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White Dwarfs in Globular Clusters

We review empirical and theoretical findings concerning white dwarfs in Galactic globular clusters. Since their detection is a critical issue we describe in detail the various efforts to find white dwarfs in globular clusters. We then outline the advantages of using cluster white dwarfs to investigate the formation and evolution of white dwarfs and concentrate on evolutionary channels that appear to be unique to globular clusters. We also discuss the usefulness of globular cluster white dwarfs to provide independent information on the distances and ages of globular clusters, information that is very important far beyond the immediate field of white dwarf research. Finally, we mention possible future avenues concerning globular cluster white dwarfs, like the study of strange quark matter or plasma neutrinos.


Introduction
The advantages of using cluster white dwarfs over field white dwarfs in studying the formation, physical properties, and evolution of these stars come from a number of properties of star clusters. i) -White dwarfs in globular or open clusters are located at the same distance and have (in general) the same reddening. Moreover and even more importantly, when moving from hot to cool white dwarfs the colours of cluster white dwarfs are systematically bluer than those of main sequence stars (see Fig. 1). This means that to properly identify cluster white dwarfs we can use the colour-magnitude diagram instead of a colour-colour plane. Therefore, the identification of cool cluster white dwarfs is not hampered by the thorny problem of colour degeneracy with main sequence stars that affects field white dwarfs ( [66]). ii) -For cluster white dwarfs we can trace back the evolutionary properties of the progenitors, since both the chemical composition and the typical mass at the turn-off of the cluster are well-known. Moreover, we can in general safely assume that cluster stars originate from the same star formation event. While there is some evidence that the most massive globular clusters (e.g. ω Cen, NGC 1851, NGC 2808, NGC 6388, NGC 6441) may have a more complicated star formation and chemical enrichment history, most globular clusters are essentially mono-metallic systems with a negligible spread in age. This provides the opportunity to constrain the initial-to-final mass relation of white dwarfs and to improve the knowledge of the physical mechanisms governing their final fate ( [67]; [90]). iii) -According to current evolutionary predictions the number of white dwarfs in a globular cluster with an age of 12 Gyr and a Salpeterlike initial mass function (α = 2.35) is about a factor of 300 larger than the number of horizontal branch stars ( [22]). This means that the expected local density of white dwarfs in a globular cluster is several orders of magnitude larger than the local densities of the halo, thick disk, and thin disk white dwarf populations, thus allowing us to observe large homogeneous samples of white dwarfs without the need for wide-field surveys.
The main drawback for white dwarfs located in globular clusters is that they are faint objects severely affected by crowding problems. Photometric observations are well possible with the Hubble Space Telescope (HST) and profit from software packages that allow to obtain precise measurements even in crowded fields. Spectroscopy, however, poses a different problem: HST is a too small telescope and lacks the multiplexing capacities that allow efficient observations in globular clusters. The disentangling of overlapping spectra in ground based observations is a rather difficult process, as the contributions from the different stars vary strongly with wavelength. Early spectroscopic investigations (e.g. [114]; [117]) were hampered by the fact that their targets were selected from HST photometry, which had usually been observed rather close to the cluster cores. Good photometry of the outer regions of globular clusters will facilitate spectroscopic observations enormously, as the problem of background subtraction is immensely reduced if there are no bright stars close to the white dwarfs.
In a recent investigation [40] called attention to the evidence that the radial distribution of young white dwarfs in NGC 6397 is significantly more extended than the radial distribution of both older white dwarfs and the most massive main sequence stars. To account for this peculiar trend they suggest that the white dwarfs in this cluster do not experience a quiescent birth, but they receive a natal kick. This scenario has been supported by theoretical investigations of [74,75,76]. In particular he found that asymmetric winds on the asymptotic giant branch can generate a kick affecting the trajectory of the resulting white dwarfs. This mechanism would explain why young white dwarfs are less centrally concentrated than their progenitors. If this effect is indeed present in other globular clusters as well, it will be very helpful for the study of white dwarfs in globular clusters, as it would put the youngest (and therefore brightest) white dwarfs into the less crowded outer regions.
Beyond the obvious observational complications, we still lack a detailed understanding of the impact of the high density environment of globular clusters on the formation and evolution of cluster white dwarfs ( [118]).
As the exploration of white dwarfs in globular clusters is an extremely active and rapidly growing field we want to state here that this review contains information from papers or preprints (accepted for publication) available by March 2008.

Searches and Detections
As already mentioned above, white dwarfs in globular clusters are not the most easily observable stars. Their direct detection is hampered by the severe crowding problems in observations deep enough to locate white dwarfs, which explains why it took so long to really identify the first white dwarfs in a globular cluster.

