ABSTRACT

The Very Large Array (VLA) was used to observe 30 globular clusters at a frequency of 43 GHz. The aim of the observation was to identify Silicon Monoxide (SiO) Maser emission associated with evolved stars belonging to the clusters. If such radio sources were to be detected, it would facilitate making improved distance and proper motion measurements during subsequent observations. More accurate distance measurements would improve absolute magnitude estimates for stars at the main sequence turn-off point and hence better determination of cluster age. It would also facilitate a more accurate understanding of matter distribution in the Galaxy through kinematic analysis of cluster motion. Data from the observation was divided amongst 10 postgraduate students for analysis. This paper presents the analysis of data for NGC 4147, NGC 5272 (M3), and NGC 6838 (M71). In those clusters, no SiO Maser emission was detected. Possible reasons for a null detection are discussed, along with suggestions for future research.

INTRODUCTION

Globular clusters are dense collections of old stars that are found in a tightly packed spherical grouping and orbiting the parent galaxy outside of the galactic plane. For example, Figure 1 is a Charge Coupled Device (CCD) image taken at optical wavelengths of NGC 5272 (M3). As can be seen in the figure, NGC 5272 exhibits the tight grouping of stars characteristic of globular clusters.

The distance to globular clusters has previously been estimated using the period-luminosity relationship of Cepheid, RR Lyrae, and Mira variable stars contained within them [Reid et al., 1996; Menzies and Whitelock, 1985]

The present study has attempted to determine if SiO masers exist in evolved cluster stars, since these would allow accurate distance measurements to be made using high-resolution parallax observations at radio wavelengths. Accurate measurements of cluster distances could help constrain the age of the universe since the universe itself cannot be younger than any cluster. Moreover, if accurate distance measurements were combined with proper motion studies, SiO radio sources in the clusters could be used in conjunction with existing Galactic rotation curves to better infer the distribution of matter in the Galaxy.

FIGURE 1 Charge Coupled Device (CCD) image of the globular cluster NGC 5272 (M3) at optical wavelengths. Image of M3 copyright © 2000 by Wil Milan (http://www.astrophotographer.com/). Used by permission.

 

 

BACKGROUND

This paper will begin by presenting relevant background information and reviewing related research and observations.

Distance and Proper Motion

Trigonometric parallax can be used to determine the distance to nearby objects by measuring the extent to which those objects appear to shift position relative to more distant objects when viewed from two locations along a baseline of known distance. In the case of determining the distance to astronomical objects, taking multiple observations over a six-month period provides a suitable baseline since the diameter of the Earth's orbit about the sun is well known. The technique is further described in Appendix A.

The trigonometric parallax technique requires the use of high-resolution instruments capable of measuring small apparent shift.

For example, Hipparcos satellite data at optical wavelengths enabled the distance to nearby stars to be measured with unprecedented accuracy. Due to resolution and other design limitations, however, astrometry data was limited to 100, 000 stars, although distance measurement had a relative accuracy of better than 10% for all stars within 50 parsecs [Perryman et al., 1995]

In comparison, Milky Way globular clusters range in distance from 2.2 thousand to 121.9 thousand parsecs from the Sun [Harris, 1996]. All are too far away to have their distance determined through parallax measurements at optical wavelengths.

Instead of using trigonometric parallax, Cepheid, RR Lyrae, and Mira-type variable stars have been used to measure the distance to globular clusters using the well known period-luminosity relationship, the inverse square law and measurements of apparent brightness [Menzies and Whitelock, 1985; Clement and Hogg, 1977].

Early in the twentieth century, this technique was used to measure the distance to Milky Way globular clusters and plot their distribution. This exercise provided the first direct evidence that the Sun is not at the centre of the Galaxy and the first estimate of the distance to the Galactic centre [Reid et al., 1996].

Modern radio interferometers like the VLA have sufficient resolution to make proper motion and parallax measurements of radio sources near the Galactic centre directly. Furthermore, observations at radio wavelengths can penetrate the intervening dust that obscures the Galactic centre when viewed at optical wavelengths.

The distance to the centre of the Milky Way has been measured by the kinematic analysis of proper motion data for objects near the Galactic centre as radio sources orbit a common central point [Reid et al.,1996]. The trigonometric parallax of radio objects near the Galactic centre is also being measured [Reid et al., 1998; Shapley, 1918].

