## Cosmology on its beam-ends?

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , on June 14, 2010 by telescoper

Interesting press release today from the Royal Astronomical Society about a paper (preprint version here) which casts doubt on whether the Wilkinson Microwave Anisotropy Probe supports the standard cosmological model to the extent that is generally claimed. Apologies if this is a bit more technical than my usual posts (but I like occasionally to pretend that it’s a science blog).

The abstract of the paper (by Sawangwit & Shanks) reads

Using the published WMAP 5-year data, we first show how sensitive the WMAP power spectra are to the form of the WMAP beam. It is well known that the beam profile derived from observations of Jupiter is non-Gaussian and indeed extends, in the W band for example, well beyond its 12.’6 FWHM core out to more than 1 degree in radius. This means that even though the core width corresponds to wavenumber l ~ 1800, the form of the beam still significantly affects the WMAP results even at l~200 which is the scale of the first acoustic peak. The difference between the beam convolved Cl; and the final Cl is ~ 70% at the scale of the first peak, rising to ~ 400% at the scale of the second.  New estimates of the Q, V and W-band beam profiles are then presented, based on a stacking analysis of the WMAP5 radio source catalogue and temperature maps. The radio sources show a significantly (3-4σ) broader beam profile on scales of 10′-30′ than that found by the WMAP team whose beam analysis is based on measurements of Jupiter. Beyond these scales the beam profiles from the radio sources are too noisy to give useful information. Furthermore, we find tentative evidence for a non-linear relation between WMAP and ATCA/IRAM 95 GHz source fluxes. We discuss whether the wide beam profiles could be caused either by radio source extension or clustering and find that neither explanation is likely. We also argue against the possibility that Eddington bias is affecting our results. The reasons for the difference between the radio source and the Jupiter beam profiles are therefore still unclear. If the radio source profiles were then used to define the WMAP beam, there could be a significant change in the amplitude and position of even the first acoustic peak. It is therefore important to identify the reasons for the differences between these two beam profile estimates.

The press release puts it somewhat more dramatically

New research by astronomers in the Physics Department at Durham University suggests that the conventional wisdom about the content of the Universe may be wrong. Graduate student Utane Sawangwit and Professor Tom Shanks looked at observations from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite to study the remnant heat from the Big Bang. The two scientists find evidence that the errors in its data may be much larger than previously thought, which in turn makes the standard model of the Universe open to question. The team publish their results in a letter to the journal Monthly Notices of the Royal Astronomical Society.

I dare say the WMAP team will respond in due course, but this paper spurred me to mention some work on this topic that was done by my friend (and former student) Lung-Yih Chiang. During his last visit to Cardiff we discussed this at great length and got very excited at one point when we thought we had discovered an error along the lines that the present paper claims. However, looking more carefully into it we decided that this wasn’t the case and we abandoned our plans to publish a paper on it.

Let me show you a few slides from a presentation that Lung-Yih gave to me a while ago. For a start here is the famous power-spectrum of the temperature fluctuations of the cosmic microwave background which plays an essential role in determining the parameters of the standard cosmology:

The position of the so-called “acoustic peak” plays an important role in determining the overall curvature of space-time on cosmological scales and the higher-order peaks pin down other parameters. However, it must be remembered that WMAP doesn’t just observe the cosmic microwave background. The signal it receives is heavily polluted by contamination from within our Galaxy and there is also significant instrumental noise.  To deal with this problem, the WMAP team exploit the five different frequency channels with which the probe is equipped, as shown in the picture below.

The CMB, being described by a black-body spectrum, has a sky temperature that doesn’t vary with frequency. Foreground emission, on the other hand, has an effective temperature that varies with frequency in way that is fairly well understood. The five available channels can therefore be used to model and subtract the foreground contribution to the overall signal. However, the different channels have different angular resolution (because they correspond to different wavelengths of radiation). Here are some sample patches of sky illustrating this

At each frequency the sky is blurred out by the “beam” of the WMAP optical system; the blurring is worse at low frequencies than at high frequencies. In order to do the foreground subtraction, the WMAP team therefore smooth all the frequency maps to have the same resolution, i.e. so the net effect of optical resolution and artificial smoothing produces the same overall blurring (actually 1 degree).  This requires accurate knowledge of the precise form of the beam response of the experiment to do it accurately. A rough example (for illustration only) is given in the caption above.

Now, here are the power spectra of the maps in each frequency channel

Note this is Cl not l(l+1)Cl as in the first plot of the spectrum. Now you see how much foreground there is in the data: the curves would lie on top of each other if the signal were pure CMB, i.e. if it did not vary with frequency. The equation at the bottom basically just says that the overall spectrum is a smoothed version of the CMB plus the foregrounds  plus noise. Note, crucially,  that the smoothing suppresses the interesting high-l wiggles.

