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Three dimensional velocity tomography in the core of Messier 71 Samra, Raminder Singh 2013

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Three Dimensional Velocity Tomography in the Core of Messier 71 by Raminder Singh Samra B.Sc., The University of British Columbia, 2009 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Astronomy) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2013 c© Raminder Singh Samra 2013 Abstract Using the Gemini North Telescope at Mauna Kea we have obtained astro- metric and spectroscopic data for stars in the core of the galactic globular cluster Messier 71 (NGC 6838). This data has allowed us to for the first time ever to obtain three dimensional velocity profiles for stars in the vicin- ity of centre of a globular cluster. Using the Near Infrared Imager with Adaptive Optics and a 3.8 year baseline for our astrometric study we have resolved the internal proper motion dispersion. The proper motion disper- sion is found to be 179±17µarcsec year−1, we have put a strict limit to the size of any central Intermediate Mass Black Hole at ∼150M" at 90% confidence, additionally we find no evidence of core anisotropy. Using our GMOS Integrated Field Unit spectroscopic data we have obtained a radial velocity dispersion of 3.54±0.64 km s−1. Combining our proper motion and radial velocity dispersions we find the geometric distance to the cluster to be 4.1±1.2 kpc. We then compare our geometric distance to a distance found from fitting stellar evolution models. We have developed a new technique for fitting models, using this technique we find the stellar evolution model distance to be 3.9±0.2 kpc. We then discuss how this technique can easily be applied to other clusters in any future work. ii Preface A substantial portion of this work was published in the May 2012 edition of the Astrophysical Journal Letters. All image processing, reduction and analysis was done entirely by myself with the guidance of my supervisor and co-authors of our article. The manuscript preparation and submission was done entirely by myself with the guidance of my supervisor and co-authors. The work published in the journal is included in the second and third chapter of this thesis. Works in chapters four and five are new techniques and are subjected to potential future publications. • Samra, Raminder S et al. Proper Motions and Internal Dyanmics in the Core of the Globular Cluster M71, The Astrophysical Journal Letters, Volume 751, Issue 1, article id. L12, 5 pp. (2012). iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Globular Clusters . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Colour Magnitude Diagrams . . . . . . . . . . . . . . . . . . 2 1.3 Distances to Globular Clusters . . . . . . . . . . . . . . . . . 4 1.4 Proper Motions . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Intermediate Mass Black Holes . . . . . . . . . . . . . . . . . 7 1.6 Messier 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6.2 Recent Work . . . . . . . . . . . . . . . . . . . . . . . 10 2 Data Reduction and Processing of Astrometric Data . . . 12 2.1 Adaptive Optics . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.1 Making the Medianed Image and Finding List . . . . 18 2.4.2 Making the Point Spread Functions . . . . . . . . . . 20 iv Table of Contents 2.4.3 Running ALLFRAME . . . . . . . . . . . . . . . . . 23 3 Analysis of Proper Motion Data . . . . . . . . . . . . . . . . 27 3.1 Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 Improving the Photometry . . . . . . . . . . . . . . . 27 3.1.2 Colour Cuts . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Proper Motion Distribution . . . . . . . . . . . . . . . . . . . 32 3.2.1 High Proper Motion Stars . . . . . . . . . . . . . . . 34 3.2.2 Proper Motion Isotropy . . . . . . . . . . . . . . . . . 36 3.3 An Upper Limit to the Mass of any Central IMBH . . . . . . 39 3.4 Summary of Proper Motion Analysis . . . . . . . . . . . . . 43 4 Reduction of Integrated Field Unit Data . . . . . . . . . . . 44 4.1 Introduction to Spectroscopy . . . . . . . . . . . . . . . . . . 44 4.1.1 Different Types of Astronomical Spectroscopy . . . . 45 4.2 Gemini Multi Object Spectrograph Integrated Field Unit . . 47 4.3 Messier 71 IFU Data . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Reduction of M71 IFU Data . . . . . . . . . . . . . . . . . . 51 4.5 Radial Velocities . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.6 Radial Velocity Dispersion . . . . . . . . . . . . . . . . . . . 68 5 The Distance to Messier 71 . . . . . . . . . . . . . . . . . . . 71 5.1 Geometric Distance . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 Stellar Model Distance . . . . . . . . . . . . . . . . . . . . . 71 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Appendices A NIRI Proper Motion Data . . . . . . . . . . . . . . . . . . . . 81 B IFU Radial Velocity Data . . . . . . . . . . . . . . . . . . . . 88 C Bulk Motion of Messier 71 . . . . . . . . . . . . . . . . . . . . 91 D Installation of DAOPHOT . . . . . . . . . . . . . . . . . . . . 94 E Extra Photometric Work . . . . . . . . . . . . . . . . . . . . . 98 v List of Tables 2.1 Exposure times for observations . . . . . . . . . . . . . . . . . 14 A.1 NIRI Proper Motion Data, the photometry is from the Ad- vanced Camera for Surveys . . . . . . . . . . . . . . . . . . . 87 B.1 Radial velocity data from the GMOS IFU, the photometry is from the Advanced Camera for Surveys. . . . . . . . . . . . . 90 vi List of Figures 1.1 A Colour Magnitude Diagram (CMD) of 47 Tuc. This CMD of 47 Tuc has the Hubble Space Telescope’s F606 filter plot- ted against the difference between the F606W and the F814W magnitudes. This CMD has not been cleaned for proper mo- tions and as a result is not exclusive for cluster members, therefore it shows the main sequence of the Small Magallenic Cloud stream which is located near the vicinity of the cluster. 2 1.2 A CMD of 47 Tuc with three different isochrones over plotted. The isochrones are for stars with similar abundances as 47 Tuc and only differ in age between themselves. No robust fitting technique was employed to make this plot. . . . . . . . . . . . 4 1.3 To calculate a geometric distance to a cluster, one has to assume circular orbits and the proper motion dispersion is equal to the radial velocity dispersion. . . . . . . . . . . . . 5 1.4 Relationship between various velocity components of a star. The object is located at a distance d from the Sun and has proper motion of µ radians s−1, vt = d × µ, where vt is the transverse velocity. . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Various black hole models are plotted against the velocity dispersion of NGC 6388. The best fit model is for an IMBH of mass ∼18*103M". Data for figure is from Lutzgendorf (2011) [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 The colour magnitude diagram of M71, data for figure is from Cuffey (1943) [7] . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 An image of the core of M71 using the 8m Gemini Telescope without the use of adaptive optics. The same field with adap- tive optics can be seen in figure 2.4. . . . . . . . . . . . . . . 13 2.2 Image from the Hubble Space Telescope of M71 image is 3.35’ x 3.35’ the rough location of the NIRI/ALTAIR AO image is the red square . . . . . . . . . . . . . . . . . . . . . . . . . . 15 vii List of Figures 2.3 Raw NIRI image of the core of M71 in inverted color to demonstrate the artifacts that were removed during the re- duction steps. The green circles are ghosting artifacts that appeared on some of the images. They are caused by internal reflections in the optical system. The ghosting artifacts were removed by employing a 12 step dither pattern. . . . . . . . . 16 2.4 A median combined image using the NIRI/Altair adaptive optics image in the K band. The green circle represents the cluster centre and the size of the circle represents the approxi- mate uncertainty. Note this image has been rotated compared to figure 2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 A contour plot of a star’s intensity near the edge of the field . 21 2.6 A contour plot of a star’s intensity near the centre of the field 22 2.7 The relative location of one cluster member across the field in each of the three imaging epochs. The colored dots represent the derived locations from each ALLFRAME run. The error in the final position is determined from the spread in the points for each epoch. . . . . . . . . . . . . . . . . . . . . . . 24 2.8 The X and Y positions of the same star as a function of time. The proper motion was found from fitting a straight line through those points, the slope of the line multiplied by the NIRI f/32 plate scale gives the proper motion. The dashed lines represent one-sigma errors. . . . . . . . . . . . . . . . . . 25 2.9 Proper Motion plot for 220 stars in our NIRI field. The mo- tions have been corrected for right ascension and declination. 26 3.1 Colour Magnitude Diagram of the NIRI field . . . . . . . . . 27 3.2 Colour Magnitude Diagram of Messier 71 obtained from the ACS Survey of Globular Clusters. The field here is the same from figure 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Colour Magnitude Diagram of Messier 71 obtained from the ACS Survey of Globular Clusters with the stars from our NIRI field (black circles) and the ones from Cudworth (black squares). The line at V = 17 is the limit for both datasets. For the NIRI data all stars brighter than 17 were saturated, whereas for Cudworth’s data V = 17 was the limit for detect- ing stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 Colour criteria for our proper motion sample. The black points represent our NIRI field stars whereas the green stars are Cudworth’s. . . . . . . . . . . . . . . . . . . . . . . . . . . 31 viii List of Figures 3.5 Left: Proper motions diagrams for both the NIRI field and Cudworth’s stars for which we have ACS photometry. Right: The proper motions of stars which survived the colour cut and the subsequent error cut from figure 3.4. The circle represents the cluster’s escape proper motion. As with figure 3.4 the black points are our proper motion data whereas the green are Cudworth’s. . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 A simulation of the galactic field for the same galactic coor- dinates of M71. For stars with V ≤ 17, a field 100x the ACS field was simulated. For stars V ≤ 17 a field 100x our NIRI field was simulated. The red stars are the ones that meet the colour cuts from figure 3.4. . . . . . . . . . . . . . . . . . . . 35 3.7 The proper motion vectors for the escaping stars that sur- vived the color and proper motion error cuts. The vectors are plotted to show the trajectory of the stars over the next 5000 years. The X marks the centre of the cluster. . . . . . . 36 3.8 Histogram of the proper motion angle with respect to the center of the cluster. Blue histograms are for stars in the NIRI field, and the dashed red line histogram is for stars from [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.9 Histograms for the values Qnr/Qnt resulting from the boot- strap resample of the data. The radial and tangential values of Qn are consistent with unity within 1σ for all stars. . . . 38 3.10 The observed proper motion dispersion and three different IMBH models. . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.11 The results from bootstrapping the proper motion data 25,000 times. The IMBH mass from each fit is binned here. The left- most bin from 0 ≤M" ≤ 5 peaks at 20,500 counts, implying that a very small central IMBH is the preferred fit. The red line represents the 90th percentile at 150M". . . . . . . . . . 40 3.12 A dispersion map of the field, obtained by running a circle with a 4′′ diameter across the field and calculating the dis- persion in each area. Observationally, there are no signs of radial dependence or an increase in dispersion towards the center which is represented by the X. . . . . . . . . . . . . . 42 4.1 An example of how an integrated field unit (IFU) works. The hexagons represent lenslets which have the ability of captur- ing a spectrum individually. . . . . . . . . . . . . . . . . . . . 46 ix List of Figures 4.2 GMOS IFU example data of a dwarf galaxy. At the top is the reconstructed IFU image with the left panel showing the sky field. Bottom shows the raw CCD image. The sky and object fields are arranged into alternating blocks on the CCD. Also prominent in the image are the chip gaps between the three GMOS CCDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 The transmission curve for the Calcium Triplet Filter at Gem- ini North . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 Examples of calibration images from the IFU. Top: The raw bias image supplied by Gemini. Bottom: A Raw GCAL flat from one of the nights of observations. . . . . . . . . . . . . . 51 4.5 Top: Calibration Copper-Argon arcs. Bottom: The raw twi- light image. There is a discontinuity in all IFU images in the centre chip. This is the location where the red slit’s dispersion ends and the blue slit’s starts. . . . . . . . . . . . . . . . . . . 52 4.6 Flowchart detailing the steps for IFU data reduction. The arrows have the Gemini IRAF task required for the steps. The red boxes denote final reduced files required extracting science data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7 Top: The Gemini Calibration flat after the results of step 1 is seen above. The chip gaps have been accounted for and the two slits have been stitched together. Bottom: The reduced twilight flat prior to wavelength calibration. . . . . . . . . . . 54 4.8 The response image. This is the final flat field. . . . . . . . . 55 4.9 Copper-Argon arc spectrum . . . . . . . . . . . . . . . . . . . 55 4.10 Wavelength calibration of the arc spectrum by fitting vari- ous functions. Having too many fitting parameters can cause erroneous fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.11 The effect of applying the wavelength transform onto the twi- light flats. The top figure shows the twilight flat prior to wave- length calibration. The bottom figure is the final calibrated flat. The Calcium Triplet lines are easily observed here as the three bright vertical lines in the image. Wavelength in- creases from left to right. The vertical axis represents the spectra from individual IFU fibers. The horizontal split in the bottom figure is due to the two slits used in the IFU. . . 57 4.12 Raw science image. Stellar spectra are the bright bands that run from left to right. . . . . . . . . . . . . . . . . . . . . . . 58 x List of Figures 4.13 Science image after all data reduction. Wavelength increases from left to right. Each of the 1500 IFU fibers are shown here increasing from bottom upwards. . . . . . . . . . . . . . . . . 59 4.14 Top: Map of the six IFU fields stitched together. There is no overlap between the fields. Each of the six fields appears to be split in half. This is due to the scaling of the image and the differences in throughput of the two IFU slits. Bottom: IFU map of the sky field located 1 arcminute away from the larger field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.15 Image of the cluster obtained by one of the three GMOS CCDs used for target acquisition. Red represents the two IFU fields, yellow represents the NIRI field also found in fig- ure 2.4. The blue is the field of the ACS from figure 2.2. . . 61 4.16 Cross correlation of two signals. Where the signals overlap there is a maximum in the correlation function. If these were two spectra, the radial velocity would be the offset of the peak of the correlation function. This is analogous to a sliding dot product of two signals. . . . . . . . . . . . . . . . . . . . . . 62 4.17 Twilight Spectra. The figure on the right shows a close up of the three regions of cross correlation when the lines are used individually. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.18 The spectra of one IFU fiber and the corresponding star from which the fiber was from. Brighter stars have many more illuminated fibers. . . . . . . . . . . . . . . . . . . . . . . . . 63 4.19 Spectra of a single IFU fiber for four different stars. Stars fainter than V = 20 did not have strong enough Calcium Triplet lines for velocity measurements. . . . . . . . . . . . . 64 4.20 The correlation function of two spectra. The fitting function here is a gaussian represented by the dashed curve. . . . . . 65 4.21 The response from CCD flexure. The left panel shows the arc spectrum with individual emission lines coloured. In the two figures on the right hand side, we see the result of cross correlating the coloured region against a median combined arc of that same region. The bottom panel is a zoom of the top panel to show how CCD flexure varies across the chip. . 