"Space... is big. Really big. You just won't believe how vastly hugely mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space."
The Hitchhiker's Guide to the Galaxy
Since ancient times, humans have looked to the heavens and contemplated our place in the Universe. Many of our religious and cultural traditions have placed the Earth and humankind at the centre of a cosmos brought into existence in a loving act of divine creation.
Overtime, however, we have learned that our place in the cosmos is not special. The Earth is not at the centre of the Solar System. The Sun is not at the Centre of the Milky Way Galaxy. The Galaxy is not at the "centre" of the Universe.
As science has replaced the myth and legends of a more innocent time, we have come to realise that we do not hold a special place in the Universe. We live on a small planet orbiting an average star on the outskirts of a typical barred spiral galaxy; a galaxy like countless others.
Remarkably, modern science can pinpoint our position in the Galaxy with increasing accuracy:
To map our position so precisely has required old ideas and notions to be abandoned, and the development of a scientific methodology in which an increasingly accurate model of the Universe is tested and refined through direct observation.
This process began when Galileo Galilei first pointed his telescope to the sky and produced irrefutable observational evidence that celestial bodies do not necessarily orbit the Earth in divinely perfect celestial spheres (Galilei, 1610). Although controversial at the time because his observations seemed to contradict the teaching and religious doctrine of those in authority, Galileo's observations mark a turning point in astronomy as an observational science. Direct observations seemed to suggest that the Earth was not necessary the centre of the cosmos.
Since Galileo's time, many innovations in technology, methodology, and theory have enabled our position in the Galaxy to be precisely determined.
What are these new methods that have enabled the distance to the centre of the galaxy to be measured? What new technology has enabled these measurements to be made with increasing accuracy and confidence? Why is this knowledge important?
Early in the 20th century, Harlow Shapley attempted to estimate the distance to the centre of the Galaxy by analysing the distribution of Globular Clusters which he assumed to be symmetrically distributed about the Galactic centre.
Shapley's method was as follows (Shapley, 1918; Reid 1993):
Shapley concluded (Universe, 1998; Reid, 1993):
Modern estimates place the Galaxy centre closer to 8 kiloparsecs from the Sun, so Shapley's estimate was incorrect by a factor of around 1.6. This error was largely the result of neglecting the effects of interstellar dust. Dust scatters and absorbs light, causing the apparent brightness to be less than that predicted by the inverse square law. This is known as interstellar extinction (Universe, 1998, pages 495, 614, 617 ).
In 1989, Racine and Harris attempted to produce better estimates of globular cluster distance and the related distance to the Galactic centre by mathematically correcting for the effects of interstellar extinction. They determined that the Galactic centre is 7.5 kiloparsecs from the Sun, plus or minus 0.9 (Reid, 1993).
In 1976 and 1980, Harris attempted to reduce the effects of extinction by excluding clusters close to the Galactic plane from the distribution analysis. He reasoned that clusters further from the Galactic plane were less affected by extinction since there was less intervening dust to absorb or scatter light. However, excluding clusters in this manner had the side effect that it reduced the sample size, thereby increasing the statistical uncertainty of the result (Reid, 1993).
Unlike Shapley, Harris did not use variable stars to measure cluster distance. Instead, he noted the point at which the cluster's stars depart the main sequence and turn onto the horizontal branch when plotted on a Hertzspung-Russel (H-R) diagram. This point on the main sequence determines the luminosity of cluster stars at the main sequence turn-off point and enables the distance to be calculated from the corresponding luminosity indicated on the vertical axis of the H-R diagram. The method assumes that all stars in the cluster are roughly the same age and at the same distance from the observer. Using Harris' technique, the distance to the Galactic Centre was found to be 8.5 kiloparsecs, plus or minus 1.6 (Reid, 1993).
A sample of results from studies attempting to determine the distance to the Galactic centre by analysing the distribution of Globular Clusters are summarised in Table 1.
| Distance to Galactic Centre (s) |
Distance Calibration Technique |
Comments |
| 13 | RR Lyrae | Shapley's method, not excluding effects of interstellar extinction. |
| 8.5 +/- 1.6 | H-R Horizontal branch | Harris' method, uses mean distribution of clusters and excludes clusters close to the galactic plane |
| 7.5 +/- 0.9 | RR Lyrae | Mathematically eliminate extinction effects |
| 7.0 | RR Lyrae | Harris' method excluding clusters close to the Galactic plane, but calibrated using RR Lyrae variable stars. |
Table 1. Estimates of the distance to the Galactic Centre made by analysing the distribution of Globular Clusters with various calibration techniques and methodology refinements. For a more exhaustive list, see Reid (1993).
