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Deep IR adaptive optics imaging of the core of M71 Ruberg, Andres 2008

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Deep IR Adaptive Optics Imaging of the Core of M71 by Andres Ruberg  B.Sc., The University of British Columbia, 2006  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate Studies (Astronomy)  The University Of British Columbia (Vancouver) August, 2008  ©  Andres Ruberg 2008  Abstract Data collected in H and K bands from Gemini North observatory using the NIRI/ALTAIR adaptive optics (AO) system, have been used to draw a number of new conclusions about the globular cit ster M71. K band obser vations were made in 2 epochs, separated by a 1.81 year baseline, allowing for the separation of field stars from cluster stars based on proper motion. A color-magnitude diagram (CMD) made using only cluster stars agrees well with current models. A stellar density profile was also constructed and appears to flatten at small radii, suggesting that a multimass King profile does describe the cluster quite accurately, a result contrary to that found in other work. Most significantly, the distance to M71 was calculated using the measured velocity dispersion compared to the radial dispersion measured for giant stars. The distance measured was 3.36 ± 0.71 kpc.  11  Table of Contents Abstract  ii  Table of Contents  iii  List of Figures  v  Acknowledgements  xiii  Dedication  xiv  1  Introduction 1.1 Globular Clusters 1.1.1 Colour Magnitude Diagrams 1.1.2 King Models 1.2 M71 1.2.1 History 1.2.2 Recent Work  2  Reduction 2.1 The Data 2.2 Processing 2.3 Reduction 2.3.1 Detection and Measurement 2.3.2 Registration and Co-addition 2.3.3 Creating a Finding List 2.3.4 Photometry and Astrometry 2.4 Proper Motion Measurement 2.4.1 Registration 2.4.2 Error Measurement 2.4.3 Proper Motion Calculation and Measurement of Ve locity Dispersion 2.5 Locating The Center of M71  1 1 2 4 5 5 6 13 13 13 14 15 15 17 18 31 31 34 35 39  111  Table of Contents 2.5.1 2.5.2 3  4  Motivation Procedure  39 40  Results 3.1 Proper Motions and the CMD 3.2 Surface Density Profile 3.3 Calculating the Geometric Distance to M71 Using Proper Mo tions  43 43 46  Discussion and Conclusions  49  Bibliography  46  51  Appendices A NIRI Array Characteristics  54  iv  List of Figures 1.1  1.2  From Richer et al’s 2007 paper [26), this CMD plots the mag nitude of Hubble filter F814W against the difference in mag nitudes measured in the F606W and F814W filters. This CMD for NGC 6397 is narrower than most due to the proper motion selection of cluster stars and exclusion of field stars. Labeled are the various aspects of a CMD. All stars spend the majority of their active lives on the main sequence, with the more massive stars inhabiting the upper end (lower mag nitudes) and the less massive stars inhabiting the lower end (higher magnitudes). As the stars process their elements they migrate off the main sequence up the red giant branch; this is what results in the main sequence turnoff. During this phase they shed much of their outer material and lose a large frac tion of their mass. Following this phase they carry on up the red giant branch to the assyasymptoticnt branch and eject their outer mass envelope. Finally, they come down the hor izontal branch, eventually cooling and becoming white dwarfs CMD from Hartwick and Arp’s 1971 paper [3]. Stars that were identified from photographic plates are filled circles. Those which had photoelectric measurements taken are represented by the other symbols. Their meanings are as follows: un filled circles represent main sequence stars, crosses represent blue stragglers, X’s represent horizontal branch stars, trian gles represent giants, turned triangles represent asymptotic branch stars and squares represent bright blue stars  3  7  V  List of Figures 1.3  1.4  1.5  2.1  Figure from [27]. This plot shows the number of stars found in M71 plotted against magnitude. The global luminosity function for M71 (solid histogram) is plotted alongside that of 47 Thc (broken line). The two functions are normalized at V=18.5, and M71’s function represents all stars brighter than V=24 from the center out to 3.4 arcminutes, while the data from 47 Thc represents a field near 41 cote radii Figure from [27]. This plot shows the number of stars found in M71 plotted against magnitude for a range of annuli. The global luminosity function for M71 (dashed line) is plotted alongside local luminosity functions (solid line) for 5 different annuli. The plot represents the normalized number of stars in a given magnitude bin. From the diagrams it is clear that there is mass segregation in this cluster as one finds fewer faint stars in the annuli closer to the cluster center than at larger distances. This is strong evidence that the cluster is dynamically relaxed. The luminosity functions are normal ized at V=18.5 Figure from [12]. These plots illustrate tFie surface density profiles for the two most luminous mass classes observed in M71. The filled circles represent stars with masses 0.85 < 0 < 0.89, where the open circles represent stars with M/M 0 < 0.85. The uppr data points rep masses 0.71 < M/M resented by crosses are displaced upwards.0.5 dex and rep resent the sum of the other two sets of data. (a) and (b) show the same data, but in (b) a multirnass King model is overlaid. Both mass samples show a higher, degree of concen tration than expected in the model, with .a large amount of the discrepancy coming from the higher mass stars This graph displays the number of objects found as a function of finding threshold in sigma. When using DAOFIND, if one does not know beforehand what threshold to use, this plot is consulted and typically from the knee of this graph one determines an appropriate threshold level. The black line and crosses represent the K band data  9  10  12  19  vi  List of Figures 2.2  2.3  2.4  2.5  This figure is the initial CMD of M71 plotting K magnitude against H-K colour. This plot represents the results of aper ture photometry performed on the combined H and K images and represents nearly 500 objects. Many faint objects would later prove to be artifacts that were not renoved in the pro cessing Output from IRAF. This is an isophotal contour plot of a bright star near the guide star on the combined H image, to be compared with figure 2.4, as an example of the varying PSF in the NIRI/ALTAIR data Output from IRAF. This is an isophotal contour plot of a brighter star found near the top of the combined H image. It is readily seen that the PSF is quite vertically stretched when compared with figure 2.3. The magnitude arid direction of the distortion is a function of radial distance from the guide star and location on the image. Objects displaced horizontally from the guide star show horizontal strefthing and objects in the corners show stretching along a diagonal axis. This same phenomenon is observed in the K data This figure illustrates the effect of the radial variability in the PSF in the H data, with each data point representing a star. On one axis is plotted the difference between the aperture and psf magnitude measurements. On the, other axis the ra dial distance from the guide star is plotted in pixels. It is apparent that there is a trend with the magnitude difference linearly declining with distance. PSFs become distorted when measured further from the center of the image and the result ing magnitude is affected. So long as one uses a large enough aperture, the aperture magnitude does not suffer significantly from this effect. A clear linear trend can be ascertained from this data, and the necessary magnitudes added back into the PSF results. The fit to this plot indicates that 0.00032 mag nitudes per radial pixel need to be added back into the psf magnitude data. At the corner of the image this corresponds to more than 0.2 magnitudes  20  22  23  24  vii  List of Figures 2.6  2.7  2.8  This figure illustrates the effect of anioplanisity in the K data, with each data point representing a star. On one axis is plotted the difference between the aperture and psf mag nitude measurements and on the other the radial distance from the guide star in pixels. It is apparent that there is a trend with the magnitude difference linearly declining with distance. PSFs become distorted when measured further from the center of the image and the resulting magnitude is af fected, whereas, so long as one uses a large enough aperture, the aperture magnitude does not suffer significantly from this effect. A clear linear trend can be ascertaliled from this data, and the necessary magnitudes added baèk into the PSF re sults. The fit to this plot indicates that 0.00022 magnitudes per radial pixel need to be added back into the psf magnitude data. At the corner of the image this corresponds to nearly 0.15 magnitudes This figure represents a CMD derived from the PSF photom etry of the combined H and K data. Small corrections to the data have been made in way of a radial correction and a more accurate calibration than that performed with the aperture photometry. Especially encouraging is the tightening of the sequence at brigher magnitudes This plot shows the number of frames a star was found on against un-calibrated magnitudes. ALLFRAME reports on how many frames a given object is found. It was discovered that the spurious objects in our data were found on fewer frames than actual objects, making them easy to discard based on this criterion. This figure represents the number of H frames a star was found on as a function of magnitude. Rather than allow any spurious objects tO infiltrate our data a cut was made just under 210, where the maximum number of frames an object could appear on was 218. In addition, it was clear that at the faint end objects wo’Lild not be found on every frame due to their faintness. Therefore, a small excep tion was made that stars fainter than 17.1 magnitude only needed finding on 170 frames. Similar c1ts were made in the second filter and in the second epoch  25  27  29  viii  List of Figures 2.9  The final calibrated version of our CMD using the same pho tometry results as presented in figure 2.7. The only difference being that nearly 200 objects have been removed due to their not appearing on the required number of frames as illustrated in figure 2.8. Also, this CMD is plotted on a different scale than those previous to better demonstrate its shape 2.10 Proper motion plot for the core of M71. The plate scale for this data is 0.022”, Both axes represent pixel movement over a 1.81 year baseline. Errors come from the fit to the proper motions of stars that were measured both on the Gemini and CFHT fields. As the CFHT data did nt probe as faint as the Gemini data, errors were extracted for many stars based on a fit of error versus magnitude (see figure 2.12). For a more detailed examination of the data near 0,0 please refer to figure 2.11 2.11 Proper motion plot for the core of M71. The plate scale for this data is 0.022”. Both axes represent pixel movement over a 1.81 year baseline. Errors come from the fit to the proper motions of stars that were measured both on the Gemini and CFHT fields. As the CFHT data did not probe as faint as the Gemini data, errors were extracted for many stars based on a fit of error versus magnitude (see figure 2.12). For a more extended examination of the data near please refer to figure 2.10 2.12 This figure represents the errors added in quadrature of the x(t) and y(t) fits against magnitude. EriOrs on the proper motion for each star are based on a linear fit to the 3 (x,y) coordinates from the 2 sets of Gemini data and the 1 set of CFHT data. A linear fit was performed In x(t) and in y(t). The slope of each of these fits represents the pixels per year the star had been moving. The errors oh these two slopes were added in quadrature to calculate the errors represented above. The solid line represents a linear fit to this error data, with a slope of .0016 (pixels/year) per magnitude  30  32  33  36  ix  List of Figures 2.13 This plot shows o- in our stars’ motion in the x direction about 0 over a 1.81 year baseline versus iEnagnitude, where the magnitudes were binned into equal sized bins between 15th and 23rd magnitude. For each bin cr, or dispersion, was calculated as outlined in 2.4.3. The higher values found for brighter stars can be attributed to the small number of objects in these bins, where as the fainter magnitudes higher dispersion are possibly attributed to a fw sources. First, these stars have larger errors in their motion, therefore, it is no surprise that they occupy a larger area, in proper motion space. Secondly, the fainter stars are of lower mass and as a result are expected to occupy a larger area in proper motion space. Lastly, a large fraction of these faiiiter objects occupy the same space on the proper motion diagram quite near the field and may represent some sort of field population moving together through space. All of these effects taken together likely explain the large dispersion found fOr the fainter stars. 