Cluster AgeS Experiment (CASE): Deficiency of observed dwarf novae in globular clusters

We present the results of a search for dwarf novae (DNe) in globular clusters (GCs). It is based on the largest available homogeneous sample of observations, in terms of the time span, number of observations and number of clusters. It includes 16 Galactic GCs and yielded two new certain DNe: M55-CV1 and M22-CV2. All previously known systems located in our fields were recovered, too. We surveyed M4, M5, M10, M12, M22, M30, M55, NGC 288, NGC 362, NGC 2808, NGC 3201, NGC 4372, NGC 6362, NGC 6752, omega Cen (NGC 5139) and 47 Tuc (NGC 104). The discovery of two DNe, namely M55-CV1 and M22-CV2, was already reported by Kaluzny et al. (2005) and Pietrukowicz et al. (2005), respectively. In the remaining 14 GCs we found no certain new DNe. Our result raises the total number of known DNe in the Galactic globular clusters to 12 DNe, distributed among 7 clusters. Our survey recovered all three already known erupting cataclysmic variables (CVs) located in our fields, namely M5-V101, M22-CV1, and V4 in the foreground of M30. To assess the efficiency of the survey, we analyzed images with inserted artificial stars mimicking outbursts of the prototype dwarf novae SS Cyg and U Gem. Depending on the conditions, we recovered between 16-100 percent of these artificial stars. The efficiency seems to be predominantly affected by duty cycle/time sampling and much less by distance/magnitude. Except for saturated tiny collapsed cores of M30, NGC 362 and NGC 6752 (and also the dense core of NGC 2808) crowding effects in the V band were avoided by our image subtraction technique augmented with auxiliary unsaturated B-band images. Our results clearly demonstrate that in GCs common types of DNe are very rare indeed. However, great care must be taken before these conclusions can be extended to the CV population in GCs.


INTRODUCTION
The dense central regions of globular clusters constitute rich environments for the study of dynamical processes in stellar systems. It is well established on theoretical grounds that close binary stars play a significant role in the dynamical evolution of GCs (Stodolkiewicz 1986;Hut et al. 1992). For example, the presence of the binary stars can delay or halt the evolution of a cluster toward high stellar density, which is known as 'core collapse'. The gravitational encounters between passing binaries and single stars ⋆ E-mail: pietruk@camk.edu.pl may produce tightly bound systems forming a variety of exotic objects. These include active and quiescent low-mass X-ray binaries (LMXBs) with a neutron star primary, millisecond pulsars (MSPs), cataclysmic variables (CVs) and blue stragglers (BSs).
Cataclysmic variables are interacting binaries containing a main-sequence or slightly evolved secondary star losing mass via Roche lobe overflow onto a white dwarf primary. The binaries with the magnetic field of the white dwarf strong enough (B > 10 7 G) to channel the mass-flow along the field lines directly onto the surface of the white dwarf are called AM Her-type or polar CVs. In the nonmagnetic systems (B < 10 5 G), an accretion disc forms around the primary. In the mildly magnetic systems, 10 5 < B < 10 7 G, termed intermediate polars or DQ Her-type systems, the accretion disc is truncated by the white dwarf's magnetic field at a distance from the white dwarf. It is believed that the accretion disc thermal instability is the cause of repetitive outbursts observed in some CVs called dwarf novae (DNe). The electronic edition of The Catalog and Atlas of Cataclysmic Variables (Downes et al. 2001) contains 480 certain DNe among 1117 reliable CVs. There are 86 and 50 certain polars and intermediate polars in the database, respectively. Thus, one can say that almost half of all known field CVs exhibit outbursts, whereas at least 1/8 is of a magnetic nature. However, one should also stress that the sample of known field CVs suffers from strong, heterogeneous and rather unquantifiable selection effects (see, e.g., Gänsicke 2004;Pretorius, Knigge & Kolb 2007).
The issue of presence and formation of CVs in globular clusters has been extensively studied on theoretical grounds. According to Bailyn, Grindlay & Garcia (1990), we should not expect dynamically formed CVs in clusters due to unstable mass transfer in such systems. Later, Di Stefano & Rappaport (1994) predicted the existence of more than 100 CVs in both 47 Tuc and ω Centauri and several thousand in the Galactic globular cluster system. Recently, Ivanova et al. (2006) investigated CV formation channels in GCs in detail. Using numerical simulations they estimate the total number of CVs in the core of 47 Tuc at the level of ≈ 200 binaries.
The number of known CVs in GCs is small. Over the last few years observations collected with the orbiting X-ray telescopes yielded merely several tens of candidate CVs for Chandra (e.g. Hannikainen et al. 2005;Heinke 2005;Lugger et al. 2007) and XMM-Newton (e.g. Webb et al. 2004;Webb, Wheatley & Barret 2006). At present, there are just a few spectroscopically confirmed CVs in GCs: the dwarf nova V101 in M5 (Margon, Downes & Gunn 1981), CV1-4 in NGC 6379 (Grindlay et al. 1995;Edmonds et al. 1999), a CV in NGC 6624 (Deutsch et al. 1999), and the objects V1, V2 and AKO9 in 47 Tucanae (Knigge et al. 2004). Dwarf nova outbursts were observed only in 12 objects (see Table 1). Among the latter, two DNe, namely CV1 in the globular cluster M55 and CV2 in M22, were discovered in the extensive photometric survey by the CASE collaboration (Kaluzny et al. 2005a;Pietrukowicz et al. 2005).
CVs constitute a heterogeneous class of stars studied with an assortment of tools, from X-ray and UV satellites, QSO/blue excess photometric and emission line surveys and by variability surveys, but these methods suffer from severe and varying selection effects. The magnitude of these effects has never been reliably estimated, as illustrated by the astronomer's failure to either prove or reject the hibernation hypothesis, postulating over factor 100 increase of the space density of CVs (e.g. Shara et al. 1986). For these reasons the results of our search of dwarf nova outbursts in the globular clusters should not be compared to studies of other CV sub-types and/or by other methods. Additionally, certain subtypes of DNe were identified only after a half century of efforts at many observatories. Thus, despite the lack of evidence to show an abundance of possibly numerous but rarely detected subtypes, this scenario cannot be ruled out. Among others, this does apply to WZ Sge stars having outbursts separated by decades of years.
It must be stressed that a restricted survey still suffices to claim that the properties of the field and cluster DNe differ, provided certain conditions are met. Namely, it must be proven that (i) the survey is sensitive to detection of a popular group of DNe, (ii) their relative counts in two samples differ markedly. Thus it is our aim to demonstrate that our survey is sensitive to SS Cyg/U Gem-type stars and that their count observed by us in the globular clusters is below expectations. While our survey is restricted in the above sense, it must be stressed that it is based on the most extensive photometric survey of the globular clusters yet available.
In this paper we present the results of our search for DNe by CASE in the 16 Galactic globular clusters. The observation and reduction procedures are described in Sect. 2. The data and results for the individual clusters are presented in Sect. 3. Simulations were performed to assess the completeness of our search. We inserted artificial DNe into the frames of three selected clusters. Results of these simulations are presented in Sect. 4. In Sect. 5 we discuss implications of our search for DNe in GCs, and our summary and conclusions are presented in Sect. 6.