The apparent brightness of globular clusters may be attenuated due to interstellar extinction, but at least we can see them since they orbit the centre of the Milky Way outside the dusty Galactic plane. This is fortunate, because a direct view of the Galactic centre from our position within the plane of the Milky Way's is completely obscured at visual wavelengths.
Modern observations at longer wavelengths are able to penetrate the dust that obscures our view at visual wavelengths. For example, observations at infrared wavelengths have only recently revealed the central bulge of the Milky Way in the middle of the flat Galactic plane; a characteristic distinctive of spiral galaxies. Observations at other wavelengths are equally compelling.
Interferometry is the technique of combing observations from multiple instruments to produce a single virtual instrument of large size and resolution. At wavelengths longer than those in the visual range, interferometry enables radio astronomers to "see" through the dense layers of dust in Galactic plane and make direct observations of structures near the centre of the Milky Way with remarkable resolution and accuracy.
For example, the microwave signature of water can be detected when microwave radiation emanating from a source near a molecular cloud of water is amplified by natural processes occurring with the cloud. Molecular clouds emitted amplified microwave radiation are known as masers.
The process by which a maser amplifies microwave radiation is similar to that employed by a laser working at visual wavelengths. In a maser, a molecular cloud is bombarded with infrared radiation emanating from a dense layer of dust cocooning hot sources of gamma radiation. This energy excites electrons in the molecular cloud to a higher energy state. The cloud emits a photon and drops to a metastable state. It remains in this state until it encounters a microwave photon. A second microwave photon is emitted as the electron drops to the ground state. This process cascades along, amplifying microwave emission.
By studying the proper and radial motion of many molecular clouds in the same region, the common centre of the cloud can be determined. Sagittarius (Sgr) B2(North) is a radio source thought to be within 0.3 parsecs of the Galactic centre. Proper motion studies of water maser associated with Sgr B2(North) suggest that the distance to the Galactic centre is 7.1 kiloparsecs, plus or minus 1.5 (Reid, 1993).
Interestingly, observations of water masers is not limited to our own Galaxy. Astronomers have also used the technique to determine the distance to water masers near the centre of other distant galaxies. This is fortunate, since it provides a means of crosschecking and validating other standard candle measurements used to determine the distance to extra-galactic objects (NARO, HREF 1999B).
In the closing years of the 20th century, astronomers using the Very Long Baseline Array (VLBA) have utilised trigonometric parallax to determine the distance to Sgr A*. This object is a strong radio source believed to enshroud a supermassive black hole at the centre of the Milky Way (Reid, et al., 1999; NRAO, HREF 1999A).
Trigonometric parallax measurements require the observer to make multiple accurate, high-resolution observations of an object over the course of more than six months. During successive observations, the object appears to shift its position in the sky due to the changing position of the observer. Applying basic high school trigonometry enables the distance to the object to be determined, using the Earth and the Sun to establish a baseline of known distance.
In 1838, Friedrich Bessel used trigonometric parallax to determine the distance to 61 Cygni. However, he and his contemporaries could only estimate the distance to the closest stars given the limitations imposed by the optical resolution of available instruments.
Modern trigonometric parallax observations made by the Hipparcos satellite have measured the distance to stars within 300 parsecs from the sun to an accuracy of 10 percent. Without long wavelength interferometry, however, accurate distance to objects farther than 300 parsecs from the Sun can't be determined using current instruments.
Fortunately, the VLBA does not suffer from these limitations. The VLBA combines data from ten identical antennas between Hawaii and the US Virgin Islands, producing a single virtual instrument that spans the Earth. When operating at high frequency, the VLBA is capable of seeing through intervening dust to the Galactic centre with mili-arcsecond resolution.
In the closing years of the 20th century, thanks to the accuracy and resolution of the VLBA, astronomers finally have the methodology, technology, and instrumentation to pinpoint our location in the Galaxy. We now know with great certainty that we are some 8 kiloparsecs from the centre of the Milky Way, making one complete rotation about the Galactic centre every 226 million years (NRAO, HREF 1999A).
It has taken roughly one century for astronomers to refine our methodologies, evolve our technology, and improve our instrumentation to enable us to determine our position in the galaxy so accurately.
OK. So now we know where we are; but why is this important?