I haven’t got space-time enough to go into how the foreground subtraction is carried out, but once it is done it is necessary to “unblur” the maps in order to see the structure at small angular scales, i.e. at large spherical harmonic numbers l. The initial process of convolving the sky pattern with a filter corresponds to multiplying the power-spectrum with a “window function” that decreases sharply at high l, so to deconvolve the spectrum one essentially has to divide by this window function to reinstate the power removed at high harmonics.

This is where it all gets very tricky. The smoothing applied is very close to the scale of the acoustic peaks so you have to do it very carefully to avoid introducing artificial structure in Cl or obliterating structure that you want to see. Moreover, a small error in the beam gets blown up in the deconvolution so one can go badly wrong in recovering the final spectrum. In other words, you need to know the beam very well to have any chance of getting close to the right answer!

The next picture gives a rough model for how much the “recovered” spectrum depends on the error produced by making even a small error in the beam profile which, for illustration only, is assumed to be Gaussian. It also shows how sensitive the shape of the deconvolved spectrum is to small errors in the beam.

Incidentally, the ratty blue line shows the spectrum obtained from a small patch of the sky rather than the whole sky. We were interested to see how much the spectrum varied across the sky so broke it up into square patches about the same size as those analysed by the Boomerang experiment. This turns out to be a pretty good way of getting the acoustic peak position but, as you can see, you lose information at low l (i.e. on scales larger than the patch).

The WMAP beam isn’t actually Gaussian – it differs quite markedly in its tails, which means that there’s even more cross-talk between different harmonic modes than in this example - but I hope you get the basic point. As Sawangwit & Shanks say, you need to know the beam very well to get the right fluctuation spectrum out. Move the acoustic peak around only slightly and all bets are off about the cosmological parameters and, perhaps, the evidence for dark energy and dark matter. Lung-Yih looked at the way the WMAP had done it and concluded that if their published beam shape was right then they had done a good job and there’s nothing substantially wrong with the results shown in the first graph.

Sawangwit & Shanks suggest the beam isn’t right so the recovered angular spectrum is suspect. I’ll need to look a bit more at the evidence they consider before commenting on that, although if anyone else has worked through it I’d be happy to hear from them through the comments box!

## The Seven Year Itch

Posted in Bad Statistics, Cosmic Anomalies, The Universe and Stuff with tags , , , on January 27, 2010 by telescoper

I was just thinking last night that it’s been a while since I posted anything in the file marked cosmic anomalies, and this morning I woke up to find a blizzard of papers on the arXiv from the Wilkinson Microwave Anisotropy Probe (WMAP) team. These relate to an analysis of the latest data accumulated now over seven years of operation; a full list of the papers is given here.

I haven’t had time to read all of them yet, but I thought it was worth drawing attention to the particular one that relates to the issue of cosmic anomalies. I’ve taken the liberty of including the abstract here:

A simple six-parameter LCDM model provides a successful fit to WMAP data, both when the data are analyzed alone and in combination with other cosmological data. Even so, it is appropriate to search for any hints of deviations from the now standard model of cosmology, which includes inflation, dark energy, dark matter, baryons, and neutrinos. The cosmological community has subjected the WMAP data to extensive and varied analyses. While there is widespread agreement as to the overall success of the six-parameter LCDM model, various “anomalies” have been reported relative to that model. In this paper we examine potential anomalies and present analyses and assessments of their significance. In most cases we find that claimed anomalies depend on posterior selection of some aspect or subset of the data. Compared with sky simulations based on the best fit model, one can select for low probability features of the WMAP data. Low probability features are expected, but it is not usually straightforward to determine whether any particular low probability feature is the result of the a posteriori selection or of non-standard cosmology. We examine in detail the properties of the power spectrum with respect to the LCDM model. We examine several potential or previously claimed anomalies in the sky maps and power spectra, including cold spots, low quadrupole power, quadropole-octupole alignment, hemispherical or dipole power asymmetry, and quadrupole power asymmetry. We conclude that there is no compelling evidence for deviations from the LCDM model, which is generally an acceptable statistical fit to WMAP and other cosmological data.

Since I’m one of those annoying people who have been sniffing around the WMAP data for signs of departures from the standard model, I thought I’d comment on this issue.

As the abstract says, the  LCDM model does indeed provide a good fit to the data, and the fact that it does so with only 6 free parameters is particularly impressive. On the other hand, this modelling process involves the compression of an enormous amount of data into just six numbers. If we always filter everything through the standard model analysis pipeline then it is possible that some vital information about departures from this framework might be lost. My point has always been that every now and again it is worth looking in the wastebasket to see if there’s any evidence that something interesting might have been discarded.

Various potential anomalies – mentioned in the above abstract – have been identified in this way, but usually there has turned out to be less to them than meets the eye. There are two reasons not to get too carried away.

The first reason is that no experiment – not even one as brilliant as WMAP – is entirely free from systematic artefacts. Before we get too excited and start abandoning our standard model for more exotic cosmologies, we need to be absolutely sure that we’re not just seeing residual foregrounds, instrument errors, beam asymmetries or some other effect that isn’t anything to do with cosmology. Because it has performed so well, WMAP has been able to do much more science than was originally envisaged, but every experiment is ultimately limited by its own systematics and WMAP is no different. There is some (circumstantial) evidence that some of the reported anomalies may be at least partly accounted for by  glitches of this sort.

