## Eddington in Cardiff 100 years ago today: the first proposal that stars are powered by fusion

Posted in Cardiff, History, The Universe and Stuff with tags , , on August 24, 2020 by telescoper

Here’s a fascinating bit of astrophysics history by former Cardiff colleague Bernard Schutz: one hundred years ago today, Arthur Stanley Eddington gave a talk in Cardiff in which he, with great prescience, proposed the idea that stars might be powered by nuclear fusion.

One hundred years ago today, on 24 August 1920, with over 1000 people gathered in Cardiff for the annual meeting of the British Association, Arthur Eddington gave his address as the incoming president of the physical and mathematical sciences section. He elected to speak on the subject of the “Internal Constitution of the Stars”. When I first came across the text of the address last year (published in Nature in 1920), I was amazed to find as early as this such an insightful proposal that stars are powered by the synthesis of helium from hydrogen. But what really brought me up short was this sentence:

If, indeed, the sub-atomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfilment our dream of controlling this latent power for the well-being of the human race – or for…

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## Stars, by Emily Brontë

Posted in Poetry with tags , , on July 30, 2020 by telescoper

Ah! why, because the dazzling sun
Restored our Earth to joy,
Have you departed, every one,
And left a desert sky?

All through the night, your glorious eyes
Were gazing down in mine,
And, with a full heart’s thankful sighs,
I blessed that watch divine.

I was at peace, and drank your beams
As they were life to me;
And revelled in my changeful dreams,
Like petrel on the sea.

Thought followed thought, star followed star,
Through boundless regions, on;
While one sweet influence, near and far,
Thrilled through, and proved us one!

Why did the morning dawn to break
So great, so pure, a spell;
And scorch with fire the tranquil cheek,
Where your cool radiance fell?

Blood-red, he rose, and, arrow-straight,
His fierce beams struck my brow;
The soul of nature sprang, elate,
But mine sank sad and low!

My lids closed down, yet through their veil
I saw him, blazing, still,
And steep in gold the misty dale,
And flash upon the hill.

I turned me to the pillow, then,
To call back night, and see
Your worlds of solemn light, again,
Throb with my heart, and me!

It would not do—the pillow glowed,
And glowed both roof and floor;
And birds sang loudly in the wood,
And fresh winds shook the door;

The curtains waved, the wakened flies
Were murmuring round my room,
Imprisoned there, till I should rise,
And give them leave to roam.

Oh, stars, and dreams, and gentle night;
Oh, night and stars, return!
And hide me from the hostile light
That does not warm, but burn;

That drains the blood of suffering men;
Drinks tears, instead of dew;
Let me sleep through his blinding reign,
And only wake with you!

by Emily Brontë (1818-1848; she was born on 30th July)

## Watch “Why the Universe is quite disappointing really – Episode 2” on YouTube

Posted in The Universe and Stuff, YouTube with tags , , on May 8, 2020 by telescoper

Episode 2, in which I explain how stars limp along unimpressively, making very poor use of the resources available to them, not doing a very good job at what they’re supposed to be doing, and then they die.

Just like people really…

## Euclid Updates

Posted in The Universe and Stuff with tags , , , , on June 17, 2019 by telescoper

Following the Euclid Consortium Meeting in Helsinki a couple of weeks ago, here are a couple of updates.

First, here is the conference photograph so you can play Spot The Telescoper:

(The picture was taken from the roof of the Finlandia Hall, by the way, which accounts for the strange viewpoint.

The other update is that the European Space Agency has released a Press Release releasing information about the location on the sky of the planned Euclid Deep Fields. Here they are (marked in yellow):

These deep fields amount to only about 40 square degrees, a small fraction of the total sky coverage of Euclid (~15,000 square degrees), but the Euclid telescope will point at them multiple times in order to detect very faint distant galaxies at enormous look-back times to study galaxy evolution. It is expected that these fields will produce several hundred thousand galaxy images per square degree…

Selecting these fields was a difficult task because one has to avoid bright sources in both optical and infrared (such as stars and zodiacal emission) so as not to mess with Euclid’s very sensitive camera. Roberto Scaramella gave a talk at the Helsinki Meeting showing how hard it is to find fields that satisfy all the constraints. The problem is that there are just too many stars and other bits of rubbish in the sky getting in the way of the interesting stuff!

## Why the Universe is extremely overrated.

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

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

Take this thing, for example:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## A Problem of Gravity

Posted in Cute Problems with tags , , on May 9, 2017 by telescoper

Here’s a nice one for the cute problems folder.

