The WordPress.com stats helper monkeys prepared a 2012 annual report for this blog.
Here’s an excerpt:
About 55,000 tourists visit Liechtenstein every year. This blog was viewed about 460,000 times in 2012. If it were Liechtenstein, it would take about 8 years for that many people to see it. Your blog had more visits than a small country in Europe!
Click here to see the complete report.
Follow @telescoperI thought I’d take a short break from doing absolutely nothing to post a quick little item about gravitational lensing. It’s been in my mind to say something about this since I mentioned it in one of the lectures I gave just before Christmas, but I’ve been too busy (actually too disorganized) to do it until now. It’s all based on a paper posted to the arXiv in December which was led by Jo Woodward (née Short) who did her PhD with me in Cardiff and is now in a postdoctoral research position in Durham (which is in the Midlands). The following pictures were take from her paper.
This figure shows the geometry of a gravitational lens system: light from the source S is deflected by the gravitational potential of the lens L so that an image I appears at a position on the sky which is different from the actual position when viewed by the observer O:
There’s a critical radius (which depends on the mass and density profile of the lens) at which this can lead to the formation of multiple images of the source. Even if multiple images are not resolved, lensing results in an increase in the apparent brightness of the source.
A great deal of cosmological information can be gleaned statistically from lensing with even limited knowledge of the properties of the source and lens populations and with incomplete information about e.g. the actual angular deflection produced by the lens or the lens mass. To illustrate this, just consider the expression for the differential optical depth to lensing (related to the probability that a source at redshift 
The first two terms are cosmological, accounting geometrical and expansion effects. Roughly speaking, the larger the volume out to a given redshift the higher the probability is that a given source will be lensed. The third term involves the mass function of lens systems. In the framework of the standard cosmological model this can be computed using Press-Schechter theory or one of the variations thereof. According to current understanding, cosmological structures (i.e. galaxies and clusters of galaxies) form hierarchically so this mass function changes with redshift, with fewer high mass objects present at high redshift than at low redshift, as represented in this picture, in which masses are given in units of solar masses, the colour-coding representing different redshifts:
The last term represents the lensing cross-section of an object with a given mass. This depends on the internal structure of the lens – an object in which the mass is highly concentrated produces lensing effects radically different from one that isn’t. Two simple models for the mass distribution are the singular isothermal sphere (SIS) and the Navarro-Frenk-White profile (NFW). The latter is thought (by some) to represent the distribution of cold dark matter in haloes around galaxies and clusters which is more diffuse than that of the baryonic material because it can’t dissipate energy which it needs to do to fall into the centre of the object. The real potential of a galaxy in its central regions could be more like the SIS profile would predict, however, because baryons outweigh dark matter there.
Now time for a bit of historical reminiscence. In 1997 I published a book with George Ellis in which we analysed the evidence available at the time relating to the density of matter in the Universe. It was a little bit controversial at the time, but it turns out we were correct in concluding that the density of matter was well below the level favoured by most theorists i.e. only about 20-30% of the critical density. However we did not find any compelling evidence at that time for a cosmological constant (or, if you prefer, dark energy). Indeed one of the strongest upper limits on the cosmological constant came from gravitational lensing measurements, or rather the dearth of them.
The reason for this negative conclusion was that, for a fixed value of the Hubble constant, in the presence of a cosmological constant the volume out to a given redshift is much larger than if there is no cosmological constant. That means the above integral predicts a high probability for lensing. Surveys however failed to turn up large numbers of strongly-lensed objects, hence the inference that the universe could not be dominated by a cosmological constant. This is, of course, assuming that the other terms in the integral are well understood and that the reason significant numbers of lensed systems weren’t found wasn’t just they are tricky to identify…
Meanwhile, huge advances were made in other aspects of observational cosmology that established a standard cosmological model in which the cosmological constant makes up almost 75% of the energy budget of the Universe.