OBSERVATIONS AND DATA ANALYSIS
The CASE project commenced at Las Campanas Observatory in 1996 and is continuing until now (Kaluzny et al. 2005b). For the survey we employ the 1.0-m Swope telescope. In 1996 only the globular cluster NGC 6752 was observed using two CCD cameras: FORD and SITE1. All observations since 1997 have been obtained with a 2048 × 3150 pixel SITE3 CCD camera. With a scale of 0.435 arcsec/pixel the field of view is 14. ′ 8 × 23 ′ . However, images of clusters were usually taken with a smaller sub-raster (see Table  3 for details). The observations of the globular cluster 47 Tucanae (NGC 104) were obtained in the year 1993 as a by-product of the early stage of Optical Gravitational Lensing Experiment (OGLE, Udalski et al. 1992) using the Swope telescope. Some GCs were also observed with the TEK5 direct CCD camera attached to the 2.5-m du Pont telescope.
Over 25,000 frames in total were obtained for the CASE survey. Most of them, usually between 75 and 95% per cluster, were taken in the Johnson V filter. The rest of the frames were taken through the Johnson B filter and rarely through Johnson U and Cousins I filters. The exposure times ranged from a few seconds to 600 s. For the present search of DNe we used only V -band images with the exposure times in excess of 80 s, numbering ∼19,700. The number of V -band frames taken per cluster per night ranged from 1 to 116. The best seeing measured in this band reached 0.97 arcsec. Table 2 lists basic observational and physical parameters of the 16 observed globular clusters. In Table 3 we give general information on analysed data. Note that for 47 Tucanae and ω Centauri, two separate fields were monitored. Effectively we have no V -band data on the very small cores of collapsed clusters M30, NGC 362 and NGC 6752. Their cores of radii listed in Table 2 were saturated on most of our deep frames (Sect. 3.6, 3.9 & 3.14). This deficiency is largely compensated for NGC 362 (and also NGC 2808), whose central field 2. ′ 9 × 2. ′ 9 was observed in the B band. In the B band giants in the collapsed core do not saturate and blue outbursts of DNe would be easily detected.
In our search procedure we used the Difference Image Analysis Package (DIAPL). The package was written by Wozniak (2000) and recently modified by W. Pych 1 . It is an implementation of the method developed by Alard & Lupton (1998). To get better quality of photometry each frame was split into 410 × 410 pixel subfields.
For each cluster we selected the nights where at least one Vband image with seeing better than 1. ′′ 61 (3.7 pixels for the SITE3 camera) was available. Table 3 gives the total number of nights as  Table 2. General information on analysed globular clusters. All values without footnotes, except distances d (column 6) and expected number of CVs in cores (column 9), were taken from Harris (1996). The distances were calculated basing on distance modulus (m − M ) V and reddening E(B − V ), and assuming absorption A V = 3.2 · E(B − V ). The predicted number of CVs in cores of the clusters was scaled to N CV = 200 for 47 Tucanae according to formula, given by Pooley et al. (2003), that the encounter rate Γ ∝ ρ 1.5 0 r 2 c , where ρ 0 is the central luminosity density (also adopted from Harris 1996).  well as the total number of exposures per cluster used in the analysis. For each cluster a reference image was constructed by combining 5 to 23 individual frames taken during dark time on one selected night. For each night in the data set we combined up to 5 of the best images (with good seeing and relatively low background) to form an average image. We thus obtained a sequence of frames, each representing one night. The combined frames were remapped to the reference image coordinate system and subtracted from the convolved reference image using DIAPL. The resultant frames were searched with DAOPHOT (Stetson 1987) for the presence of any stellar-like residuals. Any residuals which appeared in two subsequent frames (including breaks in observations up to 4 days) and were separated by no more than 0.25 pixels (≈ 0. ′′ 109) were se-lected for further examination. We omitted from the search regions corresponding to the locations of saturated stars or to known variables (more extended lists based on CASE results will be published elsewhere). Subsequently, we extracted light curves in units of residual counts on subtracted images. This was done with DI-APL. Finally, the light curves were examined by eye.
Such a procedure would fail to detect a DN in eruption on the reference night due to negative residuals on subtracted images. For this reason for each cluster we selected a subtracted image separated by 20-40 days from the reference night. The image was inverted and then searched for the presence of positive stellar-like residuals. For all positive residuals we extracted light curves and examined them visually. Remarks: a cluster observed with the SITE1, SITE3 and FORD CCD cameras, and not analysed with the subtraction method, b cluster observed only with the LORAL CCD camera, * due to small and crowded core the magnitude applies only to area outside the core

