GALAXIES Prof Steve Phillipps Physics Room 4.12 Level H Spring 2007 Galaxies in the Universe Galaxies are basically large systems of stars (though we will see as we go along that there is more to them than that). The Sun and all the stars which we can see at night are part of one such system, the Milky Way Galaxy, usually referred to these days as the Galaxy. As self-contained units, generally well separated from one another, galaxies represent the building blocks of the universe, i.e the link between the large scale cosmological distribution of matter in the universe and the (relatively) small scale structures such as the Sun and Solar System and our neighbouring stars. From a cosmological point of view, galaxies have two key attributes; they are (often) very luminous and there are a vast number of them distributed throughout the universe. Galaxies both trace the large scale structure of the universe and are visible at immense distances. Furthermore, since light travels at a finite speed, we see distant objects as they were in the past, at the time when the photons we see now left the object. Light from the nearest stars takes only a few years to traverse the distance to the Earth, but distant galaxies are seen as they were millions or billions of years ago. This is particularly important when we consider that galaxies today are the endpoints of an evolutionary process which had its origin immediately after the Big Bang. Since then, as the universe has expanded, galaxies have somehow managed to form and develop, becoming ever more structured and allowing the formation of stars, planets and ourselves. A Brief History of Galaxies Up to about 2000 stars are visible at any one time. From a dark site well away from artificial lights you can also see a pale cloudy band crossing the sky. This is the Milky Way, which Galileo first discovered is made up of vast numbers of faint stars. The reason why these stars appear as a band around the sky was correctly deduced by Thomas Wright c. 1750. The stars around the Sun are distributed in a flattened system so when we look in directions in the plane of this disc we see many stars along the same line of sight, but out of the plane on either side we see relatively few stars. Towards the end of the 18th century this observation was quantified by William Herschel, following his star gauging (i.e. counting) in different directions on the sky. From the Southern Hemisphere, you can also see separate patches of cloud away from the Milky Way itself. These are the Large and Small Magellanic Clouds, (named after the explorer Ferdinand Magellan). The Magellanic Clouds are separate stellar systems, now known to be smaller satellites or companion galaxies of our own Galaxy. In the Northern Hemisphere, an even smaller cloudy patch is just visible to the naked eye in the constellation of Andromeda. This is the Andromeda Nebula which turns out to be the nearest external giant galaxy comparable to (in fact slightly larger than) our own. Starting with Messier s (1784) catalogue (from which names such as M31 for the Andromeda Nebula arise), numerous nebulae were discovered during the 18th and 19th centuries, many by William and John Herschel. By 1905 Dreyer s New General Catalogue (NGC) and Index Catalogue (IC) contained around 13 000 nebulae and star clusters. However, astronomers were divided as to whether they were small systems within our Galaxy, or large star systems outside it - the island universe hypothesis. By 1850 Lord Rosse had discovered spiral structure in some nebulae, such as M51 (the Whirlpool ). Some astronomers took this to imply small nearby systems, as they resembled a popular theory of the formation of planetary systems around stars. In the 1860s, early spectroscopy indicated that some nebulae were gas clouds (and hence nebulae in the modern usage of the term), and to add to the 1
problems for the island universe side, it was shown that the distribution of nebulae on the sky largely avoided the Milky Way disc, evidence for some physical connection. In 1885 a nova, S And, was seen in the Andromeda Nebula. This had a luminosity around one tenth of that of the whole nebula. Other novae had been seen in our Galaxy and their approximate luminosities were known. If the nova in Andromeda was similar, then its apparent brightness implied that it must be well within the Galaxy. Thus the discovery that M31 actually had a spectrum like a star (or large number of stars) was not seen as convincing evidence for an external star system. At this time, the Galaxy was thought to be 5-10 kpc in diameter, so if the same was true for M31, then its angular size θ of about 1 degree (or 0.02 radians) and physical size d implied a distance D = d/θ 250 500 kpc. (1) The discussion was sidetracked when internal motions within the spiral M101 were reported. If the spiral nebulae really were at very large distances, it should have been impossible for anything to move fast enough to generate a measurable change in position on the sky over a few years. However, this remained a controversial observation and ultimately proved to be in error. Evidence had begun to sway towards the island universe theory with, for instance, the discovery of what appeared to be many more novae in spiral nebulae. They were thousands of times fainter than S And and compatible with distances of order Mpc for the nebulae if they, and not S And, were the equivalents of Galactic novae. 