Quasar structures: a postscript

A few days ago I discussed the purported 'spooky' alignment of quasar spins and the cosmological principle here. So as to focus better on the main point, I left a few technical comments out of that discussion which I want to mention here. These don't have any direct bearing on the main argument made in that post — rather they are interesting asides for a more expert audience.

Quasars can't prove the Universe is homogeneous

Readers of the original post might have noticed that I was quite careful to always state that the distribution of quasars was statistically homogeneous, but not that the quasars showed the Universe was homogeneous. The reason for this lies in the properties of the quasar sample itself.

There are two main ways of constructing a sample of galaxies or quasars to use for further analysis, such as testing homogeneity. The first is that you simply include every object seen by the survey instruments within a certain patch of sky that lies between two redshifts of interest. But these objects will vary in their intrinsic brightness, and the survey instruments have a limited sensitivity, so can only record dim objects when they are relatively close to us. Intrinsically bright objects are rarer, but if they are very far away we will only be able to see the rare bright ones. So this strategy results in a sample with very many, but largely dim, galaxies or quasars relatively close to us, and fewer but brighter objects far away. This is known as a flux-limited sample.

The other strategy is to correct the measured brightness of each object for the distance from us, to determine its 'intrinsic' brightness (otherwise known as its absolute magnitude), and then select a sample of only those objects which have similar absolute magnitudes. The magnitude range is chosen in accordance with the range of distances such that within the volume of the Universe surveyed, we can be confident we have seen every object of that magnitude that exists. This is called a volume-limited sample.

Testing the homogeneity of the Universe requires a volume-limited survey of objects. For a flux-limited sample the distribution in redshift (i.e., in the line-of-sight direction) would not be expected to be uniform in the first place: the number density of objects would ordinarily decrease sharply with redshift. But looking out away from Earth also involves looking back in time; so if the redshift range of the survey is large, the farthest objects are seen as they were at an earlier time than the closest ones. If the objects in question had evolved significantly in that time, near and far objects could represent significantly different populations even in a volume-limited sample, and once again we wouldn't expect to see homogeneity along the line of sight, even if the Universe were homogeneous.

So to really test the cosmological principle without having to assume homogeneity at the outset,¹ we really need a volume-limited sample of galaxies that cover a very large volume of the Universe but span a relatively narrow range of redshifts. Such surveys are hard to come by. For example, the study confirming homogeneity in WiggleZ galaxies (see here and here) actually used a flux-limited sample, so required additional assumptions. In this case one doesn't obtain a proof, rather a check of the self-consistency of those assumptions — which people may regard as good enough, depending on taste.

Anyway, the key point is that the DR7QSO quasar sample everyone uses is most definitely flux-limited and not volume-limited (I was myself reminded of this point by Francesco Sylos Labini). Despite this, the redshift distribution of quasars is remarkably uniform (between redshifts 1 and 1.8). So what's going on? Well, unlike certain types of galaxies that live much closer to home, distant quasar populations are expected to evolve rather quickly with time. And the age difference between objects at redshifts 1 and 1.8 is more than 2 billion years!

It would appear that this effect and the flux-limited nature of the survey coincidentally roughly cancel each other out for the sample in question. A volume-limited subset of these quasars would be (is) highly inhomogeneous — but then because of the time evolution the homogeneity or otherwise of any sample of quasars says nothing much about the homogeneity or otherwise of the Universe in general.

Luckily this is only incidental to the main argument. The fact that the distribution of these (flux-limited) quasars is statistically homogeneous on scales of 100-odd Megaparsecs despite claims for the existence of Gigaparsec-scale 'structures' simply demonstrates the point that the existence of single structures of any kind doesn't have any bearing on the question of overall homogeneity. Which is the main point.

Homogeneity is sample-dependent 

Of course the argument above cuts both ways.

Let's imagine that a study has shown that the distribution of a particular type of galaxy — call them luminous red galaxies — approaches homogeneity above a certain distance scale, say 100 Megaparsecs. Such a study was done by David Hogg and others in 2005. From this we may reasonably conclude (though not, strictly speaking, prove) that the matter distribution in the Universe is homogeneous above at most 100 Mpc. But we are not allowed to conclude that the distribution of some other sample of objects — radio galaxies, quasars, blue galaxies etc. — approaches homogeneity above the same scale, or indeed at all!