2.14 This plot shows o in our stars’ motion In the y direction about 0 over a 1.81 year baseline versus magnitude, where the magnitudes were binned into equal sIzed bins between 15th and 23rd magnitude. For each bina o, or dispersion, was calculated as outlined in 2.4.3. The higher values found for brighter stars can be attributed to the small number of objects in these bins, where as the faintei magnitudes higher dispersion are possibly attributed to a few sources. First, these stars have larger errors in their motion, therefore, it is no surprise that they occupy a larger area in proper motion space. Secondly, the fainter stars are of lOwer mass and as a result are expected to occupy a larger area in proper motion space. Lastly, a large fraction of these fainter objects occupy the same space on the proper motion diagram quite near the field and may represent some sort of field population moving together through space. All of these effects taken together likely explain the large dispersion found for the fainter stars.  37  38  x  List of Figures 2.15 Plotted is an un-calibrated CMD from 2Q06 ACS data on M71. Using points along the edge of the main sequence, an upper and lower cut was made on all of the stars in order to better ensure cluster membership for the sample being stud ied. A cut was also made at magnitudes 21 and 16.25 where the shape of the main sequence was no longer thought to be well defined. The stars passing the cut are displayed in red. These stars were then used in determining the cluster center 2.16 Contour map showing the quality factor for various pixels on the ACS plane. This does not represent the entire ACS chip, only the central region near where the center is thought to be based on past observations and calculations. From the 2-d Gaussian fit, the center is thought to lie at approximately = 19: 53 : 46.98 ± .15 and ö = 18 : 46: 46.5± 1.0. These errors represent far greater precision than previous measurements, and the center varies by nearly 10 arcseçonds from Harris’ value. However, the center of the cluster does still fall within our field 3.1  3.2  41  42  This figure is identical to figure 2.9, except with a line overplotted. The model overlaid in blue represents a model for a globular cluster with a [Fe/H] =-0.70 and Age= 12.0 Gyr. This model was projected to the distance of M71 using a distance modulus of 13.79 in V and E(B-V)=0.25, bOth from Harris [17]. 44 The points in this figure represent the same as those in figure 2.9 except it only includes points that made the proper mo tion cut. The model overlaid in blue represents a model for a globular cluster with a [Fe/H] =-0.70 and Age= 12.0 Gyr. This model was projected to the distance of M71 using a distance modulus of 13.79 in V and E(B-V)=0.25, both from Harris [17]. It is clear that the model arid main sequence do not over lap entirely, but the agreement is good. When compared to figure 3.1 the sequence is both tighter and better conforming to the model, especially around 19th to 20th magnitude. 45 .  .  .  xi  List of Figures 3.3  The surface density profile for M71. Plotted is surface density in number of stars per pc 2 against radius in pc, on a log-log scale. Our data is plotted in black, and Drukier’s [13] in red. Our data suffers from having incomplete annuli, therefore, lower number statistics, but has the advantage of probing closer to the core of the cluster. Drukier’s scaling of 2.01 pc per 1.88’ was adopted to put our data on the same scale. Also note, we did not perform any incompleteness tests, therefore all values we obtained should be taken as lower limits on the actual number densities  47  xli  Acknowledgements There are many individuals deserving acknowledgment for the assistance they provided at all steps of the research process.. First, I would like to acknowledge Dr. Harvey Richer who both suggested the project and helped shape its direction along the way. Harvey assisted me in deciding which paths were worth pursuing and which were likely dead ends, and also assisted greatly in pointing out papers and other individuals who I needed to contact in order to sort out the various issues I encountered during the research. Saul Davis was extremely helpful throughout thy research, often provid ing me with the tools I needed to complete various tasks. Saul patiently explained various routines and techniques and provided me with sample code that was extremely useful in performing my research. Dr. Jeremy Heyl assisted in the assessment Gf the quality of our re sults and in providing valuable suggestions concerning the proper motion reduction. Ronald Gagne provided me with the data from CFHT in a fully reduced and read-to-use format for purposes of calculating proper motions. Dr. Aaron Dotter helped both in developing models for M71 as well as assisting in the data calibration. Dr. Tim Davidge gave useful advice in the ptocessing and reduction of ALTAIR data from Gemini and was very helpful when I encountered problems in the data reduction. Dr. James Brewer provided me with reduction routines that he devel oped for ACS data. These formed the framework of my own reduction routines, and were extremely useful. Dr. Peter Stetson could be relied upon to answer any email within hours in regard to his DAOPHOT software package, and helped immensely in understanding how the software functioned and how best to interpret and make use of its output.  xiii  Dedication This work is dedicated to my supportive and loving wife Cindy, without whose support I don’t suppose I would have finished at all. Her patience and understanding during my graduate work was incredible and the mark of an outstanding lady.  xiv  Chapter 1  Introduction 1.1  Globular Clusters  The Ivlilky Way is home to more than 160 globular star clusters. Globular clusters are roughly spherical, dust-free, stellar populations which contain thousands to millions of stars. These objects exhibit a wide range of sizes, densities and metallicities. Most exhibit only a single star formation stage, allowing for very accurate age estimates to be obtained. Because of this property, globular clusters provide some of the most accurate estimates for the ages of early generation stars. They have also been used in determin ing the position of the Sun in relation to the center of the Milky Way by observing their distribution on the sky [29]. Gas free collections of stellar objects, with relatively simple dynamics, containing relatively few objects make globular clusters excellent candidates for observation and modeling. As such, they have provided excellent testbeds for stellar dynamics and star formation theories. These many properties make globular clusters an excit ing area of study, and before discussing the details of cluster M71, below is a brief introduction to these systems. The clusters of the Milky Way are divided into two major groups; the disk, and halo populations. The difference between the two is most easily seen in the metallicity of the clusters, which ranges from [Fe/H] —2.5 for the metal-poor clusters examined by Geisler [16} to the metal-rich Lillier 1 cluster, found to have [Fe/H] = +0.25 ± 0.3, observed by Frogel [14]. [Fe/H] is defined in equation 1.1. [Fe/H]  loglo(NFe/NH)  —  loglo(Nfr€/NH)o,  (1.1)  where the 0 denotes a solar quantity. The distinction between the two metallicity classes was first noted by Kinman in 1959 [20], when he observed that the metal-rich clusters form a more highly-flattened, rapidly rotating population. This was confirmed in 1985 by Zinn [32], who made a quantitative distinction between the two systems, defining disk clusters as those with Fe/H —0.8 and halo clusters as those with Fe/H —0.8. The difficulty in imaging low latitude fields 1  Chapter 1. Introduction  (due to extinction and field star contamination 1) means that until recently it was difficult to accurately determine the parameters of many disk population globular clusters. For a detailed study and comparison of the two globular cluster families one should refer to Armandroff’s 1989 work [2].  1.1.1  Colour Magnitude Diagrams  Much of the information one can infer from a globular cluster comes from a cluster’s colour-magnitude diagram (CMD). This diagram represents the individual stars of a cluster as points on a plot that .give information about that particular star’s brightness and colour. Typically these axes are defined by filters that are used to selectively collect light from specific wavelength ranges. A star’s value on the vertical axis is its biightness in a given filter, where the horizontal axis value represents the difference in brightness be tween two filters. A random sample of stars in the sky will form a pattern on this plot but it will be scattered due to the fact that these stars have all been born at different times, are located at different distances and are of different metallicity. However, when the stars of a population all born at the same time and place are plotted on a CMD they form a narrowly defined sequence, that has great explanatory power and hformation. A globular cluster is such a system, where all the stars are thought to have been born at the same time and from the same material; most CMDs of gobu1ar clus ters are characterized by these narrow sequences. Refer to Figure 1.1 for an example of a CMD of a globular cluster. The distance to a cluster can usually be determined by the locations of the main sequence and sub-giant branch. The locations of the main sequence and sub-giant branch depend strongly on the met allicity of the cluster, which is usually measured from the spectra of individuài cluster stars. Once the metallicity is measured, it is possible to determine he distance to the cluster by fitting known main sequence stars of the same metallicity and age of the cluster. This fit is done using the brightnesses and colours of metalpoor nearby sub-dwarf stars whose distances have been accurately been determined by parallax measurements. Using sub-dwarf stars is a necessity due to most globular clusters being extremely old and consisting primarily of low-mass stars. A CMD is typically modeled using isochrones. These are theoretical curves which attempt to simulate the lives of stars that all start on the ‘Since the Milky Way is a disk galaxy, the non-cluster star density increases when you observe fields at low galactic latitude making it difficñlt to distinguish cluster from non-cluster stars.  2  Chapter 1. Introduction  10  I  —  co  20  25  30 —1  0  1  2  P606W  3  4  5  6  P814W  Figure 1.1: From Richer et al’s 2007 paper [26], this CMD plots the magni tude of Hubble filter F814W against the difference in magnitudes measured in the F606W and F814W filters. This CIVID for NGC 6397 is narrower than most due to the proper motion selection of cluster stars and exclusion of field stars. Labeled are the various aspects of a CMD. All stars spend the majority of their active lives on the main sequence, with the more massive stars inhabiting the upper end (lower magnitudes) aüd the less massive stars inhabiting the lower end (higher magnitudes). As the stars process their el ements they migrate off the main sequence up the ted giant branch; this is what results in the main sequence turnoff. During this phase they shed much of their outer material and lose a large fraction of their mass. Following this phase they carry on up the red giant branch to the assyasymptoticnt branch and eject their outer mass envelope. Finally, they come down the horizontal branch, eventually cooling and becoming white dwarfs. 3  Chapter 1. Introduction main sequence at the same time, at the same metallicity. One evolves these stars using the stellar evolution model of their chdice, and then produces a CMD for an appropriate age and metallicity. UsIng these isochrones along with other data, one can fit the data from globular clusters to determine their age and distance, as well as the amount of reddening between that cluster and the observer. Also, in the event that a cluster is not comprised from a single age population of stars, more than one isochrone may be used to determine how long the star formation stage lasted.  