It would be possible to apply similar techniques to measure the distance and proper motion of Globular Clusters assuming that a bright, compact radio source could be identified in the clusters. No suitable radio source is currently known; a fact that was the principal motivation for the present study.

Rationale

Accurate measurements of globular cluster distance and proper motion using a suitable radio source would have many applications. These include the following:

• Mass Distribution- Galactic rotation curves plot the velocity of stellar rotation in the galactic plane as a function of the distance from the galactic centre [Nikiforov, 2000]. Such a curve demonstrates that 90% of the matter of the universe is unaccounted for; the so-called dark matter [Kaufmann and Freedman, 1999, pp 659-660]. Unfortunately, galactic rotation curves characterise the motion of stars in the galactic plane only. Since globular clusters do not orbit in the galactic plane, accurate distance and proper motion data would enable the distribution of matter and the dark matter halo to be studied with greater accuracy.
• Calibrating Standard Candles- Cepheid, RR Lyrae, and Mira-type variable stars are known to pulsate according to the so-called Period-Luminosity relationship [Kaufmann and Freedman, 1999, pp 615-617]. For these stars, the longer the period, the greater the luminosity. Using the period of variation, the apparent magnitude, and the inverse square law, it is possible to calculate the distance to the star. Being able to validate this distance using other techniques to measure distance can help to calibrate the process and improve confidence in the calculated results.
• Determining the Age of Clusters- If it is assumed that all stars in a cluster are about the same distance from the sun, then plotting apparent magnitude versus surface temperature produces a Colour-Magnitude diagram, which is equivalent to the HR diagram for the cluster. Stars in a given globular cluster are generally thought to have formed at about the same time. Consequently, the point at which they turn off of the main sequence on the Colour-Magnitude diagram is an indication of the cluster's age [Kaufmann and Freedman, 1999 pp 524-528; Bless, 1996, p358-363]. In 1984, the age of Omega Centauri was placed at about 18 billion years [Bell et al., 1984]. More recent data suggest that it is about 14 billion years old [Hughes and Wallerstein, 1998]. Accurately calculating the distance to the cluster would yield better determination of the absolute magnitude at the cluster turnoff point, and hence a more accurate determination of cluster age.
• Constraining the Age of the Universe- Many methodologies have been proposed for calculating the age of the Universe [Freedman, 2000]. These estimates can be constrained and validated by measurements of the age of globular clusters, since no cluster can be older than the Universe itself. Further, many of the methodologies for dating the Universe rely on the use of standard candles. Improved confidence in the reliability of the standard candles improves confidence in the accuracy of Universe age estimates.

Previous observations

A literature search was conducted using the NASA Astrophysics Database System (ADS), the World Wide Web, and other sources to identify related prior work and observations, particularly with respect to bright, compact radio sources in globular clusters.

Biggs and Lyne [1996] conducted a targeted search for radio pulsars in globular clusters, supernova remnants, and transient X-ray sources. Of the 85 globular clusters searched, only 4 radio pulsars were found. They attributed low detection rates to the size of pulsar emission beams, the large distance to the target, and low pulsar luminosity.

SiO masers are known to exist in relative abundance near the more metal rich Galactic Centre [Izumiura et al, 1998]. SiO masers are compact and relatively bright, particularly when associated with stars of late spectral types [Cahn, 1977].

SiO masers have been associated with Mira [Phillips et al., 2000] and some Mira-type variable stars [Bobolitz et al., 1997] and have been found in relative abundance near the Galactic centre [Izumiura et al., 1998]. Mira stars are known to exist in some globular clusters, particularly those that are relatively metal rich [Clement and Hogg, 1977].

However, SiO masers do not exist or are not detectable about all Mira-type stars, and are known to be under luminous or non-existent in symbiotic systems [Schwarz et al., 1995].

Frail & Beasley [1994] conducted a search for OH Masers towards all known globular clusters north of -42 degrees, in addition to a targeted search conducted on stars near some globular clusters. Although several candidates were identified, only one positive OH Maser detection could be associated with a globular cluster with confidence, rather than merely being a line of sight coincidence.

Cohen and Malkan [1977] were similarly unsuccessful in an attempt to identify H₂0 masers in globular clusters.

