MEASURING THE DISTANCE TO THE GALACTIC CENTRE BY: Peter Starr DATE: 18/09/2004 Introduction For thousands of years, humankind has gazed in wonder at the night sky, at the glow of millions of stars stretching across the sky that resembles a backbone. Humankind has endeavoured to understand its place and importance in the cosmos. Where once Earth was considered a significant planet at the centre of a small universe, it is now known to be one of many planets at the outskirts of one galaxy: one of countless galaxies populating a vast universe. This realisation has changed as technology has developed over the past 300 years. It is important to have a means by which the Earth’s distance from the centre of the Milky Way Galaxy can be calculated accurately. This distance, or R0, enables Astronomers to determine and define other parameters of the galaxy and indeed the universe. The mass of the Milky Way, the distribution of dark matter, the rotation rate, the luminosity of the Milky Way, the astronomical distance ladder can be calibrated more accurately, the Hubble constant, and the age of the universe, can all be known more accurately by an accurate determination of R0. How do we know the distance to the centre of our Galaxy? Counting Stars In 1785, William Herschel concluded that the sun lay at the centre of the galaxy. He constructed a model of the Milky Way by counting the stars along 683 lines of sight leading away from the sun. He theorised that the concentration of stars in a galaxy would be highest at the centre and less towards the edges. His observations showed that the number of stars was consistent across the Milky Way, that the shape of the galaxy was a thick disc. Herschel concluded the sun lies close to the centre of the galaxy [7]. Jacobus Kapteyn verified Herschel’s findings in 1922 by counting the stars in addition to utilising photographic techniques, which analysed brightness and the proper motion of stars [8]. He estimated the distance to the centre of the Galaxy at 2000 light years [6] and the size of the galaxy to be 40 000 light years [8]. Globular Clusters In 1914 Harlow Shapley surveyed the globular clusters surrounding the Milky Way and estimated the distance to 93 of them by observing RR Lyrae stars (which he mistakenly thought were Cepheid variables at the time). RR Lyrae stars are low mass metal poor horizontal branch variable stars that are relatively common in globular clusters. The variation in brightness of RR Lyrae stars changes periodically (around 0.5 days and therefore are easy to spot). The period between maximum brightness is proportional to its luminosity. The distance to the star can then be calculated using the Inverse Square Law. The centre of the galaxy was estimated by finding the centre of the distribution of the globular clusters, which he believed to be symmetrically distributed about the galactic centre. He discovered that the sun does not lie within the centre of the galaxy and the centre to be in Sagittarius. Shapley estimated R0 to be 13 kiloparsecs (Kpc) [15]. Figure 2 Distribution of Globular Clusters projected on the plane of the Milky Way [10]. What Herschel, Kapteyn, and Shapely did not take into account was the gas and dust that lie in the plane of the galaxy. This is analogous to looking through a fog, dimming the light from an object far away. This can easily seen by the dark lanes and dark nebulae when viewing the Milky Way with the naked eye. The centre of the galaxy is totally obscured to visible light due to the dust and gas. This was recognised by Robert Trumper in 1930 when he found that globular clusters appeared dimmer than what there distances indicated. Bok in 1981 estimated that there was a drop of 25 to 30 magnitudes of light coming from stars at the galactic centre due to interstellar extinction. Shapley’s distance to the centre of the galaxy was revised to 8.0 ± 0.5 kpc due the interstellar extinction. Jan Oort studied the motion of stars near the sun in the 1920s. He found that stars closer to the centre of the galaxy have faster rotation speeds that stars further away. He determined that the revolving axis of the galaxy lies near Sagittarius [9]. His galactic centre was within 2 degrees of Shapley’s estimate. He also calculated the period of the sun around the Milky Way as well as the mass of the Milky Way. The estimate of R0 was 5.8kpc. The centre of the galaxy is obscured to visible light due to the dust. Walter Baade in 1937 attempted to view the galactic centre by using deep red filters and panchromatic films. Though he could not penetrate the dust and gas to view the centre, he did find an area of less obscuration close to the centre of the galaxy known as Baades Window [14]. Longer wavelengths of light can penetrate the dust. The amount of interstellar extinction is proportional to wavelength. Observations of the galactic centre can be made at infra red and radio wavelengths. However at longer wavelengths the resolution is poorer as the detector catching these waves also needs to be bigger. This has been addressed by linking many radio telescopes together, e.g the Very Long Baseline Array (VLBA). Infra red astronomy has been used to observe RR Lyrae stars close to the galactic centre. R0 was calculated to be 7.9 ± 0.3kpc. Bohdan Paczynski and Krzysztof Stanek in 1997 calculated R0 to be 8.4kpc ± 0.4 light years by observing red clump stars [4], red giants and Mira type variables which also have a period luminosity relationship. Red clump stars are metal rich horizontal branch stars [5]. Their luminosity depends on their age and chemical composition. They have similar mass to the sun but have moved off the main sequence as they are burning helium in their cores. They have a narrow range of brightness [6]. Carney and Fulbright conducted infra red observations of 60 RR Lyrae stars near the centre of the Milky Way through Baades Window. They calculated the distance to the centre to be 8.3 ± 1 Kpc. What new techniques are available to measure the distance to the centre of our galaxy? Masers Analysis of microwave emission (using very long baseline interferometry) of water in interstellar clouds has led to the determination of their proper motion. These clouds are called masers and microwave emission