67 4.22 The CMD of the IFU stars for which we have radial velocities is overlaid on the CMD of the ACS field. The cluster members are the stars which satisfy the colour criteria from figure 3.4 and the proper motion cut from figure 3.5. . . . . . . . . . . . 69 4.23 Radial velocities of the same stars from figure 4.22. . . . . . 70 xi List of Figures 5.1 The CMD from figure 3.2 with a median line running down the centre. Here V is now in Vega magnitudes. . . . . . . . . 72 5.2 Top: The fiducial cmd and the derivative of the cmd. Bottom: An 11 Gyr isochrone of stars with similar abundances as M71 and the corresponding derivative. . . . . . . . . . . . . . . . . 73 5.3 By shifting the isochrone so that the spike of the derivative matches that of the observed data, we get the distance mod- ulus. The left panel is over the entire CMD. The right panel is a close up of the turn off. . . . . . . . . . . . . . . . . . . . 74 C.1 An example of a NIRI image prior to star subtraction. . . . . 91 C.2 Four objects were found to survive both cuts in residual flux and sharpness. Three of them were found to be on the cluster CMD, the fourth was not. . . . . . . . . . . . . . . . . . . . . 92 D.1 Daophot Makefile. . . . . . . . . . . . . . . . . . . . . . . . . 95 D.2 The Makefile is now edited so Allstar is the next suite to be packaged. Run Makefile again and Allstar will be installed. . 97 E.1 Canada-France-Hawaii Telescope image of M71 from The CFHT Adaptive Optics Bonnette from 1991. With a field of view is 90′ on each side of the image, two images one in B and the other in R with a integration time of 120s for each filter. . . . 99 E.2 A CMD from the data in Figure E.1. The CMD is in uncali- brated magnitudes. . . . . . . . . . . . . . . . . . . . . . . . 100 E.3 Image of Messier 71 obtained using the Wide Field Infrared camera from CFHT. The image is 20′ x 20′. This is a H band image of the cluster which is found in the top left hand of the image. The red circle depicts a ∼ 7′ circle centred on the cluster centre . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 E.4 A CMD from the data in Figure E.3. The stars within the circle are represented with red points, they are likely cluster members, likely galatic field stars are represented by black markers, those are also the stars which were not in the circle from Figure E.3. . . . . . . . . . . . . . . . . . . . . . . . . . 102 xii List of Acronyms ACS = Advanced Camera for Surveys CCD = Charged Coupled Device CMD = Colour Magnitude Diagram FWHM = Full Width Half Maximum HST = Hubble Space Telescope GMOS = Gemini Multi-Object Spectrograph IFU = Integrated Field Unit IRAF = Image Reduction and Analysis Facility NIRI = Near Infrared Imager PSF = Point Spread Function xiii Acknowledgements This work was supported and supervised by my supervisor Dr Harvey Richer. Dr Richer’s insights and guidance in all aspects of this project allowed me to proceed down paths of discovery which ultimately made me a better scientist. I am also thankful for the numerous conversations I had with other members of the group including Dr Jeremy Heyl, Dr Kristin Woodley, Dr Gordon Walker, Dr Karun Thanjavur and fellow graduate student Ryan Goldsbury. Without everyone’s help this project would not have arrived at its current stage. I thank all those mentioned for their exceptional help and support. xiv Dedication The One who pervades the Universe also dwells in the body; whoever seeks Him, finds Him there. - Guru Granth Sahib Ji, Raag Dhanaasree, Ang 695 This thesis is dedicated to my father Gurmit Singh Samra. My dad was re- sponsible for me choosing to pursue my lifelong passion for astronomy, it was ultimately his decision that I enroll at the University of British Columbia and study astronomy. Dad your teachings and guidance are responsible for the person I’ve become. I hope I’ve made you proud. Even in these tough times your still the brightest star in my heart; I wish nothing but the best and clear skies. Additionally I would like to thank my loving wife Ravneet for her con- tinued support over the tenure of my graduate studies. Ravneet you’ve been instrumental in helping me get through the past few years and thanks for making life so fun and enjoyable. Astronomers look around for other planets and life in the universe, but to me the only one that matters is the one with you in it. xv Chapter 1 Introduction 1.1 Globular Clusters Star clusters come in two basic varieties; loosely packed open clusters and densely packed globular clusters. The two cluster types not only differ in their stellar densities but also in their ages and locations in the galaxy. Open clusters are almost always found in the disk of the Galaxy and tend to contain young stars. These clusters contain several thousand stars with a size of a few parsecs across. By contrast, globular clusters are found in a large halo surrounding the galaxy and contain some of the oldest stars in the universe. Globular clusters can have up to a million stars concentrated in a large spheroid many dozens of parsecs in size. The central regions of a globular cluster are very crowded with typical separations between stars being much less than a parsec. Our MilkyWay galaxy contains∼160 catalogued globular clusters. Larger galaxies such as the nearby Andromeda Galaxy (Messier 31) have about 500, and galaxies such as Messier 81 are thought to contain over 10,000 globular clusters [28]. The primary constituents of globular clusters are stars. There is little gas in the space between the individual stars, and there is no evi- dence for the existence of dark matter in globulars as well. As these stars were formed from the same gas cloud near the same time, they have very similar composition. Additionally, stars in the cluster can also be approx- imated to be the same distance from the Earth. It is these properties of globular clusters that make them ideal candidates for studying stellar evo- lution, stellar dynamics, galactic evolution and assist in putting an age on the universe as a whole. Generations of star formation ultimately leave a mark on the composi- tion of interstellar material, thus astronomers group stars according to their metallicity. Metallicity is expressed as [Fe/H] = log10(NFe/NH)star − log10(NFe/NH)" (1.1) Where [Fe/H], is the logarithm of the ratio of a star’s iron abundance 1 1.2. Colour Magnitude Diagrams compared to the Sun’s. Metallicity can then be used to distinguish disk populations from halo populations. Disk clusters generally have [Fe/H] ≥ -0.8 and halo clusters [Fe/H] ≤ -0.8. [31]. Clusters which are metal rich have [Fe/H] ∼ +0.25, whereas metal poor clusters have [Fe/H] ∼ -2.5. Although iron is used as a measure of metallicity, it is far from being the most abundant heavy element present. Iron’s strong spectrum in the visible band allows it to be the ideal spectral feature for identifying abundances. 1.2 Colour Magnitude Diagrams Horizontal Branch Red Giant Branch Main Sequence White Dwarfs Small Magellanic Cloud Main Sequence Turnoff Figure 1.1: A Colour Magnitude Diagram (CMD) of 47 Tuc. This CMD of 47 Tuc has the Hubble Space Telescope’s F606 filter plotted against the difference between the F606W and the F814W magnitudes. This CMD has not been cleaned for proper motions and as a result is not exclusive for cluster members, therefore it shows the main sequence of the Small Magallenic Cloud stream which is located near the vicinity of the cluster. 2 1.2. Colour Magnitude Diagrams To determine the effective temperature for a large sample of stars would require a detailed spectral line analysis for each star. However, it is much faster and efficient to determine the colour index of an individual star. Once an apparent magnitude of a star in a particular filter is measured, a colour- magnitude diagram (CMD) can be constructed. All stars will end up some- where on a CMD depending on their stage in stellar evolution. A random sample of stars will form a pattern on the diagram but will have scatter, as the stars were born at different times, have different metallicities or their distances are different. If the stars are all from the same cluster, thus formed nearly at the same time, a CMD will have a well defined narrow sequence. From this sequence, information about the stars and the particular cluster can be obtained. Globular clusters have such a sequence and it can be seen in figure 1.2. All stars will spend most of their lives on the main sequence where they undergo Hydrogen core burning. More massive stars are located higher up on the main sequence and less massive stars are found at the lower end. Once a star completes Hydrogen to Helium fusion in its core, it will reach the main sequence turn off point and migrate to the red giant branch. It is worth noting that a star will not move up or down the main sequence during its Hydrogen core burning phase, rather the main sequence turn off point will migrate downward with time. As stars leave the main sequence, they swell up and increase their size, become redder and exhibit a large increase in brightness. During this phase, hydrogen is burning in a shell around the Helium rich core. With the onset of Helium burning in the core, the star will enter the horizontal branch. Evolutionary processes are now much faster than they were when the star was on the main sequence. Once on the horizontal branch, a star will enter the asymptotic giant branch and exhibit large pulsations which cause the outer layers of the star to be shed into a planetary nebula. The core of the star remains as a hot white dwarf star. White dwarf stars are the last remains of a sun-like star and it will slowly cool with time. White dwarfs can be found on the lower left side of a CMD. The exact location of a white dwarf cooling sequence can be used with models to determine the age of a particular cluster. 3 1.3. Distances to Globular Clusters 1.3 Distances to Globular Clusters Figure 1.2: A CMD of 47 Tuc with three different isochrones over plotted. The isochrones are for stars with similar abundances as 47 Tuc and only differ in age between themselves. No robust fitting technique was employed to make this plot. One of the challenges in astronomy and astrophysics is calculating distances to celestial objects. Several methods are used to determine distance. This is dependent upon the type of object (ie: galaxy, star, star cluster or planet) and the quality of the available data. For nearby objects in the solar system, 4 1.3. Distances to Globular Clusters radar ranging is an accurate way to determine distances. This technique can- not work for anything beyond the solar system. Nearby stars can have their distance determined using parallax, which requires multiple measurements of the star’s parallax angle. For stars which are further, their distance is determined via a process known as main-sequence fitting. Once an accu- rate distance for a nearby star is known via parallax and its spectra is also established, its absolute magnitude can be determined. The same spectral type star can then be found elsewhere and after determining the apparent magnitude, its distance can then be computed. This technique can then yield stellar evolution models which can be used to construct isochrones. Isochrones are theoretical curves that simulate the life of stars, all of which have the same chemical abundances but only differ in mass; such is the case in a globular cluster. As isochrones are theoretical models, they yield absolute magnitudes versus colour curves. To determine distance, an isochrone simply has to be shifted vertically to get the distance modulus. Horizontal shifts will determine the amount of reddening between the cluster and observer. This technique can also determine a cluster’s age, however recent evidence shows that globular clusters may have multiple stellar pop- ulations. As a result this may make fitting isochrones difficult. Figure 1.3: To calculate a geometric distance to a cluster, one has to assume circular orbits and the proper motion dispersion is equal to the radial velocity dispersion. 5 1.4. Proper Motions Another method which is independent of stellar evolution models is to calculate a geometric distance to a cluster. This simply assumes that stars have isotropic orbits and the proper motion dispersion in each direction is equal to the radial velocity dispersion. Figure 1.3 shows the geometry for this method. The accuracy of the geometric distance can be increased if there are stars for which both the proper motions and radial velocities are known. Additionally, having more stars in the samples can reduce uncertainty. 1.4 Proper Motions SUN PROPER MOTION TRANSVERSE VELOCITY RADIAL VELOCITY SPACE VELOCITY µ Figure 1.4: Relationship between various velocity components of a star. The object is located at a distance d from the Sun and has proper motion of µ radians s−1, vt = d× µ, where vt is the transverse velocity. As stars travel through space, their true space velocity can be measured by the observer in two orthogonal components; radial velocity and proper motion (see figure 1.4). The radial velocity of a star is the line of sight ve- locity measured directly via the doppler effect using a spectroscope. Proper 6 1.5. Intermediate Mass Black Holes motions is the angular change of a star’s position with time. It can be mea- sured with respect to background stars or objects of known proper motion. Proper motions are measured in seconds of arc per year and require multi- ple epochs of imaging. Traditionally, proper motions were measured using images with baselines decades apart. However, with the onset of modern CCD cameras and telescopes, baselines of just a few years can be used to determine proper motions of stars. Proper motions are instrumental for studying the dynamics of star clus- ters. As a star cluster has its own bulk proper motion, the proper motions of its stars are distinct from galactic field stars. Therefore, cluster members can be isolated for a sample of cluster only stars. From studying the motions of stars near the core of a globular cluster or galaxy, it is possible to obtain the mass of any central dark mass. Proper motion studies of stars in the vicinity of the galactic centre have been used to determine the existence of a super massive black hole SGR A* [11]. Similarly, proper motions can be used to determine the existence of a central massive black hole at the centre of a globular cluster. 1.5 Intermediate Mass Black Holes It is well established that there are two known mass ranges of black holes. Stellar mass black holes are the remnants of massive stars and can be ob- served in accreting binary systems. There is also evidence for the existence of large super massive black holes (SMBHs) at the centers of galaxies. These typically have masses that range from ∼106M" to ∼109M". SMBHs have a tight correlation between their mass and the velocity dispersion of the galaxy which they reside. Extrapolating this relation down to velocity dispersions typically found for globular clusters, black holes with masses of ∼103−4M" could exist. As there is little gas to accrete in a globular cluster, detection via radio and X-ray emission is challenging. A more efficient method is to explore the kinematics of the central regions of a cluster. Wyller (1970) [30] proposed this method more than forty years ago, however it was limited by the quality of the observations. To detect a central black hole, spatial resolution on the order of the sphere of influence of the black hole must be achieved; typically 1-2′′for globular clusters. Instruments such as the Hubble Space Telescope and ground based observatories with adaptive optics can resolve the internal motions of stars, whereas multi object spectroscopes and integrated field units can also provide the necessary resolution. 7 1.5. Intermediate Mass Black Holes Evidence for the existence of IMBHs is still debatable. Noyola et al. (2008) [15] found evidence of an IMBH in ω Centauri, the largest globular cluster in the Milky Way galaxy. However, ω Cen. may not be a typical globular cluster rather the core of a dwarf spheroidal galaxy. Additionally, this claim is met with skeptism as Anderson and van der Marel (2009) [2] show evidence that counters this claim. They claimed that Noyola et al (2007) were not at the correct centre of ω Cen and calculated a different cluster centre which is 12′′ away, therefore they found no evidence for a central IMBH in ω Cen. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 10 12 14 16 18 20 22 24 26 28 30 log r (arcsec) V rm s  ( k m /s )   M BH  = 0 M BH  = 18 x 10 3 M BH  = 44 x 10 3 Figure 1.5: Various black hole models are plotted against the velocity disper- sion of NGC 6388. The best fit model is for an IMBH of mass ∼18*103M". Data for figure is from Lutzgendorf (2011) [14] Another globular cluster NGC 6388 has evidence for a central black hole. Using the kinematic signature of the central velocity dispersion in the core of this cluster, Lutzgendorf et al (2011) [14] show evidence for the existence 8 1.6. Messier 71 of a ∼18*103M" IMBH. 1.6 Messier 71 1.6.1 History Messier 71 (NGC 6838) was discovered by in 1746 by Swiss astronomer Philippe Loys de Chseaux as the thirteenth object in his catalogue. M71 was subsequently rediscovered by Gottfried Koehler in 1772 and by Pierre Mechain on June 28th 1780. Charles Messier would classify it as his 71st object in his catalogue of faint celestial objects. Messier did not see any stars in the cluster, as his first claims were “its light is very faint and it contains no star; the least light makes it disappear”. 0.5 1 1.5 2 2.5 11 12 13 14 15 16 17 Red Colour Index A p p a re n t R e d  M a g n it u d e Figure 1.6: The colour magnitude diagram of M71, data for figure is from Cuffey (1943) [7] 9 1.6. Messier 71 Messier 71 was classified as a condensed open star cluster until the 20th century. Harlow Shapley had classifed it as the densest of all types in his classification scheme for open clusters. Cuffey (1943) [7] performed photom- etry and made a colour-magnitude diagram of red giant branch members. He recognized that M71’s CMD (see figure 1.6.1 ) resembled that of a globular cluster. He also calculated the distance to be about 4000 parsecs. 1.6.2 Recent Work In 1971 Arp and Hartwick [3] published the first modern photographic and photoelectric observations. They used the UBV system to yield a CMD that was typical of a metal rich cluster that exhibited a short red horizontal branch and a gently sloping giant branch. Additionally, they calculated the distance modulus (m−M)o = 13.07 ± 0.21, [Fe/H] = -0.30±0.2 and an age of 7.6(+3.1,-2.3) x 109 years. The age derived was younger than most halo globular clusters. In 1984, Cudworth [6] performed photometry and studied proper motions of 350 stars with V ≤ 16 in the cluster [6]. Proper motions were used to clean the cluster CMD and he noted that the horizontal branch and lower giant branch resembled that of 47 Tuc. However, the upper part of the branch was bluer and brighter in M71. Proper motions were used to detect an internal velocity dispersion. He also studied the cluster’s space velocity and determined it to be a very low, ∼50 km/s, characteristic of a disk-population object. The first modern CCD observations were conducted by Richer and Fahlman in 1988 [18] as they carried out U and V band CCD imaging in the centre of the cluster to 205′′ away. They found over 10,000 stars and investigated radial effects in the mass to luminosity relationship. They found that the global luminosity function was found to be flatter than 47 Tuc, a cluster with similar chemical abundances. The luminosity function favours the idea that the cluster is dynamically relaxed as the function shows an increase in the number of low luminosity stars at larger distances. By comparing the cluster’s mass to light ratio, they found that a significant fraction of the cluster’s mass is contained in stars outside the range of luminosities covered. Models placed the dark mass as either neutron stars, white dwarf stars or low mass sub-dwarf stars. Current modern values for M71 can be found in Harris’ 1996 catalogue [13]. The cluster’s centre was found by Goldsbury et al (2010) [12], it is at right ascension, RA = 19h53m46s.25 and declination DEC = +18◦46’46′′.7 at J2000 coordinates. Harris places the distance to be 4.0 kpc from the Sun, 10 1.6. Messier 71 [Fe/H] = -0.73, half light radius rh = 1.65′, tidal radius, rt to be at 8.96′ from the core. The core radius is rc = 0.63′, larger than 70% of all galactic globulars. This large core radius was one motivation for our study as it could be “fluffy”due to a central black hole. 11 Chapter 2 Data Reduction and Processing of Astrometric Data 2.1 Adaptive Optics Prior to the development of adaptive optics, ground based observatories had their resolution limited to that of the sky conditions at the observation site. To unlock the full potential of a telescope and operate near the diffraction limit telescopes had to be placed above the atmosphere in orbit. However, there are technical and financial limitations to the size of telescopes that can be placed in space. With the onset of modern adaptive optics, large optical telescopes now have the capability to operate at the diffraction limit. Adaptive optics work by reducing the effect of wavefront distortions by measuring the distortions using a wavefront sensor and compensating for the distortions via a deformable mirror. As starlight enters the Earth’s atmosphere it experiences turbulence from various temperature layers and wind speeds. As a result, the angular resolution suffers to that of the seeing conditions. Adaptive optics can correct for this using natural and laser guide stars. Often the science target is too faint to be used as a reference star for the measurement of wavefront. As a result, a nearby bright star must be used. Light from a reference star passes through approximately the same atmospheric turbulence as the science target so the same correction can be used. However, by having a nearby bright star (typically 12-15 V magnitude) in addition to the limitations of adaptive optics to small fields, only a small area of the sky can be used for natural guide stars. Laser guide stars offer an alternative to natural guide stars. They work by employing a 589 nm sodium laser to excite sodium atoms 90 km high in the mesosphere. The sodium atoms glow as a result and are perceived as a star by the ground-based telescope which can use the wavefront distortions of the laser guide star for correcting the distortions in the science data. Figure 12 2.2. Data 4.1 shows the core of Messier 71 as imaged by the 8m Gemini Telescope without the use of adaptive optics. Figure 2.1: An image of the core of M71 using the 8m Gemini Telescope without the use of adaptive optics. The same field with adaptive optics can be seen in figure 2.4. 2.2 Data In three separate imaging epochs we obtained H (centered at 1.65 microns) and K band (centered at 2.2 microns) imaging of the inner 22 x 22 arc- seconds of M71 (see figure 2.2). The images were obtained by using the NIRI/ALTAIR Adaptive Optics system on the 8m Gemini North Telescope. For best imaging results, imaging was only conducted during the best see- ing conditions at the summit of Mauna Kea. For all three imaging epochs, the set up was identical. The Near Infrared Imager (NIRI) was set to f/32 with a CCD size of 1024 by 1024 pixels corresponding to a plate scale of 0.0219′′ pixel−1. This yielded a field of view of 22′′ x 22′′ centred on star 13 2.3. Data Reduction AH-81 ([3]), a twelfth magnitude star close to the cluster centre. A twelve step dither pattern was also employed to aid in the removal of artifacts during image processing. Date Filter Exposure (ksec) FWHM (′′) August 2005 H 15 0.085 August 2005 K 16 0.081 June 2007 H 14 0.083 June 2009 K 23 0.077 Table 2.1: Exposure times for observations 2.3 Data Reduction The data for M71 was downloaded from the Canadian Astrophysical Data Centre. The processes outlined below were the same for each of the three imaging epochs and filters involved. However each epoch and filter was processed separately to account for any potential changes in the imaging system over the baseline of imaging. Data reduction of Gemini data was performed using the Gemini IRAF package which was supplied by the Gemini Observatory. Gemini gives users a generic cookbook for reduction of NIRI data. Here we go into detail on reduction of data. Figure 2.3 shows a raw science image. The first step in reduction is to use the task NPREPARE. This task updates the raw data headers and creates extensions in the multi exposure fits (MEF) images. This task requires updated settings of the detector arrays used in the imaging. It adds new header keywords which give an estimate of the gain, read noise, saturation level, array bias voltage and the threshold for data when it deviates from linearity. NPREPARE is run on all science and calibration data, and can be run simultaneously on all data. The next task is to create a master flat field image. This flat field image can correct for illumination variances across the detector and some of the streaking artifacts from the CCD construction. NIFLAT require two types of flat field images; those taken with a lamp on and off. Lamp on and off images are obtained by shining a bright lamp onto the detector array and then removing it. This allows for the separation of the thermal signature of the detector for the sensitivity response. The exposure times for the flats was 4 seconds each. Multiple exposures are used to construct a median flat field image. This is done separately for each imaging epoch and filter. 14 2.3. Data Reduction Figure 2.2: Image from the Hubble Space Telescope of M71 image is 3.35’ x 3.35’ the rough location of the NIRI/ALTAIR AO image is the red square 15 2.3. Data Reduction 200 400 600 800 1000 1200Figure 2.3: Raw NIRI image of the core of M71 in inverted color to demon- strate the artifacts that were removed during the reduction steps. The green circles are ghosting artifacts that appeared on some of the images. They are caused by internal reflections in the optical system. The ghosting artifacts were removed by employing a 12 step dither pattern. 16 2.4. Data Processing Likewise, this task is used to create a master dark frame. Darks are captured with the camera shutter still closed, essentially capturing the noise in the imaging sensor. Dark frames of 140 second exposures were used to create a median combined master dark frame. The final task is to run the IRAF task NIREDUCE. NIREDUCE takes in the raw science data, subtracts the bias and divides by the master flat and darks. After running NIREDUCE, most of the array artifacts are removed. Those which are not removed are easily distinguishable from stellar objects during the data processing. This task is done on all images from every epoch and filter individually. This results in about ∼700 images from the three imaging epochs. 2.4 Data Processing Majority of the data was processed and analyzed using DAOPHOT [26], a standalone version of the software which allows for more freedom than the IRAF version. IRAF is still used to help with the identification of stars. A detailed data processing cookbook is available in [26]. The processing steps are outlined in § 2.4.1, § 2.4.2 and § 2.4.3. These sections explain how the median image, point spread functions and ALLFRAME were run. Finding the Stars The first task was to make a medianed image. This image would be used to create a finding list for all of the objects in the field. Ideally the medianed image would also not have any artifacts from the reduction, as they would have been filtered out. Before a medianed image could be made, the stars had to be identified. DAOPHOT was used to identify the stars. IRAF’s IMEXAMINE routine was run to find the full-width-half-maximum of the stars in the field. The average FWHM was ∼ 3.5 pixels. It had little variance between the different nights of observations. Once the FWHM was known, the standalone version of DAOPHOT could be employed to find the locations of the stars on the chip. The FWHM was computed for each of the H and K filters used and IMEXAMINE was used to find the FWHM on each of the nights of observations for all three epochs. Registration As the data had been dithered to a 12 step pattern, it was important to put the data on the same coordinate system. This was done by using the DAO- 17 2.4. Data Processing MATCH and DAOMASTER routines. The data were fed into DAOMATCH and it did a basic four term match which allows for the translation, rotation and scaling of the data. This task works automatically and produces the input file for the more versatile task, DAOMASTER. DAOMASTER first asks for the minimum number of frames an object has to be on for it to consider translating it; this was set to 70%. Then the software asks for the amount of terms we wish to incorporate into a transfer function to transform the data. As there was only simple translations between the dither pattern, a simple six term transformation equation was used for registeration. The software then transforms the coordinates of each object x1, y1 into x2, y2 via equations 2.1 and 2.2. The software then asks the user to pick a matching radius, a radius of 10 pixels was originally used. This radius is the distance of which the program searches for a matching star between frames. The pro- gram will then ask the user to reduce the matching radius and outputs how many stars remain for the given criteria. The user then slowly decreases the matching radius until the program converges onto a final number of detected stars. Finally, before DAOMASTER exits, it asks for the type of output file the user wants. First a transformation file was created which contains the values of the six constants for equations 2.1 to 2.2. Additionally new .coo files were outputted. The .coo files contain the transformed coordinate lists, allowing the user to find the same star across various frames with new x and y coordinates. x2 = A+ Cx1 + Ey1 (2.1) y2 = B +Dx1 + Fy1 (2.2) 2.4.1 Making the Medianed Image and Finding List Once all the stars were on the same coordinate, list aperture photometry was performed in DAOPHOT using the PHOT command. After perform- ing aperture photometry, we had files with magnitudes of stars and their positions on each of the frames. It was now possible to construct a median image of the dataset. To make a medianed image MONTAGE2 was used. The input for this task was the transformation file outputted by DAOMAS- TER. MONTAGE2 then asks the user minimum number of frames an object must appear in before it is included. For all datasets a minimum thresh- old of 20% of the total number of frames was chosen, thus eliminating any remaining artifacts such as ghosts and hot pixels. Due to the dither pat- tern, the output median image was larger at 1100 x 1100 pixels, therefore more stars could be found on this image. The median image was then run through DAOPHOT’s FIND command to find the positions of every star in 18 2.4. Data Processing the median image. Originally, DAOPHOT returned ∼400 objects for which it had detected to be star-like. Most of these were found around the bright saturated stars. These false detections were then easily manually removed and a final list containing 220 stars was generated. The median image was made using the 2009 K band data set. This epoch was used as an anchor for finding the differential proper motions of stars. ! !" # $ % % % &! ! !' ( )* + )% % !" , -. / 0 . 1 2 3 / & "!"#$%%%&!!!'4)56)%%!"/0.123/& *+ *+7$ *+7* *+7+ *+7( *8 *87$ 6% 6$ 6* 6+ 6( *% *$ ** *+ *( 5% Figure 2.4: A median combined image using the NIRI/Altair adaptive optics image in the K band. The green circle represents the cluster centre and the size of the circle represents the approximate uncertainty. Note this image has been rotated compared to figure 2.3. 19 2.4. Data Processing 2.4.2 Making the Point Spread Functions While running the IMEXAMINE routine to check the FWHM of the objects as mentioned in section 2.4 it was noted that stars close to the edge of the frame had distorted shapes while stars closer to the centre had well define concentric ring shapes as seen in Figures 2.5 & 2.6. This is a result of anisoplanatism, that is stars near the edge of the field appear distorted compared to those in the centre. Anisoplanatism is a result of the limitations of adaptive optics. The corrections made for the stars at the centre of the field are not necessarily the same as the edge of the field. As the shapes of the stars varies across the frame the point spread function (PSF) was modeled in a way so it would also vary across the frame. 