Direct Identification
The pioneering ground-based photometric investigations concerning white dwarfs in globular clusters date back to the late 1980's ( [122] ω Cen; [137] -M 71). However, detailed investigations of globular cluster white dwarfs were undertaken only after the refurbishment of the HST with the WFPC2. Several candidate white dwarfs were then soon identified in quite a few globular clusters. One should keep in mind that the masses assigned to white dwarf sequences in globular clusters are based on comparisons to theoretical tracks and therefore depend strongly on the assumed distance modulus and reddening of the respective cluster.
ω Cen -This is the most massive Galactic globular cluster and it is therefore not surprising that the search for white dwarfs dates back to [122], who detected two dozen white dwarf candidates using EFOSC1@ESO-3.6m photometry, and to [50], who detected four white dwarf candidates using WFPC2@HST data. More recently, [118] detected more than 2,000 white dwarf candidates in three out of the nine ACS@HST pointings located across the cluster center. Moreover, deep H α measurements support the evidence that about 80% of these cluster white dwarfs are also H αbright. In order to account for this empirical evidence [118] suggested that a fraction of the white dwarf candidates might be helium-core white dwarfs, and therefore the aftermath of binary evolution. Results based on a more complete photometric data set (eight out of nine pointings) provided some 6,500 white dwarfs ( [19]; [25], see Fig. 1) supporting the preliminary results of ( [118]). In particular, they found that the ratio of white dwarf to main sequence star counts is at least a factor of two larger than the ratio of the C/O-core white dwarf cooling time to the main sequence lifetime. A fraction of He-core white dwarfs ranging from 10% to 80%, depending on their mean mass, can explain this apparent discrepancy. On the other hand, the presence of a helium-enhanced (Y =0.42, [119]; [104]; [37]; [38]) stellar population cannot account for the observed white dwarf excess. Interestingly enough, [25] also noted that candidate helium-core white dwarfs have been identified in stellar clusters showing evidence for extreme mass loss on the red giant branch, like the metalrich old open cluster NGC 6791 (presence of extreme horizontal branch stars) and the globular clusters ω Cen and NGC 2808 (presence of late hot helium flashers, cf. Sect. 4.2). Such extreme mass loss could in turn also yield stars that avoid the helium-core flash completely and thus become helium-core white dwarfs. M 71 -On the basis of deep multi-band CFHT data [137] detected a dozen white dwarfs in this metal-rich globular cluster. By adopting an apparent distance modulus of (m− M ) V = 13.70 they argued that the cluster white dwarf sequence was either too faint or too blue when compared to DA field white dwarfs, but in plausible agreement either with DB field white dwarfs or with a sequence of DA white dwarfs about 0.1 M ⊙ more massive than typical DA white dwarfs in the Galactic disk. The small number of objects and the shallow depth of the colour-magnitude diagram puts these conclusions on somewhat weak footing and deeper observations would be very helpful. Moreover, they identified a parallel sequence of blue objects, located between the white dwarf sequence and the main sequence, which they identified as a sequence of cluster cataclysmic variables. NGC 6397 -By using deep WFPC2@HST observations [124] first detected a candidate white dwarf sequence in NGC 6397, which showed good agreement with theoretical predictions for white dwarfs with a mass of 0.5 M ⊙ (assuming an apparent distance modulus of (m − M ) I = 12.2) for stars brighter than m 814 ≈ 24.5. At fainter magnitudes the observed numbers exceeded the predicted ones, probably due to contamination by, e.g., background galaxies. Independent observations of the same cluster with WFPC2@HST were collected by [34]. They also detected the white dwarf sequence, which they fit with models for M WD = 0.55±0.05 M ⊙ with an intrinsic dispersion below 0.05 M ⊙ (for a true distance modulus (m − M ) 0 = 11.9 and a reddening of E B−V = 0.18). This comparison illustrates the uncertainties associated with a straightforward fitting of observed white dwarf sequences with theoretical models. Using deep ACS@HST photometry (down to m F 814W = 28) of NGC 6397 [70] detected securely for the first time in a globular cluster the blueward turn of the white dwarf sequence expected due to collisionally induced absorption by H 2 in hydrogen-rich white dwarf atmospheres. In their paper they also provide a very good discussion of the various parameters affecting a fit of the white dwarf cooling curve with theoretical models.  In 1998 [35] detected seven centrally concentrated UV-bright objects in WFPC2@HST observations together with the bright end of the white dwarf cooling sequence. Three of the UV-bright objects had been previously identified as cataclysmic variables. While a fourth one is also a probable cataclysmic variable candidate, the remaining three show no evidence for variability (so-called "Non-Flickerers") and are good candidates for helium-core white dwarfs. In 2001 [158] found three additional "Non-Flickerers" from WFPC2@HST observations. These "Non-Flickerers" form a sequence parallel to the main white dwarf sequence, but brighter by about 2 magnitudes in V 555 . The fainter "Non-Flickerers" (V 555 ≈ 23) show strong H α absorption (H α − R 675 > 0.5). The "Non-Flickerers" are significantly more centrally concentrated than the main sequence stars. Since mass segregation in globular clusters causes the more massive stars to sink towards the center, this argues for fairly massive companions, if these objects are indeed helium-core white dwarfs. Due to the observed blue broad-band colours, which rule out all but the lowest mass main sequence stars (cf. Sect. 4.1), the most probable companions are white dwarfs. M 4 -Using WFPC2@HST data [138] found a well defined white dwarf sequence, which is again in agreement with a mean mass of the white dwarfs of 0.5 M ⊙ for an assumed distance modulus (m − M ) V = 12.65 (note that this is close to the best-fit distance of (m−M ) V = 12.57 recently derived by [68]) and an intrinsic dispersion below 0.05 M ⊙ . Here the observed number of white dwarf candidates lies below theoretical predictions at fainter magnitudes, possibly due to uncertainties in the completeness corrections, to non-DA contributions or to incorrect assumptions concerning the C/O core compositions of the white dwarfs. Subsequent deeper observations collected with the same instrument allowed [141] and [64] to trace the white dwarf sequence down to m 606W ≈ 30, which they used to derive an age for the cluster (see Sect. 5.2). 47 Tuc -By using the FOC@HST [125] found 9 objects in the white dwarf region of the colour-magnitude diagram. In 2001 [172] detected the white dwarf sequence in WFPC2@HST observations down to m 555 ≈ 27 and used it to determine the age and the distance of this cluster (see Sects. 5.2 and 5.1, respectively). UV observations with WFPC2@HST by [53] show a sequence of 12 hot white dwarf candidates (in agreement with theoretical expectations) as well as a large number of objects between the blue straggler and the white dwarf sequence. Unfortunately, [172] and [53] were published within a few months of each other so that the authors could not compare their results. The search for cluster white dwarfs in 47 Tuc has been hampered by the fact that this cluster is projected onto the wing of the Small Magellanic Cloud ( [172]). However, by adopting both FUV images collected with STIS@HST and F336W images collected with WFPC2@HST [96] detected a well defined white dwarf sequence (17) in the center of the cluster. Thanks to the strong temperature sensitiv-ity of the FUV-optical colour they also identified a sequence of candidate cataclysmic variables (16) located between the white dwarf and the main sequence stars. According to theoretical and statistical arguments they estimate that at least a half of these objects should belong to the cluster. NGC 6752 -Data collected with WFPC2@HST allowed [136] to identify the white dwarf cooling sequence and to determine the distance of the globular cluster (see Sect. 5.1). NGC 2808 -Near-and far-UV observations of NGC 2808 collected with STIS@HST ( [45], see also [23]) reveal a population of candidate hot white dwarfs (22 objects brighter than m N UV ≈ 21) and also a number of cataclysmic variable candidates lying between the white dwarf and the main sequence in the UV colour-magnitude diagram (about 50 objects, two of which are variable). M 15 -A clear identification of cluster white dwarfs was recently provided by [46] using deep FUV and NUV ACS@HST images. In particular, they identified 28 white dwarfs and ≈ 60 candidates for cataclysmic variables. These findings appear very promising, since M 15 is a very metal-poor ([Fe/H]=−2.26, [71]) globular cluster characterized by a very dense core (ρ c = 7 × 10 6 M ⊙ pc −3 , [160]) and a very high central velocity dispersion [48]. In order to account for these features the presence of an intermediate mass black hole ( [58]) or a high mass concentration caused by mass segregation of neutron stars and massive white dwarfs ( [5]) have been suggested.
In summary, observations of white dwarfs in globular clusters indicate that the cooling sequences in general agree with theoretical expectations. Unusual populations observed in other regions of the colour-magnitude diagram (most notably along the horizontal branch), however, also affect the white dwarf cooling sequence (e.g. the helium-core white dwarf candidates in ω Cen, see beginning of this section, and NGC 6791, see Sect. 4.2).

