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The White Dwarf Cooling Sequence of the Globular Cluster Messier 41

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The White Dwarf Cooling Sequence of the Globular Cluster Messier 41 SubmittedtoTheAstrophysical Journal Letters March 5, 2002. If both papers areaccepted for publication, this paper should immediately fol low the paper authoredbyRicher et al. 2002. THE WHITE DWARF COOLING SEQUENCE OF THE 1 GLOBULAR CLUSTER MESSIER 4 2;3 4 4;5 6 Brad M. S. Hansen , James Brewer , Greg G. Fahlman , Brad K. Gibson , Ro drigo 7 8 2 4 9 Ibata , Marco Limongi ,R.Michael Rich ,Harvey B. Richer ,Michael M. Shara ,Peter B. 10 Stetson ABSTRACT We present the white dwarf sequence of the globular cluster M4, based on a 123 orbit Hubble Space Telescop e exp osure, with limiting magnitude V 30, I 1 Based on observations with the NASA/ESA Hubble Space Telescop e, obtained at the Space Telescop e Science Institute, whichisoperatedby the Asso ciation of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are asso ciated with prop osal GO-8679 2 Hubble Fellow, Department of Astronomy,University of California Los Angeles, Los Angeles, CA 90095, [email protected], [email protected] 3 DepartmentofAstrophysical Sciences, Princeton University, Princeton, NJ 08544 4 DepartmentofPhysics & Astronomy, 6224 Agricultural Road, University of British Columbia, Vancou- ver, BC, V6T 1Z4, Canada, [email protected] c.ca 5 Canada-France-Hawaii Telescop e Corp oration, P.O. Box 1597, Kamuela, HA, 96743, [email protected] 6 Centre for Astrophysics Sup ercomputing, Mail No. 31, Swinburne University,P.O.Box 218, Hawthorn, Victoria 3122, Australia, [email protected] 7 Observatoire de Strasb ourg, 11, rue de l'Universite, F-67000 Strasb ourg, France, [email protected] strasbg.fr 8 Osservatorio Astronomico di Roma, Via Frascati 33, Montep orzio Catone I-00040, Italy, [email protected] orzio.astro.it 9 DepartmentofAstrophysics, Division of Physical Sciences, American Museum of Natural History,Cen- tral Park West at 79th St, New York, NY, 10024-5192, [email protected] 10 National Research Council, Hertzb erg Institute of Astrophysics, 5071 West Saanich Road, RR5, Victoria, BC, V9E 2E7, Canada, p [email protected] {2{ 28. The white dwarf luminosity function rises sharply for I> 25:5, consistent with the b ehaviour exp ected for a burst p opulation. The white dwarfs of M4 extend to approximately 2.5 magnitudes fainter than the p eak of the lo cal Galactic disk white dwarf luminosity function. This demonstrates a clear and signi cant age di erence b etween the Galactic disk and the halo globular cluster M4. Using the same standard white dwarf mo dels (Hansen 1999) to t each luminosity function yields ages of 7:3 1:5 Gyr for the disk and 12:7 0:7 Gyr for M4 (2 statistical errors). Subject headings: globular clusters: individual (Messier 4), age { stars: white dwarfs, luminosity function, Population I I { Galaxy: halo 1. Intro duction Globular clusters have b een the fundamental lab oratories for tests of stellar structure theories ever since the work of Sandage (1953). Aby-pro duct of such studies is an age determination for the cluster which is of cosmogonical interest by virtue of the large value. The study of the main sequence and giant branches has b ecome a detailed and quantitative eld (Stetson, Vandenb erg & Bolte 1996; Sara jedini, Chab oyer & Demarque 1997) and the ages thus determined o er a lower limit to the age of the Universe. In contrast, the study of the white dwarfs in globular clusters has progressed much more slowly. Their low luminosities hamp ered early searches (Richer 1978; Ortolani & Rosino 1986; Richer & Fahlman 1988; Paresce, De Marschi & Ramoniello 1995; Elson et al. 1995). Richer et al. (1995; 1997) rep orted the rst detection of a signi cant globular cluster white dwarf p opulation in the cluster M4. Here we rep ort the rst results of a very deep exp osure of the outer eld of that study, allowing b oth the detection of very faint white dwarfs and the removal of background stars and galaxies by virtue of the cluster prop er motion. The motivation for this work is severalfold. The contemp oraneous and chemically ho- mogeneous nature of the cluster sample makes it an excellent lab oratory to study the physics of white dwarf co oling, just as it has b een for main sequence and giant stars. The determi- nation of an age from the white dwarf luminosity function is particularly attractive b ecause it allows a direct comparison, using the same metho d, b etween the cluster and the Galactic disk. Furthermore, the internal physics of white dwarfs is considerably di erent from that of main sequence stars. In particular, the sensitivity of the atmospheric mo dels to metallicity is exp ected to b e unimp ortant as all elements heavier than helium sink under the in uence of the high white dwarf gravity.Thus, a comparison of ages determined from white dwarf and main sequence mo dels o ers an excellent test of systematic mo del uncertainties. {3{ Finally, the continuing interest in the existence of a halo white dwarf p opulation makes the cluster white dwarfs useful as templates to guide searches for similarly old white dwarfs which could p otentially contribute to the Galactic dark matter. 