1920 saw the so-called Great Debate at the American Society for the Advancement of Science, between Heber Curtis for the island universe side and Harlow Shapley for the single metagalaxy. Curtis countered the usual arguments against external systems by suggesting that S And was a supernova, much more luminous than conventional novae, and that nebulae were concentrated towards the Galactic polar regions because dust between the stars obscured those which would otherwise be seen through the plane of the Galaxy. Distance Measurements Most astronomers by now favoured the idea of external galaxies, but what was needed was a direct measurement of the distances to the nebulae. First consider how the scale of the Galaxy had been established. Tycho Brahe, in the 16th century, had appreciated that it should be possible to measure the distances to the stars by using trigonometric parallax, the change in the apparent direction of a star when viewed from two different positions. This method was used successfully to measure the distance to Mars, for instance, by using observers at two well separated points on the Earth. To obtain a larger baseline and hence measure greater distances, we can use the movement of the Earth around the Sun; observations six months apart give a baseline of 2AU (where 1 Astronomical Unit is the mean Earth - Sun distance, 149.6 million km). A measurement with a baseline of 1AU is called a star s annual parallax. However, due to the large distances to the stars, no successful parallax measurement was obtained until 1838, when Friedrich Bessel obtained a parallax of just 0.29 for the star 61 Cygni. Bessel chose this star because it had a large proper motion, i.e. it appeared to move across the sky (relative to the positions of neighbouring stars) at a faster rate than almost any other known star. (Assuming similar physical velocities for all stars, the closer ones will appear to move faster, though this is only a relative term, even 61 Cygni moves only about 5 per year). With the definition of the parsec as the distance at which a star would have an annual parallax of exactly 1 arc second (i.e. 206265 AU, 3.086 10 16 m), Bessel s measurement implied a distance of about 3.5 pc for 61 Cygni. Subsequent observations have confirmed Bessel s presumption that it should be one of the nearest stars to us, though Proxima Centauri, part of the α Centauri multiple star system, is actually the closest at 1.3 pc. William Herschel (and Huygens, a century earlier still) pre-empted the actual measurement of a stellar distance by making a simple argument still regularly used as a substitute for real distance measurements. The scale of the Solar System and hence the distance to the Sun was already known by Herschel s day. If we assume that the other stars are (at least on average) of similar luminosity to the Sun, we can estimate how much further away they must be in order to look as faint as they do. 2
In modern terms, given the distance D to the Sun and the measured flux of sunlight at the Earth (F = 1.37 kw/m 2 ), the luminosity of the Sun (i.e. its power output, L ) can readily be deduced by using the simple inverse square law F = L /4πD 2. (2) This gives L = 3.86 10 26 W. From the fluxes of the brightest stars and assuming L L, another application of the inverse square law shows that the brightest stars should 2 10 5 times further away than the Sun, i.e. about 1 pc away, a rather good estimate. Going a step further, if stars were 1 pc apart, then from the implied volume density of stars, and the total number of stars he could see, Herschel deduced that the overall size of the Galaxy must be about 800 pc (in the plane) by 150pc (perpendicular to the plane). By 1900, more sophisticated methods along the same lines led to the Kapteyn Universe, a star system 7000 by 1300 pc. A key breakthrough in the distance measurement problem came in 1908 as a result of Henrietta Leavitt s study of Cepheid variable stars in the Magellanic Clouds. Cepheid s have a very characteristic variation in brightness with time, and Leavitt discovered that there was a relationship between the period of the variations and the average brightness of the star. Since all the Cepheids in one of the Clouds could be assumed to be at essentially the same distance, this translated into a relationship between their periods (P ) and (relative) luminosities (L). To calibrate this relationship, we need the absolute luminosity of one or more nearby Cepheids, and to determine that, we need their distances. Cepheids are relatively rare, and none was near enough for a trigonometric parallax to be obtained, so Harlow Shapley used the method of statistical parallax (which is not really a parallax at all, but utilises the velocities of stars; see later). Once it was calibrated, Shapley could use the Cepheid P L relation to determine the luminosity of any Cepheid with an observed period and deduce its distance from its apparent brightness. In 1915, Shapley obtained distances of upto 50 kpc for a number of globular clusters (clusters of 10 6 stars, in a densely packed, almost spherical system a few pc across) in which he could find Cepheids. Shapley also used globular clusters to demonstrate that the Sun was not at the centre of the Galaxy. Though globulars are distributed all around the sky there is a preponderance in one direction. If we make the reasonable assumption that they should be symmetrically placed with respect to the centre of the Galaxy, then this observation can easily be explained if we are viewing them from an off-centre position. Since Shapley now also had a reasonable idea of the distance to many globulars, either directly from Cepheids or from other types of star calibrated with respect to them, he was able to estimate that the Sun must be around 10 kpc from the Galactic Centre. Ironically, the eventual resolution to the question of the distances to the nebulae used Shapley s Cepheid method to find in favour of his opponents. In 1923, Edwin Hubble used the new 100 telescope at Mount Wilson to discover Cepheids in M31. With the known P L relation he could then show that M31 must be at least 300 kpc away, in line with it having a size comparable to our own Galaxy. Discoveries of Cepheids in other spiral and irregular nebulae soon followed and the case for external galaxies was complete when Hubble published his results in 1925. Redshifts, Distances and Dynamics Spectroscopy had been applied to astronomy from the 1860s and this provided a way of measuring stars velocities. The Doppler Effect on sound waves the squashing up and therefore shortening of wavelength of sound waves from an approaching source (and the reverse for a receding source) was already well known, and an analagous result holds for light waves from a moving source. For a source moving away from an observer at speed v, successive wave crests, emitted a time t em apart, will have an extra distance v t em to travel so take an extra time (v/c) t em to arrive. The observer sees wave crests separated by time intervals t obs = (1 + v/c) t em, (3) so sees the wavelength of the light stretched by the factor 1 + v/c. If we define redshift z via where λ obs and λ em are the observed and emitted wavelengths, then 1 + z = λ obs /λ em (4) z = λ/λ em = v/c (5) 3
where λ = λ obs λ em is the change in wavelength seen for lines in the spectra of a source moving at speed v. (We have ignored any relativistic effects here). Stellar radial velocities were found to be typically tens of km s 1. In 1912, Slipher managed to obtain a spectrum of M31 with sufficient detail to measure its redshift (actually a blue shift the lines being shifted to shorter wavelengths due to a velocity of around 300 km s 1 towards us). Further observations showed that the large majority of spiral nebulae were moving away from us, at velocities up to 2000 km s 1, much greater than the velocities seen for stars and too large for the nebulae to be Galactic objects of any sort as their velocities exceed the escape velocity from the Galaxy. Redshifts are also used to study the internal dynamics of objects. For instance, in a rotating disc galaxy seen edge on, one side will be approaching the observer (so blueshifted) and the other receding (redshifted). As pointed out by Öpik in 1922, the observed rotation velocity for M31 can be used to estimate its distance. If the stars at the edge of its visible disc are moving in circular orbits at velocity V c around a mass M, then the gravitational force must match the centripetal acceleration GM (θd) 2 = V c 2 θd (6) where the physical radius is the measured angular radius θ times the unknown distance D. To get the mass, note that on average in our Galaxy, to produce the same power as generated by the Sun (one solar luminosity, 1 L ) we require about 3 solar masses (3 M ) of stars, since the majority of stars are smaller than the Sun and less efficient at power generation; the mass-to-light ratio M/L 3 in solar units. The luminosity of M31 is given by its distance and apparent flux F so combining all these results D = L = 4πD 2 F (7) V 2 c θ 4πGF (M/L). (8) Using the observed values for the terms on the right hand side of this equation, Öpik deduced a distance of about 450 kpc. Expansion of the Universe As we have seen, it