Even in a Universe with a homogeneous matter distribution, the scale above which a volume-limited sample of galaxies whose properties are constant with time approaches homogeneity depends on the galaxy bias. This number depends on the type of galaxies in question, and so too to a lesser extent will the expected homogeneity scale. Of course if the sample is not volume-limited, or does evolve with time, all bets are off anyway.

More generally, for each sample of galaxies that we wish to use for higher order statistical measurements, the statistical homogeneity of that particular sample must in general be demonstrated first. This is because higher order statistical quantities, such as the correlation function, are conventionally normalized in units of the sample mean, but in the absence of statistical homogeneity this becomes meaningless.

There was a time when the homogeneity of the Universe was less well accepted than it is today, and the possibility of a fractal distribution of matter was still an open question. At that time demonstrating the approach to homogeneity on large scales in a well-chosen sample of galaxies was worth a publication (even a well-cited publication) in itself. This is probably no longer the case, but it remains a necessary sanity check to perform for each galaxy survey.

¹Properly speaking, even the creation of a volume-limited sample requires an assumption of homogeneity at the outset, since the determination of absolute magnitudes requires a cosmological model, and the cosmological model used will assume homogeneity. In this sense all "tests" of homogeneity are really consistency checks of our assumption thereof.

A 'spooky alignment' of quasars, or just hype?

In the news this week we've had a story on the alignment of quasar spins with large-scale structure, based on this paper by Hutsemekers et al. The paper was accompanied by this press release from the European Space Observatory, which was then reproduced in various forms in a number of blogs and news outlets — almost all of which stress the 'spooky' or 'mysterious' nature of the claimed alignment 'over billions of light years'.

At least one of these blogs (the one at The Daily Galaxy) explicitly claims that the alignment of these quasar spins is a challenge for the cosmological principle, which is the assumption of large-scale statistical homogeneity and isotropy of the Universe, on which all of modern cosmology is based. This claim is not contained in the press release, but originates from a statement in the paper itself, where the authors say

The existence of correlations in quasar axes over such extreme scales would constitute a serious anomaly for the cosmological principle.

I'm afraid that this claim is completely unsupported by any of the actual results contained within the paper, and is therefore one of those annoying examples of scientific hype. In this post I will try to explain why.

I have actually covered much of this ground before — in a blog post here, but more importantly in a paper published in Monthly Notices last year — and I must admit I am a little surprised at having to repeat these points (especially since my paper is cited by Hutsemekers et al.). Nevertheless, in what follows I shall try not to sound too grumpy.

The immediate story started with a paper by Roger Clowes and collaborators, who claimed to have detected the 'largest structure' in the Universe (dubbed the 'Huge-LQG') in the distribution of quasars, and also claimed that this structure violated the cosmological principle. My paper last year was a response to this, and made the following points:

1. the detection of a single large structure has essentially no relevance to the question of whether the Universe is statistically homogeneous and isotropic;
2. the quasar sample within which the Huge-LQG was identified is statistically homogeneous, and approaches homogeneity at the scale we expect theoretically, thus providing an explicit demonstration of point 1;
3. the definition of 'structure' by which the Huge-LQG counts as a structure is so loose that by using it we would find equally vast 'structures' even in completely random distributions of points which (by construction!) contain no correlations and therefore no structure whatsoever; and 
4. therefore the classification of the Huge-LQG set of quasars as a 'structure' is essentially empty of meaning.

Quasar structures don't violate homogeneity

Since I am already repeating myself, let me elaborate a little more on points 1 and 2. Our Universe is not exactly homogeneous. The fact that you exist — more generally, the fact that stars, galaxies and clusters of galaxies exist — is sufficient proof of this, so it would a very poor advertisement for cosmology indeed if it were all founded on the assumption of exact homogeneity. Luckily it isn't. In fact our theories could be said to predict the existence of structure in the potential $\Phi$ on all scales (that's what a scale-invariant power spectrum from inflation means!), and even the galaxy-galaxy correlation function only goes asymptotically to zero at large scales.