M5
M5 is the only northern cluster observed by the CASE team. The observations cover 34 nights in the years 1997-1999. Our outburst search procedure easily detected the known DN M5-V101. In Fig. 3 we present its light curve. Apart from two eruptions in 1997, reported by Kaluzny et al. (1999), we detected two more outbursts in 2003 and in 2004. No new erupting objects were found in the field of M5.

M10
This cluster was monitored in 1998 (18 nights) and in 2002 (10 nights). Distribution of observations in time is presented in Fig. 4. No outbursting star was detected here.

M12
M12, another globular cluster, was observed in the years 1999-2001 on 41 nights (Fig. 5). These observations were also searched for DNe but unfortunately yielded no detection in the whole cluster.

M22
M22 was monitored during the 2000 and 2001 seasons (Fig. 6). The results of a search for erupting objects in the field of this cluster were published by Pietrukowicz et al. (2005), in which we reported the discovery of the DN M22-CV2 (located at a distance of 3.9 core radii from the centre of the cluster). The observations revealed an SU UMa type superoutburst in the year 2000. Prominent superhumps with a period of 128 minutes were observed in the superoutburst light curve during three nights. M22-CV2 has an X-ray counterpart (source #40 in Webb et al. 2004), but the cluster membership of the object remains an open question. We also registered two outbursts of the previously known DN M22-CV1. In Fig. 7 we show V -band light curves of the two CVs observed in the field of M22.

M30
M30 is one of the 30 Galactic globular clusters which, according to Harris (1996), has likely undergone core collapse. The CASE observations of this cluster cover 23 nights between June and September 2000 (Fig. 8). The core of M30, extending by 0. ′ 06 ≈ 8.3 pixels and covering roughly 30 seeing disks, was mostly saturated on our deep frames. Because of effective lack of data there it remained ignored in our search of outbursts and simulations.   Our search of DNe easily recovered the known DN of U Gem type labeled M30-V4 (α2000 = 21 h 39 m 58.5 s , δ2000 = −23 • 11 ′ 44 ′′ ). The variable was discovered by Rosino (1949). Later Machin et al. (1991) found that, on the basis of its quiescent magnitude and colours, its outburst magnitude and its radial velocity, V4 was likely to be a foreground object in the field of M30. A relatively high V -band brightness (see Fig. 9) is consistent with its foreground location. It is worth noting that M30-V4 has a likely X-ray counterpart, J2139.9-2312, detected by the ROSAT satellite (White, Giommi & Angelini 2000). The equatorial coordinates of the X-ray source are α2000 = 21 h 39 m 57.9 s , δ2000 = −23 • 12 ′ 06 ′′ , offset from the optical position of M30-V4 by (∆α = 9 ′′ , ∆δ = 22 ′′ ), well within the 50 ′′ X-ray error radius.
Additionally, in subtracted images we inspected the locations of four X-ray sources, namely A2, A3, B and C, which according to Lugger et al. (2007) have X-ray properties consistent with being CVs. We also checked two other bright X-ray sources, A1 (a very likely qLMXB) and D (probably a quasar). No variability was found within 3σ error circles around all these sources.

M55
The time distribution of the observations in Fig. 10 reveal that M55 was observed most often in the whole CASE survey. The results of our search for DNe outbursts were presented by Kaluzny et al. (2005a). In that paper we reported the discovery of the DN M55-CV1 in the core of the cluster. Over eight observing seasons spanning the period 1997-2004 we observed six outbursts of this vari-  Each point represents one night. At the cluster distance these values would correspond to the absolute magnitudes M * V given on the right vertical axis. They would be excessively bright for a dwarf nova, hence it is extremely likely this is a foreground dwarf nova. able star. The X-ray flux as well as the star location in the colormagnitude diagram for M55 are consistent with it being a DN at the cluster distance. In Fig. 11 we present the light curve of M55-CV1 in magnitudes.