1.1.2  King Models  In the 1960s Ivan King and Richard Michie developed models (now com monly called King models) that described the behavior of globular clusters based on their dynamical behavior. In a series of papers (see [22] [18], [19], [23] for example) they generated models based on the assumption that the most energetic stars in a cluster will have been removed through tidal interac tions with the Milky Way galaxy. These energetic stars represent those which travel furthest from the core of the cluster, therefore their removal, and the radius beyond which they are removed defines a tidal radius, rt. This parameter is one of two King included in the basic model describing the behavior of stellar populations in a globular cluster environment, the other being the core radius, r, defined to be the radius at which the surface brightness of the cluster has fallen to half its central value. The basic King model makes the assumption that all of the stars in the cluster are of identical mass, but this an incorrect assertion, as globular clusters are made up of stars spanning a large range of masses. From this, the problem arises that because globular clusters are very old the encounters between their constituent stars will have re-distributed their initial energies, driving them towards energy equipartition. This means that the lower mass stars will be travelling more quickly on average than the higher mass stars in the cluster. Another model was created to address this concern, known as a multimass King model, which divides the stellar population of the cluster into a number of different mass bins. The velocity dispersion of each bin is then chosen so that the kinetic energy is in equipartition throughout the cluster. The fraction of stars in each bin is chosen based on observations of the relative numbers of stars of the appropriate luminosity. Faint stars such as brown dwarfs, white dwarfs and neutron stars are not always detectable and thus difficult to model appropriately. An important property of King models is that. inside the core radius, the surface density of stars approaches a constant value. Most clusters 4  Chapter 1. Introduction exhibit this property, but some, such as M15, andpotentially M71, show rising surface density profiles into their cores. This phenomenon is often described as a cusp in the density profile, Numerical simulations made since King models were first developed, have shown that spherical, self-gravitating systems that initially start with fiat cores eventually all form these cusps, a phenomenon known as core-collapse. A suggestion for how this runaway process is halted is that a tight binary forms in the core of a cluster, providing a means of redistributing energy to halt the collapse. Another mechanism suggested for the formation of cusps is the presence of a massive black hole at the center of certain clusters. Bahcall and Wolf demonstrated in 1976 [4], that stars in such a system will produce a sufface brightness profile at small radii that follows the power law 1(R) cx . 07 very much in line with r , 5 observed cusps. The presence of a black hole would also be revealed by an increase in the random velocities of stars in its ininiediate vicinity, whereas for a core collapsed cluster this sort of increase wcrnld not be expected.  1.2 1.2.1  M71 History  M71 is a low latitude, medium metallicity globular cluster originally dis covered in 1745-46 by the Swiss astronomer Philippe Loys de Cheseaux. He published this discovery along with several others iii the Académie Francaise des Sciences. M71 was independently rediscovered twice more by Johann Gottfried Koehler and Pierre Méchain in the 1770s und on June 28, 1780 re spectively. These observations all came before OctOber 4, 1780 when Messier identified this cluster as the 71st item in his famous catalog. Messier’s corn rnents on M71 were, “its light is very faint & it cbñtains no star; the least light makes it disappear”. This difficulty that Messier had in observing M71 is likely due to its low surface brightness combined with its low galactic lat itude. Since it was initially observed and classified as a star cluster, there was debate in the early 20th century as to whether M71 was a condensed open cluster or a loose globular cluster. For instance, in 1943 Cuffey first took the stance that M71 was a loose globular cluster due to its similarity to M68 and NGC5053, but in 1959 made a CMD [6] and decided that M71 more resembled an open galactic cluster. Recent work, examined in the next section, has clarified this problem and identified M71 as a loose globular cluster.  5  Chapter 1. Introduction  1.2.2  Recent Work  In 1971, Hartwick and Arp [3] made some of the first modern observations of M71, and combined photoelectric with photographic observations in U, B and V to produce a CMD. They found this diagram typical of a metalrich cluster with only a short, red horizontal branch and a gently sloped giant branch. Other clusters exhibiting CMDs with these characteristics are NGC 6356 and 47 Thc, both of which are considered metal-rich. The pa rameters derived for M71 from Hartwick and Arp are: EB_V = 0.31 ± 0.02, (m—M)o = 13.07±0.21, [Fe/H] = —0.30±0.2, and age = 7.6(+3.1, —2.3) years. Their main sequence is included below as Figure 1.2. Most of the stars measured are unsurprising, but the large number of blue stragglers is a curiosity. At the time, these observations caused.M71 to stand out as a globular cluster, as such a large extension of the main sequence had only been observed in M3, and even that blue straggler sequence was not as con spicuous. These stars have been explained as a residual main sequence of younger, unevolved stars, but this would of course require that star forma tion needed to have been occurring over a long time relative to the age of the cluster. The other explanation is that these stars evolved in a close-binary system. This explanation makes additional sense if one believes M71 to be a member of the disk globular cluster population as these members typically contain a higher fraction of spectroscopic-binary stars [1]. The next significant work on M71 happened in 1985, when Cudworth published results illuminating new and curious information about the clus ter [5]. His observations in B and V improved upon previous work by using new photoelectric calibrations. By measuring proper motions he was able to derive cluster membership probabilities. It was discovered through this improved set of data that M71 was not so different from 47 Thc as previ ously believed. In the analysis of Arp and Hartwick [3] it was found that the horizontal branch (RB) had a greater extent in B-V and a wider red giant branch (RGB) than 47 Thc. However, Cudworth’s observations and improved calibration suggested that if one allowed for different distances and reddening, that the CMDs of the two clusters could be superimposed such that the RB’s agreed both in magnitude and in colour extent. Using this in formation, assuming that the intrinsic colours of the HB and ROB were the same in the two clusters, the reddening of M71 wa A(B V) = 0.23(±0.02) magnitudes larger than 47 Thc, resulting in a E(B — V) 0.27 for M71, a value very close to that found in Arp and Hartwick’s initial paper [3]. Also interesting in Cudworth’s work in 1985 [5] was that he measured the internal velocity dispersion of M71. Peterson and King [23] predicted —  6  Chapter 1. Introduction  12  14  IS V Is  17  19 0.0  10  B -V  Figure 1.2: CMD from Hartwick and Arp’s 1971 paper [3]. Stars that were identified from photographic plates are filled circles. Those which had photoelectric measurements taken are represented by the other symbols. Their meanings are as follows: unfilled circles represent main sequence stars, crosses represent blue stragglers, X’s represent horizontal branch stars, tri angles represent giants, turned triangles represent asymptotic branch stars and squares represent bright blue stars.  7  Chapter 1. Introduction an internal dispersion of approximately 2.5 km/s, corresponding to a proper motion dispersion of 15 mas cent 1 (milli-arcseconds per century). Using some of the brighter stars, where proper motions were measured to this ac curacy, Cudworth measured the velocity dispersion for two separate groups of stars in the cluster. Stars within a 100” radius were found to have a veloc ity dispersion of 18 ± 3 mas cent 1 (3.1 ± 0.7 km/s) and those outside that radius were found to have a dispersion of 28 ± 4 mas cent . These values, 1 especially for the outer group of stars were higher than predicted, however, no further investigation occurred at the time due to the lack of precision in the proper motions. Also, by analyzing the motions of stars in the cluster relative to the field stars, Cudworth was able to determine the space velocity of M71. The measured space velocity of the cluster, with the Sun’s peculiar velocity accounted for was (11,8, Z) = (—44 ± 14, —9 ± 10, +28 ± 14) km/s, where 11 is directed away from the Galactic center at the cluster’s location and 8 is in the direction of Galactic rotation. In Cudworth’s opinion, at the time this was possibly the best-determined space velocity of a globular cluster because of the small value and small uncertainty of secular parallaxes at low latitude. In 1988 the M71 luminosity and mass functions were explored in some detail by Richer and Fahiman [27] using CFHT data in U and V. These were unique observations at the time in that they were centered on the core of M71 arid sampled a large fraction of the mass of the duster. It was determined that the global 2 luminosity function of M71 was flatter than that of 47 Thc, a cluster very similar to M71 in metallicity. The two finctions overlaid can be seen in Figure 1.3. This luminosity function supported ideas of dynamical relaxation, as the relative number of low-luminosity stars increased with radius, as seen in Figure 1.4. Another important conclusion from this paper was the comparison of observed to predicted mass-to-light ratios (M/L) for M71. The observed M/L was about 0.57, but that inferred from dynamical studies was 1.2. This motivated the idea that there was a large dark component of M71 that had not yet been observed. The 3 candidates for this non-visible component were neutron stars (1.4M®), white dwarfs (0.6M®), and low-mass stars (0.1M ). 0 The different candidates were tested in multimass King models, and the best fit for these tests was obtained when the dark mass was primarily stored in faint low-mass stars. The only constraint on these objects was that they must be less massive than 0.33M , and must comprise between 50% and 0 90% of the mass of the cluster. global here defined as including all stars out to 205” or 3.19 half-brightness radii 2  8  Chapter 1. Introduction  4—  I  I  III  I  j  I  I I_f  M71 Global 47 Tuc---3—  >  z 0  I  I 12  14  18  i  i  I 18  I  I 20  I  I  I  22  24  V Figure 1.3: Figure from [27]. This plot shows the number of stars found in M71 plotted against magnitude. The global luminosity function for M71 (solid histogram) is plotted alongside that of 47 Tuc (broken line). The two functions are normalized at V=18.5, and M71 ‘s function represents all stars brighter than V=24 from the center out to 3.4 arcrninutes, while the data from 47 Thc represents a field near 41 core radii.  9  Global 4/  z 0  I,  12  14  16  18  20  20  24  16  18  20  2  3  2  z 0  0 152025  z 0  V  V  Figure 1.4: Figure from [27]. This plot shows the number of stars found in M71 plotted against magnitude for a range of annuli. The global luminosity function for M71 (dashed line) is plotted alongside local luminosity func tions (solid line) for 5 different annuli. The plot represents the normalized number of stars in a given magnitude bin. From the diagrams it is clear that there is mass segregation in this cluster as one finds fewer faint stars in the annuli closer to the cluster center than at larger distances. This is strong evidence that the cluster is dynamically relaxed. The luminosity functions are normalized at V18.5.  10  Chapter 1. Introduction With the luminosity function and mass-to-light ratio Richer and Fahiman were also able to develop a mass function for M71, which predicted the num ber of stars of a given mass. As M71 is a dynamically relaxed cluster it was expected that the mass function would vary with distance from the center of the cluster. A power-law did not fit the globa’ mass function or the mass function at any given radius. However, using the observed global mass func tion as input, which included the inferred low mass stars, a multimass-mass King model was employed to predict the mass function with radius from the center of the cluster. The output from this was a good fit to the observed morphology and absolute number of stars. In 1992 another study was done by Drukier et al. [13], where the surface density profile of M71 was studied in some detail. This profile represents the number of stars per unit area as a function of distance from the cluster center. In this study it was observed that a King model did not fit the surface density plot of the cluster, underpredicting the number of stars found near the core. Where the King model levels off the data kept climbing, as can be seen in figure 1.5. The modern values for the parameters describing M71 can be found in Harris 1996 [17]. This work places M71 at 4.0 kpc from the Sun, estimates its E(B-V) at 0.25, and places its metallicity [Fe/H] at -0.73. Harris also places the center of M71 at right ascension, RA=19h53m46.ls and declina tion, DEC=+18°46’42” in J2000 coordinates. Harris’ work is a collection of many catalogs and observations taken over the decade prior to its pub lication and likely represents the best estimates for many of the quantities described above, and these will be the values we adopt for this research, unless otherwise stated.  11  Chapter 1. Introduction  (a)  I 11 I 3.  3  -  I a I  a  a  I  p.  C.  