Now, 15 years later on, enter the Herschel Space Observatory, which turns out to be superb at identifying gravitational lenses. I posted about this here, in fact. Working in the far-infrared makes it impossible to resolve multiple images with Herschel – even with a 3.5m mirror in space, λ/D isn’t great for wavelengths of 500 microns! However, the vast majority of sources found during the Herschel ATLAS survey with large fluxes at this wavelengths can be identified as lenses simply because their brightness tells us they’ve probably been magnified by a lens. Candidates can then be followed up with other telescopes on the ground. A quick look during the Science Demonstration Phase of Herschel produced the first crop of firmly identified gravitational lens systems published in Science by Negrello et al.. When the full data set has been analysed there should be hundreds of such systems, which will revolutionize this field.
To see the potential (no pun intended) of this kind of measurement, take a look at these five systems from the SDP set:
These systems have measured (or estimated) source and lens redshifts. What is plotted is the conditional probability of a lens at some particular lens redshift, given the source redshift and the fact that strong lensing has occurred. Curves are given for SIS and NFW lens profiles and everything else is calculated according to the standard cosmological model. The green bars represent the measured lens redshifts. It’s early days, so there are only five systems, but you can already see that they are pointing towards low lens redshifts, favouring NFW over SIS; the yellow and light blue shading represents regions in which 68% of the likelihood lies. These data don’t strongly prefer one model over the other, but with hundreds more, and extra information about at least some of the lens systems (such as detailed determinations of the lens mass from deflections etc) we should be able to form more definite conclusions.
Unfortunately the proposal I submitted to STFC to develop a more detailed theoretical model and statistical analysis pipeline (Bayesian, of course) wasn’t funded. C’est la vie. That probably just means that someone smarter and quicker than me will do the necessary…
Follow @telescoperShocked and saddened by news of the death of former England cricket captain Tony Greig, at the age of only 66. He was a controversial character, but a fine all-rounder and skipper as a player, and also part of the finest comedy double-act in cricket history (with Geoffrey Boycott) when he became a commentator:
Follow @telescoperWater in the millrace, through a sluice of stone,
plunges headlong into that black pond
where, absurd and out-of-season, a single swan
floats chaste as snow, taunting the clouded mind
which hungers to haul the white reflection down.
The austere sun descends above the fen,
an orange cyclops-eye, scorning to look
longer on this landscape of chagrin;
feathered dark in thought, I stalk like a rook,
brooding as the winter night comes on.
Last summer’s reeds are all engraved in ice
as is your image in my eye; dry frost
glazes the window of my hurt; what solace
can be struck from rock to make heart’s waste
grow green again? Who’d walk in this bleak place?
by Sylvia Plath (1932-1963)
Follow @telescoperI gather the internet is crawling with people searching for rumours about the Planck mission. It would obviously be entirely inappropriate for me to direct my readers to any website where they might obtain access to confidential information about this experiment, the results from which are embargoed until well into the New Year. So naturally that’s what I’m going to do. Well, blog traffic doesn’t generate itself does it?
As a Telescoper exclusive I am able to offer you a sneak preview of the top secret Planck data well in advance of official release. If you want to see what Planck scientists have been looking since Planck was launched in 2009, just click here.
Follow @telescoperBack from a brief Christmas visit up North I thought I’d post a few snaps I took on our traditional Boxing Day spin around Northumberland. The weather wasn’t exactly marvellous, but it did at least stop raining for a while when we reached Amble so we got out of the car and went for a stroll around the little harbour…
Although it was a cold and wet day it wasn’t too windy. They must be tough fishermen who go out into the North Sea in those little boats, but they’re friendly folk too – waving to us landlubbers as they came in and out of the harbour.