20 2.4. Data Processing Figure 2.5: A contour plot of a star’s intensity near the edge of the field 21 2.4. Data Processing Figure 2.6: A contour plot of a star’s intensity near the centre of the field As the stars from the coordinate and the aperture photometry lists were already registered on the same coordinate system, the task of making the PSFs was dramatically easier. Candidate stars were selected automatically via DAOPHOT’s PICK routine which outputs a list of possible good PSF stars. The PSF candidate stars were then examined to see if they were suitable candidates, with the unsuitable stars being removed. Unsuitable stars were either saturated, near the frame’s edge or were in close proximity to a neighbouring star. Once a good list of PSF stars were generated, PICK was run on all of the frames from all available datasets. To construct the PSF, it was determined that using a three free parameter Moffat function would produce the best results. This was set by changing DAOPHOT’s ANALYTICAL MODEL PSF parameter to 2.00. For a full discussion on 22 2.4. Data Processing the PSF steps, see the DAOPHOT II user’s manual [27]. To test the quality of the PSF, science images had their stars subtracted. A good subtraction would render sky background in place of every subtracted star. 2.4.3 Running ALLFRAME ALLFRAME was the final step in the data processing procedure. The pro- gram requires four types of files to run: the file containing the transformation constants (§ 2.4), the master finding list (§ 2.4), individual PSFs for each frame (§ 2.4.2) and ALLSTAR headers for each file. To generate the ALL- STAR headers, run the ALLSTAR task and input the image, corresponding PSF and the aperture photometry file. ALLSTAR outputs a file that con- tains values of the read noise, gain, high and low good data values and the fitting radius for the frame. Once all of these files are ready, ALLFRAME is ready to run. To get the astrometric positions of the stars, ALLFRAME is run in groups of ∼20 files separately for each epoch with the same master finding list. This results in ∼8 positions of each object for each imaging epoch. ALLFRAME performs PSF photometry on all of the frames and calculates the positions and magnitudes of the objects identified in the master finding list. The output is a file that contains the averaged positions and magni- tudes. To find the position of a star in each of the three imaging epochs, the average of the ∼8 positions was taken and the error was the 1 standard deviation of the positions. See figure 2.7 for the position of one star across the three imaging epochs. 23 2.4. Data Processing 922.5 922.6 922.7 922.8 922.9 350.44 350.46 350.48 350.5 350.52 350.54 X Pixels Y  P ix e ls 2009 2007 2005 Figure 2.7: The relative location of one cluster member across the field in each of the three imaging epochs. The colored dots represent the derived locations from each ALLFRAME run. The error in the final position is determined from the spread in the points for each epoch. Once the astrometric positions and errors in position were found for each of the 220 stars in the NIRI field, we determined the proper motions. To calculate proper motions, linear time dependent curves were fit for each star’s position across the field. The best fitting slope gave the proper motion in x and y. To get the error in the proper motion, the position of the star in x and y for each epoch was chosen randomly weighted via the error in position. In other words, if a star has position x and error δx the new position was x′ but it had a 68% chance to remain 1σ from its calculated position x and a 95.4% chance to be within 2σ of x. After the determination of the differential proper motions of the 220 24 2.4. Data Processing 922.4 922.5 922.6 922.7 922.8 922.9 923 X  P ix e ls 2006 2008 2010 350.44 350.46 350.48 350.5 350.52 350.54 Year  Y  P ix e ls Figure 2.8: The X and Y positions of the same star as a function of time. The proper motion was found from fitting a straight line through those points, the slope of the line multiplied by the NIRI f/32 plate scale gives the proper motion. The dashed lines represent one-sigma errors. 25 2.4. Data Processing !! !" # " ! !$ !% !! !& !" !' # ' " & ()*+,)-.*/0*1-!-234567)8 ( )* + , )- . * /0 * 1 -" -2 3 4 5 67 )8 Figure 2.9: Proper Motion plot for 220 stars in our NIRI field. The motions have been corrected for right ascension and declination. stars in our field, it was now possible to construct a proper motion diagram. Figure 2.9 shows the proper motions in right ascension and declination for our stars. The swath of stars running diagonally from the bottom left to upper right are likely galactic field stars. 26 Chapter 3 Analysis of Proper Motion Data In this chapter we show the steps for the analysis of our proper motion data. Majority of this chapter was published in Samra et al (2012) [22]. 3.1 Sample Selection 3.1.1 Improving the Photometry ! !"# !"$ !"% !"& '! '' '# '( '$ ') '% '* '& '+ ,!- , ./ 01 2 34 5 6 7 1 38 9: Figure 3.1: Colour Magnitude Diagram of the NIRI field 27 3.1. Sample Selection One of the caveats of studying stars in the core of a globular cluster is the possibility of finding stars ejected by interactions with a possible central black hole. Therefore, for selection of stars for our analysis we could not simply select stars from the proper motion sample alone. Instead we de- cided selection would be based upon a star’s position on a cluster’s colour magnitude diagram. ! !"# $ $"# % %"# $! $# %! %# &!' & Figure 3.2: Colour Magnitude Diagram of Messier 71 obtained from the ACS Survey of Globular Clusters. The field here is the same from figure 2.2. From our NIRI data we had photometry in the infrared filters H and K. As there is very little separation between the two filters in wavelength space, our colour magnitude diagram was very narrow in colour space. Figure 3.1.1 28 3.1. Sample Selection shows the infrared CMD for our data. From this, it is difficult to determine which stars are field or cluster members. Fortunately, the Hubble Space Telescope had conducted observations of M71 during the ACS Survey of Galactic Globular Clusters ([1, 23]). We matched our NIRI stars with stars from the ACS using the Daophot routine DAOMASTER and obtained V and I photometry for 215 stars in our NIRI field. Figure 3.2 shows the CMD of the entire cluster. A previous proper motion study of M71 was performed by Cudworth (1985) [6]. We used the 358 stars listed in that paper’s table to verify our proper motions. We first matched Cudworth’s stars to the ACS photometry to obtain colors for 208 stars. The resulting CMD can be found in figure 3.3. 29 3.1. Sample Selection Figure 3.3: Colour Magnitude Diagram of Messier 71 obtained from the ACS Survey of Globular Clusters with the stars from our NIRI field (black circles) and the ones from Cudworth (black squares). The line at V = 17 is the limit for both datasets. For the NIRI data all stars brighter than 17 were saturated, whereas for Cudworth’s data V = 17 was the limit for detecting stars 3.1.2 Colour Cuts As discussed previously, we did not wish to make a selection of stars based upon proper motion. It is possible that a star may have a proper motion which is capable of escaping from the cluster. Therefore, if we perform a strict colour cut, stars which are likely galactic field stars will be removed. 30 3.1. Sample Selection !"# !"$ !"% & &"' &"# &"$ &"% ' '"' &! &' &# &$ &% '! '' '# (!) ( Figure 3.4: Colour criteria for our proper motion sample. The black points represent our NIRI field stars whereas the green stars are Cudworth’s. We used stars which had total proper motions less than 0.8 mas/yr (half the proper motion dispersion of all stars) to define a fiducial main sequence. Our cluster sample consists of all stars within 0.05 magnitudes in color of the main sequence fiducial. We then performed the same steps for Cudworth’s stars (see figure 3.4). Stars were then removed based upon their errors from both the NIRI and Cudworth’s winnowed samples. Stars which had proper motion errors greater than 2σ were rejected. This resulted in 150 cluster members for our NIRI field and 94 stars from Cudworth’s sample. These 94 stars ranged in radial distance between 6′′-150′′ from the cluster center, 2 of which were in our NIRI field for which we did not have proper motions due to them being saturated on our frames. Figure 3.5 has both our NIRI field proper motions and Cudworth’s proper motions included. The final proper motion sample we used for this study are the stars in the right hand side figure. 31 3.2. Proper Motion Distribution !! !" # " ! !$ !! !" # " % &' ( ) &* + ' ,- ' . *! */ 0 1 2 34 &5 %&'()&*+',-'.*"*/01234&5 !" # " ! Figure 3.5: Left: Proper motions diagrams for both the NIRI field and Cudworth’s stars for which we have ACS photometry. Right: The proper motions of stars which survived the colour cut and the subsequent error cut from figure 3.4. The circle represents the cluster’s escape proper motion. As with figure 3.4 the black points are our proper motion data whereas the green are Cudworth’s. 3.2 Proper Motion Distribution To quantify the velocity dispersion of the cluster, one is tempted to use the standard deviation. However, a single high-velocity interloping star in the sample can skew the standard deviation to arbitrarily large values. There- fore we seek an estimator of the dispersion that is robust to outliers. Some familiar robust measurements of scale are the inter-quartile range (IQR) and the median absolute deviation (MAD). The IQR is the difference between the 75th and 25th percentile of the data whereas MAD is the median of the absolute values of the difference between the data values and the overall me- dian of the data set. Rousseeuw & Croux (1991) [20] propose Qn, motivated by two of its strengths — its ability to deal with skewness and its efficiency with gaussian distributions. It is defined over all the pairs of stars in the sample, Qn = a× first quartile of (|µi − µj |) : i < j) (3.1) 32 3.2. Proper Motion Distribution where a is a constant dependent upon the size of the sample (for large sam- ples a→ 2.2219) and µi and µj are observed proper motions in a particular direction of pairs of stars in our sample. One further advantage of the Qn estimator is that it approximates the standard deviation for distributions which are significantly different from normally distributed distributions such as those close to a uniform distribution. We treat Qn as a proxy for the stan- dard deviation for the remaining analysis. For example, we correct for the errors in the observed proper motions from the estimated errors to arrive at the proper motion dispersion: Q2n = Q 2 no − 1 N ∑ $2µi (3.2) where Qn is the error corrected dispersion, Qno is the observed non-error- corrected proper motion dispersion and $µi is the error associated with the proper motion of each star. The error in the dispersion was calculated by bootstrapping the proper motions and their errors 100,000 times and taking the standard deviation of the bootstrapped dispersions. This results in a one-component core dispersion of Qn = 179 ± 17 µas/yr. Using the familiar standard deviation method to calculate the dispersion, we obtain a value of σ = 185 ± 18 µas/yr, that is after removing stars with proper motions greater than the cluster’s escape proper motion. We used Cudworth’s stars (see the right panel of figure 3.5) to determine the proper motion dispersion for stars which had radial distances greater than our NIRI field and were likely cluster members. We found for stars in the inner 70′′, the dispersion was 184 ± 37 µas/yr. For stars with distances greater than 70′′ and up to 150′′ the dispersion was 281 ± 33 µas/yr. These results are similar to the published values from Cudworth’s paper [6]. At the distance of 4 kpc, our proper motion corresponds to a velocity dispersion of 3.3 ± 0.4 km/s, a value greater than the radial velocity dis- persion of 2.0 km/s obtained by Rastorguev & Samus (1991) [17] and 2.8 ± 0.6 km/s from Peterson & Latham (1986) [16]. However, those velocity dispersions were calculated for giant stars which were far away from the center of the cluster; a constant dispersion is still within the uncertainties. Equating our measured proper motion dispersion to the velocity disper- sion from [16] we arrive at a geometric distance to the cluster at 3.47±0.84 kpc. Although it is consistent with previous distances it is risky to equate dispersions from radially different locations in the cluster, and it is expected that the dispersion may change over a large radial distance. To get a much more accurate distance one would have to use the same stars for radial ve- locities as well as proper motions. However, we will explore this further in 33 3.2. Proper Motion Distribution chapter 5.2. Relaxation Time We can then use the observed velocity dispersion and stellar density to estimate the relaxation time in the NIRI field. Spitzer (1987) [25] gives the general form for the relaxation time to be tr = v3 1.22n(4piG2m2∗) ln(0.4M/m∗) (3.3) where v is the projected root mean square velocity, n is the number density of stars in the field, and m∗ is the typical mass of a star, taken to be ∼ 0.5 M". This results in a relaxation time of∼ 39d64 Myr (where d4 is the distance to the cluster divided by 4 kpc). This value is close Harris’ estimated core relaxation time of ∼ 34 Myr. However, if we factor in the ∼ 20% discrepancy in the distance estimations, the relaxation time can be as little as 21 Myr or high as 70 Myr. 3.2.1 High Proper Motion Stars From the CMD in figure 3.4, we find 6 stars in the NIRI field which have high proper motions and survived the winnowing and error cuts. If any of these stars are escaping the cluster, we could determine the cluster’s evaporation timescale purely from observations. However our observed field lies at low Galactic latitude (b = −4.56 degrees), therefore the field may be subject to heavy contamination from the Galactic field as noted by [6]. To check for possible interlopers, we used the Besançon models of stellar population synthesis of the Galaxy from Robin et al (2003) [19]. The models depend on the Galactic coordinates, field size, photometric colors, and the extinction. The value for extinction in the direction of M71 was found to be 0.19 mag/kpc which was calculated using the reddening constant of 3.14 ± 0.10 from Schultz (1975) [24], the distance, and the reddening from Harris (1996) [13]. For a field 100 times the area of our NIRI field, the model yields about 5800 stars, 625 of which lie on our cluster’s main sequence. Therefore we can expect 6−7 of the stars in our NIRI field to be interloping field stars (see figure 3.6). It is therefore difficult to conclude if we have found any escaping stars. 34 3.2. Proper Motion Distribution ! !"# $ $"# % %"# $! $% $& $' $( %! %% %& )!* ) Figure 3.6: A simulation of the galactic field for the same galactic coor- dinates of M71. For stars with V ≤ 17, a field 100x the ACS field was simulated. For stars V ≤ 17 a field 100x our NIRI field was simulated. The red stars are the ones that meet the colour cuts from figure 3.4. We also ran a simulation for a field 150x the size of the ACS field; we found ∼1900 stars in this simulation which lie on the winnowed CMD for Cudworth’s stars. Scaling this down to the ACS field we expected to find ∼13 interloping stars. From the proper motion distribution we found 16 potential escapers. It is once again difficult to conclude we had observed any escaping stars. 35 3.2. Proper Motion Distribution 0 200 400 600 800 1,000 1,200 0 200 400 600 800 1,000 1,200 X Pixels Y  P ix e ls Figure 3.7: The proper motion vectors for the escaping stars that survived the color and proper motion error cuts. The vectors are plotted to show the trajectory of the stars over the next 5000 years. The X marks the centre of the cluster. 3.2.2 Proper Motion Isotropy Using the proper motion data, we determine the proper motion vector of the individual stars in the cluster. We calculated the proper motion angle with respect to the cluster center for three groups of stars. Half of the NIRI field contained stars within 11′′. The other half were from 11-22′′. We also calculated the angles for stars from Cudworth[6], which we determined to be cluster members. We found that stars in the three different radial distances had proper motion angles which were consistent with isotropy. 36 3.2. Proper Motion Distribution 0 20 40 60 80 100 120 140 160 0 5 10 15 20 25 Proper Motion Angle C o u n ts (a) Figure 3.8: Histogram of the proper motion angle with respect to the center of the cluster. Blue histograms are for stars in the NIRI field, and the dashed red line histogram is for stars from [6]. We performed a Kuiper test on the data from figure 3.8, which is a test similar to the Kolmogorov-Smirnov test but more sensitive to differences in the wings of the distributions. This test is better suited for distributions which are cyclic in nature as in our case. The p−value, comparing a flat distribution, is 0.17, for stars in the inner 11′′ and p=0.21 for stars in the outer 11′′, finding no significant difference when compared to a flat isotropic distribution. We have a similar result when we extend our field from the inner 22′′ up to 150′′. We then have a p-value of 0.14. Figure 3.8 shows the distributions of proper motion angles for the NIRI field and from Cudworth. 