Two spherically symmetric stars A and B of equal mass M and radius r have centres separated by a distance 6r. Ignoring any effects due to the orbital motion of the stars, determine a formula (in terms of G, M and r) for the minimum velocity with which material can be ejected from the surface of A so as to be captured by B.

Answers through the comments box please. First correct answer receives 7 points.

## A Question of Magnitude

Posted in Cute Problems, Education, The Universe and Stuff with tags , , , on January 30, 2016 by telescoper

A frequent complaint raised by students of Astronomy is that astronomers insist on using funny units. Chief among them is the use of magnitudes to quanitify the brightness of an object. Why not use the observed intensity (or brightness or flux) of the light from the star, which can be expressed straightforwardly in SI units, instead of faffing around with a clunky logarithmic measure? The reason we use the magnitude scale is primarily historical and based on the fact that the eye’s response to light is more-or-less logarithmic and that in the days before calculators it was easier to deal with very large and very small numbers using logarithms.Most relevant calculations involve divisions and multiplications which become subtractions and additions when you use logarithmic quantities.

It was Norman Pogson who first suggested that a magnitude scale be defined such that a difference of five magnitudes should correspond to a factor of 100 in actual brightess. This was because the brightest naked-eye stars – those of first magnitude – are about 100 times brighter than the faintest naked-eye stars, which are of sixth magnitude. That was in 1856 and we’ve been stuck with it ever since!

Although the magnitude system may appear strange, it’s not really that hard to use when you get used to it. A beginner really just needs to know a few key things:

1.  Bright things have lower magnitudes (e.g. first magnitude stars are brighter than second magnitude stars);
2.  If two stars have apparent magnitudes $m_1$ and $m_2$ respectively then $m_2-M_1=2.5\log_{10} (I_1/I_2)$ where $I_1$ and $I_2$ are respectively the fluxes received from the two stars;
3. The intensity of light falls off with the square of the distance from the source;
4.  The absolute magnitude is the apparent magnitude a star would have if it were 10 parsecs from the observer;
5. Most stars have roughly black-body spectra so their total intrinsic luminosity depends on the product of their surface area (i.e. on the square of the radius) and the fourth power of the surface temperature.

Got it?

To test your understanding you could try these little problems. To warm up you might look at I posted the first of them a while ago. Anyway, here we go:

1. A binary system at a distance of 100 pc has such a small separation between its component stars that it is unresolved by a telescope. If the apparent visual magnitude of the combined image of the system is 10.5, and one star is known to have an absolute visual magnitude of 9.0, what is the absolute visual magnitude of the other star?
2. Two stars are observed to have the same surface temperature, but their apparent visual magnitudes differ by 5. If the fainter star is known to be twice as far away as the brighter one, what is the ratio of the radii of the two stars?
3. A binary system consists of a red giant star and a main-sequence star of the same intrinsic luminosity. The red giant has a radius 50 times that of the main-sequence star. (i) If the main-sequence star has a surface temperature of 10,000 K, what is the surface tempature of the red giant star? (ii) If the two stars can’t be resolved the combined system has an apparent magnitude of 12, what are the apparent magnitudes the two component stars would have if they could be observed separately?

Answers through the comments box please! The first correct entry wins a year’s free subscription to the Open Journal of Astrophysics…

UPDATE: Apologies for having forgotten about this post for ages. The answers are:

1. Absolute magnitude 5.54 (apparent magnitude 10.54)
2. 5:1
3. (i) ~1400K (ii) 12.75, 12.75

## “Stars” by Kandinsky

Posted in Art with tags , on January 17, 2016 by telescoper

No time for a proper post so I thought I’d fill a bit of space with Stars, or at least with a picture of the lithograph of that title by Wassily Kandinsky made, I think, in 1938. It is certainly a different kind of image from that produced by astronomers, but it does put me in mind of star-forming regions such as the Orion Nebula..

## No Cox please, we’re British…

Posted in Television, The Universe and Stuff with tags , , , , , , , on March 29, 2011 by telescoper

The final episode of the BBC television series Wonders of the Universe was broadcast this weekend. Apparently it’s been incredibly popular, winning huge plaudits for its presenter Brian Cox, and perhaps inspiring the next generation of budding cosmologists the way Carl Sagan did thirty-odd years ago with his series Cosmos.

