Declining Rotation Curves at High Redshift?

Posted in Astrohype, The Universe and Stuff on March 20, 2017 by telescoper

I was thinking of doing my own blog about a recent high-profile result published in Nature by Genzel et al. (and on the arXiv here), but then I see that Stacy McGaugh has already done a much more thorough and better-informed job than I would have done, so instead of trying to emulate his effort I’ll just direct you to his piece.

A recent paper in Nature by Genzel et al. reports declining rotation curves for high redshift galaxies. I have been getting a lot of questions about this result, which would be very important if true. So I thought I’d share a few thoughts here. Nature is a highly reputable journal – in most fields of […]

via Declining Rotation Curves at High Redshift? — Triton Station

P.S. Don’t ask me why WordPress can’t render the figures properly.

A Picture of Theresa May 

Posted in Politics with tags , on March 19, 2017 by telescoper

Apparently our Prime Minister has requested that the following picture be removed from Google’s  image search facility.

If she’d like me to remove it from this blog, I will do so if she posts a comment below explaining why I should.

Wikipedia Update 

Posted in Biographical on March 18, 2017 by telescoper

In case you didn’t realise it, I have my very own Wikipedia page. I don’t know who set it up, or who edits it, but it does seem to get updated regularly. Fortunately these updates are reasonably sensible and generally accurate.

I recently noticed that it has been updated again:

I wouldn’t say it was “pathological”, but it is indeed the case that I don’t like harpsichords (or, to be more accurate, I don’t like the noise they produce).

One day I might edit the page myself, but other than being a cosmologist who hates harpsichords I’m not sure there’s enough else to me that’s worth putting there!

R.I.P. Derek Walcott 

Posted in Poetry on March 17, 2017 by telescoper

Out of the office all day, I heard quite late of the death at the age of 87 of the poet Derek Walcott.

Here’s one of his best-known poems, which will resonate with middle-aged men everywhere:

If you aren’t familiar with Derek Walcott, this collection is a good place to start:

A Quite Interesting Question: How Loud Was the Big Bang?

Posted in The Universe and Stuff with tags , , , , , , , on March 16, 2017 by telescoper

I just found out this morning that this blog got a mention on the QI Podcast. It’s taken a while for this news to reach me, as the item concerned is two years old! You can find this discussion here, about 16 minutes in. And no, it’s not in connection with yawning psychopaths. It was about the vexed question of how loud was the Big Bang?

I’ve posted on this before (here and here)but since I’m very busy again today I  should recycle the discussion, and update it as it relates to the cosmic microwave background, which is what one of the things I work on on the rare occasions on which I get to do anything 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.

Planck_CMB

The above image shows the variations in temperature of the cosmic microwave background as charted by the Planck Satellite. 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, because the primordial universe consists of a plasma rather than air. Moreover, the actual sound of the Big Bang contains a mixture of wavelengths with slightly different amplitudes. In fact here is the spectrum, showing a distinctive signature that looks, at least in this representation, like a fundamental tone and a series of harmonics…

Planck_power_spectrum_orig

 

If you take into account all this structure it all gets a bit messy, but it’s quite easy to get a rough but reasonable estimate by ignoring all these complications. 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 of this amplitude, i.e. 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.

cooler_decibel_chart

As you can see in the Figure above, 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. Modern popular beat combos often play their dreadful rock music much 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. The QI podcast also mentions  that blue whales make a noise that corresponds to about 188 decibels. 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.

Semper Cavete Quod Idibus Martiis

Posted in Film, History with tags , , on March 15, 2017 by telescoper

Today is the Ides of March so I thought I’d keep up the little tradition I’ve established of posting this  priceless bit of British cultural history relevant to such a fateful day.

This is from the First Folio Edition of Carry On Cleo, and stars the sublime Kenneth Williams as Julius Caesar delivering one of the funniest lines in the whole Carry On series. The joke may be nearly as old as me, but it’s still a cracker…

P.S. On a less frivolous note, today the good folks of the Netherlands are going to the polls. I hope that they use their votes wisely, but am more than a little nervous about the outcome.

 

Transferable Skills Training

Posted in Uncategorized on March 14, 2017 by telescoper

There’s an ever-increasing need for students of physics and astronomy to broaden their knowledge base by acquiring skills that might be transferable into other fields. Thinking about this the other day it occurred to me that some physicists and astronomers may not yet be able to dance the Madison, so here is an instructional video presented by Professors Jennifer Comar and Paolo Pasta Lanna, with musical accompaniment by the Ray Bryant Combo.

Watch very carefully, as there will be a test next week.