In addition to low detection rates for pulsars in globular clusters, if SiO masers were shown to exist in the clusters, then they would be superior targets for follow-up studies due to better resolution of interferometer observations at typical SiO maser frequencies.

TABLE 1. The resolution of various interferometers in arc seconds, for various baselines, frequencies, and object positions, computed using Equ 1. The spreadsheet that produced the table is available in a zip archive at: http://www.computing.edu.au/~bvk/astronomy/HET608/project/data.zip

 

The relationship between frequency and resolution in an interferometer is given by [SAO, 2000, slide 12]:

	[Equ 1]
	[Equ 2]

where:

Table 1 shows the resolution of interferometers for several baselines, object orientations and observation frequencies. 610, 925, and 1420 MHz are the frequencies used by Biggs and Lyne (1996) in a search for radio pulsars in globular clusters, supernova remnants, and transient X-ray sources. At these frequencies, Table 1 demonstrates that an interferometer has a relatively large angular resolution when compared to 43 GHz observations used to detect SiO Maser emission. As a result of the larger angular resolution, radio pulsars are ill-suited targets for precise measurement of changes in object position at various epochs.

Table 1 also shows the angular resolution of the Very Large Array in several configurations when tuned to a frequency of 43 GHz.

FIGURE 1 The Very Large Array (VLA) in the D configuration, photographed approximately one month before the observation in October 2000. Copyright © 2000 by Colleen Gino. Used by permission.

The D-Configuration possesses a relatively small baseline of only 1 kilometre compared to the 32 kilometre maximum baseline provided by the A-Configuration. Even in the D-Configuration, the VLA has sufficient angular resolution to be used in the present investigation and during follow-up observations in the event that SiO masers are eventually detected in globular clusters.

Further, when the array is in transition from the D to the A configuration, requests for observing time are less competitive. This is because the D configuration has a comparatively small baseline, and the transition to the larger configuration results in an awkward antenna configuration.

Situated in Socorro, New Mexico at an elevation of 2124 meters or almost 7000 feet, the VLA is at a comfortable, but relatively high altitude. Radio observatories, particularly those that are used for observations at shorter wavelengths, are usually built at high altitudes in locations with dry climates. This is because moisture in the atmosphere can adversely effect the observation at shorter wavelengths.

As has been demonstrated, pulsars would be poor targets for follow-up studies given resolution limitations. Both radio pulsars and OH masers are poor targets in globular clusters given the low detection rates reported in the literature [Biggs and Lyne,1996; Frail & Beasley, 1994].

Despite the apparently low probability of success, the potential scientific ramifications of positive SiO maser detection in a reasonable sample of globular clusters justified the attempt to detect them in the present investigation. Given the factors cited above, the VLA was selected as a suitable instrument for the observation.

METHODOLOGY

32 globular clusters were included in the target sample. Except as noted below, selected targets met the following criteria:

• Only clusters with declination between -20 and 70 degrees were included in the target sample.
• The distance from the sun was less than 25 kiloparsecs.
• Clusters were relatively metal rich with [Fe/H] > -1.9, in log units relative to solar.

Pyxis, NGC 6229, NGC 7006, M54, and Arp 2 were included in the target sample although they did not meet the standard selection criteria. These are possibly captured clusters that might possess characteristics dissimilar to clusters of Milky Way origin. Consequently, they were deemed to be interesting targets that complemented those meeting the standard criteria.

Pyxis was later discarded due to poor weather during the observation that resulted in corrupt data. NGC 6402 was also not considered due to errors in the file used to configure the array. This left useful data for 30 clusters in the target sample.

Data was amplitude and phase calibrated based on calibration data collected intermittently throughout the observation. Calibrator objects were selected from the VLA Calibrator Database. The primary flux calibrators used were 1331+3-5 and 0137+331.

A good primary calibrator possesses the following characteristics [Taylor, HREF]:

• low variability;
• close to the observed target, preferable within 10 degrees;
• the same calibrator is preferable used for all or most of the observation;
• frequent calibration observations. At 43 GHz, calibration observations at intervals more frequent than 30 minutes is generally recommended.

Data was phase corrected by interpolating phase changes detected in phase calibrator observations bracketing the target observation. Phase changes can occur during an observation when the signal path length changes due to factors that include atmospheric effects, electronic delays, and geometry or structural errors.

