## Why the Universe is extremely overrated.

Posted in Television, The Universe and Stuff with tags , , , , , , on June 19, 2018 by telescoper

A few weeks I read an article in Physics Today which prompted me to revise and resubmit an old post I cobbled together in response to the BBC television series Wonders of the Universe in which I argued that the title of that programme suggests that the Universe is wonder-ful, or even, in a word which has cropped up in the series a few times, awesome’.  When you think about it the Universe is not really awesome at all’. In fact it’s extremely overrated.

Take this thing, for example:

This is an example of a galaxy (the Andromeda Nebula, M31, to be precise). We live in a similar object. Of course it looks quite pretty on the surface but, when you look at it with a physicist’s eye, such a galaxy is really not as great as it’s cracked up to be, as I shall now explain.

We live in a relatively crowded part of our galaxy on a small planet orbiting a fairly insignificant star called the Sun. Now you’ve got me started on the Sun. I know it supplies the Earth with all its energy, but it does the job pretty badly, all things considered because the Sun only radiates a fraction of a milliwatt per kilogram. By comparison a human being radiates more than one watt per kilogram. Pound for pound, that’s more than a thousand times as much energy as a star.

So,  in reality, stars are bloated, wasteful, inefficient and not even slightly awesome. They’re only noticeable because they’re big. And we all know that size shouldn’t really matter. In short, stars are extremely overrated.

But even in what purports to be an interesting neighbourhood of our Galaxy, the nearest star is 4.5 light years from the Sun. To get that in perspective, imagine the Sun is the size of a golfball. On the same scale, where is the nearest star?

The answer to that will probably surprise you, as it does my students when I give this example in lectures. The answer is, in fact, on the order of a thousand kilometres away. That’s the distance from Cardiff to, say, Munich. What a dull landscape our Galaxy possesses. In between one little golf ball in Wales and another one in Germany there’s nothing of any interest at all, just a featureless incomprehensible void not worthy of the most perfunctory second thought.

So galaxies aren’t dazzlingly beautiful jewels of the heavens. They’re flimsy, insubstantial things more like the cheap tat you can find on QVC. What’s worse is that they’re also full of a grubby mixture of soot and dust. Indeed, some are so filthy that you can hardly see any stars at all. Somebody needs to give the Universe a good clean. I suppose you just can’t get the help these days.

And then to the Physics Today piece I mentioned at the start of this article. I quote:

Star formation is stupendously inefficient. Take the Milky Way. Our galaxy contains about a billion solar masses of fresh gas available to form stars—and yet it produces only one solar mass of new stars a year.

Hopeless! What a waste of space a galaxy is! As well as being oversized, vacuous and rather dirty, one is also pretty useless at making the very things it is supposed to be good at! What galaxies clearly need is some sort of a productivity drive or perhaps a complete redesign using more efficient technology.

So stars are overrated and galaxies are overrated, but surely the Universe as a whole is impressive?

No. Think about the Big Bang. Well, I don’t need to go on about that because I’ve already posted about it. Suffice to say that the Big Bang wasn’t anywhere near as Big as you’ve been led to believe: the volume was between about 115 and 120 decibels. Quite loud, to be sure, but many rock concerts are louder. To be honest it’s a bit of an anti-climax. If I’d been in charge (and given sufficient funding) I would have put on something much more spectacular.

In any case the Big Bang happened a very long time ago. Since then the Universe has been expanding, the space between galaxies getting emptier and emptier so there’s now less than one atom per cubic metre, and cooling down to the point where its temperature is lower than three degrees above absolute zero.

The Universe is a cold, desolate and very empty place, lit by a few feeble stars and warmed only by the fading glow of the heat left over from when it was all so much younger and more exciting. Here and there amid the cosmic void a few galaxies are dotted about, like cheap and rather tatty ornaments. It’s as if we inhabit a shabby downmarket retirement home, warmed only by the feeble radiation given off by a puny electric fire as we occupy ourselves as best we can until Armageddon comes.

