Globular Cluster Populations of the Milky Way and M31 By Peter Starr November 2004. Introduction. Globular clusters (GCs) are spherical congregations of several thousand to a million stars that formed at the same time in a volume of less than 100 parsecs across. They are the oldest known stellar formations. The stars are gravitationally bound where the density of stars in a GC drops as distance from the centre increases. They lie mostly in the halos of galaxies surrounding the galactic plane and also close to the bulge of the galaxy. They make up 1% of the visible Halo stars. Both of these only make a few percent of all of the stars in the whole MW galaxy [1]. The stars in a GC have a wide range of masses and therefore contain stars at most stages of stellar evolution. The wide range in stellar masses results in a wide range in spectral types, colours, luminosities, and stages of evolution. As the stars formed at the same time and GCs contain little or no gas so new star formation does not occur. This can be used to our advantage to calculate the distance to the GC, the age of the GC, and the reddening between the GC and the Earth. This also helps us determine the lower limit on the size of MW as the GCs are in the halo, the lower limit on the age of the galaxy, and clues to how galaxies form. GCs have been found in most galaxies. The Milky Way has around 150 of them [2]. There are probably more that are hidden away on the opposite side of the MW disk. Our sister galaxy, Andromeda or M31 also has GCs but in higher numbers. There at around 400 ± 55 GCs associated with M31 [2]. GCS have also been detected in elliptical galaxies and irregulars. This project will 1: Describe and compare the populations of GCs in the Milky Way Galaxy (MW) and the Andromeda Galaxy (M31). 2: The distribution of metallicities of MW and M31 will be examined from data obtained from the Harris list [4] and a catalogue of de-reddened colour indicies of M31 supplied by Duncan Forbes of Swinburne University. 3: Calculate and examine the distribution of extinction corrected B-I colour indicies for the GCs of both MW and M31. 4: Discuss of how subpopulations of the GCs formed with the formation of spiral galaxies. 1a Properties of Globular Clusters in the Milky Way GCs contain population II stars as indicated by their low metallicity. Population II stars are very old stars. Metallicity describes the abundance of elements heavier than hydrogen and helium found in stars. The stars in a GC formed at the same time from a cloud of gas that has the same low metallicity abundance. Therefore all of the stars in any one GC will have the same metallicity. Gas clouds of that metallicity existed at the time and just before the formation of the MW galaxy. Gas in the MW now is now enriched with metals produced from stars that have lived and died over 10 billion years. Therefore GCs must be very old structures. Metallicity of a GC is determined by analysing the absorption lines in the spectrum of the globular cluster. A figure is determined by the ratio of metals to hydrogen divided by the same ratio for the sun. The value is denoted by Fe/H and is a logarithimic scale. For example Fe/H = -1 means the metallicity is 10 times less than the metallicity of the sun. Metallicities for GCs in the MW are listed in the Harris List in appendix 1. Metallicities in MW range from -2.3 to 0.2. The distribution of metallicities show 2 sub populations. The first population have metallicities (Fe/H) less than –1 and are termed metal poor GCs (MPGCs) and the second population have Fe/H of more than –0.1. This population is termed metal rich GCs (MRGCs). The population of GCs in MW is therefore described as bimodal. This is examined in detail later in the project. Figure 2: Metallicity distribution of 137 Globular Clusters in the Milky Way shows 2 sub populations. [6] The metallicity affects stars by absorbing some of the light that the star is radiating. This is therefore decreasing the efficiency of the star to radiate the energy it produces. Metal poor stars therefore are hotter than metal rich stars of the same mass (more massive stars are hotter than less massive stars). As the surface temperature of a star is related to its colour (stars radiate like blackbodies, Wien’s Law) metal poor stars appear bluer than metal rich stars of the same mass. The same idea applies to GCs. Metal poor GCs are bluer than metal rich ones. This affect can be seen in the Hertzsprung - Russell (H-R) diagram for a GC. This diagram is a plot of the luminosity of a star (y axis) versus its surface temperature (and therefore colour and spectral type) (x-axis, temperature increasing to the left). When all of the stars in a GC are plotted on this diagram a pattern occurs which is all related to the stars masses and ages. More massive stars are more luminous and bluer than the less massive stars which are less luminous and redder. The hydrogen burning stars form a track called the main sequence. Helium burning stars depart to