Canberra
Astronomical Society

Guest Speaker Presentations

The Expanding Universe and the Hubble Constant

by Professor Jeremy Mould
Director, Mount Stromlo and Siding Spring Observatories

Canberra Astronomical Society meeting on 15 October 1998.

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Tonight's topic is the expanding universe, and I'll talk mainly about the work to measure the Hubble Constant or the rate of expansion of the universe. But I want to talk a little bit about the expanding world of astronomy as well, in case one or two of you have heard me before on this subject and might otherwise drift off.

Well, the universe is expanding, and what that means can be very easily described in a variety of models. You've probably seen or heard Brian Schmidt on the subject, he has a two-dimensional model of the expanding universe. I've got a one-dimensional model which I've shown CAS members before "a rubber band with galaxies attached that stretch out" and Brian has a balloon with galaxies painted on it, which when you blow it up real hard also produces the effect of the Big Bang.

But the model of the expanding universe is awfully simple, and we should understand it just as well as we understand the solar system model, which is a 400-year-old invention now, whereas the expanding universe is a mere 70- year-old invention, as we'll see. And all it asserts is that if you have a density enhancement of galaxies "that is to say, that the structure here is richer where it's red and less rich where it's blue-coloured" then the structure formed by the galaxies expands with the passing of time. That is, the space that is between the galaxies expands, and the structure that was formed by the galaxies expands. The galaxies themselves are bound by gravity, they don't expand. A very simple model, and uniform expansion fits the data very well.

Historically it goes back to Hubble and some other previous workers, but Hubble was the first to present it to the American National Academy of Science (here is his original data). Recession velocity (how fast the galaxies are travelling away from us) plotted vertically, and the distance of the galaxies according to Hubble's measurements are plotted horizontally in parsecs (remember, a parsec is about three light years) and Hubble was willing to make the bold step to say that a straight line connects those points. Astronomers continue to be bold in that sort of way, which sometimes catches them out.

Distances are the hard part to measure in this relation. Velocities as we all know are extremely easy to measure. Velocities are measured by redshift, and the physical principle that applies there is the same as applies to police radar, in which the radar-emitting car is sending pulses out towards the car which is moving away at velocity v, and the reflected pulse is reflected at a longer wavelength, and the difference between the emitted and received pulse is then measured by the clever folks in the car who calculate delta lambda, ratio it to lambda, quickly multiply it by the velocity of light and then write you a ticket.

But, though velocities are extremely easy to measure, distances are harder, and that's where the Hubble Space Telescope (HST) comes in, and the program that I'm going to talk to you about, and have talked to you about before now. We now as a twenty-person international team have taken our last data with the HST, all the time they will give us to do this project has been used, and we're busy reducing the data and hopefully will have a final result, getting pretty close to final, by early next year.

A reminder about some of the curious units of distance in astronomy, and how the closest units of distance are measured. Parallax is simply the surveyor's attempted triangulation of the universe, and we use the baseline of the Earth's orbit about the Sun to measure distances relative to one astronomical unit (that the Earth-Sun distance is by definition), and we define a parsec to be the distance of a star from which this baseline subtends an arcsecond. The measurement is a fairly straightforward one, because when you are here, the distant star appears with a set of background stars of course, but when you are on the other side of the Earth's orbit, the nearby star appears to move relative to the background stars, and you can meaure that one arcsecond angle. You're familiar with what an arcsecond is, because the size of images in typical astronomical telescopes at typical sites is arcseconds.

But of course if you tried to apply this same distance measuring technique to objects which are a lot more remote, say typical distances to stars anywhere in the galaxy, then the angle you're trying to measure if the distance to the object is kiloparsecs (thousands of parsecs) is miliarcseconds, and the problem with measuring galaxy distances is much worse, because the nearest galaxy like our own is almost a megaparsec away, and in that case we're out to measure a microarcsecond. Now, satellites are in preparation which will actually do measurements like that, but we can't do them yet. So we use other methods of measuring distances, and geometrical methods like that one are preferable.

An example of a geometrical method is provided by Supernova 1987A which a number of you will remember when it went off a little over ten years ago - a supernova in the Large Magellanic Cloud (LMC) - and a few years after that the pulse of light emitted from the central object first of all illuminated a disc around the star, and then a little while later a density enhancement of the stuff that had been emitted previously by this massive star when in its mass-losing phase, was lit up by the pulse of light. So this is an object whose actual size we know. Its actual size is simply given by the velocity of light times the time that it took the light to get out here. So we know physically in centimeters if you like, how large that ring and the other ring just like it is, so we simply have to measure the angle it subtends on the sky, and you can play your triangle game again and get the distance to the LMC from that. So that's a method that works on astronomical distances which works out to 150,000 light years quite effectively, and uses mostly geometry to make the measurement.