In my opinion the Universe would have worked out better had it been entirely empty, instead of being contaminated with such detritus. I agree with Tennessee Williams:

BRICK: “Well, they say nature hates a vacuum, Big Daddy.
BIG DADDY: “That’s what they say, but sometimes I think that a vacuum is a hell of a lot better than some of the stuff that nature replaces it with.”

So no, the Universe isn’t wonderful. Not at all. In fact, it’s basically a bit rubbish. Again, it’s only superficially impressive because it’s quite large, and it doesn’t do to be impressed by things just because they are large. That would be vulgar.

Digression: I just remembered a story about a loudmouthed Texan who owned a big ranch and who was visiting the English countryside on holiday. Chatting to locals in the village pub he boasted that it took him several days to drive around his ranch. A farmer replied “Yes. I used to have a car like that.”

Ultimately, however, the fact is that whatever we think about the Universe and how badly constructed it it, we’re stuck with it. Just like the trains, the government and the weather. There’s nothing we can do about it, so we might as grin and bear it.

It’s being so cheerful that helps keep me going.

## Celebrating the Sloan Telescope

Posted in The Universe and Stuff with tags , , , , , , , , on May 9, 2018 by telescoper

A little bird tweeted at me this morning that today is the 20th anniversary of first light through the Sloan Telescope (funded by the Alfred P. Sloan Foundation) which has, for the past two decades, been surveying as much of the sky as it can from its location in New Mexico (about 25% altogether): the Sloan Digital Sky Survey is now on its 14th data release.

Here’s a picture of the telescope:

For those of you who want the optical details, the Sloan Telescope is a 2.5-m f/5 modified Ritchey-Chrétien altitude-azimuth telescope located at Apache Point Observatory, in south east New Mexico (Latitude 32° 46′ 49.30″ N, Longitude 105° 49′ 13.50″ W, Elevation 2788m). A 1.08 m secondary mirror and two corrector lenses result in a 3° distortion-free field of view. The telescope is described in detail in a paper by Gunn et al. (2006).

A 2.5m telescope of modest size by the standards of modern astronomical research, but the real assets of the Sloan telescope is a giant mosaic camera, highly efficient instruments and a big investment in the software required to generate and curate the huge data sets it creates. A key feature of SDSS is that its data sets are publicly available and, as such, they have been used in countless studies by a huge fraction of the astronomical community.

The Sloan Digital Sky Survey’s original legacy’ survey was basically a huge spectroscopic redshift survey, mapping the positions of galaxies and quasars in three dimensions to reveal the cosmic web’ in unprecedented detail:

As it has been updated and modernised, the Sloan Telescope has been involved in a range of other surveys aimed at uncovering different aspects of the universe around us, including several programmes still ongoing.

## Gaia’s Second Data Release!

Posted in The Universe and Stuff with tags , , , on April 26, 2018 by telescoper

It seems like only yesterday that I was blogging excitedly about the first release of data (DR1) from the European Space Agency’s Gaia Mission. In fact it was way back in 2016! Anyway, yesterday came another glut of Gaia goodness in the form of the second release of data, known to its friends as DR2.

In case you weren’t aware, Gaia is an ambitious space mission to chart a three-dimensional map of our Galaxy, the Milky Way, in the process revealing the composition, formation and evolution of the Galaxy. Gaia will provide unprecedented positional and radial velocity measurements with the accuracy needed to produce a stereoscopic and kinematic census of about one billion stars in our Galaxy and throughout the Local Group. This amounts to about 1 per cent of the Galactic stellar population.

You can find links to all the DR2 science papers here, a guide to how to use the data here, and of course a link to the full Gaia Archive here.

Here’s a (brief!) list of the contents of DR2:

• The five-parameter astrometric solution – positions on the sky (α, δ), parallaxes, and proper motions – for more than 1.3 billion (109) sources, with a limiting magnitude of G = 21 and a bright limit of G ≈ 3. Parallax uncertainties are in the range of up to 0.04 milliarcsecond for sources at G < 15, around 0.1 mas for sources with G=17 and at the faint end, the uncertainty is of the order of 0.7 mas at G = 20. The corresponding uncertainties in the respective proper motion components are up to 0.06 mas yr-1 (for G < 15 mag), 0.2 mas yr-1 (for G = 17 mag) and 1.2 mas yr-1 (for G = 20 mag). The Gaia DR2 parallaxes and proper motions are based only on Gaia data; they do no longer depend on the Tycho-2 Catalogue.
• Median radial velocities (i.e. the median value over the epochs) for more than 7.2 million stars with a mean G magnitude between about 4 and 13 and an effective temperature (Teff) in the range of about 3550 to 6900 K. This leads to a full six-parameter solution: positions and motions on the sky with parallaxes and radial velocities, all combined with mean G magnitudes. The overall precision of the radial velocities at the bright end is in the order of 200-300 m s-1 while at the faint end the overall precision is approximately 1.2 km s-1 for a Teff of 4750 K and about 2.5 km s-1 for a Teff of 6500 K.
• An additional set of more than 361 million sources for which a two-parameter solution is available: the positions on the sky (α, δ) combined with the mean G magnitude. These sources have a positional uncertainty at G=20 of about 2 mas, at J2015.5.
G magnitudes for more than 1.69 billion sources, with precisions varying from around 1 milli-mag at the bright (G<13) end to around 20 milli-mag at G=20. Please be aware that the photometric system for the G band in Gaia DR2 is different from the photometric system as used in Gaia DR1.
• GBP and GRP magnitudes for more than 1.38 billion sources, with precisions varying from a few milli-mag at the bright (G<13) end to around 200 milli-mag at G=20.
• Full passband definitions for G, BP and RP. These passbands are now available for download.
• Epoch astrometry for 14,099 known solar system objects based on more than 1.5 million CCD observations. 96% of the along-scan (AL) residuals are in the range -5 to 5 mas, and 52% of the AL residuals are in the range of -1 to 1 mas. The transit observations are part of Gaia DR2 and have also been delivered to the Minor Planet Center (MPC).
• Subject to limitations (see below) the effective temperatures Teff for more than 161 million sources brighter than 17th magnitude with effective temperatures in the range 3000 to 10,000 K. For a subset of about 87 million sources also the line-of-sight extinction AG and reddening E(BP-RP) are given and for a part of this subset (around 76 million sources) the luminosity and radius are available as well.
• Classifications for more than 550,000 variable sources consisting of Cepheids, RR Lyrae, Mira and Semi-Regular Candidates as well as High-Amplitude Delta Scuti, BY Draconis candidates, SX Phoenicis Candidates and short time scale phenomena.
• Planned cross-matches between Gaia DR2 sources on the one hand and Hipparcos-2, Tycho-2, 2MASS PSC, SDSS DR9, Pan-STARRS1, GSC2.3, PPM-XL, AllWISE, and URAT-1 data on the other hand.

There’s much more to Gaia than pictures, but here’s a map of the stars in our galaxy to give you an idea:

I remember first hearing about Gaia about 17 years ago when I was on a PPARC advisory panel and was immediately amazed  by the ambition of its objectives. As I mentioned above, Gaia is a global space astrometry mission, which will make the largest, most precise three-dimensional map of our Galaxy by surveying more than a billion stars. In some sense Gaia is the descendant of the Hipparcos mission launched in 1989, but it’s very much more than that. Gaia monitors each of its target stars about 70 times over a five-year period. It is expected to discover hundreds of thousands of new celestial objects, such as extra-solar planets and brown dwarfs, and observe hundreds of thousands of asteroids within our own Solar System. The mission is also expected to yield a wide variety of other benefits, including new tests of the  General Theory of Relativity.

For the brighter objects, i.e. those brighter than magnitude 15, Gaia  measures their positions to an accuracy of 24 microarcseconds, comparable to measuring the diameter of a human hair at a distance of 1000 km. Distances of relatively nearby stars are measured to an accuracy of 0.001%. Even stars near the Galactic Centre, some 30,000 light-years away, have their distances measured to within an accuracy of 20%.

It’s an astonishing mission that will leave an unbelievably rich legacy not only for the astronomers working on the front-line operations of Gaia but for generations to come.