Figure 3. Phase Centre Rotation Coordinates. The original phase centre is labelled with coordinate (0, 0). The original phase centre was rotated to adjacent areas that are labelled as shown.

 

 

Because the source of potential SiO Maser emission is not necessarily at the centre of the target cluster, data was phase rotated to produce a 3 X 3 grid with the phase centres adjusted to maximise sensitivity in regions corresponding to those that are adjacent to the actual phase centre.

In this report, grid cells with adjusted phase centres are referred to as pointings, although these were actually derived from a single pointing of the array for each cluster. Grid coordinates for each phase rotated cell are shown Figure 3.

In addition to the globular clusters in the target sample, the star WX Serpentis (WXSER) was also observed. This star is known to possesses a strong SiO maser emission.

WXSER data facilitates target cluster data analysis in the following manner:

• The WXSER data provides an example of a strong SiO maser emission for statistical evaluation and comparison with data from target clusters.
• It demonstrates that the amplitude of a strong signal diminished when phase centres are adjusted to simulate a beam centre aligned with an adjacent off-centred region.

RESULTS

The approved observing schedule was necessarily pre-empted and rescheduled to accommodate target-of-opportunity projects conducted by other observers. This did not result in any significant loss of any data in the present study.

Data for the 30 clusters was divided amongst ten postgraduate students for analysis. The remainder of this report describes the analysis of globular clusters NGC 4147, NGC 5272 (M3), and NGC 6838 (M71) in addition to the star WXSER.

Results for WXSER and each cluster are plotted with a preliminary evaluation of the results. This is followed by a more comprehensive statistical analysis.

WXSER

WXSER is known to possess a strong SiO maser emission, which can be seen in Figure 4 Figure 5 and Figure 6. Data for the actual phase centre is plotted in the middle portion of Figure 5 and is labelled Pointing (0, 0), with plots for adjusted phase centres in adjacent regions labelled as shown in Figure 3.

A strong emission signal is seen in all pointings in channel 34, corresponding to a velocity of -1.35785 km/s. In pointing (0, 0), this channel has a peek amplitude of 6.13194 Jansky's, well in excess of the apparent noise. This amplitude is seen to fall off in each of the pointings with adjusted phase centres, as expected.

FIGURE 4. WXSER pointings (-30, 30), (-30, 0), and (-30, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 5. WXSER pointings (0, 30), (0, 0), and (0, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 6. WXSER pointings (30, 30), (30, 0), and (30, -30) in the top, middle, and bottom portion of the figure, respectively

 

NGC 4147

NGC 4147 is a globular cluster with [Fe/H] metalicity of -1.93. Existing data places it 19.3 kiloparsecs from the sun. Additional reference data is provided in Appendix B.

Amplitude is plotted as a function of velocity for NGC 4147 in Figure 7, Figure 8 and Figure 9. Data for the actual phase centre is plotted in the middle portion of Figure 8 and is labelled Pointing (0, 0), with plots for adjusted phase centres in adjacent regions labelled as shown in Figure 3.

No SiO maser signal is apparent. All amplitude fluctuations are less than 0.3 Jansky's and are indistinguishable from noise.

FIGURE 7. NGC 4147 pointings (-30, 30), (-30, 0), and (-30, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 8. NGC 4147 pointings (0, 30), (0, 0), and (0, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 9. NGC 4147 pointings (30, 30), (30, 0), and (30, -30) in the top, middle, and bottom portion of the figure, respectively

 

 

NGC 5272

NGC 5272 is a globular cluster with [Fe/H] metalicity of -1.57. Existing data places it 10.4 kiloparsecs from the sun. It is also known as M3, and is shown in a CCD image at optical wavelengths in Figure 1. Additional reference data is provided in Appendix B.

Amplitude is plotted as a function of velocity for NGC 5272 in Figure 13, Figure 14 and Figure 15. Data for the actual phase centre is plotted in the middle portion of Figure 14 and is labelled Pointing (0, 0), with plots for adjusted phase centres in adjacent regions labelled as shown in Figure 3.

No SiO maser signal is apparent. All amplitude fluctuations are less than 0.35 Jansky's and are indistinguishable from noise.