NGC 288
The globular cluster NGC 288 is located about 1 deg from the Southern Galactic Pole. Among all analysed clusters it is the most distant from the Galactic Centre (∼12 kpc). The CASE observations cover only two nights in 2004 and 7 nights in 2005 (Fig. 12). Our search for erupting objects yielded a negative result. We also carried out an independent visual inspection of the regions of optical counterparts to seven X-ray sources, CX13, CX15, CX18, CX19, CX20, CX24, CX25, listed by Kong et al. (2006). Three of the sources, namely CX13, CX20 and CX24, are CV candidates.   No brightness variations were found at the positions of all these objects.

NGC 362
The globular cluster NGC 362 lies on the sky about 2 deg away from the centre of Small Magellanic Cloud (SMC). It is a likely core-collapsed cluster. The CASE data for NGC 362 were obtained from 1997 until 2005, except for the 1999 season. The total number of analysed nights reached 90 (Fig. 13). Our search of CV outbursts yielded no detections. In the V band the collapsed core of radius 11. ′′ 4 and roughly covering 300 seeing radii was saturated, yielding no useful data. This was largely compensated by our analysis of the B-band frames of the central field of the cluster, covering 2. ′ 9×2. ′ 9. In this filter red giants do not saturate in the core and any erupting CVs should become more apparent due to their hot and luminous disc in the systems. The result of our search for this cluster is again negative.

NGC 2808
NGC 2808 is the most distant globular cluster in our sample (9.4 ± 0.6 kpc, (m − M )V = 15.56 mag, Saad & Lee 2001). The cluster was monitored in 1998 and 1999 during 33 nights in total (Fig. 14). For this cluster we analysed the large 14. ′ 8 × 14. ′ 8 field in the V band and the 2. ′ 9 × 2. ′ 9 central field in the B band. The results of our search yielded no DN outbursts for this cluster, too.

NGC 3201
In our sample of 16 GCs, NGC 3201 is one of three clusters located closer than 10 deg from the Galactic plane. The estimated value of the reddening in the direction of the cluster amounts to E(B − V ) = 0.23 (Layden 2002). Although our observations of NGC 3201 span five years, 2001-2005, they cover only 22 nights (Fig. 15). We found no erupting objects in this cluster either. Additional visual inspection of the locations of four X-ray sources, 16, 22, 23, 26 (which according to Webb, Wheatley & Barret (2006) could be CVs) revealed no brightness variations. We also note no variability within 3σ uncertainty circles around other 23 X-ray sources located in our field of view for NGC 3201.

NGC 4372
This globular cluster is located relatively close to the Galactic plane (b = −9. • 88) and suffers from reddening of E(B − V ) = 0.34 (Gerashchenko & Kadla 2004). Images of NGC 4372 were obtained on 14 nights in 2004 and on 5 nights in 2005 (Fig. 16). No DNe were detected in this cluster.

NGC 6362
The analysed observations of NGC 6362 span six years, from 1999 to 2005. The total number of nights reached 104, two thirds of   which dates to 1999 and 2001 seasons (Fig. 17). Despite the extensive observations of this cluster no DN outburst was detected.

NGC 6752
NGC 6752 was observed using three different CCD cameras (FORD, SITE1 and SITE3) on only 7 nights in 1996 and 1997 (see Fig. 18). Because of the difference in our frame format, for this cluster we performed only visual examination. For each night we selected the best seeing B and V images and subsequently we examined them by eye. None of the 11 optical identifications of X-ray sources (CX1, CX2, CX3, CX4, CX5, CX6, CX7, CX10, CX11, CX13, CX15) listed by Pooley et al. (2002) as likely CVs, revealed any brightness variations within 3σ error circles. Note that in the V band the collapsed core of radius 10. ′′ 2 and covering less than 300 seeing disks was saturated and yielded no useful data.

ω Centauri
ω Centauri is the most luminous and the most massive of all known Galactic GCs. Two partly overlapping fields, East and West, covering the central region of the cluster were monitored. The full size of the surveyed area was equal to 644 arcmin 2 . The CCD photometry of the two fields was carried out from February 1999 until June 2001. Additionally, the West field was observed in May and June 2002 (Fig. 19). Our extensive search of erupting objects in ω Centauri led to the detection of a source suffering from intriguing episodes of enhanced luminosity. The source was located in the West field at α2000 = 13 h 26 m 26. s 61, δ2000 = −47 • 26 ′ 35. ′′ 1. Fig. 21 presents the finding chart centered on its location. The ob-  ject was already recorded in the catalogue of variable stars published by Kaluzny et al. (2004). They suggest that the object (labelled as the variable NV408) is a probable CV. The object appeared on images obtained since June 3/4, 1999. It faded systematically during six consecutive nights. On July 24/25, 1999 it was bright again, albeit not as much as the maximum in June.
Our evidence is insufficient to prove that NV408 is an erupting CV. It remains undetectable on our images taken with the 2.5-m du Pont telescope. In order to check for other signatures of a CV at this location, we investigated the archival HST/ACS images covering the region of NV408. These are images in F435W (blue, in this subsection B) and F625W (red, R) wide-band filters, and F658N narrow-band filter centered on Hα line, all taken on June 28, 2002. These checks returned no object with a blue excess nor Hα emission within 2 ′′ radius from our derived position. Based on the paper by Monelli et al. (2005) we estimated the limiting magnitude for the HST/ACS images to be B ≈ 27 (R ≈ 26.2). At an apparent distance modulus to ω Centauri (m − M )B ≈ 14.2 this yields the limiting absolute magnitude MB ≈ 12.8.
We also note that NV408 has no X-ray counterpart. No gamma ray burst was listed near its position in The BATSE Current Gamma-Ray Burst Catalog 2 during its brightening between May and July 1999. Thus, the nature of NV408 still remains unsolved.
We report no brightness variations in the vicinity of three possible CV locations in ω Centauri. These are sources NGC5139-A and NGC5139-B (Carson, Cool & Grindlay 2000), and NGC 5139-31 (Rutledge et al. 2002).