results from luminous stars in the vicinity exciting water molecules. The radial velocity Vr (away or toward the observer) is measured from the Doppler shift of the spectral line at 22.2GHz. The tangential velocity Vt is also calculated. From the equation Vt = u x d, the distance can be calculated [11]. In 1993 Mark Reid measured the proper motion of masers and calculated R0 to be 6.5 ± 1.5 Kpc and 7.1 ± 1.5 Kpc from two different positions [12]. Trigonometric parallax Trigonometric parallax is a technique that can be used to measure the distance between other stars and the sun. By observing a star six months apart, it will appear to have shifted position compared to background stars that are much further away. This is analogous to observing a tree outside your window with one eye closed and the other open. By shutting the open eye and opening the other the tree appears to change position. The distance can be calculated from the tangent of half of the angle subtended and knowing the distance from the Earth to the sun. This angle is very small and is smaller the further away the object is. This was first achieved in the 1800s by Friedrich Bessel who determined 61 Cygni was located 11 light years away and Wilhelm Struve who determined Vega was 25 light years distant [5]. This technique is only reliable for distances up to 500 parsecs. To measure the distance to the centre of the galaxy using this technique, an object located at the centre of the galaxy needs to be observable and there needs to be a background reference. The centre of the galaxy is believed to be in the vicinity of Sagittarius A*. This is a very strong radio source where bright infra red stars are orbiting. This was determined by the Very Long Baseline Array (VLBA) using radio observations. The VLBA is a set of ten identical radio telescopes from Hawaii to the Virgin Islands. Sag A* is a massive object of 2.6 to 3.0 million solar masses and is believed to be a blackhole. This is also supported by observations of a strong x-ray source which indicate an accretion disk. Precise observations of the radio source from Earth over time, shows a slight shift in position (0.1 milli arcseconds [3]) with respect to background quasars. From the resultant triangle, the distance can be calculated. Reid, Readhead, and Vermuelen, and Treuhaft used the VLBA and calculated Ro to be 8.0Kpc. It is possible to measure the proper motion of Sag A* with respect to the background quasars after subtracting the parallax of our solar system about the centre of the galaxy. After 16 years of observations with the VLA a baseline of 754 AU would be obtained. Comparing this to previous parallax measurements where the baseline is 2AU (measurements 6 months apart) allows measurements of objects much further away than 500 parsces. Keplarian Orbits Stars that are in orbit around Sag A* are measured by taking measurements of the Doppler shift in the star’s spectral lines. The proper motion and radial velocity and therefore its orbital equation are determined. The distance between S2 and SGR* can be measured and the mass of SGR* (3.7 million solar masses +- 1.5 million [2]) can be calculated. This yields the distance to SGR* and therefore the centre of the galaxy. This is done by infrared imaging and solving the Keplarian orbits. A distance can be determined by 15 years of observations. An accuracy of between 1 and 5% can be achieved. This was proposed by Salim and Gould in 1999. Eisenhauer used ESO’s very large telescope in 2003 and calculated R0 to be 8.0kpc ± 0.4kpc. This was calculated by observing the star S2 that orbits the massive blackhole at the centre of the Milky Way in a highly elliptical orbit. This measurement will be refined further when the entire orbit of S2 is measured. Table 1 Technique Author R0 Plotting nearby stars William Herscel 0 kpc Proper motion Jacobus Kapteyn 0.6kpc Globular Clusters Shapley 13 kpc Globular Clusters Vaucouleurs & Buta, 1980 7.0 ± 0.7 kpc Proper Motions Jan Oort 5.8 kpc Red Clump Stars Paczynski and Stanek 8.4 ± 0.4 kpc RR-Lyrae variables in Baade's Window Carney and Fulbright 8.3 ±1 kpc Masers Reid 6.5 ± 1.5kpc Masers Reid 7.1 ± 1.5 kpc Trigonometric Parallax, VLBA Reid, Readhead, Vermuelen & Treuhaft, 1999 8.0 Keplarian Orbits Eisenhauer et al, 2003 8.0 ± 0.4 kpc Conclusion The determination of the distance to the centre of the Milky Way Galaxy has taken leaps and bounds since the time of Herschel and Shapley. With the advent of infra red and radio astronomy and long baseline interferometry the estimate of R0 is further refined. The next big step forward is to reduce the percentage error in R0. Most measurements have a deviation of 0.5 Kpc, which is quite a large percentage when R0 is about 8Kpc. The error is high due to the interstellar extinction (how uniform is it over 8Kpc), very small measurements in proper motion, parallax, and spectral analysis, the poorer resolution found with radio astronomy, and different metallicity in stars. With further improvements in technology and the building of observatories in space a more accurate and precise figure for R0 will be obtained and in turn the size and mass of the Milky Way Galaxy and the value of the Hubble constant. References [1] http://www.3towers.com/essays2.htm [2] http:/www.abc.net.au/cgi-bin/common/printfriendly.pl?/science/news/stories/s702556.htm [3] http://cfa-www.harvard.edu/~reid/trigpar.html [4] http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1998ApJ%2E%2E%2E494L%2E219P&db_key=AST&high=32bd93fcde14449 [5] www.carbonar.es/s33/Articles/Galactic-centre.pdf [6] http://zebu.uoregon.edu/~imamura/123/lecture-1/kapteyn.html [7] http://www-astronomy.mps.ohio-state.edu/~ryden/ast162_7/alternate28.html [8] http://www.ing.iac.es/PR/jkt_info/jktjacobus.html [9] http://spaceinfo.jaxa.jp/note/kagaku/e/kag123_oort_e.html [10] http://zebu.uoregon.edu/~js/ast122/lectures/lec25.html [11] Linda S. Sparke and John S. Gallagher, Galaxies in the Universe, Cambridge University Press 2000. [12] http://www.mpifr-bonn.mpg.de/staff/epolehampton/thesis/node25.html [13] Freedman, R., Kaufmann III, W., Universe, 6th Edition [14] http://www.aas.org/publications/baas/v32n4/aas197/2.htm [15] http://faculty.salisbury.edu/~jwhoward/astro108/html/lc14.htm