FIGURE 10. NGC 5272 pointings (-30, 30), (-30, 0), and (-30, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 11. NGC 5272 pointings (0, 30), (0, 0), and (0, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 12. NGC 5272 pointings (30, 30), (30, 0), and (30, -30) in the top, middle, and bottom portion of the figure, respectively

 

NGC 6838

NGC 6838, also known as M71, is a globular cluster with an [Fe/H] metalicity of -0.73. Of the three clusters analysed in this report, this cluster has the highest metal content.

Existing data places it at 3.9 kiloparsecs from the sun. Additional reference data is provided in Appendix B.

Amplitude is plotted as a function of velocity for NGC 6838 in Figure 16. Figure 17 and Figure 18. Data for the actual phase centre is plotted in the middle portion of Figure 17 and is labelled Pointing (0, 0), with plots for adjusted phase centres in adjacent regions labelled as shown in Figure 3.

No SiO maser signal is apparent. All amplitude fluctuations are less than 0.35 Jansky's and are indistinguishable from noise.

FIGURE 13. NGC 6838 pointings (-30, 30), (-30, 0), and (-30, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 14. NGC 6838 pointings (0, 30), (0, 0), and (0, -30) in the top, middle, and bottom portion of the figure, respectively

 

FIGURE 15. NGC 6838 pointings (30, 30), (30, 0), and (30, -30) in the top, middle, and bottom portion of the figure, respectively

 

Statistical Analysis

The mean and standard deviation were calculated for WXSER, NGC 4147, NGC 5272, and NGC 6838 in each phase rotated pointing according to:

	[Equ 3]
	[Equ 4]

where:

A given observation was deemed to have an emission if the amplitude of any channel was in excess of 5 standard deviations of the mean for that phase rotation pointing. The built-in Microsoft Excel functions AVERAGE() and STDEV() were used to compute the mean and the standard deviation, respectively. These values were also computed using manually entered spreadsheet formulas to verify consistency with the built-in functions.

In WXSER phase rotation pointing (0, 0), the mean was 0.3919 Jy, with a standard deviation of 1.1048. The detection threshold was placed 5 standard deviations from the mean at 5.9191 Jy. The peak amplitude of 6.13194 Jy occurred in channel 34, corresponding to a velocity of -1.35785 km/sec. Because the amplitude exceeded the detection threshold, this channel met the criteria for positive emission detection. A log plot of WXSER for phase rotation pointing (0, 0) is shown in Figure 16, with arrows indicating both the mean and the detection threshold for that pointing.

For WXSER, positive detection occurred in channel 34 corresponding to a velocity of 6.1253 km/sec for all phase rotation pointings except.(30, -30) and (30, 0). Positive detection also occurred in channel for pointings (-30, 30), (0, -30), (0, 0), (0, 30), and (30, 30).

The built-in Microsoft Excel conditional function IF() was used to automatically flag emissions that exceeded the detection threshold, as shown in Figure 17.

FIGURE 16. Log plot for WXSER, pointing (0, 0) showing an emission exceeding the detection threshold located 5 standard deviations from the mean.

 

FIGURE 17. Statistical analysis was conducted in Microsoft Excel using the built-in functions AVERAGE() and STDEV (). Conditional evaluation function IF() automatically flagged detected emissions, as highlighted on lines 34 and 35 in the figure.

 

The mean, standard deviation, and detection threshold for phase rotation pointing (0, 0) of each target are shown in Table 2.

The amplitude measured in each channel for phase rotation pointing (0, 0) of all targets is shown in Table 3.

The mean, standard deviation, detection threshold, and maximum amplitude are shown for each target and each phase rotation pointing in Table 4. Amplitudes that exceed the detection threshold for the given observation are highlighted in the table, but were only seen to occur for WXSER. NGC 4147, NGC 5272, and NGC 6838 did not meet the detection criteria for SiO masers emission in any phase rotation pointing.