47 Tucanae
Similar to NGC 362, the globular cluster 47 Tucanae is also projected onto the halo of the SMC. The observations of 47 Tucanae (NGC 104) were obtained in the year 1993 as a by-product of the Optical Gravitational Lensing Experiment (OGLE, Udalski et al. 1992), at the stage when the 1.0-m Swope telescope was used. We analysed fields A and B located west and east of the cluster center, respectively, but the cluster core was not included in these fields. All images of 47 Tuc were taken with a 2048 × 2048 pixel LORAL CCD camera with a scale of 0.435 arcsec/pixel. The distribution of our observations in time is presented in Fig. 22. Our search of DNe in this cluster yielded no detections.

SIMULATIONS
Our extensive search for DNe in 16 Galactic GCs yielded only two new objects, M22-CV2 (Kaluzny et al. 2005a) and M55-CV1 (Pietrukowicz et al. 2005) and recovered three previously known DNe. While the recovery of known DNe lends some confidence in the sensitivity of our search for outbursts, we performed simulations to assess the completeness of our search in a more quantitative way. We inserted into the frames of three clusters, M22, M30, and NGC 2808, artificial images of erupting CVs and checked whether they were detected in our search. The distance modulus (m − M )V of the selected clusters increases from the lowest value of ∼ 13.7 mag for M22 up to the highest value of ∼ 15.6 mag for NGC 2808, the most distant cluster in our sample. The number of observing nights per cluster was different for each of the three clusters: 71 nights for two years for M22, 23 nights in one year for M30, and 33 nights for two years for NGC 2808. Hence, M22 has the highest number of nights per year (35.5), while NGC 2808 has the smallest (16.5).
In the simulations we reproduced the light curves of two prototype DNe, SS Cygni and U Geminorum. The original light curves were taken from the AAVSO International Database. Outbursts of SS Cyg and U Gem repeat on average every 39 and 101 days, respectively (Warner 1995). We selected the most recent and wellcovered segments of the visual light curves of these DNe, illustrated in Fig. 23 For each cluster the prototype light curves were scaled according to its distance. In the process we used the recent distance determinations of our prototype DNe by Baskill, Wheatley & Osborne (2005). In Table 4 we list properties of these DNe and their hypothetical magnitude ranges in selected clusters. We also added two other well-known DNe. The absolute maximum brightness of SS Cygni exceeds by 2 mag that for the other three DNe. Only SS Cyg is sufficiently bright in its minimum to be detectable at cluster distances in our images.
Properties of our simulated artificial stars were randomised both in time and space. For each simulated artificial star, we selected a random time among the first 100 nights in the prototype light curve and identified it with the actual time of first observation of a given cluster in a given season. We simulated one point for each night of the actual observations. Our simulations were performed in subfields extending 410 × 410 pixel (2. ′ 97 × 2. ′ 97). In each of them   we inserted 10 SS Cyg and 10 U Gem stars. Locations of these artificial stars were chosen randomly within a given subfield. To add the artificial observation of a DNe to a set of frames we employed the ADDSTAR task of DAOPHOT (Stetson 1987). For this purpose we used the PSFs determined from a given subfield, to ensure the correct shapes of the stellar images. The complete set of simulated frames for each cluster was searched for outbursts of DNe in exactly the same manner as the search in our original data. This included additional visual inspection of the light curves obtained as the result of image subtraction. Example light curves of the detected artificial DNe are presented in Fig. 24. Note that the candidate 'DNe' were easily identifiable due to their characteristic pronounced flat minima with counts usu-ally near zero and outbursts reaching from hundreds to thousands of counts.
The results of the simulations are summarised in Table 5. They are presented graphically in Fig. 25. In Table 5 we give the initial number of synthetic DNe per cluster, the number (percentage) of the DNe whose eruptions would be potentially detectable, and the number (percentage) of finally recovered DNe. By 'potentially detectable' we mean those which erupted during our observation. The difference between the number of DNe used in the simulations for different clusters is the result of different field of view for these clusters. Our detection of all 194 artificial SS Cygni in the field of M22 may be facilitated by its proximity, best seasonal coverage and moderate core density (Fig. 26). The true efficiency of our search in this case is probably close to 100%.
At this point it is prudent to discuss whether our search is affected by stellar density and/or distance from the core centre. On the one hand, we must remember that variable temporal sampling yielded marked statistical variability of detection efficiency (Fig. 25). On the other hand, as illustrated in Fig. 26, the image subtraction is efficient in drastically reducing density of features per image. Additionally, inspection of Fig. 26 reveals that any stellar density gradient is not apparent in the subtracted image, containing mostly variable stars. A separate study of the top and bottom half of images revealed no spatial efficiency effect comparable to the temporal one. Effectively our detection algorithm is applied to sparsely populated residual images and its efficiency is dominated by temporal coverage and to a lesser degree to magnitude/distance effects. Exceptions were the tiny collapsed cores of M30, NGC 362 and NGC 6752 where, due to saturation, no V photometry was obtained and no simulations were possible.
From histograms in Fig. 25 we conclude that the DNe detection efficiency is dominated by a combination their outburst duty cycle and the number of nights per cluster. The overwhelming majority of larger duty cycle outbursts of SS Cyg-type was detected. For a fraction of smaller duty cycle of U Gem-type stars and less intensely observed clusters no outbursts occurred during observations (the white areas in Fig. 25). For the most sparsely observed cluster, NGC 2808, out of 250 U Gem-type DNe only 57 had observable outbursts and we recovered 42 of them. Thus the effect of distance and magnitude is less pronounced, in the extreme case of NGC 2808 yielding only 25% missed dwarf novae in outburst (sparsely hatched areas). Some DNe in outburst were not recovered at all. They were too faint and scattered too much, or they were placed too close to very bright stars to be detected. The radial distributions of such objects are shown in Fig. 27. It is clear that for clusters with sparse and non-saturated cores, like M22 (and here also M4,M5,M10,M12,M55,NGC 288,NGC 3201,NGC 4372,NGC 6362, ω Centauri), completeness is independent of the position in the cluster. However, for clusters with small, dense and partly saturated cores one expects rather strong radial dependence toward the centre.
We undertook additional simulations for the dense central part of the globular cluster NGC 2808. Fig. 28 shows the area adopted for the simulations. Inside a circle of radius 60 ′′ we inserted light curves of 1000 artificial SS Cyg variables, alongside 1000 artificial U Gem variables. In this run all simulated stars had outbursts in our data. We recovered 341 SS Cyg and 165 U Gem stars. However, none of the stars was detected closer than 8. ′′ 9 from the cluster centre. Evidently this is due to high number of saturated stars. The number of recovered DNe increases with the distance from the centre, as demonstrated in Fig. 29. The globular cluster NGC 2808 is the most distant of the all 16 clusters analysed in this work. Therefore estimates of completness of the search for DNe in this cluster can be treated as a worst case scenario for the whole sample.
Our simulations for the clusters M22, M30 and NGC 2808 allowed us direct estimation of the magnitude range of our DNe search. For these clusters we determined the limiting magnitude, corresponding to the faintest recovered artificial star in outbursts. For the remaining clusters the limiting magnitudes mc were extrapolated from these results using the following formula: where mM22 is the limiting magnitude for M22, tM22 and tc are the mean exposure times of the frames, while nM22 and nc are the median background levels for M22 and a given cluster, respectively. These limiting magnitudes are listed in Table 3.