## EWASS in Liverpool

Posted in Football, The Universe and Stuff with tags , , , , , on April 4, 2018 by telescoper

I’m back in Maynooth with teaching to do after the Easter recess. The Flybe schedule having just changed for the summer, I took a 7am flight from Cardiff to Dublin this morning, which meant getting up at stupid o’clock, but I got here safely enough to Maynooth at about 9.40am.

Anyway, had I not known that I would be here in Ireland I would probably have planned to visit the English Midlands in order to attend EWASS (European Week of Astronomy and Space Science) which takes place this week in Liverpool. This meeting, which is in a different country each year, this time incorporates the Royal Astronomical Society’s annual National Astronomy Meeting making it one of the biggest astronomy conferences ever held in the UK.

Sadly my teaching commitments meant I couldn’t attend EWASS2018, but I thought I’d take this opportunity to wish everyone there all the best for an enjoyable and productive week.

I’ll also mention that various short videos of press briefings etc are coming out on Youtube with little snippets from the conference, including this one about Ariel (which I blogged about recently):

You can find other videos by searching for EWASS on Youtube. I’m sure more will emerge over the next couple of days!

P.S. The event in Liverpool has clearly been planned with football fans in mind: Liverpool play Manchester City tonight, in Liverpool, in the UEFA Champions League..(UPDATE: the match finished 3-0 to Liverpool, which presumably pleased the locals).

## Equinoctial Molehills

Posted in Biographical, Bute Park, The Universe and Stuff with tags , , , on March 20, 2018 by telescoper

Very busy today, what with a return to lecturing in Cardiff and so on, so I’ve just got time for a quick post to mark the fact that the Vernal Equinox in the Northern Hemisphere took place today, Tuesday 20th March 2018, at 16.15 UTC (which is 16.15 GMT). This means that the Sun has just crossed the celestial equator on its journey Northward. Some people regard this as the first day of spring, which is fair enough as it does correspond fairly well to the end of the Six Nations rugby.

It wasn’t exactly spring weather when I walked into work this morning, as there are still bits of snow around in Bute Park.

More significantly, a huge number of molehills have appeared. Not quite a mole of molehills, but still quite a few. I’m not sure of the reason for all this molar activity. Perhaps moles have special rituals for marking the Vernal Equinox?

Incidentally I was dismayed to see that my Royal Astronomical Society diary gives the time of the 2018 Vernal Equinox as 16.16 GMT while the wikipedia page I linked to above gives 16.15 GMT. I find a discrepancy of this magnitude extremely unnerving. Or am I making a mountain out of a molehill?

## What the Power Spectrum misses

Posted in The Universe and Stuff with tags , , , , , , , on August 2, 2017 by telescoper

Just taking a short break from work I chatted over coffee to one of the students here at the Niels Bohr Institute about various things to do with the analysis of signals in the Fourier domain (as you do). That discussion reminded me of this rather old post (from 2009) which I thought might be worth a second airing (after a bit of editing). The discussion is all based on past cosmological data (from WMAP) rather than the most recent (from Planck), but that doesn’t change anything qualitatively. So here you are.

The picture above shows the all-sky map of fluctuations in the temperature of the cosmic microwave background across the sky as revealed by the Wilkinson Microwave Anisotropy Probe, known to its friends as WMAP.

I spent many long hours fiddling with the data coming from the WMAP experiment, partly because I’ve never quite got over the fact that such wonderful data actually exists. When I started my doctorate in 1985 the whole field of CMB analysis was so much pie in the sky, as no experiments had yet been performed with the sensitivity to reveal the structures we now see. This is because they are very faint and easily buried in noise. The fluctuations in temperature from pixel to pixel across the sky are of order one part in a hundred thousand of the mean temperature (i.e. about 30 microKelvin on a background temperature of about 3 Kelvin). That’s smoother than the surface of a billiard ball. That’s why it took such a long time to make the map shown above, and why it is such a triumphant piece of science.

I blogged a while ago about the idea that the structure we see in this map was produced by sound waves reverberating around the early Universe. The techniques cosmologists use to analyse this sound are similar to those used in branches of acoustics except that we only see things in projection on the celestial sphere which requires a bit of special consideration.