So let's suppose we know the distance to the LMC from this and other methods. How can we measure distances even further away? That's where the relationship between the luminosity of Cepheid variable stars and their period comes in. Cepheid stars "you may have looked at some of the closest examples, there are nice bright examples in our own galaxy" are pulsating stars, getting larger and smaller in a certain period, and since larger stars take a longer time to do that cyclical period, they also emit more luminosity.

There is a relationship between the luminosity and the period, shown schematically here, of a Cepheid variable star, in a sense that those with a period of fifty days at the top right of the diagram are very much more luminous than Cepheids with periods like five days, which is most of the range of period that Cepheids have, and so when we measure their magnitudes or fluxes we see a relationship like that. If you assume that the same relationship applies elsewhere in the universe, an assumption which is easy to say, but contains a few things which you could challenge, then the fact that a Cepheid star of say a ten-day period in a galaxy like M100 in the Virgo cluster is this much fainter than an exactly identical one in the LMC, that simply tells you how much further away M100 is than the LMC, from the simple notion that if these are separated by 105 in flux, then the galaxies will be separated by 102.5 in distance. And that is roughly how much further the Virgo Cluster is than the LMC.

So our project was to go find Cepheid variable stars in a set of galaxies in the local neighbourhood, and we used the Wide-Field & Planetary Camera (WFPC) on the HST. These pictures aren't all as beautiful as the pictures of galaxies that you see in books and on slides, and perhaps I should have brought some along to show you; but in black and white you can see that HST is resolving this galaxy, which is NGC925, plainly into stars. Life isn't perfectly simple, because you can see dust patches just like in the Milky Way in this galaxy, and some of the Cepheids will be hiding behind dust patches, something you have to take into account in our multi-colour measurements, but in this project we simply feed these images, thirteen successive images of each galaxy, into the computer, tell the computer to go find the stars, it's the same kind of software as the RAPT (Reynolds Amateur Photometry Team) project uses to enter them into the database, find those which are varying (most of the stars resolved are not varying), then find their periods, plot everything up in the period-luminosity relation and you can find the distance to that galaxy.

At the end of observing some twenty of these galaxies over the last four years, since the installation of the WFPC with its corrective optics in the Hubble, we've established what you might call trigonometric marker points or survey markers in the local supercluster, having measured their distance from us (this is actually the distribution in the supergalactic co-ordinates) and take a plane in the local neighbourhood and project the galaxies onto it. This is the distribution of galaxies that we've measured distances for in this survey, and so we have an incomplete survey of galaxies within 20 megaparsecs. A number of them are in the Virgo cluster up here, some are out in the Fornax cluster.

What do these results show when we plot their recession velocities against their Cepheid distances? Well, they show uniform expansion, just like Hubble showed back in 1929, but now we're a bit more confident of the distances measured, and those distances go out a lot further from us than in the 1930s. With this diagram we're actually plotting the expansion with redshifts out to 1500 km/s or as we saw, 20 megaparsecs, and even from the galaxies that we've plotted here, we can see that the Hubble Constant, which is the slope of this relation in units of km/s per megaparsec, km/s plotted vertically here and megaparsecs plotted horizontally the slope is quite well defined. The value that comes out by measuring the slope is 73 km/s per megaparsec; with these data we couldn't rule out values as slow as 61 or as high as 85, though if 61 was right it really is missing most of the points, and similarly with 85.

But this actually doesn't go out far enough. It's a measure of the expansion rate in the local 20 megaparsecs, but we would like to see this plotted further. So we use a second standard candle, a sort of distance indicator. This one is called the Tully-Fischer relation, which is a relationship between how bright galaxies are plotted on the vertical scale, versus how fast they rotate. We have a sample of spiral galaxies, and we find when we plot their brightnesses versus rotation speed, we get a relationship like that. We use that as a standard candle relationship in the same way as we used Cepheids before, but instead of period of the Cepheid, galaxy rotation speed is what defines the standard candle. So if we have a galaxy rotating at a certain rate, at a distance we know, and we see one rotating at the same rate but 100 times fainter, we know that it's 10 times further away. The trick here is that we use the HST to measure nearby galaxies, and put them on a relationship like this, then we can use that relationship to measure things which are much further away. That allows us to step out a good deal further in distance.