had been found that almost all other galaxies were moving away from ours, and by the early 1920s it was suggested that the recession of the nebulae might be associated with Einstein s recently developed General Theory of Relativity (GR). Continuing his use of Cepheids in nearby galaxies and then using the brightest stars as so-called secondary distance indicators (i.e. assuming that the most luminous stars are always physically the same, regardless of the galaxy they are in), Hubble estimated distances to 18 galaxies with redshifts up to 1000 km s 1. In a classic paper in 1929 Hubble presented a roughly linear relationship between recession velocity cz and distance D, a result extended to greater distances in a paper with Humason two years later. A few years earlier, Friedmann and Lemaitre had (independently) shown that there were solutions of Einstein s equations of GR, as applied to the universe as a whole, which allowed uniform expansion (or contraction). Hubble s observational result was immediately associated with such a general expansion, as it requires redshift proportional to distance. The key application of Hubble s law is that it provides a means of assigning a distance to any galaxy for which a redshift can be obtained, regardless of any actual distance measurement via Cepheids or any of the other methods below. Unsurprisingly, the constant of proportionality H 0 in the law cz = H 0 D (9) is now known as Hubble s constant. H 0 is conventionally written with units of km s 1 /Mpc. 4
Hubble s Constant and the Distance Scale Even inside our own Galaxy distance determinations rapidly become insecure once trigonometric parallaxes become impossible. Until the 1990s this limit was at tens of parsecs because of the practical limitation on measuring angles much less than 0.1 arc seconds (the angle subtended by a 200m diameter crater on the Moon). Since then, the precision allowed by satellite based observations, particular from Hipparcos, has enabled us to extend these measurements to stars at distances of up to 1 kpc. In the absence of such precise measurements astronomers were remarkably inventive in their attempts to measure distances and concocted a whole series of alternatives, useful for different distant ranges, and between them forming the so-called cosmic distance ladder. The moving cluster method, used to determine the distance to nearby star clusters like the Hyades, assumes that all the stars are moving around the Galaxy together, so have parallel (3-dimensional) velocity vectors. The motions of the stars will then appear to converge to some point on the sky. Combining the angular distance (θ) of a star from this convergent point with its radial velocity v r and proper motion µ, its distance (in parsecs) should be since the tangential component of the velocity (i.e. across the sky) D = v r tan θ/4.74µ (10) v t = v r tan θ (11) is also measured by the proper motion (in arcsec per year) multiplied by the distance (giving the motion in AU/year; the factor 4.74 comes from the translation between AU/year and km/sec). The statistical parallax method mentioned earlier is related to this in that we use the statistical properties of a whole set of stars. Once the overall Galactic rotation is allowed for, then on average the random velocities of the stars should be the same across the sky (where they are determined by µ and D) and in the radial direction (measured directly from Doppler shifts). Thus we can deduce the mean distance to the sample stars. Once we have the distances to some clusters, we can use the global characteristics of stellar populations. Around 1910, Hertzsprung and Russell both realised that if they plotted the temperatures of stars (from their colours) against their intrinsic luminosities (absolute magnitudes), then only certain characteristic regions of the plot (the Hertzsprung-Russell, or H-R, diagram) were populated. The majority of stars occupied a swathe from bright and blue (hot) to faint and red (cool) the stellar main sequence, on which stars spend most of their lives. If we have a relationship between the colour (or spectrum) and the luminosity of stars, calibrated by measurements on a cluster at known distance, then we can use this as a distance indicator. In the absence of any absorption of light by intervening interstellar material the colour will be independent of the distance so we can deduce L and the apparent brightness will follow the usual inverse square law. This is known as spectroscopic parallax, though again no real parallaxes are involved. This is especially profitable if we look at further star clusters, as we will essentially see our standard main sequence shifted in magnitude by the distance modulus to the cluster, the difference between the apparent magnitudes m and absolute magnitudes M, given by m M = 5 log 10 (D/10) (12) for D in pc. (Recall that the absolute magnitude is defined