37 3.2. Proper Motion Distribution 0 0.5 1 1.5 2 2.5 3 0 500 1000 1500 2000 2500 (b) Qn r /Qn t C o u n ts   Inner 50% Outer 50% Figure 3.9: Histograms for the values Qnr/Qnt resulting from the bootstrap resample of the data. The radial and tangential values of Qn are consistent with unity within 1σ for all stars. As we transform coordinates between the multiple epochs, we use cluster stars as the reference points. Therefore, any mean motion of the cluster is lost. To characterize the anisotropy of the proper motions, we measure the width of the proper motion distribution in the radial and tangential directions using Qn. The measured ratio of the radial to tangential widths Qnr/Qnt is unity for an isotropic distribution. We find the ratio of the two components Qnr/Qnt for three radial distances. For the inner 50% we have Qnr/Qnt = 1.15±0.22 and Qnr/Qnt = 1.17±0.23 for stars for the outer 50% of the NIRI field. If we extend our field up to ∼150′′ we have Qnr/Qnt = 1.03±0.13. The errors were obtained by bootstrapping our sample of measured proper motions, and accounting for errors in the cluster’s center and proper motions. Although the results for stars in our NIRI field are above unity and may indicate a stronger radial component in the proper motions, both results are still within 1σ of unity. Figure 3.9 shows the 38 3.3. An Upper Limit to the Mass of any Central IMBH distributions of the ratios of the radial and tangential dispersions from our NIRI field. 3.3 An Upper Limit to the Mass of any Central IMBH 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 Projected Distance from Centre [arcsec] D is p e rs io n  [ m a s /y r] (c)   100M sun 300M sun 1000M sun Figure 3.10: The observed proper motion dispersion and three different IMBH models. IMBHs have been suggested to exist in several globular clusters such as G1 [9, 29], NGC 6388 (Lützgendorf et al ) [14], and Omega Cen (Noyola et al)[15]. However, some of the claims are still disputed, notably the claim in Omega Cen (Anderson & van der Marel)[2]. Safonova & Shastri (2010) [21] extrapolate the SMBH correlations down to GC masses, determining a linear relation in the velocity dispersion and central black hole mass. Using their relation and our observed velocity dispersion, we obtain an upper limit 39 3.3. An Upper Limit to the Mass of any Central IMBH of a central black hole mass of 25 M" for M71. It is risky, however, to extrapolate correlations between SMBHs down to IMBHs as their formation scenarios might be significantly different. To determine if we have observed any evidence for a central IMBH in the core of M71, we divide our proper motion data for stars in the inner 22′′ into 5 radial bins. Each bin contains 30 stars. We then calculate the observed proper motion dispersion (Equation 3.2) and estimate the errors by bootstrapping and calculating the spread in the values of Qn (see Figure 3.8). The observed proper motion dispersion is nearly constant throughout the inner 22′′. 20000 21000 (d) 0 200 400 0 50 100 150 200 250 300 350 400 450 IMBH Mass [Solar Masses] C o u n ts  Figure 3.11: The results from bootstrapping the proper motion data 25,000 times. The IMBH mass from each fit is binned here. The leftmost bin from 0 ≤ M" ≤ 5 peaks at 20,500 counts, implying that a very small central IMBH is the preferred fit. The red line represents the 90th percentile at 150M". We have found that the velocity dispersion calculated by Baumgardt et 40 3.3. An Upper Limit to the Mass of any Central IMBH al (2004)[4] in clusters with a black hole at the center can be modeled sim- ply as a function of the cluster half-light radius for stars which are close to the cluster center. The resulting model contains an r−1/2 Keplerian contri- bution from the black hole and a constant dispersion from the stars only. To quantify our results, we bootstrap the observed proper motions and fit them to our model by minimizing the χ2 values and accounting for our er- ror in the cluster center. Using these bootstrapped data we find with 90% confidence, that any black hole at the center of M71 must be less massive than 150d34 M". Where d4 is the distance to the cluster divided by 4 kpc. From the histogram in figure 3.11, the most common result is the one with a very small black hole, where the proper motion distribution is constant with radius. Near the 90th percentile, the value of σ from our model vanishes and the observed proper motions obey a Keplerian r−1/2 distribution. 41 3.3. An Upper Limit to the Mass of any Central IMBH X Pixels Y  P ix e ls   (e) 2004006008001000 200 400 600 800 1000 P ro p e r M o ti o n  D is p e rs io n  [ m a s /y r] 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Figure 3.12: A dispersion map of the field, obtained by running a circle with a 4′′ diameter across the field and calculating the dispersion in each area. Observationally, there are no signs of radial dependence or an increase in dispersion towards the center which is represented by the X. One of the risks with binning data is that it is possible to over- or under- bin and mask or amplify any underlying features or noise. We approach this with two methods. First, we run a circular bin across our field and calculate the dispersion in each bin to produce a dispersion map. Figure 3.12 shows this map and it is clear the changes in dispersion are random fluctuations. Another way to check if the observed dispersion is constant, as in the case for no or a low mass black hole, is to calculate the average distance from the center, r̄ = Σr/N (3.4) 42 3.4. Summary of Proper Motion Analysis and compare it to the proper motion weighted distance from the center, r̄|µ| = Σr|µ| Σ|µ| . (3.5) If the proper motions are constant as a function of distance from the center, the two values should be equal. However, if proper motions are decreasing with increasing radial distance, larger radii get less weight so the value is less. We obtain r̄ = 11.81′′± 0.47′′ and r̄|µ| = 11.50′′± 0.83′′. The proper motion weighted distance is lower, indicative of higher proper motions at smaller radii, but a radially constant velocity dispersion is completely consistent within the uncertainties. 3.4 Summary of Proper Motion Analysis Using the Near Infrared Imager on the Gemini North Telescope we were able to resolve the internal proper motions in the core of Messier 71. With a 3.8 year baseline, we found proper motions for 215 stars, 150 of which are likely cluster members. Several of the stars exhibit high proper motions well beyond the cluster’s escape velocity. However, we are unable to say with confidence that we have observed any escaping stars because of likely contamination from field stars. The cluster’s proper motion dispersion was found to be 179±17 µas yr−1, a result similar to Cudworth (1985) [6]. By combining data from Cudworth, we are able to look for signs of anisotropy across the cluster’s inner 150′′; however we find that the distribution is consistent with the case of isotropic orbits. We then find that the observed proper motion dispersion is constant with radius and we are able to put an upper limit to any central intermediate mass black hole to be less than 150d34 M" at 90% confidence. 43 Chapter 4 Reduction of Integrated Field Unit Data 4.1 Introduction to Spectroscopy Astronomical spectroscopy is the study of the spectrum of electromagnetic radiation from astronomical objects. This can be used to derive many properties of astronomical objects such as their temperature, chemical com- position, density, luminosity, distance, mass and their relative motion via Doppler shift. To obtain spectra of an astronomical source, a diffraction grating is used to disperse the incoming light. The light is then photographed using a CCD camera. Depending on the source, various gratings in combinations with filters are used to deliver the required science goals. Gratings can come in low, medium or high resolution. The resolution of a particular grating is denoted by R, a dimensionless quantity that is a measurement of spectral purity; R = λ/∆λ. Here, λ is the wavelength of the observation and ∆λ is the smallest wavelength separation an instrument can distinguish. Spec- trographs with R ≤ 1000 are considered low resolution. Low resolution spectrographs are useful for observing faint objects and will have large spec- tral coverage. Whereas, spectographs with R ≥ 50,000 are considered high resolution. High resolution spectrographs have the advantage of delivering precise velocities or very high resolution of an objects spectrum, but at the cost of low spectral coverage and increased telescope time. The Doppler effect can be used to find the radial velocity of astronom- ical objects. The spectra of stars is not continuous. There are absorption features at known wavelengths. Absorption lines are created when electrons are excited between energy levels in the various elements found in a star’s atmosphere. These features can then be compared to a gas of the same element which also exhibits the same spectral features, however the features are slightly shifted if the star is moving. This shift can be used to calculate the object’s radial velocity via: 44 4.1. Introduction to Spectroscopy vrad = c ∆λ λ (4.1) where c is the speed of light. 4.1.1 Different Types of Astronomical Spectroscopy There are several branches of spectroscopy, depending on the instrument used and the science goals. Each has its advantages. Here we discuss three different types. Long Slit Spectroscopy Long-slit spectroscopy is used when observing an elongated celestial object through a elongated slit aperture and dispersing the light using a diffraction grating. This is particularly useful when observing extended objects such as galaxies and Herbig-Haro objects. For extended objects their rotation curve can be observed to give spatially resolved velocities. This technique can be used with high resolution gratings to deliver precise radial velocities. The drawback is only one object can be observed at a time. Multi Object Spectroscopy Multi-object spectroscopy allows for the possibility of obtaining spectra of up to several hundred objects simultaneously. This is done by precisely fab- ricating a plate with many small slits which is placed at the spectrographs’ entrance aperture or by placing fibers in the telescope’s focal plane. Integrated Field Spectroscopy Integrated field spectroscopy has recently become an important sub-discipline of astronomical spectroscopy. Traditionally, obtaining spectra of extended objects such as galaxies or many point sources such as stars in a small field, spectroscopy using a long-slit was carried out. This gave spatial resolution in the direction of the slit and the slit was then moved across the field for a second spatial dimension. However this process is slow and requires greater telescope time. Integrated field spectroscopes are used to speed up observa- tions by obtaining spectra of a two dimensional field. Recently this has been sped up with improvements in telescope resolution and with advancements in adaptive optics. 45 4.1. Introduction to Spectroscopy Integrated Field Units (IFUs) work by using one of, or a combination of three methods: lenslet array, fibers or an image slicer. For a lenslet array, an array of small lenses is placed in the image plane essentially with the lenses acting as pixels of a standard camera. The incoming light is then fed to a dispersive element and imaged via a camera. This results in a spectra for each individual lenslet. For a fiber fed spectrograph, the incoming light is captured by an array of fibers before it is dispersed and imaged by a camera. An image slicer works by slicing an image in the image plane and rearranging it so that different parts of the image fall onto a slit and dispersive grating, so that a spectrum is obtained for a larger area of interest. !"#$%#&'%(')'!'* ! " # $ %# & '% ( '+ '! '* Figure 4.1: An example of how an integrated field unit (IFU) works. The hexagons represent lenslets which have the ability of capturing a spectrum individually. 46 4.2. Gemini Multi Object Spectrograph Integrated Field Unit 4.2 Gemini Multi Object Spectrograph Integrated Field Unit The Gemini Observatory has at its disposal, the Gemini Multi Object Spec- trograph (GMOS), which can be configured for long slit, multi object or integrated field spectroscopy. Here we discuss the instrument and its capa- bilities when running the integrated field unit. 47 4.2. Gemini Multi Object Spectrograph Integrated Field Unit Figure 4.2: GMOS IFU example data of a dwarf galaxy. At the top is the reconstructed IFU image with the left panel showing the sky field. Bottom shows the raw CCD image. The sky and object fields are arranged into alternating blocks on the CCD. Also prominent in the image are the chip gaps between the three GMOS CCDs. The GMOS IFU is an optical and near infrared spectroscope which covers a wavelength range from 400-1100 nm. The IFU has two imaging fields, one for the object of study and the other for the sky. They have a 1 arcminute 48 4.3. Messier 71 IFU Data seperation. The IFU contains 1500 lenslets each of which projects 0.2′′ onto the sky. The IFU can be run in two different modes, one-slit and two-slit. In one-slit, 500 lenslets are used for the object of study and yields a 5′′ x 3.5′′ field of view and a 5′′ x 1.75′′ sky field of view. This provides extended wavelength coverage at the cost of field size. In two-slit mode, all 1500 lenslets are used, 1000 for the object and 500 for the sky. This provides a field of view of 5′′ x 7 ′′ for the object and 5′′ x 3.5′′ for the sky. Figure 4.2 shows an example of a reconstructed GMOS IFU image of a dwarf galaxy. Gemini offers various combinations of filters and medium and low resolution gratings. This allows for observing specific spectral features on science data. 4.3 Messier 71 IFU Data By using the Gemini GMOS IFU on M71, we are able to obtain spatially resolved velocities for stars in the core of the cluster. Previous studies have been conducted using an IFU to obtain radial velocities for stars in the core of globular cluster (e.g Noyola et al (2008) [15] & Lutzengdorf (2011) [14]). However, these studies always had stellar field densities much greater than ours. As a result no published study has been previously done in which individual radial velocities were measured for stars at the core of a globular cluster. M71’s extended core permits the use of an IFU to obtain uncontaminated stellar spectra. By using a medium resolution R = 5500 grating and the Calcium Triplet filter (see figure 4.3), the three Calcium Triplet lines in stellar spectrum can be observed. The triplet lines are found at λ = 850.036nm, 854.444nm and 866.452nm. 49 4.3. Messier 71 IFU Data 700 750 800 850 900 950 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ! [nm] T ra n s m it ta n c e Figure 4.3: The transmission curve for the Calcium Triplet Filter at Gemini North In 2009 we obtained six hours of observation time on the core of M71 using the GMOS IFU. The dataset was divided into six adjacent 5′′x 7′′fields with no overlap between the fields. Originally it was requested that each field be observed for one hour, however after we obtained data we found this varied between our six fields with some fields having twice as much observation time compared to others. In addition to IFU science data we were also supplied with daytime twilight flats, gemini calibration flats and Copper-Argon lamp flats for wavelength calibration. The data was were over the course of four nights on June 11 2009 and July 3-5 2009, with the twilight flats obtained only on June 11th. Additionally, the data were obtained at two central wavelengths of 855 nm and 865 nm. This was to minimize the chance that spectral features would be lost between the chip gaps in the CCD detector. 50 4.4. Reduction of M71 IFU Data 4.4 Reduction of M71 IFU Data The reduction of IFU data was done using the Gemini IRAF package. This is the same package that was used for reduction of the NIRI data in chapter 2. After acquiring the data there are four types of data files in addition to science data. They are bias, twilight, Gemini calibration flat (GCAL) and Arc. These four calibration files are essential for the reduction of the science data. Figure 4.4: Examples of calibration images from the IFU. Top: The raw bias image supplied by Gemini. Bottom: A Raw GCAL flat from one of the nights of observations. 