Indirect Identification
So far we discussed the identification of single white dwarfs in globular clusters by looking for their cooling sequence in the colour-magnitude diagrams. The detection of white dwarfs in binary systems in the clusters requires rather different methods. As the section below will show, however, ignoring them would severely bias our knowledge about white dwarfs in globular clusters.
Current theoretical predictions accounting for dynamical and evolutionary processes suggest that the binary fraction in dense globular clusters, with ages ranging from 10 to 14 Gyr, is of the order of 10% ( [82]; [39]; [79]; [55]). However, theoretical predictions concerning the evolution with time of the binary fraction in globular clusters are not very well established yet. Predictions based on full N-body simulations and including binary stellar evolution indicate that the binary fraction in the cluster core increases with time ( [79]).
On the other hand, predictions based on a simplified dynamical model and accounting for binary stellar evolution suggest that the binary fraction in clusters decreases with time ( [82]). The two different approaches to account for the fraction of binary stars detected in globular clusters require a modest and a large fraction of primordial binaries, and in turn different collisional rates. The reason for this discrepancy is not clear, but it has been suggested that the above difference is mainly due to differences in the adopted initial conditions and physical assumptions ( [54]).
On the other hand, empirical evidence based on continuous photometric monitoring (8.3 days) with WFPC2@HST of some 46,000 main sequence stars in 47 Tuc indicates that the overall binary frequency is about 14 ± 4% ( [1]). This estimate accounts for detached eclipsing binaries and for contact binaries and might still be a lower limit. From the overluminous white dwarfs in M 4 [68] estimate a binary fraction among the white dwarfs of 0.11±0.05, in agreement with the percentage of hard binaries among field white dwarfs (soft binaries would be destroyed in M 4). By using the colour distribution of main sequence stars, based on deep ACS images for 13 low-density globular clusters, [156] found that the current minimum fraction of binary stars is of the order of 6% inside the core radius, while the global fraction ranges from 10% to 50%. According to the above numbers it is not surprising that globular clusters should host a broad range of exotic objects that show up as faint X-Ray sources. Of those, the following have been identified in globular clusters so far: low-mass X-Ray binaries (a neutron star accreting from a companion) and their progeny, the millisecond pulsars; chromospherically or magnetically active binaries (two main sequence stars or a main sequence star and an evolved companion); and cataclysmic variables (a white dwarf accreting from a low-mass companion). The formation rate of these objects in globular clusters is expected to be orders of magnitude higher than in the Galactic disk ( [92]; [33]). The advent of the Chandra X-Ray Observatory and of HST provided the opportunity to investigate these objects in the central regions of globular clusters (see [162] for an extensive review of X-ray sources in globular clusters). The cataclysmic variables appear to be the progeny of either primordial binaries or stellar encounters and they have been identified in several globular clusters. In particular, Chandra X-ray observations in combination with HST photometry identified nine cataclysmic variables in NGC 6397 ( [158]), 22 in 47 Tuc ( [72]; [73]), and two (possibly three) in M 4 ( [4]). Optical and FUV data collected with HST and covering long time intervals (several years) also provided the opportunity to identify outbursting cataclysmic variables in a few globular clusters ( [149], [150]). This approach is very useful to unambiguously identify cluster CVs, since the spectroscopic follow-up of candidates located in the crowded central regions is difficult ( [97]).
On the basis of these X-ray and optical surveys of a dozen globular clusters a remarkable correlation has been found between the stellar encounter rate and the number of X-ray sources in the cores of globular clusters ( [132]). Simulations by [151] showed that the production rate of cataclysmic variables (CVs) in globular clusters is comparable to that observed in the field. Due to the high density environment in globular clusters, however, hard binaries dominate there, which have a faster evolution. Moreover, the simulations also predict a new class of cataclysmic variables that are formed by exchange interactions, i.e. without a common envelope phase. Such cataclysmic variables are formed preferably with donor masses on the main sequence of more than 0.7 M ⊙ and are short-lived when compared to classical field CVs. These generally shorter lifetimes for globular cluster CVs imply a reduction in their expected number, at any given time, by roughly a factor of three. Another interesting prediction of these simulations is that the canonical 2-3 hours period gap observed among field CVs should be smeared out in the dynamically formed globular cluster CVs.
Numerical simulations by [83] accounting for binary formation via physical collisions (based on smoothed particle hydrodynamics) and for the metallicity dependence in the formation and evolution of close binaries also predict that the formation rate of cataclysmic variables and AM CVn systems (white dwarf binaries with one of the two white dwarfs undergoing a Roche lobe overflow) in the field and over the entire cluster are very similar. The formation channels, however, are more varied than those of the field counterparts: primordial binaries, post-exchange binaries, and physical collisions between main sequence and red giant stars.

Spectral Types
Photometric observations alone are generally not sufficient to distinguish DA from non-DA stars, although hydrogen-rich DAs and helium-rich DBs in principle can be distinguished by their photometric properties alone in the temperature range 10,000 K ≤ T eff ≤ 15,000 K (see [15]). Based on this method [136] classified two white dwarfs in NGC 6752 as DBs. However, without a spectral classification, those two stars can also be explained as high-mass DA white dwarfs, possibly a product of merging. Reference [139] speculate that the brightest white dwarf in M 4 (V =22.08) might be a hot (27,000K) DB star. In 1999 [49] showed an FOS@HST spectrum covering the H β region of a "Non-Flickerer" in NGC 6397, which clearly showed that the spectrum was hydrogen-rich. In 2000 [114] published the first ground-based spectra of four white dwarfs in a globular cluster (NGC 6397) observed with FORS1@ESO-VLT, which covered the range from 3800Å to more than 5000Å. All stars were DA white dwarfs. Later [117] also showed FORS1@ESO-VLT spectra of five white dwarfs in NGC 6752, all of which were again hydrogen-rich.
In 2005 [88] showed GMOS@Gemini and LRIS@Keck spectra of 21 white dwarfs in the young (650 Myr) open cluster NGC 2099 (>30% of the known white dwarfs in that cluster), none of which was helium-rich. Cluster members have estimated effective temperatures between 13,000 K and 18,000 K in the observed magnitude range. Allowing for 4-5 contaminating field stars, one would expect to find 4 DBs from the 4:1 DA:non-DA ratio observed among field white dwarfs of similar temperatures ( [145]). It was noted by [6] that the mass distribution of field DB stars lacks the high mass tail observed for DA white dwarfs. Newer observations by [164], on the other hand, find no difference in the mass distribution between DB and DA stars. Spectroscopic analyses by [87] yield rather high masses of up to 1.1 M ⊙ for the bright white dwarfs in NGC 2099, consistent with the youth of that cluster. Several explanations for the possible lack of DB stars among massive white dwarfs were discussed by [88]: i) -More massive white dwarfs have thicker hydrogen layers, which may prevent the formation of a convection zone mixing helium to the hydrogen layer. Such a convection zone has been suggested to cause the appearance of DB stars at about 30,000 K ( [105]; [66])). This explanation, however, has no quantitative support so far and the currently assumed hydrogen layers are much thicker than those assumed by [105]. ii) -The removal efficiency for the hydrogen layer depends on mass. iii) -Binary evolution may result preferably in DA white dwarfs (in binary systems and also as single stars, [107]).
Also LRIS@Keck spectroscopy of white dwarfs in NGC 6791 by [89], showed only hydrogen-rich spectra for all nine targets with sufficient S/N.
The situation changed recently, when [168] and [90], both using LRIS@Keck, detected DB type white dwarfs in the open clusters NGC 6633 (0.5 Gyr) and NGC 6819 (1.5 Gyr), respectively. Additional deeper spectroscopic observations in older open clusters and in globular clusters will definitely be needed to get a better handle on the DA:non-DA ratio in clusters.