I 4)  4) .0  £2  ri  2  2  z o  0  .12<Vcl8 o15<V<20 “12<V<20 1  1  I —1  —0.5  0  log r (PC)  0.5  —1  —0.5  0  0.5  log r (pc)  Figure 1.5: Figure from [12]. These plots illustrate the surface density profiles for the two most luminous mass classes observed in M71. The filled circles represent stars with masses 0.85 < M/M 0 < 0.89, where the open circles represent stars with masses 0.71 < M/M 0 < 0.85. The upper data points represented by crosses are displaced upwards 0.5 dex and represent the sum of the other two sets of data. (a) and (b) show the same data, but in (b) a multimass King model is overlaid. Both mass samples show a higher degree of concentration than expected in the model, with a large amount of the discrepancy coming from the higher mass stars.  12  Chapter 2  Reduction 2.1  The Data  In August 2005, observations were made in both H and K of the inner 22 by 22 arcseconds of M71. The central wavelengths of the H and K filters are 2.20 and 1.65 microns respectively. These observations included 6.1 hours of observation in the K band and 4.7 hours of observation in the H band in order to probe to equal depth in both filters. This breaks down to 220 lOOs exposures in K and 170 lOOs exposures in H. The data were collected from Gemini North using the NIRI/ALTAIR infrared imaging and adaptive optics system. The camera used was 1024 by 1024 pixels. We used the f/32 camera resulting in a .02” platescale. In addition to the science data, images of standard star FS 149 were collected each night of observing, and exposures of a blank field were also taken for later calibration. Dithering was performed in a 10 position pattern so that artifacts could be removed later in the data analysis. In June 2007, further observations were made of the same field in M71, but only using the H filter for a total of 3.3 hours. The second set of observations was primarily for a proper motion study, therefore an additional filter was not necessary.  2.2  Processing  Note that the processes discussed in this section were only applied to the second epoch of data obtained in 2007 as Gemini provided fully processed images prior to this period. From our understanding this was the same processing performed by Gemini on the first epoch of data. Using the Gemini package in IRAF, the first step was to run the NPRE PARE task on the raw calibration images, which added essential header keywords and computed the variance and data quality planes. NIRI writes data taken with multiple digital averages, multiple non-destructive reads, and multiple co-additions. NPREPARE reads from the image header what  13  Chapter 2. Reduction sort of data was taken and modifies the data to ensure that the output from the task has numbers corresponding to the total number of electrons detected divided by the gain. The data quality frame is constructed with flags for various quality issues: 1 for bad pixels, 2 for non-linear pixels, and 4 for saturated pixels. NIFLAT was then run to create the flat field and the bad pixel mask. Flat field exposures were taken both with the dome lamps on and off. NIFLAT takes these two sets of exposures and combines them sepeseparatelyhe combined “lamps off” exposures measure the ther mal background of NIRI and are subtracted from the combined “lamps on” image before normalization. The “lamps off” exposures were also used to identify hot pixels for the bad pixel mask. The new bad pixel mask was then incorporated into the NPREPARE routine, which was run on the raw science data this time. NISKY was then utilized to construct a sky frame to use as a dark from the partially processed science data. The sky frame made for .a better dark measurement as it was taken alongside the science data. Following the construction of the sky frame, NIREDUCE was run on the science data which subtracted the sky and divided the flat. In this step the median of the sky frame was added so that all pixels had positive values, as future processing steps would require all pixel values to be positive. At this point the science data were ready for use, and the NIRI array characteristics outlined in Appendix A had mostly been accounted for. Unfortunately certain artifacts not removed included stellar-like objects that were in fact the left-over light from saturated stars on the previous exposure. In addition to these were spurious objects that resulted from reflected light in the telescope. Details on how these were dealt with are included throughout the following sections.  2.3  Reduction  The data reduction was a lengthy multi-step process necessitating various subsections to describe completely. The initial detection and photometry was purely for purposes of aligning the data for the task of co-addition ( 2.3.2). After this step a meticulous finding list was made from the com bined images ( 2.3.3). Finally, using this finding list, psf photometry was performed on the individual frames, and those measurements were averaged to arrive at a position and magnitude for each object ( 2.3.4).  14  Chapter 2. Reduction  2.3.1  Detection and Measurement  DAOPHOT was the software used for nearly all of the ensuing analysis, and it will be noted where alternative software was employed. It should be noted that instruction in the use of the DAOPHOT reduction software was found primarily in the DAOPHOT User’s Manual as well as in Peter Stetson’s guide to DAOPHOT [31]. To begin the detection process, the IMEXAMINE routine in IRAF was used to determine the FWHM of the stars in our field. With a few hundred stars to work with only a few needed direct measuring to determine an aver age FWHM of approximately 3.5 pixels, corresponding to .075 arcseconds. Looking at frames taken on various nights this number did not change by more than 20% and for the most part was fairly constant in the data col lected during both the first and second epoch. In addition to this parameter and the relevant array parameters, DAOFIND requires a finding threshold expressed in sigma. As the sky level is not entirely unaffected by the process ing, a sigma level does not necessarily correspond to a physically relevant quantity. As a result, the best way to determine a reasonable finding thresh old is by viewing a graph with number of objects detected plotted against finding threshold, and using a threshold near the knee of that graph. Too high a threshold and actual objects are omitted from the finding, but too low and many spurious detections are included. As thisstage was not intended to find all the objects of interest, a rough threshold of 15 was determined by use of this method (see figure 2.1 for an example). During detection on the final combined frame this threshold was chosen more carefully as will be discussed in section 2.3.3. These parameters resulted in roughly 750 objects being found per lOOs exposure. A magnitude was then assigned to the individual objects using DAOPHOT which does aperture photometry on the output of DAOFIND. An aperture of 3.5 pixels was used, with an inner sky radius set at 15 pixels and an outer sky radius set at 20 pixels. In this way individual aperture photometry files were made for each of the 220 K band and 170 H band images.  2.3.2  Registration and Co-addition  Matching the individual exposures was extremely important as the averag ing of the individual frames would ideally rid the data of nagging artifacts imposed by the CCD (discussed in Appendix A). A 12 term transforma tion was deemed ideal, the transformation coefficients of which allowed for the transforming of coordinates x , Yl into x2, Y2 acording to equations 2.1 1 15  Chapter 2. Reduction  through 2.6.  X2  =  +  Cl  C3 X Xi  +  C5 X  Ill +  C7 X Xa  +  Cg X X1 X  Yi +  C X Va  +  Cio X X1 X  Yi +  C12 X  (2.1)  Y2  =  C2  + c4  X Xi  + c6  X  Vi +  Cs X Za  Va  (2.2)  where,  Xa  =  1.5 x (x 2 ) 5  Va  =  1.5>< (Vs) 2  —  —  0.5  (2.3)  0.5  (2.4)  and where, Vs  =  2 x (yl  =  1 2 x (x  —  —  1.)/(1024) 1.)/(1024)  —  1  (2.5)  1  (2.6)  where the 1024 is the number of columns and rows in the NIRI CCD array. DAOMATCH made an initial match of only 4 terms, which allows for the translation, rotation and scaling of the data. This works more or less automatically on the photometry files and produces a basic transformation which is then fed into DAOMASTER. This software asks for the number of frames on which it is required to find an object in order to take it into account when calculating the transformation. This fraction was set to 80% in both filters in order to ensure that as few false detections as possible were used in the registration. Again, a 12 term transformation was used, and when prompted for the matching radius an initial value of 10 pixels was used. This sets the distance to which the program will search for a match for a given star between the frames. The program then enters an interactive 16  Chapter 2. Reduction mode, where the user is allowed to reduce the matching radius and view how many matched stars remain given the user’s criteria. A matching radius of 1 pixel was eventually used with a few more than a hundred stars being matched on more than 80% of the frames. The output of this exercise was a new transformation file, which made it possible to put all of the frames on a common coordinate system. The frames were transformed using MONTAGE2, using the transforma tion file from DAOMASTER, but not immediately combined. IRAF was employed for the co-addition of the frames. Some significant work was done in deciding the best means of co-addition, in partIcular which rejection al gorithm to use. It was apparent that many of the frames contained stellar objects that were not real, but in fact resulted from saturated pixels not being totally discharged during the COD readout. Seeing as these spurious objects were related to the dither pattern, they were only strongly present in 1 out of 10 frames and it was thought that by using a mm/max rejection algorithm these defects might be corrected. Of course, this also resulted in good data being thrown out, and ultimately this algorithm was rejected in favor of sigma-clipping. A high/low sigma of 3, .5 and 7 were all tested eventually with a high/low clip of 5 being used in the final combination of the frames, which were combined by averaging. As a figure of merit, the FWHM was computed for various stars in the combined frames, and was again found to be approximately 3.5 pixels, which was reassuring. These averaged, sigma-clipped frames were then used to create a deep finding list.  2.3.3  Creating a Finding List  With the combined images it was possible to detect much fainter stars than on the individual frames alone and DAOFIND was used once again to locate objects on both H and K images. The overall objective was to find all objects of interest on the combined frame, then run psf photometry on the individual frames, and finally average those measurements tO arrive at a position and magnitude for each object. Again, as in the case of the individual frames, there was some debate as to how high a finding threshold to use. Another graph was made of threshold against number of objects detected and can be seèr in figure 2.1. From the knee of this plot, which is similar in H and K, an optimal finding threshold was found for both ifiters. For K, a threshold of 12, and for H, a threshold of 10 were found to be the best. This resulted in nearly 2000 objects being found per filter, and upon comparing the lists, a nearly complete finding list was made. However, a number of stellar objects that were observed by 17  Chapter 2. Reduction eye in the image had were not detected using this. finding threshold. This resulted in allowing a much lower finding threshàld with the intention of removing false objects using the results of the psf photometry. Ultimately, finding thresholds of 5 and 6.5 were used for the combined H and K images respectively, and this resulted in the finding of around 8000 objects in each frame, many of which were obvious artifacts or false detections which we planned to eliminate during the photometry. 2.3.4  Photometry and Astrometry  Initially it was supposed that aperture photometry on the individual com bined images would provide accurate enough photometry and astrometry. As an initial rejection criteria, only objects which ppeared on both frames would be considered. The initial rejection resulted in a list of objects that appeared widely scattered in a CMD, and also poQrly measured in position. This made it impossible to measure proper motions between the epochs. Following this reduction attempt PSF photometry was performed on the combined images. Despite an improvement in the CMD, positional accuracy was still too poor for proper motion measurement. Finally PSF photometry was performed on the individual frames, and the measurements averaged to obtain high precision position measurements. The first two photometry attempts and reasons for their dismissal will be discussed briefly and the final photometry effort discussed in greater detail. Aperture Photometry on Combined Images Aperture photometry was performed on the combined images in both epochs using DAOPHOT, using an aperture of 3.5 pixels, and an inner and outer sky radius of 15 and 20 pixels respectively. Calibration was performed using standard star FS 149, which from the NIRI standards table has magnitudes H= 10.061 ± 0.018 and Kz= 10.061 + 0.015. The results of the photometry and calibration can be seen in the CMD displayed in figure 2.2. In addition to the CMD being of low quality and little use scientifically, the astrometry from DAOFIND was not particularly good and was not im proved upon when performing the aperture photometry. Therefore, PSF photometry was prevailed upon to provide a better result. PSF Photometry on Combined Images The photometry techniques used were partially derived from the treatment of similar data found in [9], [8] and [7]. It was initially thought that perform18  Chapter 2. Reduction  Threshoid Plot  t3 C  0 0 5 0  0 0 C,  0  E 0  z  0  10  20  30  40  50  Threshold in sigrno  Figure 2.1: This graph displays the number of objects found as a function of finding threshold in sigma. When using DAOFIND, if one does not know beforehand what threshold to use, this plot is consulted and typically from the knee of this graph one determines an appropriate threshold level. The black line and crosses represent the K band data.  19  Chapter 2. Reduction  Aperture Photometry CD 14  16  11111111  11  11111111  —  18  2O •  ••.  •  1.••.  22  ••  :  a  .  :‘  24  26  —2  I  I  I  I  I  I  I  I —1  rr  I  I  I  I  0 H—K  I  I  I  I  I  I  I  I 1  2  Figure 2.2: This figure is the initial CMD of M71 plotting K magnitude against H-K colour. This plot represents the results of aperture photome try performed on the combined H and K images and represents nearly 500 objects. Many faint objects would later prove to be artifacts that were not removed in the processing.  20  Chapter 2. Reduction ing PSF photometry on the combined images would result in both better photometry and positional certainty, and while the former hope proved true the latter did not. While exploring the possibility of doing the PSF pho tometry, it was pointed out that there would be strong PSF variability in the data. Using a variable PSF would arcount for some of this but likely not a radial variability in the PSF that resulted from the NIRI optics. Fig ures 2.3 and 2.4 illustrate the phenomenon of the variable PSF. The radial variability was dealt with by a method outlined in [30], whereby aperture magnitudes were compared with PSF magnitudes. A difference between the two as a function of distance from the guide star was linearly fit. The procedure to deal with the radial variability in the PSF was to first compute PSF magnitudes using a non-varying PSF. This was accomplished using DAOPHOT. A PSF was generated using the DAOPHOT PICK and “PSF” commands, which find stars suitable for usage in generating a PSF and then interactively prompt the user to confirm the stars chosen. Once the PSF was generated, ALLSTAR was employed to perform the actual PSF photometry (ALLSTAR being another piece of the DAOPHOT soft ware suite). A fitting radius of 3 was used, and an inner and outer sky radius of 15 and 20 pixels respectively. The results of this photometry were then compared to the earlier aperture photometry results (this time with an aperture size of 15 pixels), and as aforementioned the difference between the magnitudes as a function of distance from the image center was computed. The results of this analysis are displayed in figures 2.5 and 2.6. PSF photometry was then performed using a quadratically varying PSF and again with a fitting radius of 3 pixels. After performing the PSF pho tometry, and accounting for the radial correction, the CMD looks much improved when compared with the aperture magnitudes, as can be seen in figure 2.7. The sequence is much tighter, and although a large spread re mains at the faint end, even those objects seem to exist within a smaller envelope. A problem still existed however with the positional measurements in this data. When compared to the second epoch of H data taken 2 years later, there is great uncertainty in the proper motion measurements. Despite the great improvement in the CMD it was deemed necessary to perform PSF photometry on the individual lOOs frames. The average values from these measurements would be used in order to obtain greater positional accuracy with which to perform the proper motion measurements. A more careful calibration was carried out with the PSF magnitudes than with the aperture magnitudes. Five apparently isolated stars were se lected across the M71 field. Then single lOOs exposures were selected based on their proximity in time to the standard star exposures. Aperture pho 21  Chapter 2. Reduction  Figure 2.3: Output from IRAF. This is an isophotal contour plot of a bright star near the guide star on the combined H image, to be compared with figure 2.4, as an example of the varying PSF in the NIRI/ALTAIR data.  22  Chapter 2. Reduction  Figure 2.4: Output from IRAF. This is an isophotal contour plot of a brighter star found near the top of the combined H image. It is readily seen that the PSF is quite vertically stretched when compared with figure 2.3. The magnitude and direction of the distortion is a function of radial distance from the guide star and location on the image. Objects displaced horizontally from the guide star show horizontal stretching and objects in the corners show stretching along a diagonal axis. This same phenomenon is observed in the K data.  23  Chapter 2. Reduction  H Magnitudes lost as function of radius —0.0  I  a a a  0.1  a  at  aa  aa  U-. (F) U (0  0 I),  V .  -0.2  -  0 0  —0.3 100  200  300  400 500 Dstonce from center  600  700  Figure 2.5: This figure illustrates the effect of the radial variability in the PSF in the H data, with each data point representing a star. On one axis is plotted the difference between the aperture and psf magnitude measure ments. On the other axis the radial distance from the guide star is plotted in pixels. It is apparent that there is a trend with the magnitude difference linearly declining with distance. PSFs become distorted when measured fur ther from the center of the image and the resulting magnitude is affected. So long as one uses a large enough aperture, the aperture magnitude does not suffer significantly from this effect. A clear linear trend can be ascertained from this data, and the necessary magnitudes added back into the PSF re sults. The fit to this plot indicates that 0.00032 magnitudes per radial pixel need to be added back into the psf magnitude data. At the corner of the image this corresponds to more than 0.2 magnitudes.  24  Chapter 2. Reduction  K Magnitudes lost as functior of radius 0.00  -  D  —0.05  I  -  a  LI) 0 — ci,  —0.10  0 0)  ci, 0 D C  —0.15  -  —0.20 100  •.  200  I  300  I  I  400 500 Distance from center  I  600  700  Figure 2.6: This figure illustrates the effect of anioplanisity in the K data, with each data point representing a star. On one axis is plotted the difference between the aperture and psf magnitude measurements and on the other the radial distance from the guide star in pixels. It is apparent that there is a trend with the magnitude difference linearly declining with distance. PSFs become distorted when measured further from the center of the image and the resulting magnitude is affected, whereas, so long as one uses a large enough aperture, the aperture magnitude does not suffer significantly from this effect. A clear linear trend can be ascertained from this data, and the necessary magnitudes added back into the PSF results. The fit to this plot indicates that 0.00022 magnitudes per radial pixel need to be added back into the psf magnitude data. At the corner of the image this corresponds to nearly 0.15 magnitudes.  25  Chapter 2. Reduction tometry was performed on the five stars using a large range of apertures from 2 pixels up to 30. A similar treatment was applied to the lOs standard star frames, which were usually taken shortly after or before the lOOs ex posures being examined. The magnitudes of the five M71 stars were found to level off at about an aperture of 12, and the magnitude of the standard star at an aperture of 15. The difference is attributable to the adaptive optics being active in the lOOs exposures, but not in the lOs exposures of standard star FS 149. The standard star magnitude was then scaled to a lOOs exposure time, and the difference between this magnitude and the published apparent magnitude found in [21] was taken to be the calibration for the lOOs exposure. This calibration put the lOOs exposure stars all on the correct apparent magnitude system, and the difference between these and the combined PSF magnitudes gave the calibration for our CMD data. This calibration was performed using 2 nights of standard star exposures per filter. Although the standard star was observed for 3 nights per filter, 1 night the standard star appeared to be saturated. PSF Photometry on Individual Images It was decided that performing PSF photometry on the individual un transformed images would produce the highest accuracy astrometry. Both epochs of data can be assumed to have through identical reduction unless otherwise stated. The first step was to generate individual PSFs for all of the individuaj lOOs exposures. This was done by means of a PSF star coordinate list that could be found on every image and could be used to generate individual PSFs. Since we were working on the un-transformed data it was difficult to apply the same coordinate list to each frame because of the dither pattern. As a small translation should not affect the PSFs of the stars, all of the frames were crudely aligned by simple X-Y shifts and then using a com mon list a PSF was generated for all of the frames using DAOPHOT’s PSF command. This time more care was given to ensure the modeling of the exact shape and variability of the PSF. After some experimentation it was determined that using a Moffat function with 3 free parameters provided the best model of our PSF. This corresponds to the ANALYTIC MODEL PSF parameter being set to 2.00 in the DAOPHOT parameter file. Details on the exact function used can be found in the DAOPHOT User’s Manual. In addition it was discovered that using a purely analytic model PSF best accounted for the variability of the PSF across the chip. Again, the exact meaning of this model can be found in the DAOPHOT User’s Manual. Us 26  Chapter 2. Reduction  PSF Photometry CMD 111111111  111611111..!  I  16  ...i... 18  ..  . •  2O  .4.. S.  • •  •  22  . •.  •  .•:  •.•  24  26 —2  .  I  I  I  I  I  I  I  I  I  I —1  •  .  I  p  0  I  I  I  I  I  1  I  I  I  I  -  I  I  2  H—K  Figure 2.7: This figure represents a CMD derived from the PSF photometry of the combined H and K data. Small corrections to the data have been made in way of a radial correction and a more accurate calibration than that performed with the aperture photometry. Especially encouraging is the tightening of the sequence at brigher magnitudes.  27  Chapter 2. Reduction ing these settings the PSF subtracted images looked very promising, and even the radial effect which needed modeling before seemed to have been accounted for. Still using the finding list from the initial detection on the combined frames, ALLFRAME was used to perform psf photometry on all of the indi vidual frames and provide an output that included the averaged magnitudes, magnitude errors and positions of all the objects that conformed to the in dividual PSFs. To use ALLFRAME, one needs to. provide it with a finding list which is aligned with a reference image, a transfOrmation file which con tains transformation coordinates for each image that registers that image to the reference frame, and a PSF for each individual image. The finding list and transformation file were already complete by this stage. All that was required was a PSF to be generated for each image, the procedure for which is outlined above. Further instructions on• the use of ALLFRAME were found both in the DAOPHOT User’s Manual as well as in the “Cook ing with ALLFRAME” manual. Approximately 10% of the objects in the finding list did not converge during this process. as a result of either not conforming with the psf or not being detected on enough individual frames. Upon inspection of the photometry results it was clear that scattered light and ghosts were still contaminating the data. What made this clear was a repeated pattern of objects near almost evety bright star, which was not noticed until this stage of the process; it was clear that there was actu ally a much higher level of contamination than originally thought. Looking carefully at the ALLFRAME photometry results, it was clear that all of the spurious objects could be dealt with by increasing the number of frames we expected an object to appear on in order to be counted. Looking at figure 2.8 it is apparent many objects were found on very few frames. Upon visual inspection these proved to be most of the contaminants and by making a cautious cut one could eliminate all objects thought to be caused by scat tered light and residual charge. It should be noted that due to the dithering, many real objects were also not found on nearly every frame, but to extract these from the rogues was a daunting task, and it was much simpler to just make a prudent cut. The criterion was that bright stars needed finding on approximately 95% of the frames in question, while faint stars needed finding on roughly 80% of the frames. This extraction proved the best for elimi nating the false objects while preserving the largest sample of real objects. The result of this process was the elimination of roughly half our finding list, leaving us with just over 200 objects, now with accurate photometry and astrometry. The CMD that results from this cut can be seen in figure 2.9, which uses the combined image PSF photometry results. 