The second point relates to basic statistical theory. Generally speaking, an anomaly A (some property of the data) is flagged as such because it is deemed to be improbable given a model M (in this case the LCDM). In other words the conditional probability P(A|M) is a small number. As I’ve repeatedly ranted about in my bad statistics posts, this does not necessarily mean that P(M|A)- the probability of the model being right – is small. If you look at 1000 different properties of the data, you have a good chance of finding something that happens with a probability of 1 in a thousand. This is what the abstract means by a posteriori reasoning: it’s not the same as talking out of your posterior, but is sometimes close to it.

In order to decide how seriously to take an anomaly, you need to work out P(M|A), the probability of the model given the anomaly, which requires that  you not only take into account all the other properties of the data that are explained by the model (i.e. those that aren’t anomalous), but also specify an alternative model that explains the anomaly better than the standard model. If you do this, without introducing too many free parameters, then this may be taken as compelling evidence for an alternative model. No such model exists -at least for the time being – so the message of the paper is rightly skeptical.

So, to summarize, I think what the WMAP team say is basically sensible, although I maintain that rummaging around in the trash is a good thing to do. Models are there to be tested and surely the best way to test them is to focus on things that look odd rather than simply congratulating oneself about the things that fit? It is extremely impressive that such intense scrutiny over the last seven years has revealed so few oddities, but that just means that we should look even harder..

Before too long, data from Planck will provide an even sterner test of the standard framework. We really do need an independent experiment to see whether there is something out there that WMAP might have missed. But we’ll have to wait a few years for that.

So far it’s WMAP 7 Planck 0, but there’s plenty of time for an upset. Unless they close us all down.

## Another take on cosmic anisotropy

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , on October 22, 2009 by telescoper

Yesterday we had a nice seminar here by Antony Lewis who is currently at Cambridge, but will be on his way to Sussex in the New Year to take up a lectureship there. I thought I’d put a brief post up here so I can add it to my collection of items concerning cosmic anomalies. I admit that I had missed the paper he talked about (by himself and Duncan Hanson) when it came out on the ArXiv last month, so I’m very glad his visit drew this to my attention.

What Hanson & Lewis did was to think of a number of simple models in which the pattern of fluctuations in the temperature of the cosmic microwave background radiation across the sky might have a preferred direction. They then construct optimal estimators for the parameters in these models (assuming the underlying fluctuations are Gaussian) and then apply these estimators to the data from the Wilkinson Microwave Anisotropy Probe (WMAP). Their subsequent analysis attempts to answer the question whether the data prefer these anisotropic models to the bog-standard cosmology which is statistically isotropic.

I strongly suggest you read their paper in detail because it contains a lot of interesting things, but I wanted to pick out one result for special mention. One of their models involves a primordial power spectrum that is intrinsically anisotropic. The model is of the form

$P(\vec{ k})=P(k) [1+a(k)g(\vec{k})]$

compared to the standard P(k), which does not depend on the direction of the wavevector. They find that the WMAP measurements strongly prefer this model to the standard one. Great! A departure from the standard cosmological model! New Physics! Re-write your textbooks!

Well, not really. The direction revealed by the best-choice parameter fit to the data is shown in the smoothed picture  (top). Underneath it are simulations of the sky predicted by their  model decomposed into an isoptropic part (in the middle) and an anisotropic part (at the bottom).

You can see immediately that the asymmetry axis is extremely close to the scan axis of the WMAP satellite, i.e. at right angles to the Ecliptic plane.

This immediately suggests that it might not be a primordial effect at all but either (a) a signal that is aligned with the Ecliptic plane (i.e. something emanating from the Solar System) or (b) something arising from the WMAP scanning strategy. Antony went on to give strong evidence that it wasn’t primordial and it wasn’t from the Solar System. The WMAP satellite has a number of independent differencing assemblies. Anything external to the satellite should produce the same signal in all of them, but the observed signal varies markedly from one to another. The conclusion, then, is that this particular anomaly is largely generated by an instrumental systematic.

The best candidate for such an effect is that it is an artefact of a asymmetry in the beams of the two telescopes on the satellite. Since the scan pattern has a preferred direction, the beam profile may introduce a direction-dependent signal into the data. No attempt has been made to correct for this effect in the published maps so far, and it seems to me to be very likely that this is the root of this particular anomaly.

We will have to see the extent to which beam systematics will limit the ability of Planck to shed further light on this issue.

## Another Day at the ArXiv..

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , , , on October 8, 2009 by telescoper

Every now and again I remember that this is supposed to be some sort of science blog. This happened again this morning after three hours of meetings with my undergraduate project students. Dealing with questions about simulating the cosmic microwave background, measuring the bending of light during an eclipse, and how to do QCD calculations on a lattice reminded me that I’m supposed to know something about stuff like that.