DISCUSSION

Possible explanations for no SiO masers detection in observed clusters are listed below:

• Low Metalicity- Elements heavier than helium are generally less abundant in globular clusters. Without a significant quantity of heavy elements silicon and oxygen, SiO molecules and SiO masers will not exist.
• Low Mira count in Globular Clusters- While Mira-type stars are known to exist in globular clusters [Clement and Hogg, 1977], most clusters have comparatively few, particularly those that have been studied in any depth [Andrews et al., 1974].
• Age and evolution of cluster variables- Globular clusters generally consist of old stars. Mira-type stars in globular clusters may therefore represent a latter evolutionary stage than is seen in non-cluster counterparts. In this instance, molecular clouds associated with maser emission may have been blown away by strong stellar winds.
• SiO Maser variability- Masers are dynamic structures exhibiting ongoing structural changes [Diamond and Kemball, 1998]. It is possible, however unlikely, that maser emission existed but was not detected due to unusual structural features of the maser at the time of the observation.
• SiO masers may exist in GC Mira-type stars, but not be observable- Cahn [1977] has shown that there is a correlation between absolute SiO maser luminosity at maximum light in Mira-type stars and the mean spectral type at normal maximum. His works suggest that every Mira may turn out to be a SiO maser, but only be observable if the star is of a late spectral type and sufficiently close.
• Consistent with other masers searches in globular clusters- The lack of SiO maser emission detection is consistent with the previous results of Frail and Beasley [1994] who attempted to identify OH masers in globular clusters. Similarly, Cohen and Malkan [1977] were unsuccessful in an attempt to find H₂0 masers in globular clusters. SiO masers may be rare in globular clusters for the same reasons that OH and H₂0 masers are also rare.

TABLE 2. Statistical analysis for phase rotation pointing (0, 0) for all targets.

 

TABLE 3. Amplitude expressed in Janskys for pointing (0, 0) of each target. Highlighted items in channels 33 and 34 for WXSER met the criteria for positive emission detection since they exceed the threshold cited in Table 2.

TABLE 4. The mean, standard deviation, maximum amplitude, and an indication if an emission was detected for each phase rotation pointing for WXSER, NGC 4147, NGC 5272, and NGC 6838, occurring when the maximum amplitude exceeds the threshold.

 

FIGURE 18. The maximum WXSER signal amplitude in each pointing exceeded the detection threshold located 5 standard deviations from the mean for seven of the nine pointings.

 

FIGURE 19. Threshold test demonstrating that the maximum amplitude in each pointing for NGC 4147, GNC 5272, and NGC 6838 was well below the detection threshold located 5 standard deviations from the mean.

FUTURE WORK

SiO , OH and H₂O masers are relatively plentiful towards the Galactic centre. As a result of the present study and the prior work of Frail and Beasley [1994] and Cohen and Malkan [1979], we now know that masers are non-existent, rare, or under luminous in globular clusters.

Future work should be undertaken to definitively explain the lack of success in detecting globular cluster masers. It would be interesting to map the distribution of known masers of various molecular species to look for a correlation with respect to metal content, structure, location, density luminosity, and other attributes.

CONCLUSIONS

No evidence for SiO Masers emission was seen in the NGC 4147, NGC 5272 (M3), or NGC 6838 (M71) data analysed in this report. Other postgraduate students analysing data in conjunction with this study but analysing data for other clusters report similar findings.

ACKNOWLEDGEMENTS

Dr. Tony Beasley is gratefully acknowledged for his patient support, advice, and counsel throughout the semester.

Many thanks to classmates Wil Milan and Colleen Gino, the copyright holders who kindly granted their permission for inclusion of their images as Figure 1 and 2, respectively.

Appreciation is also extended to other classmates who provided thoughtful discussions related to this research and related topics via e-mail and the Swinburne Astronomy Online Newsgroups.

REFERENCES

Andrews, PJ, Feast, MW, Evans, LT, Thackeray, AD, and Menzies, JW. (1974) Mira variables in four metal-rich globular clusters, The Observatory, Vol. 94, p. 133-135.

Bell, RA, Cannon, RD, Harris, GLH, Hesser, JE (1984) The age of the globular cluster Omega Centauri, Bull. American Astron. Soc., 16, 734.

Biggs, JD and Lyne, AG (1996) A Search for Radio Pulsars in Globular Clusters, Supernova Remnants and Transient X-Ray Sources, Monthly Notices of the Royal Astronomical Society, Volume 282, Issue 2, pp. 691-698.

Bless, RC (1996) Discovering the Cosmos, University Science Books, ISBN 0-935702-67-9.

Bobolitz, DA, Diamond, PJ, and Kemball, AJ (1997) R Aquarii: First Detection of Circumstellar SiO Maser Proper Motions, The Astrophysical Journal (Letters), 487:L147-L150.

