Globular Cluster Systems William E Harris Department of Physics Astronomy McMaster University Hamilton ON LS M Canada Abstract The basic features of the globular cluster system of the Milky Way are summarized the total p opulation sub division of the clusters into the classic metalp o or and metalrich comp onents and rst ideas on formation mo dels The distance to the Galactic center is derived from the spatial distribution of the inner bulge clusters giving R kp c 0 The calibration of the fundamental distance scale for globular clusters is re viewed Dierent ways to estimate the zero p oint and metallicity dep endence of the RR Lyrae stars include statistical parallax and BaadeWesselink measurements of eld RR Lyraes astrometric parallaxes white dwarf cluster sequences and eld sub dwarfs and main sequence tting The results are compared with other distance measurements to the Large Magellanic Cloud and M Radial velo cities of the Milky Way clusters are used to derive the kinematics of various subsamples of the clusters the mean rotation sp eed ab out the Galactic center and the lineofsight velo city disp ersion The inner metalrich clusters b e have kinematically and spatially like a attened rotating bulge p opulation while the outer metalrich clusters resemble a thickdisk p opulation more closely The 1 metalp o or clusters have a signicant prograde rotation to km s in the R No identiable inner halo and bulge declining smo othly to nearzero for R 0 subgroups are found with signicant retrograde motion The radial velo cities of the globular clusters are used along with the spheri cally symmetric collisionless Boltzmann equation to derive the mass prole of the 11 Milky Way halo The total mass of the Galaxy is near M for r kp c Extensions to still larger radii with the same formalism are extremely uncertain b e cause of the small numb ers of outermost satellites and the p ossible correlations of their motions in orbital families The luminosity functions GCLF of the Milky Way and M globular clus ters are dened and analyzed We search for p ossible trends with cluster metallicity or radius and investigate dierent analytic tting functions such as the Gaussian and p owerlaw forms The global prop erties of GCSs in other galaxies are reviewed Measureable distributions include the total cluster p opulation quantied as the sp ecic fre quency S the metallicity distribution function MDF the luminosity and space N distributions and the radial velo city distribution W E Harris The GCLF is evaluated as a standard candle for distance determination For giant E galaxies the GCLF turnover has a mean luminosity of M on a V distance scale where Virgo has a distance mo dulus of and Fornax is at with galaxytogalaxy scatter M mag Applying this calibration to more V 1 1 remote galaxies yields a Hubble constant H km s Mp c 0 The observational constraints on globular cluster formation mo dels are sum 5 6 marized The appropriate host environments for the formation of M clusters are suggested to b e kiloparsecsized gas clouds SearleZinn fragments or 89 sup ergiant molecular clouds of M A mo del for the growth of proto cluster clouds by collisional agglomeration is presented and matched with observed mass distribution functions The issue of globular cluster formation eciency in dierent galaxies is discussed the sp ecic frequency problem Other inuences on galaxy formation are discussed including mergers accre tions and starbursts Mergers of disk galaxies almost certainly pro duce elliptical galaxies of low S while the highS ellipticals are more likely to have b een N N pro duced through in situ formation Starburst dwarfs and large active galaxies in which current globular cluster formation is taking place are compared with the key elements of the formation mo del App endix Some basic principles of photometric metho ds are gathered to gether and summarized the fundamental signaltonoise formula ob jective star nding ap erture photometry PSF tting articialstar testing detection com pleteness and photometric uncertainty Lastly we raise the essential issues in pho tometry of nonstellar ob jects including image moment analysis total magnitudes and ob ject classication techniques INTRODUCTION When the storm rages and the state is threatened by shipwreck we can do nothing more noble than to lower the anchor of our peaceful studies into the ground of eternity Johannes Kepler Why do we do astronomy It is a dicult frustrating and often p erverse business and one which is sometimes costly for so ciety to supp ort Moreover if we are genuinely serious ab out wanting to prob e Nature we might well employ ourselves b etter in other disciplines like physics chemistry or biology where at least we can exert exp erimental controls over the things we are studying and where progress is usually less ambiguous Kepler seems to have understo o d why It is often said that we pursue astronomy b ecause of our inb orn curiosity and the need to understand our place and origins True enough but there is something more Exploring the Globular Cluster Systems universe is a unique adventure of profound b eauty and exhilaration lifting us far b eyond our normal selfcentered concerns to a degree that no other eld can do quite as p owerfully Every human generation has found that the world b eyond the Earth is a vast and astonishing place In these chapters we will b e taking an allto obrief tour through just one small area of mo dern astronomy one which has ro ots extending back more than a century but which has reinvented itself again and again with the advance of b oth astrophysics and observational technology It is also one which draws intricate and sometimes surprising connections among stellar p opulations star formation the earliest history of the galaxies the distance scale and cosmology Fig Left panel Palomar a globular cluster ab out kiloparsecs from the Sun in the outer halo of the Milky Way The picture shown is an I band image taken with the CanadaFranceHawaii Telescop e see Harris et al c The eld size is arcmin or parsecs across and the image resolution seeing is arcsec Right panel A globular cluster in the halo of the giant elliptical galaxy NGC kiloparsecs from the Milky Way The picture shown is an I band image taken with the Hubble Space Telescop e see G Harris et al the eld size is arcmin or parsecs across and the resolution is arcsec This is the most distant globular cluster for which a colormagnitude diagram has b een obtained The sections to follow are organized in the same way as the lectures given at the SaasFee Advanced Course held in Les Diablerets Each one represents a well dened theme which could in principle stand on its own but all of them link together to build up an overview of what we currently know ab out globular cluster systems in galaxies It will I hop e b e true as in any active eld that much of the material will already b e sup erseded by newer insights by the time it is in print Wherever p ossible I have tried to preserve in the text the conversational style of the lectures in which lively W E Harris interchanges among the sp eakers and audience were p ossible The literature survey for this pap er carries up to the early part of A globular cluster system GCS is the collection of all globular star clus ters within one galaxy viewed as a subp opulation of that galaxys stars The essential questions addressed by each section of this review are in sequence What are the size and structure of the Milky Way globular cluster system and what are its denable subp opulations What should we use as the fundamental Population II distance scale What are the kinematical characteristics of the Milky Way GCS Do its subp opulations show traces of dierent formation ep o chs How can the velo city distribution of the clusters b e used to derive a mass prole for the Milky Way halo What is the luminosity mass distribution function for the Milky Way GCS Are there detectable trends with subp opulation or galacto centric distance What are the overall characteristics of GCSs in other galaxies total numb ers metallicity distributions correlations with parent galaxy typ e How can the luminosity distribution function GCLF b e used as a stan dard candle for estimation of the Hubble constant Do we have a basic understanding of how globular clusters formed within protogalaxies in the early universe How do we see globular cluster p opulations changing to day due to such phenomena as mergers tidal encounters and starbursts The study of globular cluster systems is a genuine hybrid sub ject mixing elements of star clusters stellar p opulations and the structure and history of all typ es of galaxies Over the past two decades it has grown rapidly along with the sp ectacular advances in imaging technology The rst review article in the sub ject Harris Racine sp ent its time almost entirely on the globular clusters in Lo cal Group galaxies and only briey discussed the little we knew ab out a few Virgo ellipticals Other reviews Harris ab b demonstrate the growth of the sub ject into one which can put a remarkable variety of constraints on issues in galaxy formation and evolution Students of this sub ject will also want to read the recent b o ok Globular Cluster Systems by Ashman Zepf which gives another comprehensive overview in a dierent style and with dierent em phases on certain topics I have kept abbreviations and acronyms in the text to a minimum Here is a list of the ones used frequently CMD colormagnitude diagram