Instead we have the assumption of statistical homogeneity and isotropy, which means that we assume that when looked at on large enough scales, different regions of the Universe are on average the same. Clearly, since this is a statement about averages, it can only be tested statistically by looking at large numbers of different regions, not by finding one particular example of a 'structure'. In fact there is a well-established procedure for checking the statistical homogeneity of the distribution of a set of points (the positions of galaxies or quasars, in this case), which involves measuring its fractal dimension and checking the scale above which this is equal to 3. I've described the procedure before, here and here, and Peter Coles describes a bit of the history of it here.

The bottom line is that, as I showed last year, the quasar distribution in question is statistically homogeneous above scales of at most $\sim130h^{-1}$Mpc. There is therefore no 'structure' you can find in this data which could violate the cosmological principle. End of story.

Scaled number counts in spheres as a measure of the fractal dimension of the quasar distribution. On scales where this number approaches 1, the distribution is statistically homogeneous. From arXiv:1306.1700.

Structures and probability

Of course, there are many different ways of being statistically homogeneous. It is perfectly possible that within a statistically homogeneous distribution one could find a particular structure or feature whose existence in our specific cosmological model (which is one of many possible models satisfying the cosmological principle) is either very unlikely or impossible. This would then be a problem for that cosmological model despite not having any wider implications for the cosmological principle. But to prove this requires some serious analysis, which should include a proper treatment of probabilities — you can't just say "this structure is big, so it must be anomalous."

In particular, any serious analysis of probabilities must take into account how a 'structure' is defined. Given infinitely many possible choices of definition, and a very large Universe in which to search, the probability of finding some 'structure' that extends over billions of light years is practically unity. In fact the definition used for the Huge-LQG would be likely to throw up equally vast 'structures' even if quasar positions were not at all correlated with each other (and we know they must be at least somewhat correlated, because of gravity). So it really isn't a very useful definition at all.

'Spooky' alignments

This brings us to the current paper by Hutsemekers et al. The starting assumption of this paper is that the Huge-LQG is a real structure which is somehow distinguished from its surroundings. This assumption is manifest in the decision that the authors make to try to measure the polarization of light from only those quasars that are classified as part of the Huge-LQG rather than a more general sample of quasars. This classic case of circular reasoning is the first flaw in the logic, but let's put it to one side for a minute.

The press release then tells us that the scientists

found that the rotation axes of the central supermassive black holes in a sample of quasars are parallel to each other over distances of billions of light years

and that the spins of the central black holes are aligned along the filaments of large-scale structure in which they reside.

I find this statement extremely problematic. Here is a figure from the paper in question, showing the sky positions of the 93 quasars in question, along with the polarization orientations for the 19 which are used in the actual analysis:

Quasar positions (black dots) and polarization alignments (red lines). From arXiv.1409.6098.

Do you see the alignment? No, me neither. In fact, looking at the distribution of angles in panel b, I would say that looks very much like a sample drawn from a perfectly uniform distribution.

So what is the claim actually based on? Well, for a start one has to split up the (arbitrarily defined) 'structure' into several (even more arbitrarily defined) 'sub-structures'. Each of these sub-structures then defines a different reference angle on the sky:

Chopping the data to suit the argument (Figure 4 of arXiv:1409.6098). On what basis are sub-structures 1 and 2 defined as separate from each other?

And now one has to measure the angles between the quasar polarization direction and the reference direction of the particular sub-structure, and the direction perpendicular to the reference direction, and choose the smaller of the two. In other words, rather than prove that quasars are aligned parallel to each other over distances extending over billions of light years (the claim in the press release), what Hutsemekers et al. are actually doing is attempting to show that given arbitrary choices of some smaller sub-structures and reference directions, quasars in different sub-structures are typically aligned either parallel to or perpendicular to this direction. This is a much less exacting standard.