28  Chapter 2. Reduction  Frames found vs. MagnftUde I I  -H-++W  +  -++*--1H- ii ! iin.l,IIIII. iiI •IIffiuI1# ..  +  ++*  200 +  + +  ÷  +  150 -  +  +  +  +:  +  +  I.  ±  H±  -  +  +  100 ++ +++ + +  +;  -  + 50  +  ++++ ++  +++  ++*±4  +  r  0  8  I  I  I  10  12  14 Ma0nitude  +  I  I 18  20  Figure 2.8: This plot shows the number of frames a star was found on against un-calibrated magnitudes. ALLFRAME reports on how many frames a given object is found. It was discovered that the spurious objects in our data were found on fewer frames than actual objects, making them easy to discard based on this criterion. This figure represents the number of H frames a star was found on as a function of magnitude. Rather than allow any spurious objects to infiltrate our data a cut was made just under 210, where the maximum number of frames an object could appear on was 218. In addition, it was clear that at the faint end objects would not be found on every frame due to their faintness. Therefore, a small exception was made that stars fainter than 17.7 magnitude only needed finding on 170 frames. Similar cuts were made in the second ifiter and in the second epoch.  29  Chapter 2. Reduction  PSF Photometry CMD 1z  p  i  I  p  I  I  I  I  I  14  :  16  ....  18  20  .  ...  22  I  —0.5  I  I  I  I  I  0.0  I  0.5  I  I  I  1.0  H—K  Figure 2.9: The final calibrated version of our CMD using the same pho tometry results as presented in figure 2.7. The only difference being that nearly 200 objects have been removed due to their not appearing on the required number of frames as illustrated in figure 2.8. Also, this CMD is plotted on a different scale than those previous to better demonstrate its shape.  30  Chapter 2. Reduction  2.4  Proper Motion Measurement  Using the astrometry results from ALLFRAME, tile two epochs of data from Gemini were registered to each other, and positions of the stars compared between the two epochs. The difference in the epochs was 1.81 ± .01 years, the spread due to the fact that observations were taken over several evenings. It was expected that over this timeframe the cluster stars would have moved relative to field stars a large enough amount that they could be distinguished. In addition to the Gemini data, a CFHT dataset from 1996 was used to corroborate the proper motions and estimate the errors. This data was taken 9.26 ± .01 years prior to the first Gemini data, and included 2 frames in V and 2 in I. Reduction of the data was performed by Ronald Gagne, who provided me with positions of stars from each of the 4 frames.  2.4.1  Registration  Very important in measuring the proper motion was the registration be tween the two epochs. Ideally one would like to have identical camera po sitioning and response between the two sets of Gemini measurements, but naturally things do not usually work out this way, as was the case with our data. It appears that a slight magnification was introduced between the epochs, amongst other smaller distortions, all of which needed characteri zation if the relative positions were to be measured accurately. A 20 term transformation was chosen, first using all of the 200 stars in our list. The intention was to recalculate the transformation based solely on the cluster members, which could hopefully be extracted from the first proper motion measurement based on the initial 20 term transformation. The initial set of proper motions was encouraging, and by selecting what were thought to be only cluster members, a second 20 term transformation was made between the two epochs. It turned out not to make a sigtiificant difference in the transformation, nor in the proper motion measurethents. The results of the second 20 term transformation can be seen in figute 2.10 where Lx is plot ted against Ly for each star. This plot shows the motion over the 1.81 year baseline between the 2 Gemini epochs with high-metion stars moving up to a pixel over this timeframe, corresponding to a mOvement of .022”. Most stars exhibited motion less than 0.1 pixels; these lOw proper motion stars can be better viewed in figure 2.11. How errors were derived is explained in subsection 2.4.2.  31  Chapter 2. Reduction  Proper Motion Plot 1.0  I  I  I  I  I  I  I  I  I  I  I  p  *  0.5  —  N  .0  *  0.0—  I Il)  a,  C 0 .0  0  —0.5  —  —1.0 —1.0  I  I  I  I  I  I  I  —0.5  0.0 Change in x coordinate in pixels  0.5  1.0  Figure 2.10: Proper motion plot for the core of M71. The plate scale for this data is 0.022”. Both axes represent pixel movement over a 1.81 year baseline. Errors come from the fit to the proper ifiotions of stars that were measured both on the Gemini and CFHT fields. As the CFHT data did not probe as faint as the Gemini data, errors were extracted for many stars based on a fit of error versus magnitude (see figure 2.12). For a more detailed examination of the data near 0,0 please refer to figure 2.11.  32  Chapter 2. Reduction  —0.10  —0.05  0.00  0.05  0.10  Chonge n x coordinate a pixet  Figure 2.11: Proper motion plot for the core of M71. The plate scale for this data is 0.022”. Both axes represent pixel movement over a 1.81 year baseline. Errors come from the fit to the proper motions of stars that were measured both on the Gemini and CFHT fields. A the CFHT data did not probe as faint as the Gemini data, errors were extracted for many stars based on a fit of error versus magnitude (see figure 2.12). For a more extended examination of the data near please refer to figure 2.10.  33  Chapter 2. Reduction  2.4.2  Error Measurement  The errors in the proper motion measurement depend strongly on the errors in the positional measurement of the stars in the two Gemini epochs and the one CFHT epoch. From these errors, fits of x and y as a function of time can be made using the three data points, the siopes of which are the proper motions in pixels per year. The errors on the slope can then be interpreted as the errors in the proper motions themselves. The errors on the position measurements of the two Gemini epochs was taken to be the standard deviation between the ALLFRAME calculated average and the individual measurements that went into that average, ac cording to equation 2.7. These errors were calculated separately for both x and y in both of the epochs. Errors were approximately 0.01 pixels for the first epoch on each the x and the y measurements, and roughly 0.015 for the second epoch. The error on the CFHT data was calculated in a similar way. From 4 frames (2 in V and 2 in I), an average position for each star was calculated and then an error assigned based on the standard deviation of the individual measurements from the average. As the data was of lower quality and stars were not always found on all 4 exposures, the errors were on the whole larger than those of the Gemini data, but rarely more than 5 times as large. With a baseline approximately 6 times larger than that between the Gemini epochs this error was certainly reasonable, and allowed for quality fits to be obtained. =  —  (2.7)  The fit on the x and y data was done through the IDL routine UNFIT. This routine takes a vector pair (in this case (x, t) Or (y, t)), and then fits it to the model x = a x t + b, by minimizing the chi-scpiare error statistic, given by equation 2.8, where u represents the error in the position measurement xi. 2 (xZ—a—bt)  (2.8)  i=O N—i  Using linear fitting routines outlined in Numerical Recipes [25], the fit also provides the user with the errors on the fit parameters b and a. The error on the slope, b, is then taken to be the error on the proper motion in the direction being examined. This is done for both x and y, and the errors added in quadrature to give an error on the bulk proper motion of the object 34  Chapter 2. Reduction in question. The results of these fits and error extractions can be viewed in figure 2.12, where error is plotted against magnitude. Here a linear trend can be detected and extracted. As not all stars from the Gemini data were matched with the CFHT data, errors can be attributed to all stars in the Gemini dataset based on the fit of error as a function of magnitude, thus resulting in errors on all the stars in the Gemini sample. The result of this fit Was PM = —0.0216 + K x 0.0016. For purposes of determining the proper motion: dispersion of the stars it was important to have some idea of the average error on the stars we use to determine that dispersion. This sub-sample includes all stars fainter than K magnitude of 19 and having a proper motion less than .046 pixels over 1.81 years. The average error on this sample is .006 pixels.per year, corresponding to an error of .0 109 pixels over 1.81 years. This is .an important result that came from the error analysis and will be referred to later.  2.4.3  Proper Motion Calculation and Measurement of Velocity Dispersion  Deciding where to draw the line on which stars were cluster members and which were not was a difficult decision and ultimately- a 2cr cut on bulk proper motion was used to determine outliers in the proper motion space diagram seen in figure 2.11. A ci was calculated in a regressive way first starting with the entire sample of stars. A ci about zero was calëulated based on all of the stars in the sample, and then a 2cr cut was made, and the stars that made this cut were subjected to the same calculation made previously. In this way we iteratively zeroed in on the core of the stars in proper motion space, until the returned value of ci remained the same over several iterations (this value was achieved after roughly 5 iterations). Eventually we were sampling solely the stars in the core of our sample and calculating o- based on these stars alone. From this calculation of ci a final 2cr cut was made, and those inside this cut were considered high confidence cluster members. When this procedure was performed on specific magnitude bins, it became clear that the higher motions associated with the fainter stars factored significantly into their inclusion or rejection in this sample. For fainter stars a higher multiple of sigma was required in determining cluster membership. The results of this study can be seen in figures 2.13 and. 2.14. The net result of this study was that to determine the dispersion (or ci) of the cluster we would use only the bright low error stars (K magnitude less than 19). The dispersions in x and y for stars in this sample are cr = 0.0230 and a 9 = 0.0234 in units of pixels per 1.81 years. Based on the idea that all of 35  Chapter 2. Reduction  12  14  16 K Magnitude  16  20  Figure 2.12: This figure represents the errors added in quadrature of the x(t) and y(t) fits against magnitude. Errors on the proper motion for each star are based on a linear fit to the 3 (x,y) coordinates from the 2 sets of Gemini data and the 1 set of CFHT data. A linear fit wa performed in x(t) and in y(t). The slope of each of these fits represents the pixels per year the star had been moving. The errors on these two slopes were added in quadrature to calculate the errors represented above. The solid line represents a linear fit to this error data, with a slope of 0.0016 (pixels/year) per magnitude.  36  Chapter 2. Reduction  I  Dispersion Function using 2 sigiho cut I I I I  0.20  0  0.15 0. C  x C C  0 0 0  0.10 0  0.05  0.00 14  I  I  I  I  18  20 1<  22  24  mog  Figure 2.13: This plot shows a in our stars’ motion in the x direction about 0 over a 1.81 year baseline versus magnitude, where the magnitudes were binned into equal sized bins between 15th and 23rd magnitude. For each bin a a, or dispersion, was calculated as outlined in 2.4.3. The higher values found for brighter stars can be attributed to the sniäll number of objects in these bins, where as the fainter magnitudes higher dispersion are possibly attributed to a few sources. First, these stars have larger errors in their motion, therefore, it is no surprise that they occupy a larger area in proper motion space. Secondly, the fainter stars are of lower mass and as a result are expected to occupy a larger area in proper motion space. Lastly, a large fraction of these fainter objects occupy the same space on the proper motion diagram quite near the field and may represent some sort of field population moving together through space. All of these effects taken together likely explain the large dispersion found for the fainter stars. 