Anyway, looking for something to post about while I eat my lunchtime sandwich, I turned to the estimable arXiv and turned to the section marked astro-ph, and to the new submissions category, for inspiration.

I’m one of the old-fashioned types who still gets an email every day of the new submissions. In the old days there were only a few, but today’s new submissions were 77 in number, only about half-a-dozen of which seemed directly relevant to things I’m interested in. It’s always a bit of a struggle keeping up and I often miss important things. There’s no way I can read as widely around my own field as I would like to, or as I used to in the past, but that’s the information revolution for you…

Anyway, the thing that leapt out at me first was an interesting paper by Dikarev et al (accepted for publication in the Astrophysical Journal) that speculates about the possibility that dust grains in the solar system might be producing emission that messes up measurements of the cosmic microwave background, thus possibly causing the curious cosmic anomalies seen by WMAP I’ve blogged about on more than one previous occasion.

Analyses of the cosmic microwave background (CMB) radiation maps made by the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed anomalies not predicted by the standard inflationary cosmology. In particular, the power of the quadrupole moment of the CMB fluctuations is remarkably low, and the quadrupole and octopole moments are aligned mutually and with the geometry of the Solar system. It has been suggested in the literature that microwave sky pollution by an unidentified dust cloud in the vicinity of the Solar system may be the cause for these anomalies. In this paper, we simulate the thermal emission by clouds of spherical homogeneous particles of several materials. Spectral constraints from the WMAP multi-wavelength data and earlier infrared observations on the hypothetical dust cloud are used to determine the dust cloud’s physical characteristics. In order for its emissivity to demonstrate a flat, CMB-like wavelength dependence over the WMAP wavelengths (3 through 14 mm), and to be invisible in the infrared light, its particles must be macroscopic. Silicate spheres from several millimetres in size and carbonaceous particles an order of magnitude smaller will suffice. According to our estimates of the abundance of such particles in the Zodiacal cloud and trans-neptunian belt, yielding the optical depths of the order of 1E-7 for each cloud, the Solar-system dust can well contribute 10 microKelvin (within an order of magnitude) in the microwaves. This is not only intriguingly close to the magnitude of the anomalies (about 30 microKelvin), but also alarmingly above the presently believed magnitude of systematic biases of the WMAP results (below 5 microKelvin) and, to an even greater degree, of the future missions with higher sensitivities, e.g. PLANCK.

I haven’t read the paper in detail yet, but will definitely do so. In the meantime I’d be interested to hear the reaction to this claim from dusty experts!

Of course we know there is dust in the solar system, and were reminded of this in spectacular style earlier this week by the discovery (by the Spitzer telescope) of an enormous new ring around Saturn.

That tenuous link gives me an excuse to include a gratuitous pretty picture:

It may look impressive, but I hope things like that are not messing up the CMB. Has anyone got a vacuum cleaner?

## Lessening Anomalies

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , on September 15, 2009 by telescoper

An interesting paper caught my eye on today’s ArXiv and I thought I’d post something here because it relates to an ongoing theme on this blog about the possibility that there might be anomalies in the observed pattern of temperature fluctuations in the cosmic microwave background (CMB). See my other posts here, here, here, here and here for related discussions.

One of the authors of the new paper, John Peacock, is an occasional commenter on this blog. He was also the Chief Inquisitor at my PhD (or rather DPhil) examination, which took place 21 years ago. The four-and-a-half hours of grilling I went through that afternoon reduced me to a gibbering wreck but the examiners obviously felt sorry for me and let me pass anyway. I’m not one to hold a grudge so I’ll resist the temptation to be churlish towards my erstwhile tormentor.

The most recent paper is about the possible  contribution of  the integrated Sachs-Wolfe (ISW) effect to these anomalies. The ISW mechanism generates temperature variations in the CMB because photons travel along a line of sight through a time-varying gravitational potential between the last-scattering surface and the observer. The integrated effect is zero if the potential does not evolve because the energy shift falling into a well exactly balances that involved in climbing out of one. If in transit the well gets a bit deeper, however, there is a net contribution.

The specific thing about the ISW effect that makes it measurable is that the temperature variations it induces should correlate with the pattern of structure in the galaxy distribution, as it is these that generate the potential fluctuations through which CMB photons travel. Francis & Peacock try to assess the ISW contribution using data from the 2MASS all-sky survey of galaxies. This in itself contains important cosmological clues but in the context of this particular question it is a nuisance, like any other foreground contamination, so they subtract it off the maps obtained from the Wilkinson Microwave Anisotropy Probe (WMAP) in an attempt to get a cleaner map of the primordial CMB sky.

The results are shown in the picture below which presents  the lowest order spherical harmonic modes, the quadrupole (left) and octopole (right) for the  ISW component (top) , WMAP data (middle) and at the bottom we have the cleaned CMB sky (i.e. the middle minus the top). The ISW subtraction doesn’t make a huge difference to the visual appearance of the CMB maps but it is enough to substantially reduce to the statistical significance of at least some of the reported anomalies I mentioned above. This reinforces how careful we have to be in analysing the data before jumping to cosmological conclusions.