Cohen, NL and Malkan, MA (1979), A search for H2O maser emission from globular clusters, Astronomical Journal, vol. 84, Jan. 1979, p. 74-76.

Diamond, PJ and Kemball, AJ (1998) A Stellar movie: VLBA monitoring of SiO masers around the Mira variable TX Cam, American Astronomical Society Meeting #193, #69.03

Frail, DA and Beasley, AJ (1994) Stellar OH Masers toward Globular Clusters, Astronomy and Astrophysics, 280:796-802.

Freedman, WL, (2000) The Hubble constant and the expansion age of the Universe, Physics Reports, 333, 13-31.

Harris, WE (1996) A Catalog of Parameters for Globular Clusters in the Milky Way, Astronomical Journal v.112, p.1487

http://physun.physics.mcmaster.ca/~harris/mwgc.dat

Hughes, JD and Wallerstein, G (1998) Age and Metallicity Effects in Omega Centauri I: Stromgren Photometry, American Astronomical Society Meeting #193, #68.09

Izumiura, H, Deguchi, S, and Fujii, T (1998) SiO Forest at the Galactic Center, The Astrophysical Journal (Letters), 494:L89-L92

Kaufmann, WJ and Freedman, RA (1999) Universe, 5^th ed. WH Freeman and Company, ISBN 0-7167-3495-8.

Menzies, JW, and Whitelock, PA (1985) A period-luminosity relation for Mira variables in globular clusters and its impact on the distance scale, Royal Astronomical Society, Monthly Notices (ISSN 0035-8711), vol. 212, Feb. 15, 1985, p. 783-797.

Nikiforov, I (2000) Milky Way Rotation Models from Neutral Hydrogen and Molecular Clouds: Galactic Constants, Common Details and Differences, Small Galaxy Groups: IAU Colloquium 174, ASP Conference Series, Astronomical Society of the Pacific, Volume 209, p. 403.

Perryman, MAC Lindegren, L, Kovalevsky, J; Turon, C; Hoeg, E, Grenon, M, Schrijver, H, Bernacca, PL, Creze, M, Donati, F, Evans, D, Falin, JLm Froeschle, M, Gomez, A, Grewing, M, van Leeuwen, F, van der Marel, H, Mignard, F, Murray, C A, Penston, MJ, Petersen, C, Le Poole, RS, Walter, HG, (1995) Parallaxes and the Hertzsprung-Russell diagram for the preliminary HIPPARCOS solution H30, Astron. Astrophys. 304, 69.

Phillips, RB, Boboltz, DA (2000) 86 GHZ SIO Masers toward Mira, The Astronomical Journal, Volume 119, Issue 6, pp. 3015-3018.

Reid, M, Menten, K, Eckart, A, and Genzel, R (1996) "Where is the Galactic Center?, American Astronomical Society Meeting, 189, #61.05,

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. JA Zensus, GB Taylor, & JM Wrobel, p. 335-33.

Schwarz, HE, Nyman, LA.; Seaquist, E.R, and Ivison, RJ (1995) A search for SiO maser emission from symbiotic Miras, Astronomy and Astrophysics, v.303, p.833.

Shapley, H (1918) Globular Clusters and the Structure of the Galactic System, Publications of the Astronomical Society of the Pacific, Vol. 30, No. 173, p.42.-54.

Taylor, G (HREF) Hints and Strategies for Successful Phase Calibration, http://www.aoc.nrao.edu/~gtaylor/calman/hints.html

Appendix A- Parallax and Distance

Parallax measurements enable the distance to nearby objects to be calculated as they appear to shift position over time relative to more distant objects which appear fixed. The geometry that enables distance to be calculated is demonstrated in Figure B-1, which shows two observations of the same nearby object separated in time by six months.

From the Figure A-1, it can be seen that:

	[Equ A-1]
	[Equ A-2]

where:

Since the parallax angle is very small:

	[Equ A-3]
	[Equ A-4]

Since the amount of shift is very small, parallax measurements require instruments of high resolution and small field of view.

For more details, see http://www.computing.edu.au/~bvk/astronomy/HET603/atlas/

Figure A-1Parallax geometry, demonsrating how the distance to nearby objects can be measured by observing how they appear to shift position over the course of six months relative o other more distant objects that appear fixed.

 

 

Appendix B- Cluster Reference Information