From Kepler's Third Law, it can be shown that the mass of the Milky Way Galaxy is a function of the Sun's distance to the Galactic centre and its orbital speed. The mass estimate predicted by this calculation is not large enough to explain the rotation curve resulting from plotting the Galaxy's orbital speed as a function of distance from the Galactic centre. This paradox tells astronomers that most of the mass of the universe is missing; the so-called dark matter.
What is dark matter? This remains one of the great-unanswered questions of modern astronomy.
Furthermore, accurately knowing the distance to globular clusters and the centre of the Galaxy enables astronomers to calibrate other "standard candles" used in measuring the distance to other remote objects. This includes calibrating the period luminosity-relationship used to determine the distance to RR Lyrae and Cepheid variable stars. The latter provides greater confidence in the "standard-candles" used to infer the distance to vastly distant galaxies, and in measuring the Hubble Constant and the age of the universe.
The techniques and measurements that have determined our position in the Milky Way have progressively led astronomers to determine the distance to other distant galaxies with increasing accuracy. By considering extra- galactic distance estimates together with their Doppler red shift, we know that the universe is expanding like the surface of an inflating balloon. Measuring the distance from the Sun to the centre of our own Galaxy was just a stepping stone leading to this inescapable conclusion.
On a cosmological scale, observational science shows us with confidence that galaxies are moving away from other galaxies at a speed proportional to the distance from the observer. Further, they are able estimate the rate of expansion and speculate about the ultimate fate of the Universe.
In a cruel twist of irony, humanity is left with the false illusion of being at the centre of the cosmos as the Universe expands and every point in the universe becomes farther away from every other point. An alien observer living on a distant planet in some other remote galaxy is left with the same illusion. If the old religious traditions are right and God did create the Universe, then at least He did so with the greatest sense of equalitarian wisdom. That is, He gave all intelligent beings everywhere some degree of security from the illusion that they are special and placed the centre of all creation.
The internet bound astronomer can investigate the importance of high-resolution observations when making trigonometric parallax observations using The Atlas of Nearby Stars: Experiments in Virtual Astronomy. This Java applet was developed by the author as part of the assessment for HET 603: Exploring the Stars and the Milky Way.
Modified 21/12/1999
Reid et al. has used masar proper motion to determine the distance to the galactic centre. Working with other colleagues, Reid has also begun an attempt to measure the distance to the galactic centre using the method of trigonometric parallax. As of this writing (November, 1999) final observations and results for the latter method have not been published, but are expected soon.
Adams, D (1979) The Hitchhiker's Guide to the Galaxy, Pocket Books, New York.
Galilei, G. (1610) Sidereus Nuncius or the Sidereal Messenger, Translated by Van Helden A, The University of Chicago Press, Chicago.
Kaufmann III, WJ, Freedman, RA (1999) Universe, 5th ed., WH Freeman and Co., New York.
NASA (HREF 1999) The Shapley-Curtin Debate in 1920, http://antwrp.gsfc.nasa.gov/diamond_jubilee/debate20.html
Nikiforov, II (1999) Modeling the Rotation Curve of the Plane Subsystem and Determination of the Distance to the Galactic Center: Analysis of Data for Gas Complexes, Astronomy Reports, 43:345.
NRAO (HREF 1999A) VLBA Detects Earth's Motion Around the Milky Way's Center, http://www.nrao.edu/pr/sagastar.html
NRAO (HREF 1999B) Radio Astronomers Set New Standard for Accurate Cosmic Distance Measurement, http://www.nrao.edu/pr/4258.distance.html
Reid, MJ, Readhead, ACS, Vermeulen, RC, and Treuhaft, RN (1998) Toward a Trigonometric Parallax of Sgr A*, Radio Emission from Galactic and Extragalactic Compact Sources, ASP Conference Series, Volume 144, IAU Colloquium 164, eds. J.A. Zensus, G.B. Taylor, & J.M. Wrobel, p. 335-336, ftp://ftp.mpifr-bonn.mpg.de/pub/user/zensus/iau164/preprints/reid.ps.gz
Reid, M, Menten, K, Eckart, A, and Genzel, R (1996) "Where is the Galactic Center?, American Astronomical Society Meeting, 189, #61.05.
Reid, MJ (1993) The distance to the center of the Galaxy, Annual Review of Astronomy and Astrophysics, 31: 345-372.
Smith, RS (1982) The Expanding Universe: Astronomy's 'Great Debate' 1900-1931, Cambridge University Press, Cambridge.