51 4.4. Reduction of M71 IFU Data Figure 4.5: Top: Calibration Copper-Argon arcs. Bottom: The raw twilight image. There is a discontinuity in all IFU images in the centre chip. This is the location where the red slit’s dispersion ends and the blue slit’s starts. The reduction of data was done individually on each of the images. This means that every night a new set of calibration images were obtained and those images were used for calibrating the science data. One concern with the data was the twilights were only obtained on the first night of observa- tions. As a result, the same twilights had to be used for calibrations despite updated calibration flats and arcs from every other night. 52 4.4. Reduction of M71 IFU Data The general IFU reductions are outlined in figure 4.6. This shows the sequence for reducing data. The numbers denote the steps performed during the data reduction. The primary IRAF task is GFREDUCE. This task has the ability for calling other Gemini IRAF tasks which can be controlled accessing the task’s parameters. Figure 4.6: Flowchart detailing the steps for IFU data reduction. The arrows have the Gemini IRAF task required for the steps. The red boxes denote final reduced files required extracting science data. The first task is to bias subtract, clip the images at the discontinuity in wavelength space then stitch the images to account for the chip gaps. There is a discontinuity in the images where the red slit ends and the blue slit starts (see figure 4.5). The top half of figure 4.7 shows the results of the first task. The second task was to perform the same steps as step 1, except this time on the twilight flat. 53 4.4. Reduction of M71 IFU Data Figure 4.7: Top: The Gemini Calibration flat after the results of step 1 is seen above. The chip gaps have been accounted for and the two slits have been stitched together. Bottom: The reduced twilight flat prior to wavelength calibration. 54 4.4. Reduction of M71 IFU Data Step 3 is to use both the reduced calibration and twilight flats to create a final flat field image. This flat field image would be applied to the science data for final reductions. Figure 4.8 shows the final response image. Figure 4.8: The response image. This is the final flat field. One of the most critical steps in the IFU data reduction is the wavelength calibration of the Copper-Argon arcs. The arc spectrum are recorded during the night of the science observations. They are obtained by shining a lamp onto the IFU with the same filter and gratings as the science data. The spectrum shows emission lines at known wavelengths and this serves as a wavelength scale for the science spectra. Step 4 in figure 4.6 shows the Gemini IRAF task required for wavelength calibration. This task also cuts the raw data at the slits and corrects for the CCD chip gaps. !"#$%$&'()*+"&',(-./,0* 1222* 1322* 1422* 1522* 1122* Figure 4.9: Copper-Argon arc spectrum 55 4.4. Reduction of M71 IFU Data Figure 4.9 shows the Cu-Ar arc spectrum used for wavelength calibration. Unfortunately there is one emission line at 8510Åwhich is miss-calibrated in the Cu-Ar lamps, therefore it must be excluded in the calibrations. !"#$%&#'('$)*+,-)*./'&01*0(2' 34.*5*#67)'84#6-70&9-:' ;<<<' ;=<<' ;2<<' ;><<' !"#$%&#'('$)*+,-)*./'&01*0(23' 45.*6*#78)'95#7-80&:-;' <333' <=33' <>33' <?33' Figure 4.10: Wavelength calibration of the arc spectrum by fitting various functions. Having too many fitting parameters can cause erroneous fits. Calibration of the Cu-Ar spectra requires fitting of polynomial functions to determine the wavelength solution. Various fitting functions were tried including cubic splines and Chebyshev polynomials. It was ultimately found that a fourth order Chebyshev polynomials provided the most robust wave- length solution. Using higher order fitting functions can cause erroneous fits 56 4.4. Reduction of M71 IFU Data as there are not enough calibration arc lines to accurately fit them. Figure 4.10 shows the difference between a good 4th order Chebyshev polynomial and a high 10th order function which did not fit accurately. Figure 4.11: The effect of applying the wavelength transform onto the twi- light flats. The top figure shows the twilight flat prior to wavelength cali- bration. The bottom figure is the final calibrated flat. The Calcium Triplet lines are easily observed here as the three bright vertical lines in the im- age. Wavelength increases from left to right. The vertical axis represents the spectra from individual IFU fibers. The horizontal split in the bottom figure is due to the two slits used in the IFU. Steps 5 and 6 of the data reduction requires applying the wavelength calibration found in step 4 to the twilight flat and the Cu-Ar arc spectra. This step produces arcs and twilights which are fully wavelength calibrated. These are the same ones that will be used in the IFU science data analysis. Figure 4.11 shows the effect of step 6 from figure 4.6. 57 4.4. Reduction of M71 IFU Data Reduction of Science Data We obtained six hours of telescope time on six different IFU fields, all within the core of M71. To reduce science data, a final flat field must be gener- ated. In addition, the wavelength calibration for each IFU aperture must be completed. Similar to all other IFU calibration data, science data has to be clipped and trimmed so that the chip gaps and the discontinuity between the two slits and be accounted for. Following this, the data is flat fielded using the twilight and GCAL flats from step 3 of figure 4.6. Here we decided to not perform sky subtraction as the sky field of the IFU is still located well within the cluster. Additionally, there are very few night sky telluric lines in the region of the Calcium Triplet lines. Therefore, sky subtraction is not crucial. The stars we found in the sky field were all fainter than V = 20, due to the very low signal to noise ratio in their spectra we did not include them in our analysis. Figure 4.12: Raw science image. Stellar spectra are the bright bands that run from left to right. 58 4.4. Reduction of M71 IFU Data Figure 4.13: Science image after all data reduction. Wavelength increases from left to right. Each of the 1500 IFU fibers are shown here increasing from bottom upwards. Following this, we preformed cosmic ray rejection and wavelength cali- bration to the raw science data which resulted in the final science data. Fig- ure 4.13 shows the effects of reduction of IFU science data. All science data were calibrated using GCAL flats and arc spectra from the same night as the science observations. Additionally, the data were processed separately depending on which central wavelength was used for the data. Following data reduction, using the IRAF task GFDISPLAY, the science data can be used to create an IFU image of the field. This task was used for each of the six IFU fields and then manually aligned to create an IFU map of the cluster. 59 4.4. Reduction of M71 IFU Data Figure 4.14: Top: Map of the six IFU fields stitched together. There is no overlap between the fields. Each of the six fields appears to be split in half. This is due to the scaling of the image and the differences in throughput of the two IFU slits. Bottom: IFU map of the sky field located 1 arcminute away from the larger field. 60 4.5. Radial Velocities Figure 4.15: Image of the cluster obtained by one of the three GMOS CCDs used for target acquisition. Red represents the two IFU fields, yellow rep- resents the NIRI field also found in figure 2.4. The blue is the field of the ACS from figure 2.2. 4.5 Radial Velocities To obtain radial velocities of stellar spectra one needs to calculate the differ- ence between wavelength of a given spectral feature to that a similar feature whose velocity is known. One technique for determining the radial velocity of a given spectrum is to cross correlate it against a template spectrum. Cross correlation is a technique used to measure lag between two signals. As the signals are correlated a correlation plot is produced. If two signals are identical, the correlation plot will have a maximum at zero. However, if there is a small shift in one of the signals the plot’s maximum will be offset. Figure 4.16 shows the basic idea behind cross correlation of two signals. 61 4.5. Radial Velocities Figure 4.16: Cross correlation of two signals. Where the signals overlap there is a maximum in the correlation function. If these were two spectra, the radial velocity would be the offset of the peak of the correlation function. This is analogous to a sliding dot product of two signals. 8000 8200 8400 8600 8800 0 5 10 15 x 10 4 ! [Angstrom] In te n s it y Twilight 8450 8500 8550 8600 8650 8700 0 2 4 6 8 10 12 x 10 4 ! [Angstrom] In te n s it y Twilight Figure 4.17: Twilight Spectra. The figure on the right shows a close up of the three regions of cross correlation when the lines are used individually. As we have strong Calcium Triplet lines in the twilight signals (see figure 62 4.5. Radial Velocities 4.17). We will use them as one of the correlation signals. The other will be the stellar spectra. From figure 4.14 we can see small hexagonal lenslets. Each of these contains a stellar spectrum. Therefore, the brighter stars will have not only stronger absorption lines in the spectrum but more spectra for measuring radial velocities. For cross correlation, we use the three triplet lines individually for stars that are brighter than ∼18.5. This provides three radial velocity measurements for these stars. Stars fainter than ∼18.5 have weak triplet lines in their spectra and therefore are correlated using all three lines at once. Figure 4.17 shows the three triplet line regions for correlation. They were from λ = 8475:8525, 8525:8560, and 8635:8685. V=16.4 V=13.0 V=14.5 V=14.2 V=18.7 Figure 4.18: The spectra of one IFU fiber and the corresponding star from which the fiber was from. Brighter stars have many more illuminated fibers. 63 4.5. Radial Velocities 8000 8200 8400 8600 8800 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 ! [Angstrom] In te n s it y V = 13 8000 8200 8400 8600 8800 0 50 100 150 200 250 300 350 400 ! [Angstrom] In te n s it y V = 16.7 8000 8200 8400 8600 8800 0 500 1000 1500 2000 2500 3000 ! [Angstrom] In te n s it y V = 14.5 8000 8200 8400 8600 8800 0 20 40 60 80 100 120 ! [Angstrom] In te n s it y V = 18.7 Figure 4.19: Spectra of a single IFU fiber for four different stars. Stars fainter than V = 20 did not have strong enough Calcium Triplet lines for velocity measurements. The number of radial velocity measurements of a particular star depends 64 4.5. Radial Velocities on the star’s brightness. The brighter the star is, the more IFU lenslets are illuminated by that star’s light, therefore we have more measurements of velocity. Some of the brighter stars can have starlight enter up to 50 lenslets, each of which offers three measurements of radial velocity. Whereas, stars fainter than V = 18 have starlight enter only one lenslet and have weak triplet lines. The general steps for measurement of velocity is as follows: cross corre- late with twilight spectrum, perform heliocentric velocity correction, add in the wavelength shifts due to telescope flexure and finally combine all radial velocities from all measurements for each individual star. To measure radial velocity, we use the IRAF task FXCOR. This task takes in two spectra and performs a cross correlation over a specified region. In our case, this is the Calcium Triplet region. Following this, FXCOR pro- duces a correlation plot which is used to determine the shift between the two signals. To get the pixel shift between the spectra, we fit a gaussian function to the correlation plot. The location of its peak gives the pixel shift and the error in the shift. We then simply convert from pixels to a wavelength shift using the scale calculated during the wavelength calibration. In our case, this was about 16.6 km/s/pixel but varied from each fiber. FXCOR is applied to all stars and every fiber for which there is stellar spectra present. !"#$%&'(")& *&+,*&+-*& ,*& *& .-& ./& .0& .1& ,& 2 3 44 $ %5 6 3 7 & ,**& -**&+,**&+-**&+8**& *& Figure 4.20: The correlation function of two spectra. The fitting function here is a gaussian represented by the dashed curve. As the Earth orbits the sun, its velocity with respect to M71 is constantly 65 4.5. Radial Velocities changing . In addition to this, our data was obtained from different nights. We therefore have to make corrections for this motion. This is done by using the IRAF task RVCORRECT. In this task, we feed in the observed velocity from FXCOR, in addition to the date, time and location of the observations, to obtain the heliocentric radial velocity of the stars. Flexure Correction The next task for our velocity calculations is to add in the shift due to CCD flexure to the velocities. When observations are carried out depending on the angle at which the telescope is situated, the CCD can experience small distortions. We correct for these using the Copper-Argon arc spectra. We first create a median combined arc spectrum. We create two different median combined arcs one for each of the IFU slits. We then use FXCOR and cross correlate a small section of the arc spectrum using the median arc as a template and each of the IFU fibers as the object. The result of the flexure response can be seen in figure 4.21. Here, all seven (including doublets) are correlated against the same region of the template. 66 4.5. Radial Velocities Figure 4.21: The response from CCD flexure. The left panel shows the arc spectrum with individual emission lines coloured. In the two figures on the right hand side, we see the result of cross correlating the coloured region against a median combined arc of that same region. The bottom panel is a zoom of the top panel to show how CCD flexure varies across the chip. We can see that the red line at λ = 8500 gives a very large shift. However, this line was ignored in our wavelength calibration due to Gemini IRAF tasks warnings. We then take the next closest line which is the green line at λ ∼ 8700 Angstroms and use this to correct for CCD flexure. The value from cross correlating the emission line at λ ∼ 8700 against a median combined arc gives the flexure correction, typically this is on the order of ∼50 m/s. Combining Radial Velocities To combine multiple radial velocity measurements of stars, we used equation 4.3. The underlying principle here is that the more accurate a measurement 67 4.6. Radial Velocity Dispersion is the greater its weight should be on the combined radial velocity.Less accurate measurements have less contribution. We can derive this by using the χ2 formula: χ2 = ∑ ( vi − v̄ σ2i )2 (4.2) Here, vi and σi are the measurements of velocity and the associated error. We then take the derivative of this function with respect to χ2 and solve for when v̄ is set to zero to obtain: v̄ = ∑ vi σ2i / ∑ 1 σ2i (4.3) The error of the measurment is obtained by taking the second derivative of χ2 and solving for σ: σ̄ = ( ∑ 1 σ2i )−0.5 (4.4) Once we have calculated the combined radial velocities for each of our stars using the above equations, we are now able to proceed to determine the radial velocity dispersion. 4.6 Radial Velocity Dispersion We have now at this point determined radial velocities for 43 stars in our IFU field. They range from V = 13 to ∼20. We have proper motions for 37 of these stars. We then perform the same colour and proper motion cuts from section 3.1 to arrive at a final cluster member only radial velocity sample. 68 4.6. Radial Velocity Dispersion Figure 4.22: The CMD of the IFU stars for which we have radial velocities is overlaid on the CMD of the ACS field. The cluster members are the stars which satisfy the colour criteria from figure 3.4 and the proper motion cut from figure 3.5. The final radial velocity sample is shown in figure 4.23. We have 36 stars which we can say are likely cluster members and we can now compute the radial velocity dispersion using equation 3.2. We find the radial velocity dispersion to be σvr = 3.54±0.64 km s−1. The error is determined by boot- strapping the sample. In comparison, this value is greater than the previous two measurements of the radial velocity dispersion. Rastorguev & Samus [17] calculate a dispersion of 2.0 ±0.6 km/s, whereas Peterson & Latham 69 4.6. Radial Velocity Dispersion [16] obtained 2.8 ± 0.6 km/s. However, both of these measurements are for stars situated far away from the cluster centre where the dispersion is expected to be lower. Our measurement of the dispersion is slightly higher than Peterson & Latham’s, however it is still within the errors. !" !# !$ !% "& "" !$& !'& !#& !(& !"& !!& & ) * + , -+ ./ ) 0 .1 2 -3 4 /5 6 7 89 : Figure 4.23: Radial velocities of the same stars from figure 4.22. 