There should also be a further contribution from fluctuations beyond the depth of the 2MASS survey (about 0.3 in redshift).  The actual ISW effect could therefore  be significantly larger than this estimate.

## The Axle of Elvis

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , , , on August 6, 2009 by telescoper

An interesting paper on the arXiv yesterday gave me a prod to expand a little on one of the cosmic anomalies I’ve blogged about before.

Before explaining what this is all about, let me just briefly introduce a bit of lingo. The pattern of variations fluctuations in the temperature of the cosmic microwave background (CMB) across the sky, such as is revealed by the Wilkinson Microwave Anisotropy Probe (WMAP), is usually presented in terms of the behaviour of its spherical harmonic components. The temperature as a function of position is represented as a superposition of spherical harmonic modes labelled by two numbers, the degree l and the order m. The degree basically sets the characteristic angular scale of the mode (large  scales have low l, and small scales have high l). For example the dipole mode has l=1 and it corresponds to variation across the sky on a scale of 180 degrees; the quadrupole (l=2) has a scale of 90 degrees, and so on. For a fixed l the order m runs from -l to +l and each order represents a particular pattern with that given scale.

The spherical harmonic coefficients that tell you how much of each mode is present in the signal are generally  complex numbers having real and imaginary parts or, equivalently, an amplitude and a phase.  The exception to this are the modes with m=0, the zonal modes, which have no azimuthal variation: they vary only with latitude, not longitude. These have no imaginary part so don’t really have a phase. For the other modes, the phase controls the variation with azimuthal angle around the axis of the chosen coordinate system, which in the case of the CMB is usually taken to be the Galactic one.

In the simplest versions of cosmic inflation, each of the spherical harmonic modes should be statistically independent and randomly distributed in both amplitude and phase. What this really means is that the harmonic modes are in a state of maximum statistical disorder or entropy. This property also guarantees that the temperature fluctuations over the sky should be described by  a Gaussian distribution.

That was perhaps a bit technical but the key idea is that if you decompose the overall pattern of fluctuations into its spherical harmonic components the individual mode patterns should look completely different. The quadrupole and octopole, for example, shouldn’t line up in any particular way.

Evidence that this wasn’t the case started to emerge when WMAP released its first set of data in 2003 with indications of an alignment between the modes of low degree. In their  analysis, Kate Land and Joao Magueijo dubbed this feature The Axis of Evil; the name has stuck.They concluded that there was a statistically significant alignment (at 99.9% confidence) between the multipoles of low degree (l=2 and 3), meaning that the measured alignment is only expected to arise by chance in one in a thousand simulated skies. More recently, further investigation of this effect using subsequent releases of data from the WMAP experiment and a more detailed treatment of the analysis (including its stability with respect to Galactic cuts) suggested that the result is not quite as robust as had originally been claimed. .

Here are the low-l modes of the WMAP data so you see what we’re talking about. The top row of the picture contains the modes for l=2 (quadrupole) and l=3 (octopole) and the bottom shows l=4 and l=5.

The two small red blobs mark the two ends of the preferred axis of each mode. The orientation of this axis is consistent across all the modes shown but the statistical significance is much stronger for the ones with lower l.

It’s probably worth mentioning a couple of neglected aspects of this phenomenon. One is that the observed quadrupole and octopole appear not only to be aligned with each other but also appear to be dominated by sectoral orders, i.e those with m=l. These are the modes which are, in a sense, opposite to the zonal modes in that they vary only with longitude and not with latitude. Here’s what the sectoral mode of the quadrupole looks like:

Changing the phase of this mode would result in the pattern moving to the left or right, i.e. changing its origin, but wouldn’t change the orientation. Which brings me to the other remarkable thing, namely that the two lowest modes also have  correlated phases. The blue patch to the right of Galactic centre is in the same place for both these modes. You can see the same feature in the full-resolution map (which involves modes up to l~700 or so):

I don’t know whether there is really anything anomalous about the low degree multipoles, but I hope this is a question that Planck (with its extra sensitivity, better frequency coverage and different experimental strategy) will hopefully shed some light on. It could be some sort of artifact of the measurement process or it could be an indication of something beyond the standard cosmology. It could also just be a fluke. Or even the result of an over-active imagination, like seeing Elvis in your local Tesco.

On its own I don’t think this is going to overthrow the standard model of cosmology. Introducing extra parameters to a model in order to explain a result with a likelihood that is only marginally low in a simpler model does not make sense, at least not to a proper Bayesian who knows about model selection…

However, it is worth mentioning that the Axis of Evil isn’t the only cosmic anomaly to have been reported. If an explanation is found with relatively few parameters that can account for all of these curiosities in one fell swoop then it would stand a good chance of convincing us all that there is more to the Universe than we thought. And that would be fun.