the upper right from the main sequence becoming redder as they expand. White dwarfs are found at the bottom right. As GC stars are essentially the same distance from Earth apparent magnitude can be used instead of luminosity. The H-R diagram of a metal rich GC will have its main sequence further to the right than a metal poor GC does. The H-R diagrams for GCs differ to that to a population of MW thin disk stars as the main sequence will be incomplete. As GCs are older than the thin disk stars and no new stars are forming or have formed since the GC formed, the more massive stars have burned their hydrogen and have left the main sequence. Massive stars burn their hydrogen quicker than less massive stars and therefore have much shorter lives. GCs will therefore have the top portion of their main sequence missing and a prominent trail of horizontal branch stars will be seen. This point is called the turn off point. The position of this turnoff point is measured on the main sequence and this position is equal to a certain mass range for a star. The age of the star is then known as the mass of a star determines how long it exists on the main sequence. Therefore an age can be determined for the whole GC once the distance to the GC is known. The distance to the GCs cannot be determined by parallax as they are too far away. Distance can only be estimated from standard candles. These exist in the form of RR Lyrae stars. Like Cepheid variable stars, there variability is proportional to their luminosity. The ages of the MW GCs have been determined. The MPGCs formed at the same time at about 15 billion years ago. The MRGCs formed about 2 billion years later [13]. The distances of the GCs from the sun in MW have been determined as well as the distance to the galactic centre. The distance to the galactic centre assumes that the sun lies 8Kpc from the galactic centre. The distances are list ed below in Appendix 1. The MRGCs all lie within 20 Kpc of the galactic centre. The MPGCs lie at all ranges out to 120 Kpc. This indicates that the MPGCs are associated with the halo and the metal rich with the bulge of the galaxy. The MPGCs have highly elliptical orbits which take them far out into the halo and then they dive back into the bulge where they speed up (500km/sec) doing so before they travel back out into the halo where they slow down (100km/sec). This can be seen in the chart where radial velocity is graphed versus distance from the galactic centre. The chart shows low velocities for GCs far out from the galactic centre and high velocities (as high as 500 km/sec) for the metal poor GCs that are currently close to the galactic centre. Some have low radial velocities close to the galactic centre, this is because there motion is across our line of sight. The MPGCs are spherically distributed and show no net rotation. Some of the MPGCs may have been captured from other smaller galaxies straying too close to MW. This is currently been seen with the Sagittarius Dwarf Galaxy being stripped by the MW.[6] Figure 3: Spatial distribution of Globular Clusters in MW. [6] The MPGCs can be broken down into two further sub populations, named old halo and young halo [13]. The old halo GCs have prograde rotation and the young halo has retrograde motion. The metal rich GCs on the other hand have dispersion velocities similar to that of the thick disk and bulge stars and have average rotational velocities of 165 km/sec [5] same as the bulge stars. The MRGCs form a flattened distribution with the galactic plane but surrounding the bulge. The MRGCs also have two poulations, thick disk and bulge which are > 5 and < 5 kpc respectively [13]. 1b Properties of GCs in M31 The Andromeda galaxy known as M31 is another spiral galaxy (Sb type) within our local group and is the closest spiral galaxy to the MW lying 770 Kpc distant. [18] It is a naked eye galaxy in dark skies. It was not revealed until the 1920s by Hubble that the MW and M31 were separate stellar systems. M31 gives us a unique perspective on studying spiral galaxies as measurements on the MW are difficult since we are imbedded in it.M31 is 50% more luminous than MW and is twice as large. It also has many more globular clusters, 460.+- 70 [3]. The disk rotates 30% faster. The bulge is larger in proportion to that of MW providing 30 to 40 % of its luminosity. The metal poor GCs of M31 have deep plunging orbits and have no ordered rotation like that of MW. [19] The metal rich GCs are younger in M31 than in MW [20] The metal rich clusters are brighter and not fainter as would be expected from the effects of metallicity. This is not seen in the MW or other galaxies. This could happen if these GCs were considerably younger. These GCs may have formed in a merger.