DISCUSSION
Our survey of DNe globular clusters is based on the largest available homogeneous sample of observations, in terms of the time span of several years, number of observations and number of clusters. It extended over 16 Galactic GCs and yielded two new certain DNe: M55-CV1 and M22-CV2. All previously known systems located in our fields were recovered, too. For 16 GCs our survey yielded on average 50 nights per cluster, much more than any survey conducted so far. Past surveys of M92, M15 and of NGC 6712 extended over 10 nights (  Unfortunately, they constitute an insufficient sample to establish general properties of the cluster DNe. Half of the objects are located inside cluster cores (see Fig. 30; c.f., distances listed in Table 1), and some systems are located several core radii away from it. Theoretical considerations predict that most CVs are concentrated inside cluster cores (see e.g. Ivanova et al. 2006). However in the crowded cluster cores many detection methods suffer from strong observational biases against CV detection. Due to use of the image subtraction, our search was little affected by image crowding. Exceptional cases were the tiny collapsed cores of M30, NGC 362 and NGC 6752, and also dense and partly saturated core of NGC 2808 (the most distant cluster in our sample). In the first three cases the cores cover from 30 to 300 seeing disks. They are mostly saturated on our deep V -band exposures, effectively yielding no data. This deficiency was partly compensated by our outburst search on B-band images of the core of NGC 362 and NGC 2808. In the B band red giants do not saturate the core image and blue DNe outbursts would easily be detected, but it must be stressed here that already in the immediate vicinity of the saturated cores our photometry performs well in the range of magnitudes discussed here and we detect eclipsing and pulsating stars, reported elsewhere. In particular, just several PSF diameters away from the saturated collapsed core of NGC 362 we found a pulsating star of V amplitude 0.3 and MV ≈ 3.5 mag. This experience from our non-CV work enhances our confidence that our detection efficiency does not depend very much on the distance from the cluster centre.
Searches for quiescent cataclysmic variables in globular clusters are also hampered due to the intrinsic faintness of these binaries. The DNe detected in GCs so far have absolute magnitudes MV in quiescence ranging from +5.4 to +9.8 mag, or fainter. Our simulations demonstrate that outbursts of amplitudes between 2 and 4 magnitudes yield improvement of their detectability also in distant clusters, albeit strongly dependent on DNe duty cycle. This may explain why all seven clusters harbouring 12 known DNe are relatively nearby, less than ∼10 kpc away, and well-covered by observations. In this context we emphasise that we detected no light variation near the locations of 56 X-ray sources and their optical counterparts, 27 of which are CV candidates.
The environment of DNe in GC depends on cluster age and metallicity. In Fig. 31 we plot these two parameters for 83 Galactic GCs (data taken from: Salaris & Weiss 2002;Gratton et al. 2003;Carretta et al. 2004;Santos & Piatti 2004), of which 7 contain DNe. Ages and metallicities for the seven clusters are given in Table 6. Inspection of Fig. 31 reveals that the clusters with DNe are not concentrated in any particular location in the plot, they appear to be scattered among all clusters. Metallicity of four out of five clusters harbouring 2 DNe, namely NGC 6397, M15, M22 and M80, is low. This statistic is insufficient to show any tendency. Such a tendency would contradict the presence of numerous field DNe in the metal rich population I.
In Table 4 we list outburst properties of prototype DNe, scaled according to cluster distances. Our simulations have confirmed that if globular clusters were populated by numerous dwarf novae resembling U Gem or SS Cyg they would be easily detected in our survey. Detection efficiency of general DNe in our simulations mostly depends on the duty cycle and observation coverage. The duty cycle is not particularly discriminating as many, perhaps most DNe have duty cycles comparable to these of U Gem or SS Cyg. On the contrary, the outburst absolute magnitude is correlated with the orbital period (Warner 1995). Thus our survey is slightly biased towards detection of brighter, U Gem-type, DNe above the period gap, and against SU UMa-type below it. For the most likely Figure 26. Images of the same central region of the globular cluster M22 taken on four nights every 10 days in Aug/Sep 2000. The area has 87 ′′ × 130. ′′ 5 (200 × 300 pixels) and is almost entirely located inside the cluster core, of radius of 85. ′′ 2. The lower panels show corresponding residual images. The black circle denotes the known dwarf nova M22-CV1 while white circles denote artificial dwarf novae inserted into frames of the cluster. The brightest stars are saturated and are covered with white, rectangular areas. The images demonstrate that in the image subtraction technique cores of some globular clusters remain sparse fields as far as variable stars are concerned.  et al. (2004) periods (distribution modes) of these types (respectively 3.8 and 1.5 hours) the average difference of absolute magnitudes in outburst amounts to roughly one magnitude. The corresponding loss in detection efficiency of SU UMa-type stars would correspond to a shift by one panel to the right in Fig. 25, amounting to no more than 25% loss of observable outbursts. Paradoxically SU UMa by itself would be discovered as easily as U Gem, because of a similar absolute brightness and (super)outburst duty cycle. About a third of SU UMa-type stars, i.e., WZ Sge stars, undergo extreme superoutbursts with large amplitude and recurrence times longer than a year. We would miss most of these superoutbursts because of their small duty cycle. However, as observed by Warner (1995), statistics of field CVs suffers from unknown and possibly large selection effects, rendering detailed quantitative comparison uncertain.