Even this claim is not particularly well supported by the evidence. That is, looking at the distribution of angles, I am really not at all convinced that this shows evidence for a bimodal distribution with peaks at 0 and 90 degrees:

Distribution of angles purportedly showing two distinct peaks at 0 and 90. Figure 5 of arXiv:1409.6098.

So in summary I think the statistical evidence of alignment of quasar spins is already pretty weak. I don't see any analysis in the paper dealing with the effects of a different arbitrary choice of sub-structures, nor do I see any error analysis (the error in measuring the polarization direction of a quasar can be as large as 10 degrees!). And I haven't even dealt with the fact that the polarization data is used for only 19 quasars out of the full 93 — in other words, for the majority of quasars in the sample the central black hole spins are aligned along some other, undetermined, direction such that we can't measure the polarization.

Extraordinary claims require extraordinary evidence

Now, it's worth repeating that we've already seen that in fact the space distribution of quasars is statistically homogeneous in accordance with the cosmological principle. That simple test has been done, the cosmological principle survives. So if you've got some more nuanced claim of an anomaly, I think the onus is on you not only to describe the measurement you made, but also say what exactly is anomalous about it. What is the theoretical prediction we should compare it to? Which model is being rejected (or otherwise) by the new data?

So, for instance, if quasar spins in sub-structures are indeed aligned either parallel or perpendicular to each other (and I still remain to be convinced that they are), is this really something 'spooky', or would we expect some degree of alignment in the standard $\Lambda$CDM model?

Such an analysis has not been presented, but even if it had, it's worth bearing in mind the principle that extraordinary claims require extraordinary evidence. I'm afraid throwing out a p-value of about 1% simply doesn't cut it. Not only is that actually not an enormously impressive number (especially given all the other things I mentioned above), such a frequentist statistic doesn't take account of all our prior knowledge.

Other people have banged this drum at length before, but the point is easily summarized: the p-value tells us the probability of getting this data given the model, but doesn't tell us the probability of the model being correct despite the new data appearing to contradict it. This is the question we really wish to answer. To do this requires a Bayesian analysis, in which one must account for the prior belief in the model, which is the result of confidence built up from all other experimental results that agree with it. We have an incredible amount of observational evidence in favour of our current model, that would probably not be consistent with a model in which gigantic structures could exist (I say 'probably' because no such model actually exists at present). 

So my prior in favour of $\Lambda$CDM is pretty high — 19 quasars and an analysis so full of holes are not going to change that so quickly.

Quasars, homogeneity and Einstein

[A little note: This post, like many others on this blog, contains a few mathematical symbols which are displayed using MathJax. If you are reading this using an RSS reader such as Feedly and you see a lot of $ signs floating around, you may need to click through to the blog to see the proper symbols.]

People following the reporting of physics in the popular press might remember having come across a paper earlier this year that claimed to have detected the "largest structure in the Universe" in the distribution of quasars, that "challenged the Cosmological Principle". This was work done by Roger Clowes of the University of Central Lancashire and collaborators, and their paper was published in the Monthly Notices of the Royal Astronomical Society back in March (though it was available online from late last year). 

The reason I suspect people might have come across it is that it was accompanied by a pretty extraordinary amount of publicity, starting from this press release on the Royal Astronomical Society website. This was then taken up by Reuters, and featured on various popular science websites and news outlets, including New Scientist, The Atlantic, National Geographic, Space.com, The Daily Galaxy, Phys.org, Gizmodo, and many more. The structure they claimed to have found even has its own Wikipedia entry.

Obligatory artist's impression of a quasar.

One thing that you notice in a lot of these reports is the statement that the discovery of this structure violates Einstein's theory of gravity, which is nonsense. This is sloppy reporting, sure, but the RAS press release is also partly to blame here, since it includes a somewhat gratuitous mention of Einstein, and this is exactly the kind of thing that non-expert journalists are likely to pick up on. Mentioning Einstein probably helps generate more traffic after all, which is why I've put him in the title as well.

But aside from the name-dropping, what about the main point about the violation of the cosmological principle? As a quick reminder, the cosmological principle is sometimes taken to be the assumption that, on large scales, the Universe is well-described as homogeneous and isotropic. 