White Dwarf Formation and Evolution
The minimum mass value for carbon ignition in the core is the so-called M up , while M mas defines the minimum mass value to ignite neon at the center. Stellar structures with initial masses smaller than M up produce degenerate C/O cores during the asymptotic giant branch phase. Current evolutionary prescriptions ( [18]; [110]; [61]; [126]) suggest that these stars finish their evolution either as C/O white dwarfs (efficient mass loss along the asymptotic giant branch) or with a carbon deflagration ( [80]; [77]) if the mass of the C/O core becomes larger than the Chandrasekhar mass (mild mass loss along the asymptotic giant branch). Stellar structures with initial masses larger than M mas experience all the nuclear burning stages and finish their evolution as iron core collapse supernovae ( [171]; [108]). Stellar structures with initial masses between M up and M mas , the so-called super-AGB stars, start to ignite carbon in a partially degenerate off-center shell. After a few shell flashes these structures eventually start to burn carbon in the center and finish their evolution either as massive O/Ne white dwarfs ([120]; [159]; [59]; [152]) or as electron-capture supernovae where the core collapse is triggered by electron captures before the neon ignition ( [166]). Evolutionary calculations indicate that the value of M up strongly depends on the assumptions adopted to deal with semi-convection and convective overshooting. By using three evolutionary codes with different mixing algorithms, [131] found that, at fixed metal abundance, the value of M up ranges from 7.5 to 9.0 M ⊙ .
White dwarfs in globular clusters thus have a broad range of progenitor masses, but they are currently produced by progenitors with stellar masses of about 0.8-1.0 M ⊙ ( [140]). Due to their long cooling times massive white dwarfs in globular clusters will generally be extremely faint. However, massive cluster white dwarfs may currently evolve from blue stragglers or from the merging of close white dwarf binaries (see, e.g., [112]). The general evolutionary properties of white dwarfs have been investigated in many papers (see, e.g., [98]; [36]; [14]; [3]; [147]; [57]; and references therein). In the following subsection we briefly discuss the formation of low-mass white dwarfs from binary evolution and otherwise.

Binary Evolution
Empirical evidence based on field white dwarfs, for which spectroscopic mass estimates are available, indicates that only a fraction of the order of 10% has masses below 0.45 M ⊙ , which is the limiting mass required to remove the electronic degeneracy and to ignite helium-core burning via the heliumcore flash ( [29]). These helium-core white dwarfs are generally considered to be the aftermath of binary star evolution, since single stars with such low masses are not expected to evolve to the white dwarf cooling sequence within a Hubble time. These objects underwent an episode of extreme mass loss, possibly caused by stellar encounters or by evolution in compact binaries, while they approach the tip of the red giant branch ( [95]).
In 2003 [65] published a study on the effects of binary evolution on the white dwarfs in globular clusters. Binary formation by exchange interactions between hard binaries and single stars in globular clusters promotes the production of helium-core white dwarfs as it increases the average secondary mass in binaries containing C/O white dwarfs or neutron stars (thereby increasing the probability of mass transfer episodes). In addition the final helium-core white dwarf will be removed preferably from these systems during ensuing exchange interactions. Tidal captures followed by mergers or direct stellar collisions involving red giants result in binaries with a red giant core (= proto helium-core white dwarf) and a more massive companion, which accreted most of the red giant's envelope (unless that was ejected). Low-mass helium-core white dwarfs are, at fixed effective temperature, brighter than typical C/Ocore white dwarfs and the cooling times of the former objects are significantly longer than the latter ones. This means that even a small fraction of heliumcore white dwarfs significantly increases the number of observed bright white dwarfs in globular clusters ( [28]; [29], see also Sect. 2.1 for ω Cen and Sect 4.2 for NGC 6791).
The globular cluster NGC 6397 shows a centrally concentrated population of UV-bright stars ( [35]; [49]; [158]; see also Sect. 2.2). Spectroscopic follow-up collected with FOS@HST by [49] indicates that the observed non-variable UV bright star is a binary system consistent with a helium-core white dwarf and an unseen massive companion being either a neutron star or a massive white dwarf. This was the first helium-core white dwarf identified in a globular cluster. Detailed investigations by [65] assuming various values for the thickness of hydrogen layers and the companion masses (neutron stars, C/O white dwarfs) suggest that the "Non-Flickerers" in NGC 6397 are young objects with C/O white dwarf companions, whereas neutron star companions do not provide self-consistent solutions. This is in agreement with the lack of X-ray emission from "Non-Flickerers" observed by [63].
In a recent exhaustive review [10] discussed the theoretical models of globular cluster evolution and the dynamical interaction between single and binary stars. The author also provides a detailed analysis concerning the formation and evolution of binary systems including one or more compact objects. The observational techniques currently adopted to detect and characterize these exotic objects are also reviewed, including the possibility to detect gravitational radiation from the relativistic binaries in globular clusters with LISA.