## Space Camp

Posted in Uncategorized with tags , , , , , on July 4, 2009 by telescoper

The other day I was looking through my copy of the Men’s Disciplinary Rubberwear Gazette (which I buy for the Spot-the-Ball competition). Turning to the advertisements, I discovered that the Science & Technology Facilities Council is conducting a review of its space facilities and operations. Always eager to push back the frontiers of science, I hurried down to their address in Swindon to find out what was going on.

ME: Hello. Is there anyone there?

JULIAN: Oh hello. My name’s Julian, and this is my friend Sandy.

SANDY: Oooh hello! What can we do for you?

ME: Hello to you both. Is this Polaris House?

JULIAN: Not quite. Since we took over we changed the name…

ME: To?

SANDY: It’s now called Polari House…

JULIAN: On account of that’s the only language spoken around here.

ME: So you’re in charge of the British Space Programme then?

JULIAN:  Yes, owing to the budget, the national handbag isn’t as full as it used to be so now it’s just me and her.

SANDY: But never fear we’re both dab hands with thrusters.

JULIAN: Our motto is “You can vada about in any band, with a satellite run  by Jules and…

SANDY: …Sand.

ME: I heard that you’re looking for some input.

SANDY: Ooooh. He’s bold, in’e?

ME: I mean for your consultation exercise…

JULIAN: Oh yes. I forgot about that. Well I’m sure we’d welcome your contribution any time, ducky.

ME: Well I was wondering what you could tell me about Moonlite?

SANDY: You’ve come to the right place. She had an experience by Moonlight, didn’t you Jules?

JULIAN: Yes. Up the Acropolis…

ME: I mean the Space Mission “Moonlite”

SANDY: Oh, of course. Well, it’s only small but it’s very stimulating.

JULIAN: Hmmm.

SANDY: Yes. It gets blasted off into space and whooshes off to the Moon…

JULIAN: …the backside thereof…

SANDY: ..and when it gets there it shoves these probes in to see what happens.

ME: Why?

SANDY: Why not?

ME: Seems a bit pointless to me.

JULIAN: There’s no pleasing some people is there?

ME: Haven’t you got anything more impressive?

SANDY: Like what?

ME:  Maybe something that goes a bit further out? Mars, perhaps?

JULIAN: Well the French have this plan to send some great butch omi to troll around on Mars but we haven’t got the metzas so we have to satisfy ourselves with something a bit more bijou…

SANDY: Hmm…You can say that again.

JULIAN: You don’t have to be big to be bona.

SANDY: Anyway, we had our shot at Mars and it went willets up.

ME: Oh yes, I remember that thing named after a dog.

JULIAN: That’s right. Poodle.

ME: Do you think a man will ever get as far as Uranus?

JULIAN&SANDY: Oooh! Bold!

SANDY: Well I’ll tell you what. I’ll show you something that can vada out to the very edge of the Universe!

ME: That sounds exciting.

JULIAN: I’ll try to get it up right now.

ME: Well…er…

JULIAN: I mean on the computer

ME: I say, that’s an impressive piece of equipment

JULIAN: Thank you

SANDY: Oh don’t encourage her…

ME: I meant the computer.

JULIAN: Yes, it’s a 14″ console.

SANDY:  And, believe me, 14 inches will console anyone!

JULIAN; There you are. Look at that.

ME: It looks very impressive. What is it?

SANDY: This is an experiment designed to charper for the heat of the Big Bang.

JULIAN. Ooer.

SANDY: The Americans launched WMAP and the Europeans had PLANCK. We’ve merged the two ideas and have called it ….PLMAP.

ME: Wouldn’t it have been better if you’d made the name the other way around? On second thoughts maybe not..

JULIAN: It’s a little down-market but we have high hopes.

SANDY: Yes, Planck had two instruments called HFI and LFI. We couldn’t afford two so we made do with one.

JULIAN: It’s called MFI. That’s why it’s a bit naff.

ME: I see. What are these two round things either side?

SANDY: They’re the bolometers…

ME: What is this this long thing in between pointing up? And why is it leaning to one side?

SANDY: Well that’s not unusual in my experience …

JULIAN:  Shush. It’s an off-axis Gregorian telescope if you must know.

SANDY: That’s your actual dish. It’s very receptive, if you know what I mean.

ME: So what does it all do?

JULIAN: It’s designed to make a map of what George Smoot called “The Eek of God”. It’s fabulosa…

SANDY: Or it would be if someone hadn’t neglected to read the small print.

ME: Why? Is there are problem?

JULIAN: Well, frankly, yes. We ran out of money.

SANDY: It was only when we got it out the box we realised.

ME: What?

JULIAN & SANDY: Batteries Not Included!

(With thanks to cosmic variance for the inspiration, and apologies to Barry Took and Marty Feldman, who wrote the original Julian and Sandy sketches for the radio show Round the Horne.)

## How Loud was the Big Bang?

Posted in The Universe and Stuff with tags , , , , , , on April 26, 2009 by telescoper

The other day I was giving a talk about cosmology at Cardiff University’s Open Day for prospective students. I was talking, as I usually do on such occasions, about the cosmic microwave background, what we have learnt from it so far and what we hope to find out from it from future experiments, assuming they’re not all cancelled.