The question of what constitutes "large scales" is sometimes not very well-defined: we know that on the scale of the Solar System the matter distribution is very definitely not homogeneous, and we believe that on the scale of size of the observable Universe it is. Generally speaking, people assume that on scales larger than about $100$ Megaparsecs, homogeneity is a fair assumption. A paper by Yadav, Bagla and Khandai from 2010 showed that if the standard $\Lambda$CDM cosmological model is correct, the scale of homogeneity must be less than at most $370$ Mpc. 

On the other hand, this quasar structure that Clowes et al. found is absolutely enormous: over 4 billion light years, or more than 1000 Mpc, long. Does the existence of such a large structure mean that the Universe is not homogeneous, the cosmological principle is not true, and the foundation on which all of modern cosmology is based is shaky?

Well actually, no. 

Unfortunately Clowes' paper is wrong, on several counts. In fact, I have recently published a paper myself (journal version here, free arXiv version here) which points out that it is wrong. And, on the principle that if I don't talk about my own work, no one else will, I'm going to try explaining some of the ideas involved here.

The first reason it is wrong is something that a lot of people who should know better don't seem to realise: there is no reason that structures should not exist which are larger than the homogeneity scale of $\Lambda$CDM. You may think that this doesn't make sense, because homogeneity precludes the existence of structures, so no structure can be larger than the homogeneity scale. Nevertheless, it does and they can.

Let me explain a little more. The point here is that the Universe is not homogeneous, at any scale. What is homogeneous and isotropic is simply the background model we use the describe its behaviour. In the real Universe, there are always fluctuations away from homogeneity at all scales – in fact the theory of inflation basically guarantees this, since the power spectrum of potential fluctuations is close to scale-invariant. The assumption that all cosmological theory really rests on is that these fluctuations can be treated as perturbations about a homogeneous background – so that a perturbation theory approach to cosmology is valid.

Given this knowledge that the Universe is never exactly homogeneous, the question of what the "homogeneity scale" actually means, and how to define it, takes on a different light. (Before you ask, yes it is still a useful concept!) One possible way to define it is as that scale above which density fluctuations $\delta$ generally become small compared to the homogeneous background density. In technical terms, this means the scale at which the two-point correlation function for the fluctuations, $\xi(r)$, (of which the power spectrum $P(k)$ is the Fourier transform) becomes less than $1$. Based on this definition, the homogeneity scale would be around $10$ Mpc.

It turns out that this definition, and the direct measurement of $\xi(r)$ itself, is not very good for determining whether or not the Universe is a fractal, which is a question that several researchers decided was an important one to answer a few years ago. This question can instead be answered by a different analysis, which I explained once before here: essentially, given a catalogue with the positions of many galaxies (or quasars, or whatever), draw a sphere of radius $R$ around each galaxy, and count how many other galaxies lie within this sphere, and how this number changes with $R$. The scale above which the average of this number for all galaxies starts scaling as the cube of the radius, $$N(<R)\propto R^3,$$ (within measurement error) is then the homogeneity scale (if it starts scaling as some other constant power of $R$, the Universe has a fractal nature). This is the definition of the homogeneity scale used by Yadav et al. and it is related to an integral of $\xi(r)$; typically measurements of the homogeneity scale using this definition come up with values of around $100-150$ Mpc.

The figure that proves that the distribution of quasars is in fact homogeneous on the expected scales. For details, see  arXiv:1306.1700. 

To get back to the original point, neither of these definitions of the homogeneity scale makes any claim about the existence of structures that are larger than that. In fact, in the $\Lambda$CDM model, the correlation function for matter density fluctuations is expected to be small but positive out to scales larger than either of the two homogeneity scales defined above (though not as large as Yadav et al.'s generous upper limit). The correlation function that can actually be measured using any given population of galaxies or quasars will extend out even further. So we already expect correlations to exist beyond the homogeneity scale – this means that, for some definitions of what constitutes a "structure", we expect to see large "structures" on these scales too.