Exotic Cases
A well defined white dwarf sequence in the old open cluster NGC 6791 was recently observed by [8] with ACS@HST. The fit with C/O white dwarf models suggested an age of 2.4 Gyr, in stark contrast to the age of 8 Gyr derived from the main sequence turnoff of this cluster. The authors ruled out an incorrect distance modulus and incorrect assumptions on the mass of the hydrogen layer or the C/O ratio in the cores of the white dwarfs as possible explanations. Helium-core white dwarfs from binary evolution also cannot explain the observed white dwarf sequence, as such white dwarfs would have low masses and would therefore be too bright.
Prompted by these findings [69] explored further possible explanations and found that two effects can contribute to explain bright white dwarfs in NGC 6791: i) -Retardation of cooling by 22 Ne sedimentation ( [16]; [44]), which would predict the peak of the white dwarf cooling sequence for C/O white dwarfs at m 606W ≈28-29 (instead of m 606W ≈29-30 from canonical models). ii) -Production of massive (>0.4 M ⊙ ) helium-core white dwarfs due to extreme mass loss on the red giant branch. The idea of increased mass loss is supported by the existence of extreme horizontal branch stars in NGC 6791 ( [91,106,102]). This second scenario can explain the peak in the luminosity function at m 606W ≈27.5 for a cluster age of 8 Gyr, assuming that more than 50% of all low mass stars with main sequence masses above 1.6 M ⊙ become helium-core white dwarfs.
Analyses of LRIS@Keck spectra of bright (V ≈22. . . 24) white dwarfs in NGC 6791 by [89] yielded masses below 0.46 M ⊙ (threshold for core helium burning) for six out of nine probable cluster members, with the remaining three having masses of 0.47 M ⊙ , 0.48 M ⊙ , and 0.53 M ⊙ , supporting the high mass loss scenario outlined by [69].
Deeper observations by [9], however, show a problem with the identification of the brightest peak in the white dwarf luminosity function as helium-core white dwarfs. In the new data the bright peak shows an extension to the blue, which is supposed to be caused by the more massive and older white dwarfs, which have smaller radii. In the case of helium-core white dwarfs, however, this would require white dwarfs with masses above 0.5 M ⊙ , i.e. above the minimum mass for helium-core burning. The new data show also a second, fainter peak for which a fit with canonical C/O white dwarfs gives an age of 6 Gyr. A possible solution to the puzzling difference with the turn-off age (8 Gyr, see their Fig. 10) would be the rotation of white dwarf progenitors. Rotation increases the minimum mass for the helium-core flash by up to 0.15 M ⊙ [113] while at the same time increasing the mass loss on the red giant branch. Current data do not allow to verify this scenario.
A few massive globular clusters (e.g. ω Cen, NGC 2808, NGC 6441) show evidence for a population of very hot and helium-rich horizontal branch stars ( [41]; [23]; [115]; [116]; [24]; [26]). The formation and evolution of these objects prompted a lively debate in the recent literature. In order to account for their photometric and spectroscopic properties the so-called "hot helium-flasher" scenario has been suggested ( [27]; [41]; [23]; [29]). In this theoretical framework red giant stars experience a violent mass-loss event, which decreases the total mass of these structures to below the limit for central helium ignition before approaching the tip of the red giant branch. The red giant stars with a mass slightly larger than this limit undergo a helium-core flash at high temperatures either during their approach to the helium-core white dwarf cooling sequence (early hot helium flasher, [27]; [41]) or along this sequence (late hot helium flasher, [23]). In 2006 [29] studied the consequences of this scenario for the white dwarf population in globular clusters. A globular cluster with a significant number of "late hot helium-flashers" will also produce a significant fraction of helium-core white dwarfs (i.e. the red giant stars with a mass smaller than the limit for central helium ignition). At luminosities greater than 0.1 L ⊙ helium-core white dwarfs have a life time comparable to typical extreme horizontal branch stars. By assuming that a fraction of 20% of the stars in a globular cluster do not evolve through a helium-core burning phase one expects twice as many white dwarfs brighter than 0.1 L ⊙ than in the canonical case (all stars undergoing central helium burning). This scenario is supported by [148], who found a deficit of the order of 20% in the number of bright RGB stars in the globular cluster NGC 2808 from ACS@HST and WFPC2@HST photometry. A few dozens of white dwarfs have already been identified in NGC 2808 by [45], but their limiting magnitude is too shallow to constrain the impact of the "missing giants".
The existence of sub-populations enriched in helium ( [119,104,37,38]), which has been suggested to explain the multiple main sequences found in ω Cen ( [7]) and NGC 2808 ( [130]) also has consequences for the white dwarfs in these clusters. Recent dynamical simulations of a globular cluster, where the first generation of stars enriches the second generation with helium, have been performed by [47]. In the case of a top-heavy initial mass function for the first generation a large number of massive white dwarfs is predicted compared to the results for a Salpeter initial mass function. Accurate number ratios of white dwarfs vs. main sequence stars would allow to verify their models.
Using deep multi-band ACS@HST and WFI@ESO/MPI-2.2m photometry of ω Cen [30] found that empirical star counts of horizontal branch stars are on average larger (30%-40%) than predicted by canonical models. The possible occurrence of helium-enhanced stars cannot account for this excess. The authors suggested that the excess of horizontal branch stars might be due to "hot helium-flashers". This working hypothesis implies that ω Cen should also host a sizable fraction of candidate helium-core white dwarfs (cf. Sect. 2.1).

Astrophysical Use of White Dwarfs in Globular Clusters
Globular cluster white dwarfs play a crucial role not only to validate current evolutionary predictions, but also as a diagnostic to constrain the ages and distances of globular clusters.

Cluster Distance Determinations
The use of the white dwarf sequence as a standard candle for determining the distance to nearby globular clusters was suggested by [135]. The approach is similar to the traditional main sequence fitting procedure using local subdwarfs with known trigonometric parallaxes. The white dwarf sequence of the cluster is compared to a sequence constructed from local white dwarfs with accurate trigonometric parallaxes. While it may seem strange to use the faintest objects in a globular cluster to derive its distance, white dwarfs offer some advantages as standard candles when compared to main sequence stars: i) -They come in just two varieties -either hydrogen-rich (DA) or heliumrich (DB)independent of their original metallicity and, in both cases, their atmospheres are virtually free of metals. So, unlike in the case of main sequence fitting, one does not have to find local calibrators with the same metallicity as the globular clusters. ii) -White dwarfs are locally much more numerous than metal-poor main sequence stars and thus make it possible to define a better reference sample.
However, the method has its own specific problems, which are discussed in great detail in [172] and in [145]. Most of the discussion below is taken from these excellent papers. Indeed, the location of the white dwarf cooling sequence depends on: • The white dwarf mass On theoretical grounds, given the observed maximum luminosity reached on the asymptotic giant branch (AGB), the mass of currently forming white dwarfs in globular clusters should be 0.53 ± 0.02 M ⊙ ( [135]; [136]). Recent homogeneous evolutionary computations ( [128]) from the pre-main sequence to the tip of the asymptotic giant branch suggest that, depending on the metallicity, progenitors with a stellar mass of 0.8 M ⊙ form white dwarfs with masses ranging from 0.55 M ⊙ (Z=0.02) to 0.575 M ⊙ (Z=0.0001). Unfortunately, there are no local white dwarfs in this mass range with directly determined masses (i.e. without using a mass-radius relationship). There is, however, a handful of local white dwarfs with spectroscopically determined masses near this value (cf. Table 1 in [172]), which allows the construction of a semi-empirical cooling sequence for M WD =0.53 M ⊙ , once relatively small mass-dependent corrections are applied to each local white dwarf. However, there are also some systematic differences between clusters ( [145]): At a given metallicity some globular clusters (e.g. NGC 6752) possess very blue horizontal branches with horizontal branch star masses as low as 0.50 M ⊙ . Such extreme horizontal branch stars evolve directly to low-mass C/O-core white dwarfs (bypassing the asymptotic giant branch, therefore also called AGB-manqué stars, [62]) and shift the mean white dwarf mass closer to 0.51 M ⊙ . Other clusters show only very red horizontal branch stars, which will evolve along the asymptotic giant branch (thermal pulsing AGB) and form preferably white dwarfs with masses of about 0.55 M ⊙ , depending on the mass-loss efficiency along the asymptotic giant branch. Also other channels may exist to produce white dwarfs with masses above or below the cluster mean, as described in Sect. 4.1. The spectroscopic determination of the white dwarf masses in a globular cluster was first attempted by [114] for white dwarfs in NGC 6397. However, the low S/N ratio of the spectra of these very faint stars did not allow them to determine the mass with sufficient accuracy. Multi-colour photometry of white dwarfs in NGC 6752 in combination with low-resolution spectra allowed [117] to estimate a most probable mass of 0.53 M ⊙ for the bright white dwarfs in this cluster (assuming a true distance modulus of (m − M ) 0 = 13.20 and a hydrogen layer mass of 10 −4 M ⊙ ).