70 Chapter 5 The Distance to Messier 71 5.1 Geometric Distance Distances to globular cluster can be measured using two main methods, fitting stellar evolution models and geometry. Clusters are generally too far away for the use of geometric parallax for modern day instruments. Instead, we can get the distance using the proper motion and radial velocity dispersions. To get the distance, we assume that stars are on isotropically distributed orbits and the absolute tangential and radial velocity dispersions are equal. Binney & Tremaine (1987, p. 280) [5] give the geometric distance as: D(kpc) = σvr[km s−1] 4.74× σµ[µas year−1] (5.1) We then select the same stars from figure 4.22, which are cluster mem- bers and have radial velocities to determine that sample’s proper motion dispersion. This is the denominator in equation 5.1. The same group of stars has a proper motion dispersion of 183 ± 33 µas year−1. By substi- tuting in the radial velocity dispersion, we arrive at a geometric distance to M71 be 4.1 ± 1.2 kpc. This distance is consistent with all other values of the distance published to date. 5.2 Stellar Model Distance We now calculate the distance to M71 using stellar evolution models from Dotter et al (2007) [8]. Using published values of metallicity and age, we generated isochrones of M71. However, fitting isochrones on a CMD can be challenging as it is difficult to fit at the main sequence turnoff. Additionally, the turn off is the most important location of the CMD to be fitted as it is most dependent upon the model parameters. Here, we devise a method to fit the turnoff by taking the derivative of the CMD with respect to colour. 71 5.2. Stellar Model Distance Our first step is to make a fiducial CMD from our data. We do this by first removing stars which are clearly off the main sequence in figure 3.2. We then run a bin down the main sequence for every 50 stars and calculate the median V magnitude and colour. This produces a fiducial main sequence down the centre of the CMD as shown in figure 5.1. !"# !"$ % %"& %"' %"# %"$ & &"& %! %& %' %# %$ &! && &' (!) ( Figure 5.1: The CMD from figure 3.2 with a median line running down the centre. Here V is now in Vega magnitudes. We now plot the CMD horizontally and the derivative of the CMD as well. 72 5.2. Stellar Model Distance !"# !"$ % %"& %"' ( ! ) %# %* %$ %+ &! &% && !% !!", ! !", - .( ! )/ 0- ( 1 2 ! " # $ % &! &" !" !&'( !& !!'( ! !'( ) * +*,-./ 0 +* ! 1/ 23 20 * & &'( " "'( * ! 1 Figure 5.2: Top: The fiducial cmd and the derivative of the cmd. Bot- tom: An 11 Gyr isochrone of stars with similar abundances as M71 and the corresponding derivative. 73 5.2. Stellar Model Distance The only difference we have here is that the model is calibrated in abso- lute magnitude and the data is in apparent magnitude. By simply shifting the models so that the spike in the derivative is aligned with the observed data we get the distance modulus. We find the distance modulus to be 13.72 ± 0.10, corresponding to a distance of 3.9 ± 0.2 kpc. The error in the distance modulus comes from the FWHM of the spike in the derivative plot. !" !# $% !$ !!&' !! !%&' % %&' ! !&' ( )* ! +, -( * . * !" !"&' !/ !/&' !# !#&' !!&" !!&0 !!&$ !! !%&# !%&" !%&0 !%&$ % %&$ ( )* ! +, -( * . * Figure 5.3: By shifting the isochrone so that the spike of the derivative matches that of the observed data, we get the distance modulus. The left panel is over the entire CMD. The right panel is a close up of the turn off. We have now calculated the distance to M71 using two independent methods. Previous measurements of the distance have been by Arp & Hartwick (1971) [3] of 4100 ± 400 pc and Geffert & Maintz (2000) [10] at 3600 ± 250 pc. Both of our measurements place M71 at distances which are consistent with previous results. 74 Chapter 6 Conclusions Using the Gemini North Observatory and two of its instruments, Near In- frared Adaptive Optics Imager (NIRI) and the Gemini Mulit Object Spec- trograph’s Integrated Field Unit (GMOS-IFU), we determined the proper motions and radial velocities of stars in the core of Messier 71. The NIRI data was obtained over a 3.8 year span and allowed us to explore the internal dynamics in the core of the cluster. In this short time span we were able to resolve the internal proper motion dispersion, a feat normally reserved for space based observatories. Previous work on M71’s proper motions from ground based telescopes required images obtained decades apart. Adaptive optics imaging in conjunction with ALLFRAME software was required to accomplish this task, therefore this thesis is a testament for the capabilities of instrumentation and computer software. From the proper motion data, we found no evidence for a central inter- mediate mass black hole and were able to put a strict upper limit of just 150M". Additionally, we found no evidence of anisotropy in the motions of stars and inconclusive evidence for any escaping stars. With the use of the GMOS-IFU, we were able to determine the radial velocities of 43 stars from our NIRI field. This is the first time that stars have had their radial velocities and proper motions measured in the core of a globular cluster. We were thus able to determine the radial velocity dispersion in the core of the cluster. By combining the radial velocity and proper motion dispersions, we are able to calculate the geometric distance to the cluster. By using the same stars for both proper motion and radial velocity measurments, we are able to simply the distance calculation and not have to incorporate uncertainties in the orbital parameters of stars. Using this method, we find the distance to be 4.1±1.2 kpc. Finally we determined the distance to M71 using stellar evolution mod- els. Normally, this task is somewhat ambiguous to perform as fitting an isochrone to a CMD is difficult to perform. We devised a new method to fit isochrones to data by taking the derivative of the CMD with respect to colour. In our observed filters, the CMD is simplified as it turns into a spike at the main sequence turn off. This spike can be used to easily fit our 75 Chapter 6. Conclusions observed data. Using this method, our distance to the cluster was found to be 3.9±0.2 kpc, consistent with the geometric distance. Some of the techniques discussed in this thesis are performed for the first time and have yet to be found in published literature. In particular, resolving proper motion dispersions using ground based telescopes in a very short timescale. Also we were the first to use the same stars for the proper motion and radial velocity dispersions for the geometric distance. Finally, using derivatives of the CMD to calculate a distance using stellar models. 76 Bibliography [1] J. Anderson, A. Sarajedini, L. R. Bedin, I. R. King, G. Piotto, I. N. Reid, M. Siegel, S. R. Majewski, N. E. Q. Paust, A. Aparicio, A. P. Milone, B. Chaboyer, and A. Rosenberg. The Acs Survey of Globular Clusters. V. Generating a Comprehensive Star Catalog for each Cluster. AJ, 135:2055–2073, June 2008. [2] J. Anderson and R. P. van der Marel. New Limits on an Intermediate- Mass Black Hole in Omega Centauri. I. Hubble Space Telescope Pho- tometry and Proper Motions. ApJ, 710:1032–1062, February 2010. [3] H. C. Arp and F. D. A. Hartwick. A Photometric Study of the Metal- Rich Globular Cluster M71. Ap.J., 167:499–+, August 1971. [4] H. Baumgardt, J. Makino, and T. Ebisuzaki. Massive Black Holes in Star Clusters. II. Realistic Cluster Models. ApJ, 613:1143–1156, October 2004. [5] J. Binney and S. Tremaine. Galactic dynamics. 1987. [6] K. M. Cudworth. Photometry, proper motions, and membership in the globular cluster M71. A.J., 90:65–73, 1985. [7] J. Cuffey. Noc 6838. A.J., 64:327–+, 1959. [8] A. Dotter, B. Chaboyer, J. W. Ferguson, H.-c. Lee, G. Worthey, D. Jevremović, and E. Baron. Stellar Population Models and Indi- vidual Element Abundances. I. Sensitivity of Stellar Evolution Models. Ap.J., 666:403–412, September 2007. [9] K. Gebhardt, R. M. Rich, and L. C. Ho. An Intermediate-Mass Black Hole in the Globular Cluster G1: Improved Significance from New Keck and Hubble Space Telescope Observations. ApJ, 634:1093–1102, De- cember 2005. 77 Bibliography [10] M. Geffert and G. Maintz. First results of a photometric and astromet- ric study of the globular cluster M 71 (NGC 6838). Astron. Astrophys. Suppl. Ser., 144:227–233, June 2000. [11] A. M. Ghez, M. Morris, and E. E. Becklin. Dynamical Evidence for a Supermassive Black Hole at the Center of the Milky Way. In D. R. Merritt, M. Valluri, and J. A. Sellwood, editors, Galaxy Dynamics - A Rutgers Symposium, volume 182 of Astronomical Society of the Pacific Conference Series, page 24, August 1999. [12] R. Goldsbury, H. B. Richer, J. Anderson, A. Dotter, A. Sarajedini, and K. Woodley. The ACS Survey of Galactic Globular Clusters. X. New Determinations of Centers for 65 Clusters. AJ, 140:1830–1837, December 2010. [13] W. E. Harris. A Catalog of Parameters for Globular Clusters in the Milky Way. A.J., 112:1487–+, October 1996. [14] N. Lützgendorf, M. Kissler-Patig, E. Noyola, B. Jalali, P. T. de Zeeuw, K. Gebhardt, and H. Baumgardt. Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. AAAP, 533:A36, September 2011. [15] E. Noyola, K. Gebhardt, and M. Bergmann. Gemini and Hubble Space Telescope Evidence for an Intermediate-Mass Black Hole in ω Centauri. ApJ, 676:1008–1015, April 2008. [16] C. J. Peterson and I. R. King. The structure of star clusters. VI. Observed radii and structural parameters in globular clusters. A.J., 80:427–436, June 1975. [17] A. S. Rastorguev and N. N. Samus. Velocity Dispersion of Stars and the Mass of Globular Clusters m4 m5 M10 M12 and M71. Soviet Astronomy Letters, 17:388, May 1991. [18] H. B. Richer and G. G. Fahlman. Star counts in the globular cluster M71. Ap.J., 339:178–194, April 1989. [19] A. C. Robin, C. Reylé, S. Derrière, and S. Picaud. A synthetic view on structure and evolution of the Milky Way. AAAP, 409:523–540, October 2003. [20] P. J. Rousseeuw and N. N. Croux. Alternatives to the Median Absolute Deviation. Journal of the American Statistical Association, 88:20, 1991. 78 [21] M. Safonova and P. Shastri. Extrapolating SMBH correlations down the mass scale: the case for IMBHs in globular clusters. APPS, 325:47–58, January 2010. [22] R. S. Samra, H. B. Richer, J. S. Heyl, R. Goldsbury, K. Thanjavur, G. Walker, and K. A. Woodley. Proper Motions and Internal Dynamics in the Core of the Globular Cluster M71. ApJl, 751:L12, May 2012. [23] A. Sarajedini, L. R. Bedin, B. Chaboyer, A. Dotter, M. Siegel, J. An- derson, A. Aparicio, I. King, S. Majewski, A. Maŕın-Franch, G. Piotto, I. N. Reid, and A. Rosenberg. The ACS Survey of Galactic Globu- lar Clusters. I. Overview and Clusters without Previous Hubble Space Telescope Photometry. aj, 133:1658–1672, April 2007. [24] G. V. Schultz and W. Wiemer. Interstellar reddening and IR-excess of O and B stars. AAP, 43:133–139, September 1975. [25] L. Spitzer. Dynamical evolution of globular clusters. 1987. [26] P. B. Stetson. DAOPHOT - A computer program for crowded-field stellar photometry. Pub.Astron.Soc.Pac., 99:191–222, March 1987. [27] P. B. Stetson. More Experiments with DAOPHOT II and WF/PC Images. In D. M. Worrall, C. Biemesderfer, and J. Barnes, editors, Astronomical Data Analysis Software and Systems I, volume 25 of As- tronomical Society of the Pacific Conference Series, page 297, 1992. [28] S. E. Strom, K. M. Strom, D. C. Wells, J. C. Forte, M. G. Smith, and W. E. Harris. The halo globular clusters of the giant elliptical galaxy Messier 87. ApJ, 245:416–453, April 1981. [29] J. S. Ulvestad, J. E. Greene, and L. C. Ho. Radio Emission from the Intermediate-Mass Black Hole in the Globular Cluster G1. ApJL, 661:L151–L154, June 2007. [30] A. A. Wyller. Observational Aspects of Black Holes in Globular Clus- ters. ApJ, 160:443, May 1970. [31] R. Zinn. The globular cluster system of the galaxy. IV - The halo and disk subsystems. Ap.J., 293:424–444, June 1985. 79 Bibliography 80 Appendix A NIRI Proper Motion Data The cluster centre is located at coordinates (x,y) = (754,806). The each pixel is 0.022′′projected onto the plane of the sky. Proper motions and proper motion errors are in milli-arcseconds year−1. Star ID x y PMx δx PMy δy V I 3 122.81 -41.08 -0.4919 0.4527 -0.1050 0.3173 17.215 16.410 4 561.78 -38.06 0.0606 0.1552 0.5228 0.2791 18.931 18.150 6 458.76 -35.75 -0.2638 0.2264 0.5746 0.2717 19.658 18.791 7 81.10 -35.01 -0.1944 0.3582 -0.3903 0.3132 20.086 19.129 8 415.44 -33.10 -0.0847 0.2421 0.1910 0.2182 20.956 19.736 9 138.32 -25.12 -0.3584 0.3569 -0.0114 0.2446 17.165 16.345 11 107.26 -17.85 -0.1851 0.2430 0.1682 0.2115 18.735 17.986 12 197.89 -17.84 -0.3468 0.3062 0.3442 0.2445 17.853 17.103 13 385.18 -16.52 -0.2374 0.2156 0.1425 0.1446 19.639 18.588 14 920.14 -17.31 0.1485 0.3967 -2.8143 1.0246 22.640 21.177 15 26.55 -15.89 -0.4826 0.3689 0.0962 0.2441 21.352 20.155 16 78.20 -7.89 -0.0270 0.2792 0.1635 0.2142 19.796 18.871 17 499.25 -6.46 0.0581 0.1063 0.2480 0.1847 18.359 17.619 18 693.83 -4.89 -0.2255 0.1806 0.8493 0.3728 22.544 21.021 20 215.69 2.31 -0.0479 0.1776 -3.6546 1.1523 17.630 16.831 22 385.76 6.56 -0.2633 0.2168 0.3945 0.2078 19.938 18.999 24 902.75 12.97 -0.0228 0.1502 0.4657 0.2231 17.858 17.147 25 752.69 15.88 -0.2009 0.1476 0.3188 0.2331 20.419 19.398 27 475.29 21.42 0.0303 0.1115 0.4136 0.1807 19.508 18.669 28 878.10 22.11 0.0389 0.1134 0.1672 0.1778 18.317 17.585 29 409.58 24.08 -1.4610 0.5933 -1.6851 0.5741 22.782 21.474 34 689.84 30.50 -2.0788 0.6503 -1.6266 0.4909 22.137 20.949 35 236.29 40.78 -0.3603 0.1989 0.1420 0.1501 20.439 19.393 36 437.86 62.58 0.1431 0.1197 0.2817 0.1337 20.485 19.453 37 422.89 73.40 0.2566 0.1812 0.4196 0.3044 23.026 21.612 38 420.62 77.61 0.0547 0.0975 0.2338 0.1220 20.078 19.135 39 929.06 80.66 0.0635 0.1183 0.1244 0.1300 19.045 18.245 81 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 40 732.86 88.89 -0.3190 0.1101 -3.5128 1.0146 17.088 16.404 41 945.92 89.93 0.0508 0.1567 0.2830 0.1368 21.365 20.125 42 295.54 95.60 -0.0793 0.1848 -0.0254 0.0864 23.025 21.263 43 806.44 96.32 0.0910 0.1070 0.3885 0.1791 18.747 17.901 44 4.07 109.97 0.4564 0.2400 0.2688 0.1672 16.541 15.939 45 850.02 122.29 0.0982 0.0917 0.2561 0.1344 19.158 18.323 46 514.09 127.58 0.2265 0.0893 0.2180 0.1056 19.074 18.278 47 910.24 136.31 0.0285 0.0804 0.3258 0.1170 21.118 19.930 48 169.70 157.53 -0.4098 0.1841 0.0150 0.0703 19.456 18.589 49 451.06 160.42 0.0163 0.0800 0.5072 0.1932 17.491 16.766 50 494.21 159.51 0.3491 0.1081 0.4634 0.1674 20.429 19.424 51 728.42 163.99 -0.1672 0.0973 0.2587 0.1977 23.054 21.535 52 532.74 165.04 0.5272 0.2347 -0.0998 0.1439 23.906 21.977 53 948.40 166.46 0.3084 0.1252 0.1446 0.0922 20.271 19.295 54 39.30 168.24 -0.0098 0.1682 -0.0340 0.0938 20.703 19.630 55 168.89 173.39 -0.2864 0.1549 -0.0933 0.0863 20.709 19.627 56 213.21 190.34 -0.1565 0.1127 0.1267 0.0724 21.216 20.006 57 862.52 193.65 -0.1970 0.0770 0.1897 0.1018 18.937 18.151 58 809.47 202.88 -0.0371 0.0780 0.0080 0.0895 16.886 16.012 59 652.08 205.16 -0.1978 0.0876 0.3009 0.1592 20.500 19.422 60 840.21 207.43 -0.0124 0.1585 0.0228 0.0746 22.243 20.776 61 430.19 -0.17 -0.4683 0.3659 0.3434 0.2775 23.840 21.977 62 594.79 211.22 0.1361 0.0783 0.3120 0.1668 18.266 17.473 63 379.49 219.08 0.1817 0.0942 0.2719 0.1120 19.530 18.651 64 476.18 221.91 -0.1280 0.1141 0.3167 0.1447 23.058 21.394 65 293.16 227.44 -1.3619 0.4619 -2.1200 0.6294 16.024 15.251 67 705.62 235.08 -0.2641 0.1008 0.5772 0.2192 22.332 20.841 68 995.18 244.74 0.2600 0.1274 -0.2514 0.1454 18.255 17.526 69 577.57 248.00 0.1501 0.0746 0.4670 0.1921 19.583 18.602 70 758.55 250.57 -0.5295 0.1325 0.4764 0.1829 21.393 20.134 71 971.16 249.54 -0.1213 0.1445 -2.9432 0.9393 21.278 20.252 72 246.69 259.50 -0.2123 0.0838 0.1140 0.1350 23.163 21.493 73 591.54 259.52 -1.1606 0.3327 -3.6548 1.0847 22.067 20.639 74 664.60 261.33 -0.0765 0.1223 0.3854 0.2041 23.458 21.559 75 216.89 272.54 -0.1143 0.0725 0.1190 0.0897 18.681 17.888 76 726.20 272.73 -0.2942 0.0937 -1.6538 0.4721 19.374 18.603 77 120.46 275.15 0.1379 0.0905 -0.0757 0.0640 18.744 17.981 82 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 78 916.21 275.11 -0.0959 0.0616 0.0855 0.0745 18.832 18.060 81 130.97 295.60 0.0067 0.0599 0.0277 0.0784 18.237 17.485 82 293.14 300.14 -0.0080 0.0874 0.0868 0.0699 21.504 20.223 83 823.52 300.14 -0.0277 0.1085 0.3958 0.2641 22.927 21.379 84 525.84 317.79 0.3590 0.1375 0.1156 0.0702 17.883 17.161 85 750.39 318.58 -0.1825 0.0848 0.1892 0.1671 21.157 19.929 86 480.20 319.56 0.1192 0.0712 -0.2301 0.0943 18.983 18.148 87 209.07 321.65 -0.3504 0.1059 -0.0912 0.0992 17.940 17.230 88 733.99 321.56 -0.0438 0.2013 0.3281 0.4832 23.800 22.075 89 395.72 333.61 0.6091 0.2194 0.1089 0.1445 23.568 21.659 93 531.69 346.05 1.8816 0.5876 -3.8401 1.2557 23.873 21.910 98 466.33 350.15 -0.0775 0.0550 0.2711 0.0896 20.072 19.128 99 922.93 350.45 -2.6708 0.8347 0.3838 0.1460 17.392 16.646 104 721.28 