it's asymmetrical or not. They apply this to the enormous ALFALFA data set, so describing this method and giving the full catalogue on such a large sample is very important. It's just not interesting yet because they don't do any scientific analysis of the results.

Anyway, I've long thought that there's potentially a lot of unexploited information in an HI spectra. For example, the classic double-horn (a.k.a. Batman) profile arises because of flat rotation curves : most of the gas in a galaxy is moving at a single, constant velocity, irrespective of its distance from the galactic centre - the very discovery that led to the idea of dark matter. So could there be other such important discoveries to be made by further exploiting the data ?

Perhaps not. But it's been difficult to examine the spectral shapes in a systematic, objective way, because the measurements are surprisingly hard. Typically, we measure the width of the line at 20% and/or 50% of the peak flux (known as the W20 and W50 parameters) , and that's about it. Nobody does much with such nuances as the shape of the profile because objectively describing the shape is rather hard. 

There's one exception. People do try and measure the asymmetry, by comparing how much flux is found either side of the central velocity. Unfortunately this is the exception that proves the rule, as here the results prove controversial. You'd expect to see wonky profiles for galaxies in dense regions, where there are lots of gravitational interactions to disturb the gas. Some people find this, but some don't, and some find there are anyway strong asymmetries even in isolated galaxies, meaning there could be internal process causing disturbances as well. It's all very confusing, the numbers vary considerably, and not at all satisfying. Nobody can agree on what constitutes a significant level of asymmetry, which is a problem.

What the authors of the present study do here is actually better explained in their previous paper (see section 3.2 and especially figure 1). They use the curve of growth method to measure the HI spectra, something which is actually quite common in optical astronomy but not much used in HI analysis.

Let me explain the problem of the existing measurements a bit more. Usually, the W50 and W20 values are in good agreement. W50 is generally better because it's measured at a higher flux level, but in a strongly asymmetric profile, this can give an estimate of the line width that's much smaller than the true value - you can end up measuring only one of the horns, for example. W20, measured at a lower flux level, is often confused with noise, so can give width estimates which are too high. Although most of the time the two measurements do agree quite well, it'd sure be nice to have something more robust.

The curve of growth method is a pleasingly simple alternative. Starting from the central velocity, the flux is integrated incrementally over larger and larger velocity widths. And all you do is then plot the cumulative flux over these increasing widths, and what you get is roughly a linear slope which then quite suddenly flattens when you hit the edge of the galaxy. Et voilĂ , a robust, objective way to determine the true velocity width of the galaxy, irrespective of the shape of the profile.

Marvellous ! But there's more. You can parameterise the width in different ways, e.g. by looking for the width that encloses, say, 85 or 90% of the total, giving objective criteria for measuring both width and total flux that account for the signal to noise. And you can do the curve of growth for each half of the spectrum separately, giving you robust flux ratios for measuring asymmetry. 

*Importantly, though the details are boring, the authors also correct for how much the signal to noise level affects the measured asymmetry, meaning you can now reliably quantify the significance level of any measured asymmetry and thus settle any arguments about how much of a flux ratio is really needed to quantify as asymmetry.

This also gives additional parameters. For asymmetric profiles, the slopes of the two curves of growth are different, so you can also compare the slopes as a measure of asymmetry as well as the flux ratio. And more complex parameters can quantify the actual shape of the profile. They favour a parameter they call K, which measures how much the integrated flux compares to the case of a linear increase : the linear case (K=0) corresponds to a flat-topped profile, while K < 0 (less flux than linear) corresponds to double-horned profiles and K > 0 happens for single-peaked profiles.

What this means is they can create reliable, quantifiable, continuous parameters for measuring both asymmetry and shape. What they stop short of doing is any sort of analysis on the results. Are double-horn profiles more common in certain environments, or dependent only on galaxy morphology ? Are there any galaxies with strong HI asymmetries but without optical disturbances ? Does K vary linearly, or does it fall into nice neat groupings ? Do these new parameters work well at low S/N levels ? Can they help with source extraction or this is strictly only for analysis ?

This paper very literally raises a lot more questions than it answers, which is a good thing in this case. Though I'd like to really have a good thorough look at how this technique works in anger, it's got definite potential for being a classic case of, "why hasn't anyone done this already ?". Even if it isn't likely to lead to another discovery as profound as dark matter, it's still likely to give rise to a veritable plethora of spin-off papers and a horde of citations so large the Mongols would be jealous. Well, maybe.

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