37  Chapter 2. Reduction Dispersion Function using 2 sih,o cut I  0.20  0.15  I  I  I  I  I  I  I  I  I  I  I  I  —  0 V 0. C  0.10  -  C  0 t0 V  0 0  0.05  -  0.00 14  I  16  I  I  I  I  18  20  -I--I  I 22  24  K mog  Figure 2.14: This plot shows u in our stars’ motion in the y direction about 0 over a 1.81 year baseline versus magnitude, where the magnitudes were binned into equal sized bins between 15th and 23rd magnitude. For each bin a a, or dispersion, was calculated as outlined in 2.4.3. The higher values found for brighter stars can be attributed to the máll number of objects in these bins, where as the fainter magnitudes higher dispersion are possibly attributed to a few sources. First, these stars have larger errors in their motion, therefore, it is no surprise that they occupy a larger area in proper motion space. Secondly, the fainter stars are of lower mass and as a result are expected to occupy a larger area in proper motiOn space. Lastly, a large fraction of these fainter objects occupy the same spate on the proper motion diagram quite near the field and may represent some sort of field population moving together through space. All of these effects taken together likely explain the large dispersion found for the fainter Stars. 38  Chapter 2. Reduction the stars in the cluster should have roughly equal eüergy, cluster membership would be based on a 2cr cut scaled for the mass Of the object in question by equation 2.9. This assumes of course that the measured dispersion is proportional to the velocity of the stars in question. This implies that we believe our errors to be less than the dispersion, which they are based on the results presented in subsection 2.4.2, where the. average error for proper motions of stars with K magnitude less than 19 was calculated to be 0.0109 pixels per 1.81 years.  2 m  1 a  (2.9)  To further convince ourselves that we had truly resolved the dispersion of the cluster itself and that our measured dispersion was not simply due to er ror, we calculated an error on our dispersion based on a bootstrapping tech nique. This technique required the generation randOm simulations of points in proper motion space where the random collectiOn of points was drawn from our data. This technique involves running thousands of such random simulations and then measuring the dispersion of each set of data. A a is then calculated of the thousands of dispersions calculated and this a would represent our confidence in our dispersion parameter. The results of this technique using 10,000 trials was a = 0.00235 alid a 0 = 0.00310, using 100,000 trials was a = 0.00236 and a 0 = 0.00310, and using 1,000,000 tri als was a 0 = 0.00235 and = 0.00310 all in units of pixels per 1.81 years. It was decided that further tests were unnecessary. Thus, our final reported dispersions with errors were a = 0.0230 ± .0024 and a = 0.0234 ± 0.0031 in units of pixels per 1.81 years.  2.5 2.5.1  Locating The Center of M71 Motivation  For purposes of viewing the velocity profile and rtiass profile of the cluster it was necessary to locate the center. Previous measurements of the cluster center, such as those reported in [17j were made primarily on the basis of isophotes, thus tracking light rather than star cOunts. In addition, these measurements were not made to be incredibly precise. As reported in [101, from which Harris used most of his positional measurements, the authors claim that the centers of most clusters were known to at best an arcsecond, and in many cases to no better than an arcminute. Mu being a fairly diffuse cluster, near the galactic center and of low mass, almost certainly falls into  39  Chapter 2. Reduction the latter category. As the field being explored in this research is only 22 by 22 arcseconds large, this amount of error wa unacceptable and a new center based on modern results was needed. 2.5.2  Procedure  For this task, ACS data were found that overlapped Our field, and a detection down to a high threshold was used to identify stars. From this finding list, a rough CMD was created, as it was important to use cluster stars only in the calculation of the center to avoid local over-densities and underdensities caused by background or foreground contathinants. A series of data points were chosen along the upper and lower edges of the main sequence to create 2 spline functions. Only stars falling inside these two curves would be considered for the center calculation. Figure 2:15 illustrates the rough ACS CMD and the spline functions used to constiain cluster membership. Using this finding list, a circular window divided into 4 sections was placed over the coordinates and slid increment1Iy in the horizontal and vertical plane, each time calculating the total number of stars found in each segment. As the segments were equal in area this translated directly into a density, and it was supposed that one could locate the center based on where the densities were both the highest and had the smallest deviation from the average. A window of radius 1000 pixels was used, which corresponds to approximately 50” on ACS. A quality parameter was derived as the quotient of the average density divided by the variance, and from this a contour map created, which could be fit by a two dimensional Gaussian. The resulting contour map can be seen in figure 2.16. The value for the center found using this technique was c = 19: 53 : 45.98 ± .15, 6 = 18: 46: 46.5 ± 1.0. However, it should be noted that a similar technique employed by Drukier in [13] used a larger area and had a higher number of stars, and for purposes of calculating the distance of stars from the center of the cluster, his center of = 19 : 53 : 45.8, 6 = 18: 46 : 43.5 will be used for the results presented in this paper.  40  Chapter 2. Reduction  CMD based on ACS Dota from 2006 14  16 I  :  I  18  >  20  22  24  —2  —1  2 v—I  Figure 2.15: Plotted is an un-calibrated CMD from 2006 ACS data on M71. Using points along the edge of the main sequence, an upper and lower cut was made on all of the stars in order to better ensure cluster membership for the sample being studied. A cut was also made at magnitudes 21 and 16.25 where the shape of the main sequence was no longer thought to be well defined. The stars passing the cut are displayed in red. These stars were then used in determining the cluster center.  41  Chapter 2. Reduction  X n ACS Pi,&  Figure 2.16: Contour map showing the quality factor for various pixels on the ACS plane. This does not represent the entire ACS chip, only the central region near where the center is thought to be based on past observations and calculations. Fom the 2-d Gaussian fit, the center is thought to lie at approximately = 19 : 53 : 46.98 ± .15 and ö = 18 : 46 : 46.5 ± 1.0. These errors represent far greater precision than previous measurements, and the center varies by nearly 10 arcseconds froni Harris’ value. However, the center of the cluster does still fall within our field.  42  Chapter 3  Results 3.1  Proper Motions and the CMD  With a sample of stars selected based on their proper motions it was ex pected that the CMD would tighten somewhat with the exclusion of noncluster stars. As mentioned in subsection 2.4.3 the proper motion cut was one that scakd with magnitude as fainter stars were expected to have a larger proper motion dispersion. Overtop of the CMD data was overlaid a model from Dotter [11], for a cluster of metallicity [Fe/H]=-0.70 and Age=12.0 Gyr. In order to project the model’s magnitudes and colours onto that of the clus ters, a distance modulus of 12.9 was added to the model’s K magnitudes and an E(H-K) of 0.068 added to the color. These come from Harris’ distance modulus of 13.79 in V and E(B-V)rz0.25 [17], combined with Schlegel et al.’s reddening estimate of A 1.01 and AK = 0.120 [28]. It should be noted that the model does not change significantly with age in the H and K bands, therefore, using the model to estimate an age is not possible. The PSF photometry of the combined H and K frames resulted in a CMD that ranged from 13.5 to 21.5 magnitude. The resultant CMD without the proper motion cut and with model overlaid can be seen in figure 3.1. The CMD with the proper motion cut and with the model overlaid can be seen in figure 3.2. It is clear that the proper motion cut cleared out many of the anomalous objects in the CMD and resulted in a tighter sequence. The model also seems to fit the cleaned CMD slightly better, giving confidence both in the model and in the proper motion cut. It is apparent that we did not detect stars as faint as the predicted hydrogen burning limit.  3.2  Surface Density Profile  To generate a surface density profile that we could compare with Drukier’s 1992 data [13], we had to limit our sample and compute our bins in a similar fashion. Stars were selected that were of the mass range 0.71 < M/MG < 0.85. This mass range represents a K magnitude range of 15.7 to 17.0,  43  Chapter 3. Results  PSF Photometry CMD I  I  I  I  14  :  16  ••  •.r.•’• • .‘.  18  20  •  22  24 —0.5  I  I  I  I 0.0  0.5  1.0  H—K  Figure 3.1: This figure is identical to figure 2.9, except with a line overplot ted. The model overlaid in blue represents a model for a globular cluster with a [Fe/H]=-O.70 and Age=12.O Gyr. This model was projected to the distance of M71 using a distance modulus of 12.9 in K and E(H-K)=O.068, both from Harris [17].  44  Chapter 3. Results  PSF Photometry CMD 1  I  14  16  •  • •i•.• ,• .  18  “:  •.••  20  22  I  —0.5  I  I  I 0.0  I  0.5  1.0  H—K  Figure 3.2: The points in this figure represent the same as those in figure 2.9 except it only includes points that made the proper motion cut. The model overlaid in blue represents a model for a globular cluster with a [Fe/HJz=-O.70 and Age=12.O Gyr. This model was projected to the distance of M71 using a distance modulus of 12.9 in K and E(H-K)=O.068. The agreement seems quite good. When compared to figure 3.1 the sequence is both tighter and better conforming to the model, especially around 19th to 20th magnitude.  45  Chapter 3. Results which represents a magnitude railge well above our faint limit and well below our saturation limit. Stars’ distances to the cluster center were computed using the conclusions of section 2.5 and then the field was divided into 6 overlapping annuli each of which measured 7” in width. As the cluster center was very near the edge of our image, this allowed us to calculate densities out to about 20”. In each annulus the stars of the specified mass were counted and then the area calculated to produce a density. The results of this analysis, plotted alongside Drukier’s results can be seen in figure 3.3. It should be noted that we did not perform any incompleteness tests, therefore our numbers represent lower bounds on the actual number density.  3.3  Calculating the Geometric Distance to M71 Using Proper Motions  We believe the proper motion dispersion of stars near 0,0 in proper motion space is in fact a physical dispersion caused by the motion of the stars within the cluster. This quantity relates to the measured radial velocity dispersion by a factor equal to the distance to the cluster. Peterson and Latham measured the radial velocity dispersion of M71 to be 3.2 ± 0.6km/s [24]. This measurement was made using giant stars within the inner 100” of the cluster with an average mass of 0.8M . This is the value we will adopt 0 for our study once adjusting for the mass difference in Cudworth’s sample and our own according equation 2.9, but substituting velocity for a. Also, as the giant stars’ radial velocities were measured out to 100”, and our own stars are all within 22”, an adjustment needs to be made for expected radial velocity based on position within the cluster. From the models examined in Drukier’s 1992 work [13], it can be inferred that from a distance of 100” to 22” the expected radial velocity dispersion increases by a factor of 2.5/2.2. The average mass of the stars used to calculate our dispersion was 0.69M , 0 calculated using the models discussed in section 3.1. Scaling the velocity dispersion to stars of our average mass and accounting for the larger radial velocity dispersion at smaller radii we arrive at an expected dispersion of 3.9 ± 0.7km/s. As aforementioned the distance should be the factor relating the angular dispersion measured in this study to the radial velocity dispersion, which has been measured to better than 20%. Using the average of our two disper sion measurements in x and y, and combining their errors in quadrature, the angular dispersion measured is 0.0233 ± 0.0020 in pixels per L8lyr. Con verting this into arcseconds per year the angular dispersion we measure is 46  Chapter 3. Results  Stellor Density Plot I  I  ‘I H1  2.5-  Ij  I  I  “III  1.0 —1.5  I  i  —1.0  I  I  I  0.0  —0.5  I  0.5  1.0  Log(R) in pc  Figure 3.3: The surface density profile for M71. Plotted is surface density in number of stars per pc 2 against radius in pc, on a log-log scale. Our data is plotted in black, and Drukier’s [131 in red. Our. data suffers from having incomplete annuli, therefore, lower number statistics, but has the advantage of probing closer to the core of the cluster. Drukier’s scaling of 2.01 pc per 1.88’ was adopted to put our data on the same scale. Also note, we did not perform any incompleteness tests, therefore oil values we obtained should be taken as lower limits on the actual number densities.  