2. The Cluster White Dwarf Sequence The data are drawn from Hubble Space Telescop e exp osures of M4 in programs GO 5461 (cycle 4) and GO 8679 (cycle 9) and are describ ed in detail in the preceding pap er, Richer et al. (2002). The photometric solutions are p erformed by the metho d of pro le tting. The deep second ep o ch is used to x the p osition centroid for cluster memb ers. The p osition (in the cluster frame of reference) is then held xed when determining the magnitude in the (shallower) rst ep o ch data. This allows the detection and measurementofmuchfainter ob jects than in Richer et al. (1997). The nal sample consists of ob jects that havebeen detected in at least three data sets (where the four p ossible sets are the V and I data at each of the two epochs). Completeness corrections were determined using arti cial star tests and require that the added stars b e recovered within 0.5 pixels of their original p ositions and within 0.5 magnitudes of their original input magnitude. The entire cluster white dwarf co oling sequence is shown in Figure 1. The resulting V- band luminosity function is shown in Figure 2. Also shown is the disk white dwarf luminosity function from Lieb ert, Dahn & Monet (1988), using the improved photometry of Leggett, Ruiz & Bergeron (1998) and a V-band distance mo dulus of 12.51. This diagram provides the clearest and most direct evidence of a signi cant age di erence b etween the Galactic disk and the Galactic halo cluster M4, predicated only on the assumption that white dwarfs co ol as they age. While this may not surprise many astronomers, until nowsuch evidence has b een remarkably unconvincing (e.g. Carraro, Girardi & Chiosi 1999). While (halo) globular cluster ages have b een estimated at > 10 Gyr (Chab oyer et al. 1998; Cassisi et al. 1999; Caretta et al. 2000; Thompson et al. 2001) for some time, age estimates (ignoring, for the moment, white dwarf-based estimates, to whichwe shall return) for the lo cal Galactic thin disk range from 8-15 Gyr (Ng & Bertelli 1998; Jimenez, Flynn & Kotonova 1998; Liu & Chab oyer 2000; Binney, Dehnen & Bertelli 2000). Another striking asp ect of the M4 luminosity function is the sharp rise in the number counts from V 26:5toV 27:5. This is the exp ected characteristic b ehaviour of the white dwarf p opulation resulting from a single burst of star formation (e.g. Hansen 2001) and is to b e contrasted with the more gradual rise and turnover at the faint end exp ected from a more extended p erio d of star formation. {4{ 3. Comparison with the mo dels To obtain a quantitative measure of this age di erence, wemust turn to theoretical mo dels of white dwarf co oling. A complete parameter study is b eyond the scop e of a Letter, but wemay obtain a rst estimate by using the current default set of mo dels. It is also imp ortantthatwe redo the age estimate for the lo cal white dwarfs with the same mo dels and in the same way in order to b e consistent. We shall assume mo dels with carb on/oxygen cores, using the mixtures of Segretain & Chabrier (1993). We shall assume a chemical comp osition uniform in layers (`onion- skin mo del') due to gravitational sedimentation, with helium surface layers of mass M He 2 10 M .We will consider mo dels b oth with no surface hydrogen layers and with a hydrogen wd 4 mass fraction of 10 on the surface. The main sequence ages are taken from the mo dels of Hurley,Pols & Tout (2000) and the white dwarf mo dels from Hansen (1999). The main sequence-white dwarf mass relation is that of Wo o d (1992). The signi cant di erence in the calculation of the cluster and disk luminosity functions is the choice of initial mass function and star formation history. The star formation rate in the Galactic disk is assumed to b e constant and the IMF is assumed to b e Salp eter (slop e =2.35). For M4, wehave assumed the star formation is a single burst and the mass function (in the white dwarf progenitor range) slop e is =1.05, based on comparing the white dwarf number count with the main sequence counts in our eld (see Richer et al.
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