We have checked the literature to count the number of erupting CVs in the solar neighbourhood. Out of 11 CVs located within the sphere of a radius of 100 pc from the Sun, seven stars (   of the known CVs exhibit outbursts. However one should remember that distances for a significant number of known field CVs are uncertain or have never been measured. Based on data from the electronic edition of the Catalogue of Cataclysmic Binaries, Low-Mass X-Ray Binaries and Related Objects (Ritter & Kolb 2003, RKcat Edition 7.9, Jan 1, 2008) we find median recurrence times of 101 and 49 days for erupting CVs with distances up to 100 pc and 200 pc from the Sun, respectively.
One can roughly calculate the number of known CVs per unit stellar mass in the solar vicinity.  . Radial distributions of recovered artificial DNe in additional simulations performed for the central part of the globular cluster NGC 2808, the most distant globular cluster in our sample. Each bin (annulus) is 6 ′′ wide. The core radius of the cluster is marked with dotted lines. It can be seen that the number of recovered stars clearly decreases toward the centre. It is also evident that fainter U Gem stars are harder to detect than brighter SS Cyg stars. into ∼ 7.4 × 10 −6 , 1.5 × 10 −6 and 0 known DNe per unit solar mass respectively in the three clusters. All these densities for the clusters are significantly smaller than those estimated for the solar neighbourhood.
While it seems reasonable to conclude that, compared to the solar vicinity, GCs are deficient in U Gem-like variables, i.e., dwarf novae with recurrence times up to a few hundreds of days, the actual cause remains obscured. Either the relative number of DNe is small or their outburst properties are different. Rare outbursts in GC CVs would correspond to small average transfer rates and dim quiescent accretion discs compared to those in CVs in our vicinity (Warner 1995, his Fig. 3.9 and Eq. 3.3). HST observations of low optical fluxes from 22 CV candidates would be consistent with such a hypothesis (Edmonds et al. 2003). An alternative explanation postulates that most CVs in GCs are magnetic and avoid outbursts as normal intermediate polars do. In these stars the magnetic field of the white dwarf truncates the inner accretion disc thus preventing or diminishing its outbursts. According to this proposal, in clusters close encounters or even stellar mergers result in a faster rotation of stellar cores and thus they facilitate growth of the magnetic field by stellar dynamo mechanism (Ivanova et al. 2006  The data for all the clusters (except NGC 6397 and 47 Tuc) come from Salaris & Weiss (2002) and Santos & Piatti (2004). The ages and metallicites for NGC 6397 and 47 Tuc were taken from Gratton et al. (2003) and Carretta et al. (2004), respectively.
(2006) do not invalidate the magnetic hypothesis as similar outbursts were observed in confirmed intermediate polars (e.g. GK Per, EX Hya). Further credit to the magnetic hypothesis was lent by the detection of intermediate polar-like 218 s oscillations in Xray source X9 in 47 Tuc (Heinke 2005). Another X-ray source in the same cluster, X10, exhibits a 4.7 hour period and an X-ray spectrum consistent with those seen in polars. Dobrotka, Lasota & Menou (2006) proposed that rare outbursts in some CVs result from the combination of low mass transfer rates (10 −13 − 10 −12 M ⊙ /year) and moderately strong white dwarf magnetic moments (> 10 30 G cm 3 ). Conversely, the mass transfer rates in GC CVs obtained in numerical simulations by Ivanova et al. (2006) exceed those proposed by Dobrotka, Lasota & Menou (2006) by two orders of magnitude. According to Ivanova et al. (2006), a field strength of 10 7 G suffices to prevent DN outbursts in all CVs with the white dwarf mass less than 1.1 M ⊙ .
In an alternative scenario, frequent stellar encounters affect stability of binary orbits, thus affecting their ability to sustain an accretion rate suitable for formation of an accretion disc. Recently, Shara & Hurley (2006) simulated a 100,000 star cluster with 5000 primordial binaries. They found that cluster CVs were affected by encounters with other cluster members. This tends to shorten their life and hence decrease the expected number of active CVs, at any given time, by a factor of 3, compared to field CVs.
Extensive observations of the known CV candidates in clusters are urgently needed to determine their average accretion rates and dominant mode of variability. In particular, it would be important to verify whether these objects are magnetic. Magnetic fields in such stars are reliably detected by Zeeman split of the lines, strong and/or variable polarisation and by presence of the cyclotron harmonics (humps) in their continuum spectra.