• The white dwarf envelope mass
In the case of DA white dwarfs the cooling sequence location depends also on the mass of the residual hydrogen-rich envelope. The thickness of the envelope is important for the energy loss rate of the white dwarf cores and also affects the white dwarf radius at a given temperature ( [145]). For ranges in envelope mass from 10 −4 M ⊙ to 10 −6 M ⊙ the cooling sequences for DA white dwarfs differ by about 0.07 in M V , whereas non-DA white dwarfs show no difference. This also affects spectroscopically derived masses (see above), with the resulting mass being about 0.04 M ⊙ higher when using the evolutionary envelope mass (10 −4 M ⊙ , [56]) as opposed to virtually zero envelope mass. This mass uncertainty corresponds to an uncertainty of 0.1 mag in the distance modulus and 1-1.5 Gyr in the age derived from the main sequence turnoff. • Spectral type DB stars are fainter than DA stars at a given colour, with the offset depending on the filter combination (i.e. the offset is greater in V vs. B − V than in I vs. V − I). In the field we find a ratio of DA:non-DA of about 4:1 ( [145]), while the number for globular clusters is currently unknown (cf. Sect. 3). As non-DAs have colour-magnitude relations different from DAs (DA white dwarfs are, at fixed luminosity, systematically cooler than DBs) their undetected presence in the white dwarf cooling sequence can bias the distance determination. Since the cooling sequences are well separated e.g. in B − V , however, this effect can be accounted for by a prudent choice of filters. However, the possible occurrence of helium-core white dwarfs makes the photometric identification of DA and DB white dwarfs a risky approach, since helium-core white dwarfs, at fixed luminosity, are also systematically cooler than DBs. • Chemical composition of the core (varying C/O profiles, helium-core white dwarfs) While the structure of the C/O-core is not well known, even large changes do not significantly affect the position of the cooling sequence ( [145]). Helium-core white dwarfs are, at fixed mass and effective temperature, brighter than C/O-core white dwarfs, but their cooling sequences can overlap in the M V , V − I plane.

• Initial-to-final mass relation
For the initial-to-final mass relation assumed by [145] white dwarfs with progenitor masses below 2.5 M ⊙ have a mass of 0.54 M ⊙ , which increases to 1.0 M ⊙ for progenitor masses of 7 M ⊙ . These high masses occupy the blueward turn expected for the coolest white dwarfs. Regardless of the assumed initial-to-final mass relation the masses of the white dwarfs are constant for the temperature range between 10,000 K and 20,000 K (although the actual value varies with the adopted initial-to-final mass relation). Also the progenitor masses are basically constant for this temperature range, since the white dwarf evolution is very fast when compared to the cluster ages. This is not true for the field stars, where due to extended star formation white dwarfs of different ages and masses can occupy a given temperature range.

• Reddening
An uncertainty of 0.01 mag in E B−V yields an uncertainty of 0.055 mag in the true distance modulus ( [145]).
The first determination of the distance to a globular cluster using its white dwarf sequence was provided by [136] using WFPC@HST data. Their distance modulus for NGC 6752 of (m−M ) 0 =13.05±0.1 was a bit lower than, but con-sistent with, the ones obtained from main sequence fitting (13.12÷13.23, see [117] for a discussion). In 2001 [172] repeated this experiment for 47 Tuc, again using WFPC2@HST. The brightnesses of the local white dwarfs were corrected to a mass of 0.53 M ⊙ assuming a hydrogen envelope mass of 10 −4 M ⊙ . They obtained a true distance modulus of (m − M ) 0 = 13.09±0.14, which was significantly shorter than all previously determined distances for 47 Tuc. They also provided a new white dwarf distance to NGC 6752, using the new value for the hydrogen layer mass, of (m − M ) V = 13.27. Shortly afterward [129] re-determined the distance to 47 Tuc from main-sequence fitting, noting possible calibration problems with previous studies. They found a best-fit value of (m − M ) 0 = 13.25 +0.06 −0.07 , which is in good agreement with the distance derived from the red clump (m − M ) 0 = 13.31 ± 0.05 and (within the mutual error bars) with the white dwarf distance derived by [172].
In 2004 [117] used FORS1@ESO-VLT spectroscopy of white dwarfs in NGC 6397 and NGC 6752 to estimate a distance modulus to NGC 6397. The average gravity obtained from multi-colour WFPC2@HST photometry for the white dwarfs in NGC 6752 (assuming a fixed distance modulus) was used to determine effective temperatures from the spectra for the white dwarfs in NGC 6397. Using the effective temperatures determined that way to estimate the distance of the cluster yielded a true distance modulus of (m − M ) 0 = 12.0±0.1, which is at the short end of the range of distances derived for NGC 6397 from main-sequence fitting (12.1 ÷ 12.2, [133,134]). This result is in agreement with the one obtained by [70] ((m − M ) 0 = 12.02±0.06) from deep ACS@HST photometry (down to m F 814W = 28) of NGC 6397 (see below for the age derived from these data).
Using WFPC2@HST data [103] determined the distance to M 5 from both the main sequence ((m − M ) V = 14.56 ± 0.10, consistent with previous determinations) and the white dwarf sequence ((m − M ) V = 14.78 ± 0.18). They ascribe the rather large error of their white dwarf distance to the low S/N of the observed white dwarfs, the small baseline in colour (V − I), and the mediocre spatial resolution of their WFPC2 data. These arguments should be considered in further attempts to determine white dwarf distances to globular clusters.