The second reason that the claim by Clowes et al. is wrong is however less subtle. Given the particular definition of a "structure" they use, one would expect to find very large structures even if density correlations were exactly zero on all scales.

Yes, you read that right. It's worth going over how they define a "structure", just to make this absolutely clear. About the position of each quasar in the catalogue they draw a sphere of radius $L$. If any other quasars at all happen to lie within this sphere, they are classified as part of the same "structure", which can now be extended in other directions by repeating the procedure about each of the newly added member quasars. After repeating this procedure over all $18,722$ quasars in the catalogue, the largest such group of quasars identified becomes the "largest structure in the Universe".

It should be pretty obvious now that the radius $L$ chosen for these spheres, while chosen rather arbitrarily, is crucial to the end result. If it is too large, all quasars in the catalogue end up classified as part of the same truly ginormous "structure", but this is not very helpful. This is known as "percolation" and the critical percolation threshold has been thoroughly studied for Poisson point sets – which are by definition random distributions of points with no correlation at all. The value of $L$ that  Clowes et al. chose to use, for no apparent reason other than that it gave them a dramatic result, was $100$ Mpc – far too large to be justified on any theoretical grounds, but slightly lower than the critical percolation threshold would be if the quasar distribution was similar to that of a Poisson set. On the other hand, the "largest structure in the Universe" only consists of $73$ quasars out of $18,722$, so it could be entirely explained as a result of the poor definition ...

Now I'll spare you all the details of how to test whether, using this definition of a "structure", one would expect to find "structures" extending over more than $1000$ Mpc in length or with more than $73$ members or whatever, even in a purely random distribution of points, which are by definition homogeneous. Suffice it to say that it turns out one would. This plot shows the maximum extent of such "structures" found in $10,000$ simulations of completely uncorrelated distributions of points, compared to the maximum extent of the "structure" found in the real quasar catalogue.

The probability distribution of extents of largest "structures" found in 10,000 random point sets for two different choices of $L$. Vertical lines show the actual values found for "structures" in the quasar catalogue. The actual values are not very unusual. Figure from arXiv:1306.1700. 

To summarise then: finding a "structure" larger than the homogeneity scale does not violate the cosmological principle, because of correlations; on top of that, the "largest structure in the Universe" is actually not really a "structure" in any meaningful sense. In my professional opinion, Clowes' paper and all the hype surrounding it in the press is nothing more than that – hype. Unfortunately, this is another verification of my maxim that if a paper to do with cosmology is accompanied by a big press release, it is odds-on to turn out to be wrong.

Finally, before I leave the topic, I'll make a comment about the presentation of results by Clowes et al. Here, for instance, is an image they presented showing their "structure", which they call the 'Huge-LQG', with a second "structure" called the 'CCLQG' towards the bottom left:

3D representation of the Huge-LQG and CCLQG. From arXiv:1211.6256.

Looks impressive! Until you start digging a bit deeper, anyway. Firstly, they've only shown the quasars that form part of the "structure", not all the others around it. Secondly, they've drawn enormous spheres (of radius $33$ Mpc) at the position of each quasar to make it look more dramatic. In actual fact the quasars are way smaller than that. The combined effect of these two presentational choices is to make the 'Huge-LQG' look far more plausible as a structure than it really is. Here's a representation of the exact same region of space that I made myself, which rectifies both problems:

Quasar positions around the "structures" claimed by Clowes et al.

Do you still see the "structures"?

One year on

It has been a long month-and-a-bit since I last had the time to write a proper post here. Primarily this is because I am not very good at doing more than one thing at a time – at least while attempting to do those things properly – and I have been working on some real research papers, which I thought I should try to do properly. As a result science communication, and blogging in general, has had to wait. But I will get back in the swing of things very soon: there are some interesting new results, some interesting rehashes of old arguments about inflation, and one of my own papers that I will write about over the next couple of weeks.