One of the things that sticks in my brain from my undergraduate years is being told that if you don’t know what you’re doing as a physicist you should start by making a Fourier transform of everything. This approach breaks down the phenomenon being studied into a set of  plane waves with different wavelengths corresponding to analysing the different tones present in a complicated sound.

It’s often very good advice to do such a decomposition for one-dimensional time series or fluctuation fields in three-dimensional Cartesian space, even you do know what you’re doing, but it doesn’t work with a sphere because plane waves don’t fit properly on a curved surface. Fortunately, however, there is a tried-and-tested alternative involving spherical harmonics rather than plane waves.

Spherical harmonics are quite complicated beasts mathematically but they have pretty similar properties to Fourier harmonics in many respects. In particular they are represented as complex numbers having real and imaginary parts or, equivalently, an amplitude and a phase (usually called the argument by mathematicians),

$Z=X+iY = R \exp(i\phi)$

This latter representation is the most useful one for CMB fluctuations because the simplest versions of inflationary theory predict that the phases φ of each of the spherical harmonic modes should be randomly distributed. What this really means is that there is no information content in their distribution so that the harmonic modes are in a state of maximum statistical disorder or entropy. This property also guarantees that the distribution of fluctuations over the sky should have a Gaussian distribution.

If you accept that the fluctuations are Gaussian then only the amplitudes of the spherical harmonic coefficients are useful. Indeed, their statistical properties can be specified entirely by the variance of these amplitudes as a function of mode frequency. This pre-eminently important function is called the power-spectrum of the fluctuations, and it is shown here for the WMAP data:

Although the units on the axes are a bit strange it doesn”t require too much imagination to interpret this in terms of a sound spectrum. There is a characteristic tone (at the position of the big peak) plus a couple of overtones (the bumps at higher frequencies). However these features are not sharp so the overall sound is not at all musical.

If the Gaussian assumption is correct then the power-spectrum contains all the useful statistical information to be gleaned from the CMB sky, which is why so much emphasis has been placed on extracting it accurately from the data.

Conversely, though, the power spectrum is completely insensitive to any information in the distribution of spherical harmonic phases. If something beyond the standard model made the Universe non-Gaussian it would affect the phases of the harmonic modes in a way that would make them non-random.

However,I will now show you how important phase information could actually be, if only we could find a good way of exploiting it. Let’s start with a map of the Earth, with the colour representing height of the surface above mean sea level:

You can see the major mountain ranges (Andes, Himalayas) quite clearly as red in this picture and note how high Antarctica is…that’s one of the reasons so much astronomy is done there.

Now, using the same colour scale we have the WMAP data again (in Galactic coordinates).

The virture of this representation of the map is that it shows how smooth the microwave sky is compared to the surface of the Earth. Note also that you can see a bit of crud in the plane of the Milky Way that serves as a reminder of the difficulty of cleaning the foregrounds out.

Clearly these two maps have completely different power spectra. The Earth is dominated by large features made from long-wavelength modes whereas the CMB sky has relatively more small-scale fuzz.

Now I’m going to play with these maps in the following rather peculiar way. First, I make a spherical harmonic transform of each of them. This gives me two sets of complex numbers, one for the Earth and one for WMAP. Following the usual fashion, I think of these as two sets of amplitudes and two sets of phases. Note that the spherical harmonic transformation preserves all the information in the sky maps, it’s just a different representation.

Now what I do is swap the amplitudes and phases for the two maps. First, I take the amplitudes of WMAP and put them with the phases for the Earth. That gives me the spherical harmonic representation of a new data set which I can reveal by doing an inverse spherical transform:

This map has exactly the same amplitudes for each mode as the WMAP data and therefore possesses an identical power spectrum to that shown above. Clearly, though, this particular CMB sky is not compatible with the standard cosmological model! Notice that all the strongly localised features such as coastlines appear by virtue of information contained in the phases but absent from the power-spectrum.

To understand this think how sharp features appear in a Fourier transform. A sharp spike at a specific location actually produces a broad spectrum of Fourier modes with different frequencies. These modes have to add in coherently at the location of the spike and cancel out everywhere else, so their phases are strongly correlated. A sea of white noise also has a flat power spectrum but has random phases. The key difference between these two configurations is not revealed by their spectra but by their phases.