[20] The metallicity distributions of GCs in M31 have two populations similar to MW. The metal poor centering around –1.4 and the metal rich centering about –0.6 [14]. Like in the MW the MPGCs are associated with the halo and the MRGCs are associated with the bulge. However data taken from appendix 2 and also from a catalogue by Barmby 2000 [15] show three peaks as depicted below in chart 2. The (B-I)o colour indexes are very similar in both MW and M31. This is depicted below in charts 9 and 10. Kinematic analysis shows that the MRGCs of M31that lie close to the bulge have similar characteristics to MW as do the mPGCs. However the MRGCs at larger distances from the bulge have the same rotation velocity or velocity dispersion [14]. The MRGCs of M31 are brighter GC Luminosity Function) than expected comparing them to MW. A possible reason for this could be that these GCs are much younger. The difference in age between the MPGCs and MRGCs could be as much as 55% [3]. This could make the age of MRGCs in M31 to be 8 billion years compared to 12 Billion for MRGCs in MW. Other possibilities are that the MRGCs formed by a merger with another galaxy that did not affect the disk of M31. Another reason is that the MPGCs formed before M31 did and the MRGCs formed with the galaxy [3]. 2 The Distribution of Metallicities of MW and M31 Metallicity data was taken from the tables in appendix 1 and entered into an excel spreadsheet. This was also done with radial velocity and distance from the galactic centre data for each of 147 GCs in the MW. Chart 1. A chart was developed from this data graphing metallicity subgroups of 0.25. The y axis is the number of GCs in each group. Two distinct populations can be seen with the MPGCs < -1 peaking at about –1.6 and the MRGCs > -1 peaking at -0.5. The 2 different metallicity poulations could infer that the 2 populations formed at different stages of the formation of the galaxy, the MPGCs being older when gas clouds were poorer in metal abundance than in later periods of the universe. The average metallicity for GCs in Mw is -1.3. Two thirds of the GCs are metal poor. Chart 2 This chart shows the distribution of metallicities in M31 overlayed with MW. Two traces are present, one from the metallicity data in appendix 2 and the other from a catalogue by Barmby in 200 [15]. The metallicities of both galaxies are similar with the metal poor GCs at around –1.5 and the metal rich at –0.5. M31 has two distinct bumps in its curve between –1 and –2.5. This may indicate M31 may have had 3 GC formation episodes? The average metallicity for M31 is –1.2 which compares closely tp –1.3 for MW. M31 has about the same proportion of MPGCs to MR GCs a does MW. Chart 3 This chart graphs metallicity versus distance from the galactic centre in parsecs. The MPGCs are in blue and the MPRGCs are in red. Chart 3 shows that all of the MRGCs are within 20 Kpc of the galactic centre . The MPGCs range out to 120 Kpc but are concentrated closer in to the galactic centre. This shows that the MPGCs exist in the halo and supports the theory that they have eccentric orbits that take them from the halo and through the bulge of the galaxy and then back out into the halo. The 2 populations show that they have different beginnings from their spatial arrangement. Chart 4 This chart shows relative distance to metallicity in M31. Distance here does not have units however it does show that the MRGCs are spread out further relative to that in the MW. Chart 5 This chart shows the position of each GC around the galactic centre of M31. This is taken from data in appendix 2. It indicates that GCs are spherically distributed about the galaxy. The same situation occurs with GCs in MW. Chart 6 This chart is graphing radial velocity versus distance from the galactic centre. The red squares are MRGCs and the blue diamonds are MPGCs. This chart also shows 2 populations. The MRGCs all have radial velocities within +- 200 km/sec. The radial velocity drops for the MRGCs that are between 5 and 10 Kpc from the galactic centre. The MPGCs have low radial velocities further out, when they are close to the bulge the velocities are very high, up to 400 and 500 km/sec. The ones with low velocities may have large proper motions that we cannot observe because of the angle we are viewing them on. 3. Photometric Analysis Of GCs. Much of the information of GCs can be derived from their colour. This is because a stars colour depends on its surface temperature which depends on its mass. Analysing the spectrum of GCs can tell us their metallicities and their radial motion. As discussed previously a H-R diagram of a GC can tell us its age and hint on its metallicity. One problem that exists for astronomers and that must be taken into account when making photometric measurements is reddening or interstellar extinction. This makes the star or GC appear dimmer and redder than it actually is [7]. The reddening is caused by gas and dust absorbing and reradiating EM radiation. This can be seen within the galaxy as emission and reflection nebulae. The amount of reddening depends on the position of the GC with respect to the Earth and the disk of the galaxy. Obviously GCs viewed through much of the disk will be significantly affected as dust and gas lies within the