One of the many things that I omitted to mention during this little break was the fact that Blank On The Map had its first anniversary a couple of weeks ago. All in all, I would say it has been quite a satisfying year of blogging, and, at least relative to my prior expectations, a reasonably successful one too. Blogger doesn't provide me with many detailed statistics, but it does tell me that despite the low recent rate of new postings, there have been roughly 23,000 clicks over the last twelve months. A sizeable portion of of this traffic came from one link on Peter Woit's blog (boy he must have a huge number of readers!) – though the majority appear to arrive via Google search, either by accident or design.

Anyway, to all those who have arrived here at some point over the last year, welcome! I hope you found what you were looking for, and enjoyed what you read. This explains what this blog is about. In case you haven't worked your way through the archives, here is a short selection of some highlights from the last year:

• Steven Weinberg and the 'Crisis of Big Science'
• An explanation of a dark matter controversy
• A question of probability
• The dog who climbed a mountain
• The Structure of a Scientific Revolution
• Explaining Planck by analogy

I should also use this post to try to get some feedback from (all three) regular readers. Do you think I should post more often? Less often? More posts about cosmology and fewer about mountaineering and other stuff in general? Or the other way round? Let me know through the comments box. Constructive criticism of the writing style or any other aspect of this blog will also be well received, though I can't promise to change ...

Type Ia single degenerate survivors must be overluminous

I noticed a paper on the arXiv today with exactly this title (well, except that I removed the superfluous capitalisation of words), that is due to be published in the Astrophysical Journal. The abstract of the paper says:

In the single-degenerate (SD) channel of a Type Ia supernovae (SN Ia) explosion, a main-sequence (MS) donor star survives the explosion but it is stripped of mass and shock heated. An essentially unavoidable consequence of mass loss during the explosion is that the companion must have an overextended envelope after the explosion. While this has been noted previously, it has not been strongly emphasized as an inevitable consequence. We calculate the future evolution of the companion by injecting $2$-$6\times10^{47}$ ergs into the stellar evolution model of a $1\,M_\odot$ donor star based on the post-explosion progenitors seen in simulations. We find that, due to the Kelvin-Helmholtz collapse of the envelope, the companion must become significantly more luminous ($10$-$10^3\, L_\odot$) for a long period of time ($10^3$-$10^4$ years). The lack of such a luminous "leftover" star in the LMC supernova remnant SNR 0609-67.5 provides another piece of evidence against the SD scenario. We also show that none of the stars proposed as the survivors of the Tycho supernova, including Tycho G, could plausibly be the donor star. Additionally, luminous donors closer than $\sim10$ Mpc should be observable with the Hubble Space Telescope starting $\sim2$ years post-peak. Such systems include SN 1937C, SN 1972E, SN 1986G, and SN 2011fe. Thus, the SD channel is already ruled out for at least two nearby SNe Ia and can be easily tested for a number of additional ones. We also discuss similar implications for the companions of core-collapse SNe.

Now, technical scientific papers are full of jargon and maybe the meaning of that paragraph isn't immediately clear to everyone (there's an accompanying Youtube video purporting to explain the content of the paper, but I didn't think it quite achieved that aim!). But I think this result is really quite interesting and probably important in a broader cosmological sense.

Black Sun

While I'm at it, let me also reblog this beautiful picture taken by Jim Lafferty:

Yes, that's the Sun. The image is recorded at the H$\alpha$ wavelength and then colour-inverted: the other black dots around it are stars.

There's a short description of the features of the photograph here.

Things To Read, 16th July

When I first decided to start collecting together links to interesting things on the internet and putting them into one blog post per week, I was envisaging something like a less frequent version of this. Instead these posts have become something slightly different: longer, because I like to add short comments on the articles I link to; and perhaps more selective. This meant that these posts were becoming a little too much work! I also don't always find enough physics links to highlight each week.

So I have decided to embrace the change: these posts will remain a regular feature, but no longer necessarily a weekly feature. Instead I shall put them out as and when I have collected enough items I'd like to point out and briefly comment on. The title of the series will also be amended to reflect this.