Cluster Age Determinations
The white dwarf sequence also provides a possibility to determine the age of a globular cluster. However, aside from the observational difficulties and the uncertainties in the cooling tracks (see [31] for more details) any error in the assumed mass affects the result. Recent very deep WFPC2@HST observations allowed the detection of the white dwarf cooling sequence in M 4 to unprecedented depths of V ≈30 ( [141]). As a preliminary result [64] derived an age of 12.7±0.7 Gyr from the white dwarf luminosity function of M 4, where the cluster membership of the stars had been verified from proper motions. This age is consistent with other independent age estimates, but one should keep in mind that their error bar does not include errors due to the uncertainty of the white dwarf mass. Their result had been questioned by [42], who claimed that the cluster membership of the white dwarfs cannot be verified down to sufficiently faint limits to obtain more than a lower limit of the age. In response to that claim [143] argued that with different methods for data reduction and analysis different limiting magnitudes can be reached using the same data.
In a more detailed paper [68] carefully studied the influence of the following parameters on the age determination: distance, reddening, atmospheric models, cooling models, main sequence lifetime, initial-to-final mass relation, core composition, atmospheric composition, and binary fraction.
To determine the age they performed a 2-dimensional modeling of the white dwarf cooling sequence, i.e. they modeled magnitude and colour. They started from a main sequence initial mass function (IMF), using an initialto-final mass relation, and then assigned colour and magnitude based on the white dwarf cooling age. This way they derived an age of 12.4 +1.8 −1.5 Gyr (2σ limits) for an IMF slope (dN/dM ms ∼ M −(1+x) ms ) of x = −0.85. Variations of the input parameters envelope mass, C/O ratio in the core, initial mass function, cooling models, atmospheric composition (hydrogen-rich vs. helium-rich), atmospheric models, binary fraction, proper motion cutoff, and distance yielded a global best fit for an age of 12.1 Gyr and an IMF slope of x = −1.2 with a 2σ lower age limit of 10.3 Gyr, in good agreement with other determinations, but with substantially larger uncertainties than their preliminary result in [64]. IMF slope and age are correlated as larger ages require that a larger fraction of the white dwarfs has cooled to below the detection limit, so that a smaller value of x is required to fit the observed star counts. One should keep in mind that the x values derived by the fitting procedure are local ones (based on one region within the globular cluster) and may be influenced by the effects of mass segregation.
They estimated a current birth rate of white dwarfs of 1.5×10 −6 yr −1 , which is consistent with the birth rate of horizontal branch stars for that cluster.
Using deep ACS@HST photometry (down to m F 814W = 28) of NGC 6397 [70] derived age, reddening, distance, and an initial-to-final mass relationship from a fit of the complete white dwarf sequence (magnitude and colour, similar to their work on M 4 [68]). Using various evolutionary sequences they arrived at an age of 11.47±0.47 Gyr (95% confidence limits) in agreement with, but more precise than, previous determinations from the main sequence turnoff. All models, however, fail to reproduce the full extent of the blueward turn at the faint end of the observed white dwarf cooling sequence. The initial-to-final mass relation which they derived simultaneously from their data is in good agreement with the empirical one from [167] and also with the white dwarf mass estimated at the bright end by [117].
On the theoretical side, [128] recently addressed the uncertainties affecting cluster age determinations based on the white dwarf luminosity function. In particular, they found that different assumptions concerning the conductive opacities might affect the ages of globular clusters at the 10% level, while the impact of the C/O ratio in the core is smaller than 5%. Interestingly enough, they also found that the cluster age is only marginally affected by the adopted initial mass function, since it does not affect the position of the peak in the luminosity function. On the other hand, the adopted initial-tofinal mass relation affects both the shape and the position of the peak of the luminosity function. The change causes an uncertainty on the cluster age of about 8%. A similar uncertainty on the cluster age is also caused by the metal abundance, and indeed for progenitors with metallicities ranging from Z=0.0001 to Z=0.001 and from Z=0.001 to Z=0.006 the difference is of the order of 10% per interval (see also [146] and [127]).
In a recent investigation [101] included Ly α red wing opacity in the pure hydrogen white dwarf atmosphere models. He found that this physical ingredient plays a relevant role in the analysis of cluster white dwarf cooling sequences. The application of the new models to NGC 6397 suggests that the white dwarfs at the end of its cooling sequence are about 160 K cooler, and in turn that the cluster is about 0.5 Gyr older than previously estimated by [70].