thin disk of the galaxy. GCs viewed straight out of the plane of the galaxy will be less affected. Reddening from the Earth’s atmosphere also has to be taken into account. Any measurements must be made to a reference star of known luminosity to calibrate the readings. The reddening must be added to the observed brightness to get the true brightness. Another problem is that reddening affects different wavelengths of light differently. Blue light is more easily scattered than red light by dust in interstellar space. Astronomers use different filters when measuring the colours of stars. The most common are U, B, and V [8]. The U filter looks at ultra violet light, B blue light, and V yellow/green light. A stars brightness is measured through each filter and recorded as bU, bB, bV. The intensity of the light is compared to the preceding filter by taking the ratio, bV/bB, bB/bU. Hot stars will have low values and cooler red stars higher values. These values are converted into colour indicies B-V and U-B using the formula B – V = 2.5 log (bV/bB). B and V are magnitudes. So B-V is magnitude of V subtracted from V. V-I and B-I are other indicies used. I is in the infra red region. Using I is advantageous for observing GCs as V-I is less affected by reddening than is B-V and that the stars in GCs are old and redder and their isochrones can be seen more easily. The data in appendix 1 gives values for colour indicies of U-B, B-V, V-R, and V-I for each GC in MW. These values are not corrected for reddening and must be to be able to examine any differences in the subpopulations in MW. Values for E(B-V) (colour excess) and V t (apparent V magnitude) are also given for each GC. The data in appendix 2 is already corrected for reddening and the B-I colour index just needs to be calculated. To correct the indicies for reddening the amount of reddening needs to be subtracted from B, V, and I to give B0, V0, and I0. To do this we need to know the total extinction for each colour, A_V, A_B, and A_I. A_V = E(B-V) x R_V, where R_V = 3.1. [11, 12] V is then converted to V0 by V0 = V - A_V A_V is related to A_B by 1.33 x A_V [12] And to A_I by 0.48 x A_V. [12] Once B0, V0, and I0 are calculated, (B-I)0 is calculated by subtracting I0 from B0. The same is done for the M31 data in appendix 2. Another way to calculate (B-I)0 is 2.36 x (B-V)0. [9,10] CHART 7 The distribution of B-I was graphed for MW GCs and separated into the metallicity subpopulations.. It can be easily seen that the MPGCs are bluer than the MRGCs. This is not surprising as metal poor stars are bluer than metal rich stars. Chart 8 This shows the distribution of B_I colour index for GCs in both MW and M31. This clearly shows that both galaxies have 2 populations of GCs, the metal poor with a bluer index and the metal rich with a redder index. Chart 9 This chart shows the relationship between metallicity and B-I0 in MW. This shows that there is correlation between B-I0 and metallicity and that MPGCs are bluer than MRGCs. Metallicity could be predicted to a an extent by finding the line of best fit and determining the equation for the curve. There is much error in this but if this correlation was true of GC systems of other galaxies, metallicities could be calculated for those GCs where the metallicity cannot be determined from the absorption lines of metals in stars because they are too far away. Chart 10 Chart 10 shows the B-I and metallicity relationship is similar in M31. Chart 11. This chart shows the relationship between B-V and B-I. As there is a correlation B-I could easily be determined by knowing B-V. 4. Formation of Galaxies. When the universe was 300 000 years old, hydrogen and helium atoms formed a gas when the photons from the Big Bang no longer had sufficient energy to keep the atoms ionised. Regions where gas was denser started to collapse into clouds with masses of 1 to 100 million solar masses (Jeans Mass [5]). The first stars began to form within these (population III stars). These stars added heavier elements into the cloud to give a concentration of metals 1 in 1000 to 100 that of the solar abundance. This is the abundance we now see in the oldest stars in the halo and in the metal poor GCs today (population II stars). The gas clouds started to rotate due to tidal forces as they have irregular shapes. The gas clouds are attracted to each other by gravity and form protogalaxies. The GCs may have formed when the gas clouds collided. This compressed the gas and many stars formed all in a short space of time. This halted any rotation developing as energy is not lost. Gas clouds lose energy when they contract and rotation results. These metal poor GCs therefore formed quickly and far enough from the MW and at the time the MW was beginning to form and the gravity well was not as well established. All of the metal poor GCs formed at this time around 13 ± 1 Billion years ago [1]. The lack of rotation and elliptical orbits of the metal poor GCs are evidence of this. The halo stars also