So the far field Hubble Constant has us looking at the expansion all the way out to 10,000 km/sec, out to 150 mpc or almost 500 million ly. The objects we're plotting here are actually clusters of galaxies named after George Abell who zealously plotted them on the Palomar Sky Survey. The same linear relationship between velocity and distance, and no surprise: the Hubble Constant is coming out not very different from when we were only looking in the last slide out this far. The uncertainty, which as we complete the project is slowly shrinking, is shown there.

There are other standard candles which are more famous, and which Brian Schmidt has probably talked to you about, such as the supernova standard candle, but we can use our Cepheid results to calibrate our standard candles in the same way we calibrated the Tully-Fischer relation. That allows you to plot the expansion out to immense distance, as Brian has probably told you. He gave me this picture of the most distant supernova found with large telescopes to date. This is the galaxy it's in, it's a one-pixel bright supernova, and that one is at a redshift approaching 1. Using Cepheids to calibrate distance indicators like this, you can map the expansion rate all the way out.

Of course, what people want to know is not the expansion rate, but the age of the universe. The expansion rate tells you the age of the universe, but you need to know more than that in order to get the age of the universe. That's because, of course, the expansion could be steady. If these are objects expanding out from the centre and the expansion is steady, that is continuing at the same rate, you'll have concentric circles; or the expansion could be slowing down, or accelerating. You need to know which, in order to get the age of the universe. The easiest assumption is that the expansion has always been at the same rate. But because of gravity it could be slowing down. Although this is our result now for the Hubble Constant - 73 + 10 km/second per megaparsec (this is a 15% uncertainty and we hope to refine this over the next few months down to a 10% uncertainty) we won't be able to go on TV and tell people what the age of the universe is without more information.

You could see it like this. This is the scale of the universe, and this is time schematically, and here we are now, the question is: When was the scale zero? That's how long it has been since the big bang. The simplest (steady expansion) assumption gives a straight line graph, with the scale always increasing at the same rate, then our measure of the Hubble Contant, which is the slope of this relation, is the slope of this straight line, and we can trace it right back simply to 14 + 2 billion years.

But perhaps the expansion is slowing down. The extreme case of that is to suppose that at infinite time, the expansion will have stopped. That is called the critical density assumption, that the density of the universe is doing the slowing down, and that if the density were any higher the expansion would after a finite time reverse; if it is less than the critical density the expansion will go forever. But the critical density case, when things come to a halt at infinite time, can be plotted there as this curve, and under that assumption the universe's age is 9 + 2 billion years. But until we know exactly what the density is, anywhere between here and here is possible.

Hence the big effort, and Brian Schmidt has probably already talked to you about it, to measure the density by measuring the brightness of supernovae and the geometry of the universe which is dependent on its density. So with more work it should be possible to narrow down the age of the universe between these two limits. Except, as Brian has no doubt told you, the supernova work has turned up a surprise which is that there may be some accelerating mechanism at work in the universe. Certainly in the early universe there was; whether there is now is still uncertain. That allows for a whole family of other curves. Nevertheless the simple answer is that the supernova data are consistent with a universe that is freely expanding, in which the gravity and acceleration are more or less in balance. So the simplest answer that we can give to how old is the universe is: 14 + 2 billion years. That would bring the supernova work with its uncertainties, the expansion rate work with its uncertainties, and also the work on the age of the oldest stars, into reasonable agreement.

That's where this work stands now on measuring the expansion rate. But I wanted to take a little time, if I may, to expand on the topic a little bit, and say something on the expanding world of astronomy. What do we expect to be doing in the next few years? Because certainly measuring the expansion rate to 10% uncertainty is a good thing to have done, and has been one of the challenges of astronomy over the last few decades. But that's only one of the challenges that astronomy can address in the coming decade. One of the things we're particularly keen to focus on concerns the evolution of the universe, and in particular what is going on over the history of the universe that we have not yet explored.