as the magnitude an object would have if placed exactly 10 pc away). This method of distance determination is known as main sequence fitting. If the cluster happens to contain a particularly useful sort of star (perhaps some characteristic type of variable star such as an RR Lyrae) then we will be able to calibrate its absolute brightness and hence use that as another standard candle (i.e. source of known brightness) to determine yet more distances. As well as the main sequence, the H-R diagram of a typical cluster will also contain a giant branch, containing the red giant stars which have evolved off the main sequence, increasing in size and luminosity. The stars at the tip of the red giant branch have quite characteristic luminosities, so this TRGB provides another distance indicator for any star cluster (or galaxy) in which individual stars can be resolved essentially a modern version of Hubble s use of the brightest stars in a galaxy. 5
Uncertainty is introduced into distance measurements by the fact that spiral galaxies such as our own not only contain stars, but also an interstellar medium (ISM), of gas and dust acting like a fog betwen the stars. This makes stars look dimmer than they would be on the basis of their distance alone so complicates all distance estimates based on apparent brightnesses and the inverse square law. Beyond the distance where individual stars could be seen, Hubble and his successors had to rely on even less direct means, such as the size of the largest HII regions (luminous regions of ionized hydrogen) in a galaxy, or the appearance of the whole galaxy. To reach the greatest distances we can try to repeat Hubble s trick with the stars, and assume that the brightest galaxy in any cluster of galaxies always has (more or less) the same absolute magnitude. Recently there has been considerable success in using supernovae as standard candles. We return to some of these methods later. Unsurprisingly, the large variety (and dubious precision) of the distance indicators led to uncertainty and controversy over the value of Hubble s constant, the ratio of recession velocity to distance. Hubble himself originally estimated that its value was 550 km s 1 Mpc 1, but this was later reduced to somewhere around 50 or 100 km s 1 Mpc 1 equivalent to a disagreement by a factor of two between the so-called long and short distance scales. With the advent of the Hubble Space Telescope (HST), however, it became possible to detect Cepheids at much greater distances, allowing direct distance estimates to many more galaxies. Working in the near infra-red (to reduce the absorption by intervening interstellar dust, either in our Galaxy or in the target galaxy), the P L relation for Cepheids can be written in terms of I-band magnitudes as M I = 1.3 3.5 log P (13) for P in days. Thus a Cepheid with a period of 100 days will have an absolute I magnitude of 8.3 and be visible with HST (which can easily reach m I = 25) out to a distance modulus m M 33, corresponding to a distance of 40 Mpc, well beyond the Virgo Cluster, the nearest really large grouping of galaxies. The HST key project on the distance scale has obtained a value which we assume hereafter. The Observable Universe H 0 = 70 ± 2 km s 1 Mpc 1. (14) Before moving on to the galaxy population itself, we should consider how far out in the universe (and back in time) we are able to observe galaxies. It is convenient to do this in terms of redshift rather than distance, since the former is directly observable and the latter is not. On local scales, we have looked on the redshift as a recession velocity. In fact this is not strictly correct, as the cosmic expansion increases the space between the galaxies without them actually moving. Thus the redshift can be arbitrarily large without conflicting with the fact that nothing can travel faster than the speed of light. As a normalisation, the redshift of the Virgo Cluster, around 20 Mpc away, is about z = 0.005. Much more distant galaxies are seen even at quite bright apparent magnitudes and by the 1950s galaxies were already known at redshifts beyond z = 0.1. In 1960, the radio source 3C295 was identified with a galaxy in a cluster and found to have a redshift of 0.46. Although this remained the furthest known galaxy for many years, the overall distance record was soon surpassed by an entirely new type of object with the discovery of quasars, e.g. 3C9 with a redshift of 2. By 1973 the most distant known object was another quasar at z = 3.73. Observations of other sorts of galaxy caught up in the 1980s and after ultra-deep imaging observations were made using the HST (the Hubble Deep Field ), one of the galaxies therein broke the z = 5 barrier. Recently the first z 6 7 quasars and galaxies have been identified. Current cosmological models imply that we are seeing these object as they were around 13 Gyr ago, < 1 Gyr after the Big Bang. 6