Anyway, since I have already started writing something for today, I will include a few items:

1. I was particularly interested in this little post by Julianne Dalcanton at Cosmic Variance, about the employment chances for physicists who choose to, or for whatever reason have to, leave the world of academia. The statistics — at least in the US — appear to be relatively encouraging, and somewhat better than for "lab-based" biologists or chemists. Julianne has her speculations as to why this should be so; I suppose they sound quite plausible.
   I think the other point she makes is really important too — students enrolling for physics PhD programmes really ought to be aware that the odds against them ever getting a permanent academic position equivalent to that of their advisor are very small. Say the average professor sees one student through to a PhD every two years. Over a career of 40 years, that's 20 completed PhDs, and yet when that professor retires, only one permanent faculty position becomes available. Odds like that mean that, unlike the UK government, every sensible PhD student should be aware of the need to have a Plan B. This applies also to those of us who have been lucky enough to get a foot on the ladder in the form of a post-doc job (though I don't seem to have taken my own advice yet!).
   
2. Tucked away in the Guardian, I saw this report on the treatment in Pakistan of Nobel-Prize-winning particle theorist Abdus Salam, both before and after his death in 1996.
3. Anyone who has been following the US Presidential elections will know that there has been some amount of kerfuffle recently about who was in charge of which company when. You could see this for a little perspective, or doubtless there are countless other places you could read about it. Anyway, that's not what interests me: I don't have a vote in this election, and if I did, I wouldn't need stories about Bain Capital to know that Romney is a ridiculous candidate.
   Instead, I think the significant occurrence from the last week was this quote from Barack Obama:

[I]f you’re a head of a large private equity firm or hedge fund, your job is to make money. It’s not to create jobs. It’s not even to create a successful business – it’s to make sure that you’re maximizing returns for your investor. Now that’s appropriate. That’s part of the American way. That’s part of the system. But that doesn’t necessarily make you qualified to think about the economy as a whole ...

Phew. At last some politician has come out and said something sensible. I would have thought it was fairly obvious that the analogy between running a country and running a business was completely wrong — after all, I doubt there is a company anywhere in the world that sells its product primarily to its own employees — but still most politicians continue to treat people like idiots. This is not restricted to the US: in Britain the analogy used by the Tories is different — that government budgets are like family budgets, complete with credit cards and tightening belts — but the underlying fallacy is basically the same (which family buys goods and services primarily from itself?). I don't know exactly what rhetorical devices politicians use in Germany, Spain, Greece and the like, but from the utter mess they have made of the Euro, one can surmise that they must be equally stupid. So one-and-a-half cheers for Obama for attempting to right that trend.

LftW: 11th June

Hello again — normal service is now resumed. Obviously having been away I have missed out on lots of interesting stuff, but I did see a few items that could be included in this week's links.

Physics links:

• The big astronomy event of last week was of course the transit of Venus. I entirely missed seeing it, mostly because I was lying in a tent listening to the rain at the time, but the wonderful thing about the modern world is that you need never really miss an event. So if like me you didn't see the real thing and don't think you'll be around in 2117, have a look at NASA's time-lapse HD video of it:

• There are also many great photographs of the event all over the internet. One of the nicest ones I saw was actually not of this transit but of the previous one, in 2004, taken by David Cortner.
• Sean Carroll: Does This Ontological Commitment Make Me Look Fat? Nice title, worthwhile discussion about objections to multiverse ideas.

Other links:

• In my opinon, BBC Radio 4 is one of the best things about the UK. Luckily, you can also listen to it from outside the UK! Last week Kamin Mohammadi gave a very interesting personal talk about the social lives of young people in Iran, as part of the Four Thought series. Her main thesis was that life under an authoritarian regime is more creative — but even if you don't agree with that, you should listen to her simply for the stories of how young Iranians use rides in shared taxis to share some physical intimacy, or use mobile phones with Bluetooth technology to chat under their parents' noses! (Incidentally, if you download the podcast version of Four Thought from here, you can also hear the questions the audience ask after the talks, which isn't included in the first link.)
• Simon Wren-Lewis: The Euro: an alternative moral tale
• Francine Prose: Getting Them Dead. On the Obama administration's tactics of assassination of terrorist suspects (and the use of the English language).
• Three Englishmen Saved from Boiling Pot by Cannibal Chief, Who Was Friend At Oxford