358.73 -0.3045 0.0827 0.2820 0.1306 16.921 16.043 106 534.13 359.77 -0.0581 0.0611 0.3494 0.1158 20.095 19.138 108 656.78 361.40 0.1104 0.0678 0.2475 0.1029 17.694 16.976 110 538.36 362.55 -2.7379 0.8079 -0.5075 0.1808 22.975 20.567 111 913.34 364.10 0.0599 0.1227 -0.0135 0.0946 20.459 19.410 114 588.66 90.66 0.3019 0.2040 0.5881 0.3059 23.970 22.167 120 835.99 374.85 2.2162 0.6952 -9.0674 2.9333 18.682 17.711 122 166.66 377.77 -0.1083 0.0617 0.0560 0.0662 18.659 17.895 127 643.58 382.07 0.1863 0.1312 -2.7166 0.8730 21.963 20.486 128 397.75 383.20 -3.1051 0.9293 -0.2260 0.1131 21.335 19.871 131 914.78 386.71 -0.1366 0.0897 -0.1495 0.1004 20.646 19.589 133 485.93 401.28 -0.0140 0.0671 -0.1527 0.1044 20.192 19.234 134 -23.90 403.62 -0.0262 0.3397 0.6111 0.2330 22.866 21.230 135 500.56 407.08 0.1182 0.1220 -0.0150 0.0650 20.119 19.178 136 586.97 411.88 0.1568 0.0742 -0.0578 0.0544 18.725 17.943 137 465.10 415.38 0.3180 0.1542 -0.3660 0.1255 18.030 17.304 138 531.58 414.74 0.0213 0.0695 0.2066 0.0875 19.255 18.436 139 188.86 423.86 -0.2073 0.0813 0.0319 0.0671 18.682 17.918 140 735.25 425.11 -0.0993 0.0682 -0.1558 0.0612 21.030 19.820 141 824.13 427.18 -0.0708 0.0759 0.3349 0.1075 19.216 18.284 142 282.46 432.33 -0.2273 0.0752 0.2195 0.0737 17.986 17.271 143 158.48 432.66 0.2872 0.2022 0.0223 0.1609 23.398 21.714 144 238.60 437.18 -0.0482 0.0644 0.0886 0.0593 18.918 18.140 145 521.47 437.42 -0.1794 0.1042 -0.0233 0.1310 19.063 18.173 83 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 147 23.08 462.78 -0.0132 0.2362 1.0600 0.4137 24.062 21.979 154 354.75 471.07 -0.0915 0.0818 0.0422 0.0665 18.364 17.556 160 605.42 476.08 -0.0946 0.2507 0.5336 0.2641 24.295 22.201 161 990.76 475.57 0.2522 0.1533 -0.1978 0.1412 20.926 19.795 174 123.23 487.13 3.1927 1.0234 -7.1140 2.1704 22.404 20.788 178 6.41 490.70 -0.1102 0.1929 0.5150 0.2488 17.069 16.453 187 202.32 495.92 -0.2027 0.0798 0.0575 0.0572 19.326 18.491 205 735.54 507.01 0.0609 0.0848 -0.0524 0.0579 20.991 19.839 219 606.00 520.16 -0.1208 0.0993 -0.1172 0.1435 22.895 21.227 220 366.93 520.56 0.1418 0.1229 0.0847 0.0580 16.375 15.500 226 835.25 531.96 -0.1796 0.0804 0.0936 0.0782 19.213 18.409 227 782.91 543.10 -0.2550 0.0845 0.2745 0.1109 19.320 18.487 228 389.76 545.18 0.0337 0.0734 0.2250 0.0760 19.026 18.193 229 899.12 547.18 -0.1011 0.0781 -0.1571 0.1165 20.820 19.697 230 228.10 548.50 -0.2654 0.1022 0.1835 0.1028 22.897 21.268 232 585.53 562.27 0.2509 0.1190 0.0832 0.0590 19.850 18.937 233 447.66 563.86 0.1827 0.1014 0.0041 0.0733 18.858 18.076 234 251.99 565.33 -0.3222 0.0912 -0.0350 0.0817 19.123 18.318 235 837.78 564.76 -0.0044 0.1691 0.5769 0.2361 24.013 21.990 236 944.25 564.89 -0.1273 0.0838 -0.0741 0.0907 19.396 18.578 237 369.45 569.74 -0.3571 0.1119 -0.3636 0.2490 23.236 21.492 238 129.95 577.83 -0.2646 0.1318 0.3097 0.1570 17.974 17.258 239 701.96 616.54 0.0897 0.0664 0.0047 0.0790 19.205 18.397 240 422.05 618.16 0.4818 0.1579 -0.0306 0.0690 20.294 19.308 241 731.79 620.22 0.1045 0.1068 0.0990 0.0746 22.469 20.757 242 145.43 636.28 -0.2488 0.1341 -0.1946 0.1287 19.026 18.235 243 804.16 642.01 -0.0899 0.1166 0.1234 0.1068 22.544 21.070 244 515.13 643.98 0.1786 0.0790 0.1423 0.0861 17.292 16.531 245 701.82 645.31 -0.5318 0.1729 -4.6913 1.5484 20.322 19.228 246 43.44 650.29 -0.4769 0.2318 0.3618 0.2368 19.200 18.326 247 499.96 649.69 0.3548 0.1692 0.4499 0.1511 21.018 19.862 248 511.41 654.84 0.0259 0.1033 0.1140 0.0904 17.962 17.237 249 557.39 658.40 -0.0363 0.0479 0.1571 0.1065 19.553 18.682 250 949.40 659.32 0.1477 0.0796 0.3665 0.1518 21.592 20.244 251 23.18 661.65 -0.2040 0.2462 0.4883 0.2744 17.767 17.053 253 538.66 672.05 0.0088 0.1071 0.2952 0.1114 22.559 21.043 257 427.61 675.70 -0.1459 0.0704 -5.2044 1.6731 20.880 19.944 84 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 259 138.49 677.83 -0.4922 0.1842 -0.1140 0.1234 17.228 16.425 264 792.84 688.40 2.3551 0.7938 -5.3182 1.7785 22.335 20.865 274 426.98 702.38 0.3123 0.1161 0.0925 0.0766 20.072 19.134 279 675.50 713.30 -0.0993 0.0818 -0.0127 0.0684 18.240 17.497 281 61.31 717.78 -0.7583 0.2820 0.0798 0.1781 17.411 16.671 283 883.21 718.51 -0.0096 0.0757 0.0404 0.0808 18.945 18.155 284 485.12 720.52 0.0765 0.0689 -0.0682 0.0622 18.644 17.830 285 700.74 720.43 0.3488 0.1908 0.1819 0.0936 22.317 20.834 286 462.75 724.38 0.3245 0.1212 0.0485 0.0756 20.089 19.141 287 570.33 724.37 -0.2162 0.2478 -0.0873 0.2356 22.100 20.992 288 179.93 733.26 0.2071 0.1644 -4.5018 1.3806 18.216 17.506 289 353.68 735.05 0.2291 0.1136 -0.1643 0.0812 18.671 17.910 290 745.62 739.26 0.1260 0.0721 0.3035 0.1382 18.726 17.966 291 618.67 741.09 0.2558 0.1598 0.1832 0.0949 19.947 19.099 292 944.18 740.81 0.0272 0.1140 0.2242 0.0841 19.202 18.396 293 148.46 742.46 -0.6697 0.2393 -0.0098 0.1352 18.490 17.743 294 731.44 743.54 0.0503 0.0592 0.2343 0.1101 19.004 18.216 295 133.39 744.37 -0.5917 0.2429 0.1651 0.1456 19.717 18.825 296 141.18 754.87 -0.5326 0.2363 0.0835 0.1723 21.044 19.887 301 661.22 758.99 -1.8647 0.6344 -2.6943 0.8720 21.693 20.715 304 249.22 762.22 -0.1990 0.1228 0.0474 0.1269 17.413 16.716 312 327.08 779.37 -0.0205 0.0972 0.1493 0.1075 19.041 18.268 316 524.35 786.65 0.1392 0.0754 0.3343 0.1175 19.833 18.921 317 448.74 791.48 0.4577 0.1442 0.0749 0.0801 21.849 20.486 318 786.60 795.94 -0.2162 0.1062 0.0376 0.1012 21.395 20.160 319 628.74 806.69 0.3696 0.1581 0.3442 0.1282 21.378 20.140 320 723.64 807.44 -0.1568 0.1069 0.4683 0.1941 17.851 17.125 325 429.96 825.94 0.1397 0.1116 0.2022 0.1425 21.115 19.932 326 755.21 827.00 -0.0912 0.1310 0.2343 0.1113 20.603 19.578 327 -2.82 832.37 -0.8890 0.6557 0.1625 0.5844 19.246 18.397 328 1022.80 837.46 0.2760 0.2918 -0.3812 0.1665 18.680 17.932 329 481.67 843.19 0.0643 0.0975 0.2986 0.1782 18.520 17.768 330 568.08 851.17 0.2540 0.1105 0.0140 0.1080 20.002 19.060 331 337.11 853.03 -0.0200 0.1316 -0.0314 0.1188 18.201 17.369 333 956.25 852.81 0.4950 0.1968 0.2784 0.1293 18.132 17.415 335 818.79 858.33 -0.4691 0.2061 -1.0644 0.3558 20.822 19.660 336 919.87 857.68 0.3338 0.1446 0.3906 0.1569 18.119 17.391 85 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 340 176.02 886.84 -0.5069 0.3739 -0.3971 0.4823 23.102 21.397 344 241.16 895.88 -0.0498 0.1740 -0.1472 0.2204 16.650 15.777 345 550.72 898.24 0.1770 0.1336 -0.0832 0.1835 18.490 17.741 347 884.18 899.93 -0.8589 0.3243 -0.3281 0.1587 21.889 20.093 399 650.69 957.33 -1.4900 0.5754 -1.6996 0.4930 23.501 21.530 402 429.19 959.80 0.4445 0.2512 -0.0314 0.2820 18.943 18.157 423 885.21 995.14 0.4538 0.2261 -0.2206 0.3353 17.149 16.314 430 566.38 1007.70 -0.0754 0.3155 -0.2410 0.5348 18.275 17.517 439 754.59 1025.50 0.3556 0.3658 0.4103 0.6816 20.321 19.281 503 764.84 522.73 0.5655 0.5497 -2.3211 0.7915 25.707 23.304 550 -40.85 575.36 -0.3063 0.5066 1.0955 0.7132 23.643 21.791 553 853.57 598.24 -2.8392 1.2462 -0.4051 0.5861 24.318 23.076 624 452.69 700.60 0.3043 0.5696 -3.0225 0.9431 25.838 23.673 650 119.15 718.91 -0.0860 1.2861 -0.3110 1.3140 25.694 23.398 722 391.13 781.89 0.3781 0.9295 -2.4170 1.1792 25.382 24.392 746 906.81 803.41 -1.6742 1.0401 0.4764 0.8558 25.129 23.808 758 316.79 809.09 0.0829 0.4301 -0.5005 0.4105 24.644 22.748 911 523.83 89.01 -2.3338 0.8104 -2.6938 0.9521 24.671 22.587 951 18.78 899.28 -0.3942 0.5877 0.0879 0.5661 17.804 17.048 966 383.72 905.30 -1.5265 0.8690 -1.1738 0.5789 27.043 23.554 967 429.12 905.44 0.7612 0.4723 -0.3359 0.5117 25.691 23.184 1015 312.20 921.35 -0.3175 0.5613 -0.1506 0.4786 24.373 22.555 1043 787.12 931.87 0.0397 0.3153 -5.9853 1.9341 25.768 23.126 1047 280.67 932.58 -0.6977 0.6668 0.8187 0.6848 24.173 22.522 1056 323.65 936.96 0.0949 0.2867 -0.2146 0.2360 19.549 18.692 1120 639.07 317.26 0.2755 0.3255 0.4769 0.3874 24.612 22.577 1126 987.92 968.20 0.3587 0.5282 -0.1298 0.4256 22.662 21.112 1207 210.49 996.54 -0.6363 0.4633 0.5155 0.5103 18.980 18.179 1258 831.19 -3.87 0.1125 0.5996 0.4963 0.4356 24.230 22.337 2101 864.92 57.89 -0.0104 0.3799 0.4559 0.2028 24.213 22.193 2122 901.86 99.63 -2.0659 0.7441 -3.3361 1.2544 26.182 23.791 2130 275.54 115.60 -1.5356 0.5295 -0.8519 0.3021 22.124 21.220 2131 317.81 116.33 -0.4945 0.2644 -0.1418 0.1721 23.923 21.981 2135 825.51 124.11 -0.1705 0.2308 0.6407 0.2741 24.059 22.106 2152 145.96 176.43 -0.1783 0.3112 0.0625 0.2956 24.556 22.655 2168 149.35 211.62 -10.0620 3.1974 1.2438 0.5194 25.610 22.655 2193 439.49 256.67 -3.3410 1.0817 3.0727 0.9902 25.249 23.414 86 Appendix A. NIRI Proper Motion Data Star ID x y PMx δx PMy δy V I 2408 158.97 477.49 -2.3141 0.9164 2.7475 0.9996 25.435 23.746 Table A.1: NIRI Proper Motion Data, the photometry is from the Advanced Camera for Surveys 87 Appendix B IFU Radial Velocity Data The cluster centre is located at the ACS coordinates (x,y) = (2882,2986). The each pixel is 0.049′′ projected onto the plane of the sky. ACS Star ID V V-I Vrad [km/s] δVrad [km/s] ACS X Pixels ACS Y Pixels Cluster Member? 5846 18.682 0.764 -28.45 2.3 2654.4 2838.2 yes 5847 19.326 0.835 -30.4 1.7 2660.5 2869.5 yes 5878 18.918 0.778 -19.5 1.92 2676.3 2843.8 yes 5879 17.986 0.715 -23.51 0.71 2695.5 2841.6 yes 5939 18.283 0.734 -18.89 2.28 2742 2818.7 no 6001 20.072 0.944 -31.91 2.17 2775.6 2805.3 yes 6002 20.192 0.958 -20.78 1.06 2784.2 2827.5 yes 6003 18.03 0.726 -23.85 0.38 2775.1 2833.7 yes 6004 20.119 0.941 -27.845 0.739 2790.6 2829.9 yes 6005 12.989 1.138 -21.774 0.043 2785.7 2868.1 yes 6037 19.063 0.89 -23.206 0.689 2799.7 2843.1 no 6038 19.255 0.819 -22.609 0.413 2804.1 2833.2 yes 6039 19.355 0.864 -29.841 0.76 2809.1 2871.7 no 6074 18.725 0.782 -27.61 1.01 2828.2 2831.8 yes 6100 17.694 0.718 -23.382 0.217 2858.6 2809.6 yes 88 A p p en d ix B . IF U R ad ial V elocity D ata ACS Star ID V V-I Vrad [km/s] δVrad [km/s] ACS X Pixels ACS Y Pixels Cluster Member? 6133 16.921 0.878 -22.932 0.248 2886.7 2808.2 yes 6167 14.361 0.972 -26.561 0.055 2919.6 2809.9 yes 10025 18.216 0.71 -23.533 0.41 2650.8 2972.9 yes 10049 19.123 0.805 -23.45 4.1 2682.3 2899.5 yes 10050 17.413 0.697 -4.814 0.81 2681.2 2985.3 no 10051 16.65 0.873 -26.243 0.089 2677.7 3043.8 yes 10077 19.041 0.773 -26.688 0.79 2715.3 2992.5 no 10079 18.201 0.832 -15.57 0.78 2719.7 3024.6 no 10081 19.549 0.857 -28.4 1.07 2713.8 3061.4 yes 10116 16.375 0.875 -20.3 0.58 2732.5 2879.7 yes 10118 19.026 0.833 -21.26 0.436 2742.5 2890.3 no 10119 18.671 0.761 -17.667 0.41637 2726.9 2973 yes 10143 18.858 0.782 -24.48 0.4776 2767.7 2898.2 yes 10146 20.072 0.938 -30.74 2.1 2758.9 2958.5 yes 10175 17.962 0.725 -25.272 0.269 2795.6 2937.6 yes 10179 18.52 0.752 -26.595 0.879 2782.8 3019.7 yes 10202 19.553 0.871 -30.359 1.109 2815.6 2938.9 yes 10204 19.833 0.912 -26.273 1.2502 2801.4 2994.9 yes 10205 20.002 0.942 -32.995 1.97 2820.5 3022.9 yes 10206 18.49 0.749 -28.406 0.759 2813 3043.6 yes 10247 19.947 0.848 -21.078 0.772 2842.4 2974.7 no 10279 18.24 0.743 -23.159 0.65 2867.2 2962.5 yes 10306 19.205 0.808 -20.166 1.435 2878.6 2920.3 yes 10310 19.004 0.788 -22.98 1.04 2891.6 2975.5 yes89 A p p en d ix B . IF U R ad ial V elocity D ata ACS Star ID V V-I Vrad [km/s] δVrad [km/s] ACS X Pixels ACS Y Pixels Cluster Member? 10312 17.851 0.726 -22.857 0.459 2888.3 3003.4 yes 10333 19.32 0.833 -26.528 2.61 2913.8 2888.1 yes 10372 16.57 0.94 -53.23 0.3345 2929.1 3010 no 10245 14.468 0.964 -20.628 0.098 2838.3 2953.7 yes 10248 14.864 0.971 -22.386 0.0872 2828.6 2988.5 yes Table B.1: Radial velocity data from the GMOS IFU, the photometry is from the Advanced Camera for Surveys. To convert from NIRI coordinates to ACS coordinates use: xACS = (A× xNIRI) +B (B.1) yACS = (C × yNIRI) +D (B.2) Here A & C = 0.438 (the NIRI plate scale divided by the ACS plate scale), B = 2636 and C = 2761.5. 90 Appendix C Bulk Motion of Messier 71 Here we attempted to derive the bulk motion of Messier 71. For this we need to calculate the bulk proper motion of the cluster. Stars with known proper motions or distant galaxies can serve as extragalactic anchors to determine the bulk motion of a globular cluster. We attempted to look for point like galaxies in our NIRI field to find an extra galactic anchor. The first task was to use our PSFs that we had created from chapter 2 and subtract stars from our images. We then look for any left over flux in the subtracted image. A point like star would have zero residual flux whereas a galaxy which is elongated would have some left over. Figure C.1: An example of a NIRI image prior to star subtraction. 91 A p p en d ix C . B u lk M otion of M essier 71 !" !# !$ !% !& !' !( !)*# !) !!*# !! !+*# + +*# ! ,-./0123-/45676849 : ; < 3 . . 6= 3 - /0 4 56 > 51 ; 6? = : @ A : B ,C D !" !# !$ !% !& !' + +*! +*) +*( +*" +*# +*$ +*% +*& +*' ! A E 1 - F - 3 . . ,-./0123-/45676849 Figure C.2: Four objects were found to survive both cuts in residual flux and sharpness. Three of them were found to be on the cluster CMD, the fourth was not. 92 Appendix C. Bulk Motion of Messier 71 From the four objects that survived the cuts in excess flux and roundness three of them were found to be on the CMD, the fourth was not. However, upon closer inspection the object is likely a visual binary star. The bulk motion of M71 can still be calculated using background galaxies, from figure 2.2 there are numerous background galaxies visible. The bulk motion of M71 has already been calculated by Cudworth (1985) [6] and it resembles the motion of a typical galactic disk cluster. 93 Appendix D Installation of DAOPHOT The installation of DAOPHOT may not be trivial to a novice user, espe- cially if the user has little experience with command line scripts and Fortran makefiles. The following explains how to install DAOPHOT on a computer running Mac OS. This is different from the DAOPHOT software that comes pre-installed on IRAF, this is a standalone version which offers more versa- tility and options for reduction of photometric and astrometric data. Prior to installation of DAOPHOT and its family of software the user will need to acquire the following software: 1. Download and install a gcc compiler 2. Install Mac Xcode developer’s tools. This is a free download from Apple Inc and also comes on the Mac OS installation DVD. 3. Download and install the cfitsio package. This is avaialbe from the High Energy Astrophysics Science Archive Research Center’s (HEASARC) software page. 4. Acquire DAOPHOT from Peter Stetson. 94 Appendix D. Installation of DAOPHOT Installing of DAOPHOT Figure D.1: Daophot Makefile. 95 Appendix D. Installation of DAOPHOT Modify the fifth line in the included Makefile to have the FITSLIB directed to the folder where libcfitsio.a is found (see figure D.1) Switch to the tsch shell in terminal, this shell is required to install DAOPHOT. Once in tsch run Makefile. This will only compile the pro- grams and not package them all into their suites. It packages only the the suite found at the top of the Makefile script. Now edit Makefile and delete the DAOPHOT code and replace it with the next package as the suite at the top of the script. Repeat the step in figure D.2 until the rest of the suites are installed. When this is finished executables for daophot, daomaster, daomatch, daogrow, allstar, montage2 and allframe should all be ready for use. 96 Appendix D. Installation of DAOPHOT Figure D.2: The Makefile is now edited so Allstar is the next suite to be packaged. Run Makefile again and Allstar will be installed. 97 Appendix E Extra Photometric Work Here we present additional colour-magnitude diagrams from two other data sets of Messier 71. Both data sets were not involved in our analysis of the data but are here to show that they are available for the interested researcher. This data is available for download from the Canadian Astro- physical Data Centre. 98 Appendix E. Extra Photometric Work Figure E.1: Canada-France-Hawaii Telescope image of M71 from The CFHT Adaptive Optics Bonnette from 1991. With a field of view is 90′ on each side of the image, two images one in B and the other in R with a integration time of 120s for each filter. 99 Appendix E. Extra Photometric Work ! !"# $ $"# % $! $$ $% $& $' $# $( $) $* $+ ,!- , ./ 01 2 34 5 6 7 1 38 9: Figure E.2: A CMD from the data in Figure E.1. The CMD is in uncali- brated magnitudes. 100 Appendix E. Extra Photometric Work Figure E.3: Image of Messier 71 obtained using the Wide Field Infrared camera from CFHT. The image is 20′ x 20′. This is a H band image of the cluster which is found in the top left hand of the image. The red circle depicts a ∼ 7′ circle centred on the cluster centre 101 Appendix E. Extra Photometric Work Figure E.4: A CMD from the data in Figure E.3. The stars within the circle are represented with red points, they are likely cluster members, likely galatic field stars are represented by black markers, those are also the stars which were not in the circle from Figure E.3. 102

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