Quite a few members of staff listened to the talk too and, afterwards, some of them expressed surprise at what I’d been saying, so I thought it would be fun to try to explain it on here in case anyone else finds it interesting.

As you probably know the Big Bang theory involves the assumption that the entire Universe – not only the matter and energy but also space-time itself – had its origins in a single event a finite time in the past and it has been expanding ever since. The earliest mathematical models of what we now call the  Big Bang were derived independently by Alexander Friedman and George Lemaître in the 1920s. The term “Big Bang” was later coined by Fred Hoyle as a derogatory description of an idea he couldn’t stomach, but the phrase caught on. Strictly speaking, though, the Big Bang was a misnomer.

Friedman and Lemaître had made mathematical models of universes that obeyed the Cosmological Principle, i.e. in which the matter was distributed in a completely uniform manner throughout space. Sound consists of oscillating fluctuations in the pressure and density of the medium through which it travels. These are longitudinal “acoustic” waves that involve successive compressions and rarefactions of matter, in other words departures from the purely homogeneous state required by the Cosmological Principle. The Friedman-Lemaitre models contained no sound waves so they did not really describe a Big Bang at all, let alone how loud it was.

However, as I have blogged about before, newer versions of the Big Bang theory do contain a mechanism for generating sound waves in the early Universe and, even more importantly, these waves have now been detected and their properties measured.

The above image shows the variations in temperature of the cosmic microwave background as charted by the Wilkinson Microwave Anisotropy Probe about five years ago. The average temperature of the sky is about 2.73 K but there are variations across the sky that have an rms value of about 0.08 milliKelvin. This corresponds to a fractional variation of a few parts in a hundred thousand relative to the mean temperature. It doesn’t sound like much, but this is evidence for the existence of primordial acoustic waves and therefore of a Big Bang with a genuine “Bang” to it.

A full description of what causes these temperature fluctuations would be very complicated but, roughly speaking, the variation in temperature you corresponds directly to variations in density and pressure arising from sound waves.

So how loud was it?

The waves we are dealing with have wavelengths up to about 200,000 light years and the human ear can only actually hear sound waves with wavelengths up to about 17 metres. In any case the Universe was far too hot and dense for there to have been anyone around listening to the cacophony at the time. In some sense, therefore, it wouldn’t have been loud at all because our ears can’t have heard anything.

Setting aside these rather pedantic objections – I’m never one to allow dull realism to get in the way of a good story- we can get a reasonable value for the loudness in terms of the familiar language of decibels. This defines the level of sound (L) logarithmically in terms of the rms pressure level of the sound wave Prms relative to some reference pressure level Pref

L=20 log10[Prms/Pref]

(the 20 appears because of the fact that the energy carried goes as the square of the amplitude of the wave; in terms of energy there would be a factor 10).

There is no absolute scale for loudness because this expression involves the specification of the reference pressure. We have to set this level by analogy with everyday experience. For sound waves in air this is taken to be about 20 microPascals, or about 2×10-10 times the ambient atmospheric air pressure which is about 100,000 Pa.  This reference is chosen because the limit of audibility for most people corresponds to pressure variations of this order and these consequently have L=0 dB. It seems reasonable to set the reference pressure of the early Universe to be about the same fraction of the ambient pressure then, i.e.

Pref~2×10-10 Pamb

The physics of how primordial variations in pressure translate into observed fluctuations in the CMB temperature is quite complicated, and the actual sound of the Big Bang contains a mixture of wavelengths with slightly different amplitudes so it all gets a bit messy if you want to do it exactly, but it’s quite easy to get a rough estimate. We simply take the rms pressure variation to be the same fraction of ambient pressure as the averaged temperature variation are compared to the average CMB temperature,  i.e.

Prms~ a few ×10-5Pamb

If we do this, scaling both pressures in logarithm in the equation in proportion to the ambient pressure, the ambient pressure cancels out in the ratio, which turns out to be a few times 10-5

With our definition of the decibel level we find that waves corresponding to variations of one part in a hundred thousand of the reference level  give roughly L=100dB while part in ten thousand gives about L=120dB. The sound of the Big Bang therefore peaks at levels just a bit less than  120 dB. As you can see in the Figure to the left, this is close to the threshold of pain,  but it’s perhaps not as loud as you might have guessed in response to the initial question. Many rock concerts are actually louder than the Big Bang.

A useful yardstick is the amplitude  at which the fluctuations in pressure are comparable to the mean pressure. This would give a factor of about 1010 in the logarithm and is pretty much the limit that sound waves can propagate without distortion. These would have L≈190 dB. It is estimated that the 1883 Krakatoa eruption produced a sound level of about 180 dB at a range of 100 miles. By comparison the Big Bang was little more than a whimper.