The situation can be summarised quite nicely in this diagram, where you begin at the big bang and time advances, and here we are 12-14 billion years later with our ground based telescopes and HST, etc., and we have the wonderful advantage that we can look back in time with our telescopes. Because these galaxies have taken billions of years to send their light to us, we see them as they were billions of years ago. We have the opportunity to trace the whole history of the universe, not in the way that paleontologists do, looking at things which have been preserved, but we can actually see how things were with no metamorphosis in between times. By looking at distant galaxies we have seen things as far back in time as one billion years since the big bang. At the present time, with the 4-metre telecopes we've been using for the last several decades, we don't quite have the oomph to get us beyond redshift 3 or 5 to enable us to look back any further than a billion years since the big bang. So there is a dark zone which larger telescopes and more sensitive detectors we will be able to explore.

It's not like we don't know something of what went before, we know there was a big bang, we see the evidence of it in the radiation left over, and actually when we look at it in detail we see this gorgeous map of the sky [on the diagram] in the microwave background radiation, and we see the density enhancements out of which galaxies eventually formed. So this red spot here in the background radiation represents a concentration of material which eventually became a stronger, more concentrated lump and eventually turned into a galaxy. At least, that's the theory. Theories are great, but what we like to do in observational astronomy is to test it by seeing what's actually there. That's one of the main challenges for the next 10 to 30 years in astronomy, or whatever it takes: to see what is going on in the epoch in which galaxies were actually formed. We see a formed galaxy here, the seeds of a galaxy there. We'd like to see the process by which galaxies actually form. And we'll be able to do it, in our students' lifetimes at any rate, using the new generation of telescopes that are being built at the moment.

I thought I'd show you a picture of the southern Gemini telescope. Remember about 6 months ago the Australian Research Council joined the international Gemini project, joining a number of other research councils from the US, UK, Canada, Chile, Argentina and Brazil, to build two of the world's largest telescopes – one in Chile and one in Hawaii. Here's the state of play off the Web today (taken in September) of the southern telescope, and our role constructionwise is going to be to build instruments for this telescope. We have in the last couple of months got a contract back from Gemini to build something we call Niki, and some partners including us, Anglo-Australian Observatory, University of NSW, University of Sydney, and some help from JPL as well. We have a contract to do a design study for an instrument called a coronagraph, which will enable us to look at nearby stars, mask them out and try to detect planets around them.

If you want to pick the two big themes of optical and infrared astronomy in the next 20 years, I mentioned one of them – that is, seeing galaxies form – but the one the public is much more interested in is trying to detect planets around nearby stars. So we are studying how best to build an infrared coronagraphic imager for the southern Gemini telescope, and we also hope this design is accepted to actually build the instrument in the workshop here. We're pretty good at building instruments, if we're allowed to blow our own trumpet a bit.

This [picture] is not an instrument we built here at the Stromlo shop, but in the Anglo-Australian Observatory's shops in Epping, Sydney: this is the famous 2-degree field instrument, which sometimes you can see on the 4-metre AAT at Siding Spring Observatory. This whole instrument is suspended up there at the prime focus of the telescope, and it has the ability to measure the redshifts of 400 stars simultaneously. So we'd like to take that technology to the next step, looking at the design study for Gemini but when the design study is completed, to put it on ESO's Very Large Telescope. Here you can see that the spectrograph has now grown. This infrared spectrograph will enable us to get spectra of galaxies in the IR while they're actually forming.

So those are some of the things we're aiming at. You may ask what we're aiming at with facilities closer to home. One of them I described in a letter I wrote to the CAS newsletter a little while back: one of the new projects we've put to the Australian Government looking for support is an IR telescope at the South Pole, that's a project we would like to see in the next few years.

But there's an even more ambitious project which is on the radio astronomers' drawing board, the 1 kilometre telescope, with 1 square km of collecting area, compared with the Parkes telescope which has a 210-foot dish (that's not 1 square km or even a fraction of it) in collecting area. The design, which has been worked on internationally and at CSIRO Australia Telescope headquarters in Sydney has an array of small dishes (not so small actually) distributed. Some of the outlying elements of the array in this design are actually 500 km from the centre. The thinking of the designers of the 1 km telescope is that they need to find a site where you can have this amount of space 500 km away from sources of radio interference and so on and certainly given the long radio wavelengths, the atmosphere in Australia is perfectly benign for this kind of observation. Australia would be a very good site for a telescope of this scale in the southern hemisphere. The price tag will require an international partner to be found, because it's in the hundreds of millions of dollars, not the ten million dollar scale which the south polar telescope would take.

So plenty of ambitious plans, lots of interesting projects to do with these facilities, focusing on the history of the universe and also focusing on such interesting questions as "Is there life out there?" and I thought you might be interested in what we're talking about for the future.

Thank you.