Future Perspectives
While several recent photometric and spectroscopic investigations of cluster white dwarfs significantly improved our knowledge of these objects we are still facing longstanding problems. The right instruments to properly address these problems will be future extremely large telescopes like the European Extremely Large Telescope (E-ELT, [78]; [20]; http://www.eso.org/projects/e-elt/), the Thirty Meter Telescope (http://www.tmt.org/), or the Giant Magellan Telescope (http://www.gmto.org/). The use of multi-conjugate adaptive optic systems ( [111]) will provide near-infrared (NIR) images with a full width at half maximum (FWHM) of the order of a few hundredths of arcseconds, a field of view (FoV) of a few arcminutes squared and very high spatial resolution (from 0.005" to 0.01", see, e.g., [51]). The same outcome applies to James Webb Space Telescope (JWST, http://www.stsci.edu/jwst/). This telescope will be equipped with a NIR Camera (NIRCam, http://ircamera.as.arizona.edu/nircam/) covering the wavelength range from 0.6 to 5 µm with a FoV of 4.52' for simultaneous observations in two wavelength ranges. The short wavelength (λ ≤ 2.4 µm) channels have a spatial sampling of 0.03"/px, while the long ones have 0.06"/px with Nyquist sampling at 2 and 4 µm ( [144]). In addition the NIR spectrograph covers the same wavelength region at low spectral resolution (R≈3000). The key advantage of this choice is the possibility to collect spectra of faint targets located close to bright sources ( [109]). This is a very typical situation in the crowded central regions of globular clusters. There are several fields where these observational equipments might play a crucial role.
i) Variable Stars -The 30m-40m class telescopes will provide the unique opportunity to collect multi-band photometry of globular cluster white dwarfs with an unprecedented time resolution. This means that we should be able to investigate in situ the topology of the instability strips located along the cooling sequence of cluster white dwarfs ( [93]). Variable white dwarfs are multi-periodic non-radial oscillators with periods ranging from a few tenths to roughly 1000 seconds ( [154]) and present small luminosity amplitudes. Starting at the hot end of the white dwarf cooling sequence we first find the instability strip of hot (80,000 K ≤ T eff ≤ 170,000 K) either pre-white dwarfs or central stars of planetary nebulae. They are called DOV or GW Vir stars and the prototype is PG1159−035. The instability strip of DBV stars is located at cooler effective temperatures (22,000 K ≤ T eff ≤ 28,000 K). Eventually, we approach the instability strip of the DAV or ZZ Ceti variables at even cooler effective temperatures (11,000 K ≤ T eff ≤ 12,500 K). Note that the current knowledge on variable white dwarfs is based on local objects only, which are affected by uncertainties in the progenitor mix, the distance, the reddening, and the effective temperature. Cluster variable white dwarfs will provide firm constraints on the driving mechanisms and the possible occurrence of static stars inside the various instability strips ( [155]). Moreover, the detection of cluster DBVs might provide fundamental constraints on plasmon neutrinos. The neutrino produced in the decay of plasmons cannot be observed in physics laboratories ( [81]). However, current theoretical predictions indicate that half of the luminosity of a hot white dwarf (T eff ≈ 25,000 K) is carried away by neutrino emission ( [121]; [94]). This means that accurate measurements of period changes over time for DBV stars can constrain plasmon neutrino rates ( [169]). The great advantage of using cluster DBVs is the possibility to compare the plasmon neutrino rates based on pulsation observables with those based on evolutionary observables (white dwarf luminosity function). Current luminosity functions of white dwarfs in globular clusters do not allow to put firm constraints on this mechanism as the critical temperature range of the cooling sequence is too poorly populated. Cluster white dwarf variables can also play an important role for even more fundamental physics. It has been suggested ( [2]) that compact objects, such as neutron stars, might consist of Strange Quark Matter (SQM). SQM is a particular form of quark matter with a strangeness per baryon value of about −1 ( [17]; [170]). Theoretical predictions indicate that SQM may also exist in the cores of white dwarfs ( [60]; [161]). Two different observational approaches have been suggested to constrain the existence of exotic white dwarfs with SQM cores and envelopes of normal matter. i) The mass-radius relation. However, the difference between normal and exotic white dwarfs is too small to be observable (see Fig. 4 in [123]). ii) Gravity modes. Pulsations are very sensitive to density profiles and [11], [12], and [13] demonstrated that white dwarf models with SQM cores show a completely new resonant cavity for gravity modes. This causes the period spacing between consecutive modes in exotic white dwarfs to be shorter than one second, while in normal white dwarfs it is of the order of several tens of seconds. Moreover, the number of modes inside the different clusters of periods strongly depends on the size of the SQM core. The observational signature of this effect is that the Fourier spectrum of exotic white dwarfs should show peaks that are characterized by an intrinsic width, while those of normal white dwarfs become sharper with increasing time coverage. Cluster white dwarf variables will provide the large homogeneous samples required to constrain the possible occurrence of these phenomena. Longer time series data covering several hours will also provide fundamental constraints on the number of cataclysmic variables in globular clusters as well as on the frequency of dwarf novae.
ii) Metals and IR Excess -White dwarfs have metal-poor atmospheres. Whatever the metal abundance of the progenitor, heavy elements in their atmosphere can only survive for a short period (≈ 10 7 yr). This empirical evidence is supported by the plain physical argument that radiative levitation is stronger than gravitational settling only at the hot end of the white dwarf cooling sequence (T eff ≥ 20,000 K, [32], and references therein). Cooler white dwarfs are characterized by diffusion timescales that are several orders of magnitudes shorter than the cooling lifetime. Therefore, the occurrence of metal lines in the photospheres of cool white dwarfs must be due either to the inward growth of the convective region that dredges-up carbon ([52]) or to accretion of interstellar matter ( [99]). Detailed theoretical calculations indicate that the diffusion timescale of Ca, Mg, and Fe in "metal-rich" DA (DAZ) white dwarfs are 3-4 orders of magnitude shorter than for "metal-rich" non-DA (DZ) white dwarfs (10 6 yr, [100]). This means that DAZ white dwarfs provide a unique opportunity to measure the actual accretion rate and to constrain small scale variations of the composition of the interstellar medium by comparing the composition of the white dwarfs (dominated by accretion while moving through the interstellar medium) to the local properties of the interstellar medium. The detection of cluster DAZ white dwarfs will provide the opportunity to measure the efficiency of pollution and in particular to probe the extent and composition of intra-cluster material. This questions becomes even more intriguing if one accounts for the fact that one scenario to explain the nature of the contaminating elements envisages the tidal disruption of an asteroid and an ensuing infrared excess ( [84]). This working hypothesis is supported by the discovery of several systems in the field showing both metal lines and a well defined infrared excess during the last few years ( [85]; [163]). Moreover, recent investigations suggest that the millisecond pulsar PSR B1620−26 in the globular cluster M 4 is a triple system including a white dwarf and a third body with a mass value of the order of a few Jupiter masses ( [153]; [142]). The detection of a planet in a globular cluster of intermediate metallicity is relevant not only for constraining planetary formation mechanisms but also to investigate their survival rate in old dense stellar systems. The possible occurrence of planets in globular clusters might also have an impact on the evolutionary properties of cluster stars. It has been suggested by [157] that the presence of planets could affect the evolution of the parent stars, and in turn the morphology of the horizontal branch and the presence of low-mass white dwarfs. The occurrence of infrared excess among white dwarfs is typically explained as the presence either of dust (disks, circumstellar envelope) or of a lowluminosity companion. Thanks to near-infrared (2MASS) and mid-infrared (Spitzer) photometric surveys a sizable fraction of white dwarfs hosting both stellar and sub-stellar (brown dwarfs) companions have been identified ( [165]; [86]; [43], and references therein). The detection of cluster white dwarfs that show a well defined near-IR excess can provide useful constraints on the current fraction of binary stars, but also on the evolutionary properties of brown dwarfs in metal-poor regimes. The current and the next generation of near-IR adaptive optics systems at the 10m class telescopes will allow to tackle this important experiment. The quality of the images (FWHM≤0.1" in the K-band) and the field of view (12') provide the opportunity to perform accurate photometry for large samples in crowded cluster regions down to limiting magnitudes of K ≈21.5-22 with exposure times of less than one hour ( [21]). Preliminary results suggest that a handful of white dwarfs with near-IR excess have been recently identified in the globular cluster ω Cen (A. Calamida, priv. comm.).
iii) Spectral Classification -Thanks to its superb spatial resolution and its larger collecting area the 30m-40m class telescopes will allow us to observe spectra of much fainter white dwarfs than today. This will be essential to answer the question of the ratio DA:non-DA in globular clusters.
iv) Missing Physical Ingredients -The comparison between theory and observations is a fundamental step in constraining the plausibility and the accuracy of the physical assumptions adopted to construct stellar models. With respect to globular cluster white dwarfs we are still facing several open problems. The mismatch between the observed blue hook of the white dwarf cooling sequence in NGC 6397 and synthetic colour-magnitude diagrams indicates that theory shows a smoother transition to bluer colours than is observed. A plausible culprit of this discrepancy might be an underestimate of the collision-induced absorption (CIA) from molecular hydrogen. This working hypothesis is supported by recent theoretical investigations suggesting that new DA white dwarfs atmosphere models accounting for the Ly α red wing opacity are systematically redder that the old ones ( [101]). One of the two anonymous referees properly noted that quantitative constraints on the currently adopted CIA have also significant impact on the predictions of planetary spectra. Circumstantial empirical evidence indicates that globular clusters with extremely hot horizontal branch stars (hot helium flashers, cf. Sec. 4.2) present an excess of white dwarfs when compared with main sequence turnoff stars. It has been suggested that a fraction of helium-core white dwarfs might account for current star counts. However, the number of globular clusters for which sufficiently accurate and deep data are available is quite limited and we still also lack firm constraints on the accuracy of cooling lifetimes in the high temperature range ( [25]).
Summarizing the previous sections we feel quite confident that the coming years will provide ample material for new reviews on white dwarfs in globular clusters -and we look forward to reading them!