47  Chapter 3. Results 0.000277 ± 0.000024 “/yr. From this one needs to subtract in quadrature the errors on the proper motions which have acted to expand the actual dispersion. The average error as reported in subsection 2.12 was 0.006 pix els per year corresponding to .00013 “/yr. Subtracting this in quadrature, one arrives at an angular dispersion of 0.000246 ± 0.000024 “/yr. Relating this to the radial velocity measurement, one calculates the distance to the cluster to be (1.04 ± 0.22) x 1017 km or 3.36 ± 0.71 kpc, the error coming from adding the percent error in the dispersion to the percent error in the radial velocity in quadrature.  48  Chapter 4  Discussion and Conclusions The PSF photometry of the combined 11 and K frames resulted in a CMD that included stars from magnitude 13.5 all the way to 21.5 in the K band. The proper motion cleaning did an excellent job in removing almost all the CMD outliers, leaving a fairly clean and tight main sequence. This in itself is encouraging and is proof of concept that infrared data from the NIRI/ALTAIR adaptive optics system can achieve state of the art astrom etry, allowing for the distinguishing of cluster from field stars in a baseline as short as 1.81 years for a nearby cluster moving at moderate speed with respect to the Sun. The overlap of the model on our color-magnitude data is encouraging, although it is unfortunate that our data did not go so deep as the hydrogen burning limit. It is possible that further analysis with this dataset and a better understanding of the reflected light and optical ghost pattern could result in adding as much as a magnitude to the CMD. Thus the faintest main sequence stars in this cluster could be examined, however these stars might be very sparse in the core due to their high velocity dispersion, and high likelihood of being stripped from the cluster. The agreement of the model with our data does lend confidence to the claim that M71 has a [Fe/HI —0.73 as reported in Harris 1996 1171, but does not place any strong constraint on the age of the cluster. The extension of the data presented by Drukier et al. in 1992 [13] is also an interesting result. At the time that the original results were presented it appeared that M71 did not have a well behaved stellar density profile. In the core the profile did not flatten as multimass King models predict. Our data points to the contrary in that the density profile is observed to flatten close to the core of M71. Although our data agrees with Drukier et al. up to their inner data point, we extend the data all the way down to the core and observe a flattening rather than a rising density profile. The discrepancy in the findings may be due to the fact that we were able to measure proper motions, and thus remove field stars from our data. However, it should be noted that our statistics are poorer, having counted fewer stars due to our smaller field of view. In addition, we did not account for incompleteness in 49  Chapter 4. Discussion and Conclusions our sample of stars, therefore our numbers represent lower bounds. Also, we were unable to probe the upper mass range observed by Drukier et al. which they claim adds significantly to the cusp they observed. However, it should be pointed out that the high mass stars exist in significantly smaller numbers (they are half as frequent as the lower mass range), and are unlikely to change the overall shape of the stellar density profile we observed. Perhaps the closer analysis of the short exposure data in the future would allow for the comparison of the high-mass stars, and this could be explored in greater detail. In addition, completeness tests could be made that would allow for higher confidence in the comparison of the two sets of data. Most exciting perhaps was that we believe that we measured a physical dispersion in the cluster stars’ proper motions. We measured a dispersion of 0.000246±0.000024 “/yr, which is equivalent to 25 mas cent’, a higher value than that expected by King and measured by Cudworth (see [23] and [5]). The error on the stars motion and error on the dispersion were low enough that one could use the measured dispersion in x and y and relate it to the measured radial dispersion of giant stars to extract a geometric distance to M71. This represents the first time data of this sort has been used to make this type of measurement. The measured distance of 3.36±0.71 kpc is a little lower than Harris’ value of 4.0 kpc [17], however does just fall within Harris’ error on this value, which is 10%. This error is based on the work done by Geffert and Maintz in 2000 [15] from which many Of Harris’ reportings on M71 are based. Our result is probably low due to the simplified treatment of the velocity anisotropy relating the radial velocities of giants found at larger radial extent to the tangential velocities of lower mass stars in the core. Also, it is worth nothing that with a higher confidence radial velocity measurement the error on our value could be brought down significantly.  50  Bibliography [1] H. A. Abt and S. G. Levy. The frequency of spectroscopic binaries among high-velocity dwarf stars. A.J., 74:908—916, 1969. [2] T. E. Armandroff. The properties of the disk system of globular clusters. A.J., 97:375—389, February 1989. [3] H. C. Arp and F. D. A. Hartwick. A Photometric Study of the MetalRich Globular Cluster M71. Ap.J., 167:499—+, August 1971. [4] J. N. Bahcall and R. A. Wolf. Star distribution around a massive black hole in a globular cluster. Ap.J., 209:214—232, October 1976. [5] K. M. Cudworth. Photometry, proper motions, and membership in the globular cluster M71. A.J., 90:65—73, 1985. [6] J. Cuffey. Noc 6838. A.J., 64:327—+, 1959. [7] T. J. Davidge. Adaptive Optics Observations of Stars in Globular Clus ters and Nearby Galaxies. In W. Brandner and M. E. Kasper, editors, Science with Adaptive Optics, pages 323—+, 2005. [8] T. J. Davidge, K. A. G. Olsen, R. Blum, A. W. Stephens, and F. Rigaut. Deep ALTAIR+NTRI Imaging of the Disk and Bulge of M31. A.J., 129:201—219, January 2005. [9] T. J. Davidge and F. Rigaut. Photometric Variability among the Bright est Asymptotic Giant Branch Stars near the Center of M32. Ap.J.l, 607:L25—L28, May 2004. [10] S. Djorgovski and G. Meylan. The Galactic Globular Cluster Systems a List of the Known Clusters and Their Positions. In S. G. Djorgovski and G. Meylan, editors, Structure and Dynamics of Globular Clusters, volume 50 of Astronomical Society of the Pacific Conference Series, pages 325—+, January 1993. -  51  Bibliography [11] A. Dotter, B. Chaboyer, J. W. Ferguson, H.-c. Lee, G. Worthey, D. Jevremovié, and E. Baron. Stellar Population Models and Indi vidual Element Abundances. I. Sensitivity of Stellar Evolution Models. Ap.J., 666:403—412, September 2007. [12] G. A. Drukier, C. G. Fahlman, and H. B. Richer. Towards the Com parison of Observations of Globular Clusters and Fokker-Planck Sim ulations. In K. Janes, editor, The Formation and Evolution of Star Clusters, volume 13 of Astronomical Society of the Pacific Conference Series, pages 385—+, 1991. [13] G. A. Drukier, G. G. Fahlman, and H. B. Richer. Fokker-Planck models and globular cluster evolution The problem of M71. A. J., 386:106— 119, February 1992. -  [14] J. A. Frogel, L. E. Kuchinski, and C. P. Tiede. Infrared array pho tometry of metal rich globular clusters. 2: Liller 1—the most metal rich cluster? A.J., 109:1154—1168, March 1995. [15] M. Geffert and G. Maintz. First results of a photometric and astromet nc study of the globular cluster M 71 (NGC 6838). Astron. Astrophys. Suppi. Ser., 144:227—233, June 2000. [16] D. Ceisler, D. Minniti, and J. J. Claria. Washington photometry of globular cluster giants The most metal-poor clusters. A .J., 104:627— 644, August 1992. -  [17] W. E. Harris. A Catalog of Parameters for Globular Clusters in the Milky Way. A.J., 112:1487—+, October 1996. [18] I. King. The structure of star clusters. I. an empirical density law. A. J., 67:471—+, October 1962. [19] I. R. King. The structure of star clusters. III. Some simple dynamical models. A.J., 71:64—+, February 1966. [20] T. D. Kinman. Globular clusters, III. An analysis of the cluster radial velocities. M.N.R.A.S., 119:559—+, 1959. [21] S. K. Leggett, M. J. Currie, W. P. Varricatt, T. C. Hawarden, A. J. Adamson, J. Buckle, T. Carroll, J. K. Davies, C. J. Davis, T. H. Kerr, 0. P. Kuhn, M. S. Seigar, and T. Wold. JHK observations of faint stan dard stars in the Mauna Kea Observatories near-infrared photometric system. M. N. R. AS., 373:781—792, December 2006. 52  Bibliography [11] A. Dotter, B. Chaboyer, J. W. Ferguson, H.-c. Lee, G. Worthey, D. Jevremovié, and E. Baron. Stellar Population Models and Indi vidual Element Abundances. I. Sensitivity of Stellar Evolution Models. Ap. J., 666:403—412, September 2007. [12] G. A. Drukier, G. G. Fahlman, and H. B. Richer. Towards the Com parison of Observations of Globular Clusters and Fokker-Planck Sim ulations. In K. Janes, editor, The Formation and Evolution of Star Clusters, volume 13 of Astronomical Society of the Pacific Conference Series, pages 385—+, 1991. [13] G. A. Drukier, G. G. Fahiman, and H. B. Richer. Fokker-Planck models and globular cluster evolution The problem of M71. Ap.J., 386:106— 119, February 1992. -  [14] J. A. Frogel, L. E. Kuchinski, and G. P. Tiede. Infrared array pho tometry of metal rich globular clusters. 2: Liller 1—the most metal rich cluster? A.J., 109:1154—1168, March 1995. [15] M. Geffert and G. Maintz. First results of a photometric and astromet nc study of the globular cluster M 71 (NGC 6838). Astron. Astrophys. Suppl. Ser., 144:227—233, June 2000. [16] D. Geisler, D. Minniti, and J. J. Claria. Washington photometry of globular cluster giants The most metal-poor clusters. A. J., 104:627— 644, August 1992. -  [17] W. E. Harris. A Catalog of Parameters for Globular Clusters in the Milky Way. A.J., 112:1487—+, October 1996. [18] I. King. The structure of star clusters. I. an empirical density law. A.J., 67:471—+, October 1962. [19] I. R. King. The structure of star clusters. III. Some simple dynamical models. A.J., 71:64—+, February 1966. [20] T. D. Kinman. Globular clusters, III. An analysis of the cluster radial velocities. M.N.R.A.S., 119:559—+, 1959. [21] S. K. Leggett, M. J. Currie, W. P. Varricatt, T. G. Hawarden, A. J. Adamson, J. Buckle, T. Carroll, J. K. Davies, C. J. Davis, T. H. Kerr, 0. P. Kuhn, M. S. Seigar, and T. Wold. JHK observations of faint stan dard stars in the Mauna Kea Observatories near-infrared photometric system. M. N.R. A.S., 373:781—792, December 2006. 52  Bibliography [22] R. W. Michie. Structure and Evolution of Globular Clusters. +, May 1961.  ,  133:78 1—  [23] 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. [24] R. C. Peterson and D. W. Latham. Stellar velocity dispersions for four low-concentration globular clusters. Ap.J., 305:645—650, June 1986. [25] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical recipes in FORTRAN. The art of scientific computing. Cam bridge: University Press, —c1992, 2nd ed., 1992. [26] H. B. Richer, A. Dotter, J. Hurley, J. Anderson, I. King, S. Davis, G. G. Fahlman, B. M. S. Hansen, J. Kalirai, N. Paust, R. M. Rich, and M. M. Shara. Deep Advanced Camera for Surveys Imaging in the Globular Cluster NGC 6397: the Cluster Color-Magnitude Diagram and Luminosity Function. A.J., 135:2141—2154, June 2008. [27] H. B. Richer and G. G. Fahlman. Star counts in the globular cluster M71. Ap.J., 339:178—194, April 1989. [28] D. J. Schlegel, D. P. Finkbeiner, and M. Davis. Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds. Ap. J., 500:525—+, June 1998. [29] H. Shapley. Studies based on the colors and magnitudes in stellar clusters. VII. The distances, distribution in space, and dimensions of 69 globular clusters. Ap.J., 48:154—181, October 1918. [30] C. D. Sheehy, N. McCrady, and J. R. Graham. Constraining the Adap tive Optics Point-Spread Function in Crowded Fields: Measuring Pho tometric Aperture Corrections. Ap.J., 647:1517—1530, August 2006. [31] P. B. Stetson. DAOPHOT A computer program for crowded-field stellar photometry. Pub. A stron. Soc. Pac., 99:191—222, March 1987. -  [32] R. Zinn. The globular cluster system of the galaxy. IV disk subsystems. Ap.J., 293:424—444, June 1985.  -  The halo and  53  Appendix A  NIRI Array Characteristics Raw NIRI images contain various features, mostly due to pixel sensitivity variation on the CCD. Common issues include, but are not limited to: • Vertical “stripes” which are the result of the manufacturing of the array. These typically flatten. • A circular ripple patter in the upper left of the array which also flattens out. • 3 regions of bad pixels roughly 10 pixels wide, 2 of which are associated with a partially bad column. These are the result of a procedure used to excise the photon-emitting defects from the array. These are correctable with a large enough dither pattern. • A few hundred hot pixels in the upper left and bottom middle of the array, again usually corrected with the dithers. • A crack in the array substrate, observed as a line of bad pixels in the bottom right. • A large-scale bright area in the center of the array with darker regions above and below. • Offsets in sensitivity at the quadrant boundaries.  54  

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