On the way home we stopped at Benwell, not a picturesque place but the part of Newcastle in which I was brought up. I’ve posted about the little house where my first memories live here, and there’s an old photograph of it here:
The house itself (ours was the one on the left on this picture) was built of brick but to the left hand side you can just see a stone wall. The two cottages were demolished some time ago, along with Pendower School which was behind them as viewed from the picture. The whole area has now been covered with new houses, but for some reason they left the stone wall. I hopped out of the car to take a couple of pictures, as this is all that remains of the first place I can remember living. These were both taken from Ferguson’s Lane, which is immediately behind the stone wall I mentioned earlier, i.e. to the left of the two cottages in the old photograph.
In the second picture you can see the filled in outlines of the door which led to our backyard (on the right) and (on the left) the holes through which the coalman used to deliver the coal that was the only form of heating in the house. There was no central heating and no heating at all upstairs, incidentally, so we had very cold bedrooms in winter!
Follow @telescoperWell, I made it back to Cardiff more-or-less in one piece despite the best efforts of Cross Country Trains. The train I took from Newcastle was three carriages shorter than expected, so my reserved seat was in a carriage that didn’t exist. Obviously not many people travel at Christmas so they thought they didn’t need a full size train. I had decided to treat myself to a First Class ticket to make the long journey to Newcastle and back as pleasurable as possible, but I ended up having to scramble for a seat in second class. By the time we reached Darlington it was standing room only throughout the train, including First Class, and each station stop took ages as scores of travellers tried to board the already packed carriages.
The train was 45 minutes late into Birmingham, but the connecting train from there to Cardiff was also delayed so I managed to catch it. However, never willing to let any cloud show its silver lining, Cross Country Trains decided to terminate the Cardiff train at Newport so I had to scramble again onto another train with a host of similarly disgruntled passengers. You might have thought they would have tried their best to help their customers out on a day that the whole railway network has been in chaos, but no.
Anyway, I got home only an hour late so perhaps shouldn’t complain too much. Expectations must be kept low when travelling on the British railway network. At least I got a lovely view along the Severn in the late afternoon as the train headed towards Newport…
It’s nice to be home. I think I’ll chill out this evening and defer writing my claim for compensation until tomorrow!
Follow @telescoperHaving spent most of the afternoon setting up a new laptop and wireless router, and installing various bits of software on the computers here at the old family home, I thought the least I could do is sign in for a moment and wish you all a very Merry Xmas while we prepare for dinner.
If your Christmas Day has been half as good as mine, then mine has been twice as good as yours!
Follow @telescoperWell, I’m up early to get the train Up North, so I thought I’d just sign off for the holiday with a little gift. I have posted this before but, on the grounds that you can’t have too much of a good thing, here it is again. Plus, of course, this will be my last Christmas in Wales…
There are only two kinds of people in the world: those who have heard Dylan Thomas reading his wonderful short autobiographical story A Child’s Christmas in Wales; and those who haven’t. I’ve heard it hundreds of times, like a favourite piece of music. Technically it’s a prose work, but it’s prose that’s so close to poetry that it really defies categorisation. Either way, the language certainly has a musical quality, and the author’s voice brings it to life in a way nobody else has ever been able to. It’s also shot through with flashes of a dry offbeat humour that tickles my fancy any time of the year but at Christmas time I think it’s just magical.
Follow @telescoperIt’s with some trepidation that I find myself facing the long journey to Newcastle tomorrow. There’s been heavy rain overnight (even leading to a Flood Alert along the Taff near my house) and quite a lot of disruption on the railways today as a consequence. Nevertheless I’m determined to make an attempt to get into the Christmas spirit. If Fats Waller can’t do it, nobody can. Here’s his classic version of Jingle Bells on which the general atmosphere of hilarity and inspired chaos allows his superb musicianship to shine all the more brightly. Few ever managed to play Harlem Stride piano as well as Fats Waller, and he’s on top form in the opening choruses of this record.
Will I make it home on Christmas Eve? In the immortal words of Mr Waller “One never knows, do one?”
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In the Dark 
