Archive for May 4, 2012

Milky Way Satellites and Dark Matter

Posted in Astrohype, Bad Statistics, The Universe and Stuff with tags , , , , on May 4, 2012 by telescoper

I found a strange paper on the ArXiv last week, and was interested to see that it had been deemed to merit a press release from the Royal Astronomical Society that had been picked up by various sites across the interwebs.

The paper, to appear in due course in Monthly Notices of the Royal Astronomical Society, describes a study of the positions and velocities of small satellite galaxies and other object around the Milky Way, which suggest the existence of a flattened structure orientated at right angles to the Galactic plane. They call this the “Vast Polar Structure”. There’s even a nifty video showing this arrangement:

They argue that this is is evidence that these structures have a tidal origin, having been thrown out   in the collision between two smaller galaxies during the formation of the Milky Way. One would naively expect a much more isotropic distribution of material around our Galaxy if matter had fallen into it in the relatively quiescent way envisaged by more standard theoretical models.

Definitely Quite Interesting.

However, I was rather taken aback by this quotation by one of the authors, Pavel Kroupa, which ends the press release.

Our model appears to rule out the presence of dark matter in the universe, threatening a central pillar of current cosmological theory. We see this as the beginning of a paradigm shift, one that will ultimately lead us to a new understanding of the universe we inhabit.

Hang on a minute!

One would infer from this rather bold statement that the paper concerned contained a systematic comparison between the observations – allowing for selection effects, such as incomplete sky coverage – and detailed theoretical calculations of what is predicted in the standard theory of galaxy formation involving dark matter.

But it doesn’t.

What it does contain is a simple statistical calculation of the probability that the observed distribution of satellite galaxies would have arisen in an exactly isotropic distribution function, which they conclude to be around 0.2 per cent.

However, we already know that galaxies like the Milky Way are not exactly isotropic, so this isn’t really a test of the dark matter hypothesis. It’s a test of an idealised unrealistic model. And even if it were a more general test of the dark matter hypothesis, the probability of this hypothesis being correct is not what has been calculated. The probability of a model given the data is not the same as the probability of the data given the model. To get that you need Bayes’ theorem.

What needs to be done is to calculate the degree of anisotropy expected in the dark matter theory and in the tidal theory and then do a proper (i.e. Bayesian) comparison with the observations to see which model gives the better account of the data. This is not any easy thing to do because it necessitates doing detailed dynamical calculations at very high resolution of what galaxy like the Milky Way should look like according to both theories.

Until that’s done, these observations by no means “rule out” the dark matter theory.


The Tallis Scholars

Posted in Music with tags , , , , , on May 4, 2012 by telescoper

I’ve always wanted to be at a live performance of the legendary 40 part motet  Spem in Alium by Thomas Tallis, not only  because it’s a gorgeous piece of music but also because I’ve always wondered what the conductor is supposed to do with his hands when there are so many independent parts. It’s such a complicated and demanding work, however, that opportunities to hear it live are rather limited. Last night’s concert at St David’s Hall by the Tallis Scholars (supplemented by a local choir; the Tallis Scholars number only ten singers) actually involved two performances of Tallis’ most famous work, first at the beginning and then again right at the end.

If you’ve never heard Spem in Alium before, then you really should make the effort. It’s an extraordinary piece of music in many different ways. Most writers focus on its complexity, but that shouldn’t make you think Tallis was just showing off when he wrote it, or distract you from the fact that it’s so very beautiful to listen to. The forty parts  involved are divided into eight choirs, each of five voices. The piece starts with one voice from the first choir, and slowly evolves to incorporate all forty voices, waving each individual vocal line into a gorgeous musical tapestry. At times all the voices seem to be acting independently within the overall harmonic framework, at others the choirs act as the basic unit; there’s a wonderful passage, for example, when choirs throw phrases backwards and forwards between them. There are also moments when all the evolving parts come back into phase so that all voices sing the same words at the same time. The effect of this is indescribable; it sent cold shivers down my spine.

There is so much going on in this piece that it’s difficult to understand how Tallis managed to stop the different parts interfering destructively with each other, but Spem in Alium  never dissolves into a shapeless melisma. As the piece unfolds, the various patterns that appear and disappear are always held in sharp focus. It’s a masterpiece, and although the large space of St David’s Hall probably isn’t ideal for performing a work like this, my long wait to hear a live performance of this masterpiece was well worth it.

The concert wasn’t just about Spem in Alium.  The Tallis Scholars performed a number of other works on their own, including pieces by Tallis’ old mate William Byrd and part of one of my other favourite Tallis works, The Lamentations of Jeremiah. The programme called for various combinations of the singers drawn from the ten in the basic line-up, producing a wide range of texture and colour.

It was all extremely enjoyable, but my lasting memory will be the piece that started and ended the show. There’s so much to discover listening to Spem in Alium that the second performance of it that ended the concert made me want to hear a third straight away.

PS. One of the other pieces performed during the concert was Tallis’ Miserere, which aptly described Cardiff City’s performance at home to West Ham in their play-off semi-final which was being played at the same time as the concert!