Grumpy old cosmologists (i.e. people like myself) who have watched it are a bit baffled by the peculiar choices of location – seemingly chosen simply in order to be expensive, without any relevance to the topic being discussed – the intrusive (and rather ghastly) music, and the personality cult generated by the constant focus on the dreamy-eyed presenter. But of course the series wasn’t made for people like us, so we’ve got no right to complain. If he does a great job getting the younger generation interested in science, then that’s enough for me. I can always watch Miss Marple on the other side instead.

But walking into work this morning I suddenly realised the real reason why I don’t really like Wonders of the Universe. It’s got nothing to do with the things I mentioned above. It’s because it’s just not British enough.

I’m not saying that Brian Cox isn’t British. Obviously he is. Although I do quibble with him being labelled as a “northerner”. Actually, he’s from Manchester. The North is in fact that part of England that extends southwards from the Scottish border to the Tyne. The Midlands start with Gateshead and include Yorkshire, Manchester and Liverpool and all those places whose inhabitants wish they were from the North, but aren’t really hard enough.

Anyway, I just put that bit in to inform non-British readers of this blog about the facts of UK geography. It’s not really relevant to the main point of the piece.

The problem with Wonders of the Universe is betrayed by its title. The word “wonders” suggests that the Universe is wonder-ful, or even, in a word which has cropped up in the series a few times, “awesome”. No authentic British person, and certainly not one who’s forty-something, would ever use the word “awesome” without being paid a lot of money to do so. It just doesn’t ring true.

I reckon it doesn’t do to be too impressed by anything on TV these days (especially if its accompanied by awful music), but there is a particularly good reason for not being taken in by all this talk about “Wonders”, and that is that the Universe is basically a load of rubbish.

Take this thing, for example.

It’s a galaxy (the Andromeda Nebula, M31, to be precise). We live in a similar article, in fact. Of course it looks quite pretty on the surface, but when you look at them with a physicist’s eye galaxies are really not all they’re cracked up to be.

We live in a relatively crowded part of our galaxy on a small planet orbiting a fairly insignificant star called the Sun. Now you’ve got me started on the Sun. I know it supplies the Earth with all its energy, but it does so pretty badly, all things considered. The Sun only radiates a fraction of a milliwatt per kilogram. That’s hopeless! Pound for pound, a human being radiates more than a thousand times as much. All in all, stars are drastically overrated: bloated, wasteful, inefficient and  not even slightly awesome. They’re only noticeable because they’re big. And we all know that size shouldn’t really matter.

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

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

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

And then there’s the Big Bang. Well, I don’t need to go on about that because I’ve already posted about it. Suffice to say that the Big Bang wasn’t anywhere near as Big as you’ve been led to believe. The volume was between about 115 and 120 decibels. Quite loud, but many rock concerts are louder. Very disappointing. If I’d been in charge I would have put on something much more spectacular.

In any case the Big Bang happened a very long time ago. The Universe is now a cold and desolate place, lit by a few feeble stars and warmed only by the fading glow of the heat given off when it was all so much younger and more exciting. It’s as if we inhabit a shabby downmarket retirement home, warmed only by the feeble radiation given off by a puny electric fire as we occupy ourselves as best we can until Armageddon comes.

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

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

We British just don’t like showy things. It’s in our genes. We’re fundamentally a rather drab and dowdy race. We don’t really enjoy being astonished either. We prefer things we can find fault with over things that intimidate us with their splendour. We’re much more likely to tut disapprovingly than stare open-mouthed in amazement at something that seems pointlessly ostentatious. If pushed, we might even write a letter of complaint to the Council.

Ultimately, however, the fact is that whatever we think about it, we’re stuck with it. Just like the trains, the government and the weather. Nothing we can do about it, so we might as well just soldier on. That’s the British way.

So you can rest assured that none of this Wonders of the Universe stuff will distract us for long from getting on with the important things in life, such as watching Coronation Street.

Professor Brian Cox is 43.

## Off the Main Sequence…

Posted in Biographical, The Universe and Stuff with tags , , , , , , , on July 22, 2010 by telescoper

When I was at School, one of my English teachers enjoyed setting creative writing challenges for homework. One of the things he liked to do was to give us two apparently separate topics and get us to write a short story that managed to tie them together. Although I seldom got good marks I now realise that this is quite a useful skill to develop.  Sometimes, when I’ve been at a loss for something  to blog about, I’ve taken two items from the news and tried to link them somehow. That’s also how a lot of satire works – many of the best Private Eye skits involve putting two pieces of news together in a way that’s deliberately back to front. In fact many writers have commented along similar lines,  the most famous being E. M. Forster, whose advice to a young writer was “Only Connect”.