formed at this time as the MW protogalaxy was forming. The thick disk and metal rich GCs formed about 2 billion years later [1]. At this time the gas cloud had given up much of its energy on collapse to form the rotating disk. The thin disk formed 2 billion years after this when more gas was contracting therefore forming a flatter disk. This gas had been enriched with metals from stars to have an abundance 20% of the solar metallicity. It is not known how the bulge formed but it contains the most metal rich stars. The MW is still forming as smaller galaxies fall victim and merge with the MW. The GCs contain no gas so no new stars are forming and so the GCs are metal poor. Only the old metal poor population II stars exist. The gravity of a GC system may not be strong enough to hold its gas and metals produced by any supernovae from the larger mass stars. Therefore no new stars form. The disk contains much gas and stars are continually made and return metals back into the gas in the disk when they end their lives. These are metal rich and are called population I stars. Conclusion The Globular Cluster system of the Milky Way Galaxy has been studied in great detail and provides clues to the formation of spiral Galaxies. The Andromeda Galaxy provides a good test on whether the GC properties are typical of spiral galaxies. From the research undertaken and the data analysis it can be concluded that the MW and M31 GC systems are in the main very similar. This is shown in the bimodal populations of metallicity, a spatially extended metal poor system and a metal rich system concentrated close to the bulge of the galaxy. Difference lies in the relative ages in the 2 populations with the MRGCs of M31 being possibly much younger than those of MW; the MRGCs of M31 extend out further into the halo than for MW, and M31 contains many more GCs than M31. The bimodal GC populations show that the formation of spiral galaxies is not a single formation event but one where the MPGCs form before the galaxy is forming or has a considerable gravity well and the MRGCs form with the formation of the galaxy thick disk and bulge in a clumpy collapse.. Bibliography [1] Issues in the formation of globular cluster systems., William E Harris,, arXiv:astro-ph/9801201 v1 21 Jan 1998. [2] The Chemical Properties of Milky Way and M31 Globular Clusters: I. A Comparative Study, M.Beasley et al, astro-ph/0405009v2 12 July 2004. [3] Globular Cluster Systems of Spirals, Pauline Barmby, arXiv:astro-ph0210629v1 29 Oct 2002 [4] http://physwww.mcmaster.ca/~harris/mwgc.dat [5] A short History of The Universe, Joseph Silk, Scientific American Library [6] http://nedwww.ipac.caltech.edu/level5/Harris2/Harris_contents.html [7] Basic Astronomical Data, Stars and Stellar systems vol III, Edited by K. Strand, University of Chicago Press. [8] R. Freedman and W. Kaufmann III, Universe, 6th ed, p 430. [9] http://www.aerith.net/astro/color_conversion.html [10] F. Natali, G. Natali, E. Pompei, and F. Pedichini, Astron. Astrophys. 289, 756-762 (1994 [11] http://aa.springer.de/papers/0359001/2300347/sc2.htm [12] data provided by Prof Duncan Forbes, Swinburne University. [13] http://astronomy.swin.edu.au/staff/dforbes/pucon.ppt [14] M31 Globular Clusters: Colors and Metallicities, P.Barmby, J. Huchra, astro-ph/9911152v1 9 Nov 1999. [15] http://cfa-www.harvard.edu/~pbarmby/m31gc/m31gc.dat [16] The M31 Globular Cluster Luminosity Function, P.Barmby, J. Huchra [17] Harris, W.E. 1996, AJ, 112, 1487 [18] http://www.3towers.com/Andromeda.htm [19] Galaxies in the Universe, An Introduction, L.Sparke, J,Gallagher. [20] M31 globular cluster metallicities and ages, Pauline Barmby, arXiv:astro-ph/0106389 v1 21 Jun 2001 Other papers used for general reading and research: The Elliptical Galaxy Formerly Known as the Local group: Merging the Globular Systems; D.Forbes, K. Masters, D. Minniti, P. Barmby; astro-ph/0001477 v1 27 Jan 2000 http://www.astro.ku.dk/~milvang/Master/more/thesis/node74.html http://springer.de/papers/9346003/2300721/sc5.htm System Effects on Photometric Parallaxes for FGK Dwarfs and Subdwarfs; C. Jordi, E. Masana, X. Luri, J. Torra, F. Figueras; Dept. d’ Astronomia I Meterologia, Univ. de Barcelona, Avda. Diagonal 647, E-08028 Barcelona, Spain http://www.macalester.edu/astronomy/research/phys40/M15/M15.html M31 Globular Clusters in the HST Archive: I. Cluster Detection and Completeness; P.Barmby, J Huchra; astro-ph/0107401 v1 20 July 2001 M31 Globular Clusters in the HST Archive: II. Structural Parameters; P.Barmby; astro-ph/0201253 v1 15 Jan 2002 http://www.google.com.au/search?q=cache:ssOyhJwZ8AEJ:astronomy.swin.edu.au/staff/dforbes/book.ps+globular+cluster+populations+of+the+milky+way+and+M31&hl=en Antlia: An Outskirt Locala Group Galaxy, M. Castellani et al; astro-ph/0008080 v1 4 Aug 2000 The remarkable M31 globular cluster 037-B237 revisited; P. Barmby, K. Perrett, T. Bridges; astro-ph/0109533 v1 27 Sep 2001 M31 Globular cluster metallicities and ages, P. Barmby; astro-ph/0106389 v1 21 Jun 2001