Fortunately there is nothing quite as wacky as a picture of the Earth in the real data, but it makes the point that there are more things in Heaven and Earth than can be described in terms of the power spectrum!

Finally, perhaps in your mind’s eye you might consider what it might look lie to do the reverse experiment: recombine the phases of WMAP with the amplitudes of the Earth.

If the WMAP data are actually Gaussian, then this map is a sort of random-phase realisation of the Earth’s power spectrum. Alternatively you can see that it is the result of running a kind of weird low-pass filter over the WMAP fluctuations. The only striking things it reveals are (i) a big blue hole associated with foreground contamination, (ii) a suspicious excess of red in the galactic plane owing to the same problem, and (iiI) a strong North-South asymmetry arising from the presence of Antarctica.

There’s no great scientific result here, just a proof that spherical harmonic phases are potentially interesting because of the information they contain about strongly localised features

PS. These pictures were made by a former PhD student of mine, Patrick Dineen, who has since quit astrophysics  to work in the financial sector for Winton Capital, which has over the years recruited a number of astronomy and cosmology graduates and also sponsors a Royal Astronomical Society prize. That shows that the skills and knowledge obtained in the seemingly obscure field of cosmological data analysis have applications elsewhere!

## Yellow Stars, Red Stars and Bayesian Inference

Posted in Bad Statistics, The Universe and Stuff with tags , , , , , , on May 25, 2017 by telescoper

I came across a paper on the arXiv yesterday with the title Why do we find ourselves around a yellow star instead of a red star?’.  Here’s the abstract:

M-dwarf stars are more abundant than G-dwarf stars, so our position as observers on a planet orbiting a G-dwarf raises questions about the suitability of other stellar types for supporting life. If we consider ourselves as typical, in the anthropic sense that our environment is probably a typical one for conscious observers, then we are led to the conclusion that planets orbiting in the habitable zone of G-dwarf stars should be the best place for conscious life to develop. But such a conclusion neglects the possibility that K-dwarfs or M-dwarfs could provide more numerous sites for life to develop, both now and in the future. In this paper we analyze this problem through Bayesian inference to demonstrate that our occurrence around a G-dwarf might be a slight statistical anomaly, but only the sort of chance event that we expect to occur regularly. Even if M-dwarfs provide more numerous habitable planets today and in the future, we still expect mid G- to early K-dwarfs stars to be the most likely place for observers like ourselves. This suggests that observers with similar cognitive capabilities as us are most likely to be found at the present time and place, rather than in the future or around much smaller stars.

Athough astrobiology is not really my province,  I was intrigued enough to read on, until I came to the following paragraph in which the authors attempt to explain how Bayesian Inference works:

We approach this problem through the framework of Bayesian inference. As an example, consider a fair coin that is tossed three times in a row. Suppose that all three tosses turn up Heads. Can we conclude from this experiment that the coin must be weighted? In fact, we can still maintain our hypothesis that the coin is fair because the chances of getting three Heads in a row is 1/8. Many events with a probability of 1/8 occur every day, and so we should not be concerned about an event like this indicating that our initial assumptions are flawed. However, if we were to flip the same coin 70 times in a row with all 70 turning up Heads, we would readily conclude that the experiment is fixed. This is because the probability of flipping 70 Heads in a row is about 10-22, which is an exceedingly unlikely event that has probably never happened in the history of the universe. This
informal description of Bayesian inference provides a way to assess the probability of a hypothesis in light of new evidence.

Obviously I agree with the statement right at the end that Bayesian inference provides a way to assess the probability of a hypothesis in light of new evidence’. That’s certainly what Bayesian inference does, but this informal description’ is really a frequentist rather than a Bayesian argument, in that it only mentions the probability of given outcomes not the probability of different hypotheses…

Anyway, I was so unconvinced by this description’ that I stopped reading at that point and went and did something else. Since I didn’t finish the paper I won’t comment on the conclusions, although I am more than usually sceptical. You might disagree of course, so read the paper yourself and form your own opinion! For me, it goes in the file marked Bad Statistics!