Yesterday the news was full of stories emanating from the discovery of a very massive star, in fact the most massive one ever found.  This news also got the Jonathan Amos treatment on the  BBC science website too. I think it’s quite an interesting discovery but it  didn’t generate much enthusiasm from Lord Rees who wrote in a Guardian article

I don’t view this discovery as a big breakthrough. It’s a bit bigger than other stars of this kind that we’ve seen and it’s nice that it involves British scientists and the world’s biggest telescope. It’s a step forward, but it is not more than an incremental advance in our knowledge.

What’s interesting about this star is that it may shed some light – actually, rather a lot of light, because it’s 10,000,000 times brighter than the Sun – on the properties of very big stars as well as possibly how they form.

There was even an item on local radio last night, which reported

The biggest star ever discovered was recently found by astronomers in Sheffield.

You’d think if it was that bright and so nearby somebody in Sheffield would have noticed it long before now…

A star this big – about 300 times the mass of the Sun – operates on the same basic mechanism as the Sun but the quantitative details are very different. Its surface temperature is about 40,000 Kelvin compared to the Sun’s, which is only about 6000K, so the radiation field it generates is very much more powerful. It’s also very much larger, probably about 50 times the Sun’s radius, so there’s more surface area to radiate. It’s a very big and very bright beastie.

The name of this star is R136a1 but given its new status as media star, it really needs a better one. In fact, there’s a suggestions page here. Let me see. Overweight and prominent in the media? No Eamonn Holmes gags please.

A star is basically just a ball of hot gas which exerts pressure forces that balance the force of gravity, which tries to make it collapse, in a form of hydrostatic equilibrium. With so much mass to hold up the pressure in the centre of the star has to be very large, and it therefore has to be very hot. The energy needed to keep it hot comes from nuclear reactions that mainly burn hydrogen to make helium (as in the Sun), but the rate of these processes is sensitively dependent on the temperature and density in the star’s core. The Sun is a relatively sedate pressure-cooker that will  simmer away for billions of years. A monster like the one just found guzzles fuel at such a rate that its lifetime will only be a few million years. Like megastars in other fields, this one will live fast and die young.

Nobody really knows how big the biggest star should be. Very big stars are produce such intense radiation that radiation pressure is more important than gas pressure in supporting the star against collapse, but if the star is too big (and therefore too hot) then the radiation field will blow the star apart. This is when the so-called Eddington Limit is reached.  Where the line is drawn isn’t all that clear. The new star  suggests that it is a bit higher up the mass scale than previously thought. I think it’s interesting.

I’ve written about this star partly to make a point about how wonderful astronomy is for teaching physics. To understand how a star works you need to take into account thermal physics, gravity, nuclear physics, radiative transport and whole load of other things besides. Putting all that physics together to produce a stellar model is a great way to illustrate the much-neglected synthetic (rather than analytic) side of (astro)physical theory education. Stars are good.

Cue cheesy link to another item.

The single biggest step towards the understanding of stellar structure and evolution was the Hertzsprung-Russel diagram, or HR diagram for short, which shows that there is a Main Sequence of stars (to which the Sun belongs). Main sequence stars have luminosities and temperatures that are related to each other because they are both determined by the star’s mass. That’s because they’re all described by the same basic physics – hydrostatitic equilibrium, nuclear burning, etc – but just come in different masses. They adjust their temperature and luminosity in order to find an equilibrium configuration.

Not all stars are main sequence stars, however. There are classes of stars with different things going on and these lie in other regions of the HR diagram.

With this in mind, the Astronomy Blog has constructed an amusing career-related version of the HR diagram which I’ve reproduced here:

Instead of plotting temperature against luminosity (or, to be precise, colour against magnitude) as in the standard version this one plots academic publications against google hits, which purport to be a measure of “fame”. A traditional academic will presumably acquire fame through their publications only, thus defining a main sequence, whereas some lie off that sequence because of media work, blogging, or (perhaps) involvement in a juicy sex scandal. I don’t think fame and notoriety are distinguished in this calculation.

I know quite a few colleagues have been quietly calculating where they lie on the above diagram, as indeed have I. Vanity, you see, is very contagious. I’m not named on the version shown, but I can tell you that I’m much more famous than Andy Lawrence, who is. So there.