PS. If you would like to read more about the actual sound of the Big Bang, have a look at John Cramer’s webpages. You can also download simulations of the actual sound. If you listen to them you will hear that it’s more of  a “Roar” than a “Bang” because the sound waves don’t actually originate at a single well-defined event but are excited incoherently all over the Universe.

## Ecliptic Anomalies

Posted in Cosmic Anomalies, The Universe and Stuff with tags , , , , on February 12, 2009 by telescoper

Once a week the small band of cosmologists at Cardiff University have a little discussion group during which we look at an interesting and topical subject. Today my PhD student Rockhee chose an interesting paper by Diego et al entitled “WMAP anomalous signal in the ecliptic plane”. I thought I’d mention it here because it relates to an ongoing theme of mine, and I’ll refrain from commenting on the poor grammatical construction of the title.

The WMAP referred to is of course the Wilkinson Microwave Anisotropy Probe and I’ve blogged before about the tantalising evidence it suggests of some departures from the standard cosmological theory. These authors do something very simple and the result is extremely interesting.

In order to isolate the cosmic microwave background from foreground radiation produced in our own Galaxy, the WMAP satellite is equipped with receivers working at different frequencies. Galactic dust and free-free emission dominate the microwave sky temperature at high frequencies and Galactic synchotron takes over at low frequencies. The cosmic microwave background has the same temperature at all frequencies (i.e. it has a thermal spectrum) so it should be what’s left when the frequency-dependent bits are cleaned out.

What Diego et al. did was to make a map by combining the cleaned sky maps obtained at different frequencies obtained by WMAP in such a way as to try to eliminate the thermal (CMB) component. What is left when this is done should be just residual noise, as it should contain neither known foreground or CMB. The map they get is shown here.

What is interesting is that the residual map doesn’t look like noise that is uniformly distributed over the sky: there are two distinct peaks close to the Ecliptic plane delineated by the black tramlines. Why the residuals look like this is a mystery. The peaks are both very far from the Galactic plane so it doesn’t look like they are produced by Galactic foregrounds.

One suggestion is that the anomalous signal is like an infra-red extension of the Zodiacal light (which is produced inside the Solar System and therefore is too local to be confined to the Galactic plane). The authors show, however, that a straightforward extrapolation of the known Zodiacal emission (primarily measured by the IRAS satellite) does not account for the signal seen in WMAP. If this is the explanation, then, there has to be a new source of Zodiacal emission that is not seen by IRAS but kicks in at WMAP frequencies.

Another possibility is that it is extragalactic. This is difficult to exclude, but is disfavoured in my mind because there is no a priori reason why it should be concentrated in the Ecliptic plane. Coincidences like this make me a bit uncomfortable. Some turn out to be real coincidences, but more often than not they are clues to something important. Agatha Christie would have agreed:

“Any coincidence,” said Miss Marple to herself, “is always worth noting. You can throw it away later if it is only a coincidence.”

On the other hand, the dipole asymmetry of the CMB (thought to be caused by our motion through a frame in which it is isotropic) is also lined up in roughly the same direction:

The dipole has a hot region and a cold region in places where the residual map has two hot regions and anyway it’s also a very large scale feature so the chances of it lining up by accident with the ecliptic plane to the accuracy seen is actually not small. Coincidences definitely do happen, and the rougher they are the more commonly they occur.

Obviously, I don’t know what’s going on, but  I will mention another explanation that might fit. As I have already blogged, the WMAP satellite scans the sky in a way that is oriented exactly at right angles to the Ecliptic plane. If there is an as yet unknown systematic error in the WMAP measurements, which is related in some way to the motion of the satellite, it could at least in principle produce an effect with a definite orientation with respect to the Ecliptic.

The only way we can rule out this (admittedly rather dull) explanation is by making a map using a different experiment. It’s good, then, that the Planck satellite is going to be launched in only a few weeks’ time (April 16th 2009). Fingers crossed that we can solve this riddle soon.

## Power isn’t Everything

Posted in The Universe and Stuff with tags , , , , , , , on January 6, 2009 by telescoper

Courtesy of NASA/WMAP science team

The picture above shows the latest available 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’ve 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 few days 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 a physicist doesn’t know what they are doing they should start by making a Fourier transform. This breaks down the phenomenon being studied into a set of independent plane waves with different wavelengths corresponding to 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 an argument by mathematicians). The latter representation is the most useful one for CMB fluctuations because the simplest versions of inflation predict that the phases 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 peak) plus a couple of overtones. 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 insenstive 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.

So far, so good. It sounds like it should be a straightforward job to work out whether the WMAP phases are random or not. Unfortunately, though, this task is heavily complicated by the presence of noise and systematics which can be quite easily cleaned from the spectrum but not from more sophisticated descriptors. All we can say so far is that the data seem to be consistent with a Gaussian distribution.

However, I thought I’d end with a bit of fun and 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 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 harmonics can be fun.

PS. These pictures were made by a former PhD student of mine, Patrick Dineen, who has since quit astronomy to work in high finance. I hope he is weathering the global financial storm!