SUMMARY
We report the results of our extensive photometric survey by the CASE collaboration of 16 Galactic GCs with the aim of detecting DN outbursts. Our early discovery of two DNe, namely CV1 in the globular cluster M55 and CV2 in M22 were reported in Kaluzny et al. (2005a) and in Pietrukowicz et al. (2005), respectively, where we find that the former object is likely to be a U Gemtype DN, while the latter one is an SU UMa DN, and their X-ray counterparts were detected by the XMM-Newton satellite. Their positions in the color-magnitude diagrams of the clusters and their X-ray fluxes are consistent with their cluster membership.
In the present paper we report that a similar search of DNe in the remaining 14 GCs yielded no new DNe. Our search was sufficiently sensitive to easily detected outbursts of all three well-known DNe in our fields: V101 in the globular cluster M5, CV1 in the core of M22, and the DN V4 in the foreground of the globular cluster M30. We investigated further the nature of the enigmatic erupting source NV408, located ∼ 2 ′ from the centre of ω Centauri, but found no evidence confirming its CV nature.
It is remarkable that we detected no outbursts nor any detectable variability near positions of 27 known CV candidates. To verify the efficiency of our survey we performed simulations by inserting into real frames artificial stars with light curves mimicking those of SS Cygni and U Geminorum-type DNe. The results for M22, M30, and NGC 2808 demonstrated we were able to recover between 16-100% of artificial DNe, depending on their duty cycle and observation coverage. For larger duty cycle SS Cyg-type stars our coverage was sufficient to obtain very close to 100% recovery rate. However, some U Gem type stars with a smaller duty cycle had no outbursts on our nights and hence for extremely poor sampling up to 70% of them were missed. Any effects of stellar crowding were diminished by the application of the image subtraction technique for relatively sparse cores of some clusters, like M22, M55 or ω Centauri. For clusters with very dense (and usually partly saturated) cores, the number of recovered stars decreases toward the centre, as was demonstrated in additional simulations for the central part of NGC 2808.
The results of our extensive survey provide new evidence confirming early suggestions, based on more fragmentary data, that ordinary DNe are indeed very rare in GCs. On one hand, up to 150 candidate CVs were proposed in GCs, mostly from X-ray surveys. On the other hand our survey combined with earlier results yielded only 12 confirmed DNe in total in the substantial fraction of all Galactic globular clusters. Such a fraction of DNe among CVs appears extremely low by comparison to the field CVs, of which half are DNe. Thus our observations acutely question why outbursts of dwarf novae are rare in GCs. We quote some recent evidence that most cluster CVs could be magnetic and thus exhibit little or no outbursts. However, any conclusions must await a thorough study of all cluster CV candidates.

ACKNOWLEDGMENTS
We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST), which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. The observations are associated with the programme #9442. PP was supported by Polish MNiI grant number N203 019 31/2874 and the Copernicus Foundation for Polish Astronomy. PP and JK acknowledge support from the Domestic Grant for Young Scientists and from the Grant MASTER of the Foundation for Polish Science, respectively. The CASE project is supported by the NSF grant AST 05-07325 and by Polish MNiI grant 1P03D 001 28. It is also a pleasure to thank Michael Shara and Sophia Khan for remarks on the draft version of this paper. We are grateful to the referee for very quick and detailed report on the paper.