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Mon. Not. R. Astron. Soc. 000, 000­000 (0000)

Printed 29 September 2011

A (MN L TEX style file v2.2)

The long term optical b ehaviour of helium accreting AM CVn binaries
Gavin Ramsay1, Thomas Barclay1,2, Danny Steeghs3, Peter J. Wheatley3, Pasi Hakala4 Iwona Kotko5 Simon Rosen6 1
2 3 4 5 6

Armagh Observatory, Col lege Hil l, Armagh, BT61 9DG Mul lard Space Science Laboratory, University Col lege London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT Department of Physics, University of Warwick, Coventry, CV4 7AL ¨ Finnish Centre for Astronomy with ESO (FINCA) , University of Turku, V¨isal ¨ntie 20, FI-21500 PIIKKIO, Finland a¨a Astronomical Observatory, Jagiel lonian University, Cracow, Poland Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH

Accepted MNRAS 2010 Sept 29.

ABSTRACT

We present the results of a two and a half year optical photometric monitoring programme covering 16 AM CVn binaries using the Liverpool Telescope on La Palma. We detected outbursts in seven systems, one of which (SDSS J0129) was seen in outburst for the first time. Our study coupled with existing data shows that 1/3 of these helium-rich accreting compact binaries show outbursts. The orbital period of the outbursting systems lie in the range 24­44 mins and is remarkably consistent with disk-instability predictions. The characteristics of the outbursts seem to be broadly correlated with their orbital period (and hence mass transfer rate). Systems which have short periods (<30 min) tend to exhibit outbursts lasting 1­2 weeks and often show a distinct `dip' in flux shortly after the on-set of the burst. We explore the nature of these dips which are also seen in the near-UV. The longer period bursters show higher amplitude events (5 mag) that can last several months. We have made simulations to estimate how many outbursts we are likely to have missed. Key words: Physical data and processes: accretion discs; Stars: binary - close; novae - cataclysmic variables

1

INTRODUCTION

AM CVn systems are accreting binaries consisting of a white dwarf accretor and a degenerate (or semi-degenerate) secondary. They are notable for at least two reasons: they have an extremely short orbital p eriod (Porb < 70 mins) and are almost entirely hydrogen deficient (see Solheim 2010 for a recent review). There are currently 27 known AM CVn systems of which half a dozen have b een found to exhibit at least one outburst, where they increase in brightness typically by 3­4 magnitudes. Indeed, some systems were discovered through sup ernovae surveys (eg V406 Hya =2003aw, Wood-Vasey et al. 2003). It is thought that the origin of these outbursts is similar to those seen in hydrogen accreting dwarf novae (eg Osaki 1996). Much observational and theoretical work has b een done in trying to understand the origin and nature of the outbursts in the hydrogen accreting systems (eg Lasota 2001). In contrast, our understanding of
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the cause of the outbursts seen in AM CVn systems is much more limited. On the observational side, this is largely due to the lack of information on their long term b ehaviour. On the theoretical side, progress has b een more limited compared to the work on hydrogen accreting systems. However, the work of Smak (1983), who describ ed a thermal instability model, Whitehurst (1988) and Tsugawa & Osaki (1997) who develop tidal instability models and Lasota, Dubus & Kruk (2008) and Kotko, Lasota & Dubus (2010) who take into account irradiation effects, are some notable advances in modelling hydrogen deficient accreting binaries. Accretion discs in AM CVn binaries can b e thermally stable in a hot state ­ the temp erature of the disc is always greater than the ionisation temp erature of helium ­ and can also b e thermally stable in a low state ­ the temp erature of the disc is always lower than the ionisation state of helium. Systems which lie b etween these states are exp ected to b e unstable. It is thought that the longer p eriod systems


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Source HM Cnc V407 Vul ES Cet SDSS J190817.07+394036.4 A M CV n HP Lib CR Bo o K L Dr a PTF1 J0719+4858 V803 Cen SDSS J092638.71+362402.4 CP Er i V406 Hya (2003aw) 2QZ J142701.6-012310 SDSS J012940.05+384210.4 SDSS J124058.03-015919.2 SDSS J080449.49+161624.8 SDSS J141118.31+481257.6 GP Com SDSS J090221.35+381941.9 SDSS J155252.48+320150.9 V396 Hya SDSS J120841.96+355025.2 SDSS J152509.57+360054.5 SDSS J164228.06+193410.0 SDSS J172102.48+273301.2 SDSS J204739.40+000840.1 Period (mins) 5.4 9.5 10.4 15.6 17.1 18.4 24.5 25.0 26.8 26.9 28.3 28.4 33.8 36.6 :37 37.4 44.5 :46 46.6 48.3 56.3 65.1 LT Target? # # 16.5­16.8 # # 13.6­13.7 13.8­17.0 16.0­19.6 # # 16. 16. 14. 20. 14. 19. 17. 19. 15. # 20.2­20.6 # 18.9­19.4 19.8­20.2 # 20.4­20.7 17.0­17.4 20.53 17.13 0.17 0.03 19.09 19.91 0.07 0.11 20.44 0.10 6­19. 2­20. 5­19. 0­20. 5­20. 0­19. 8­19. 4­19. 9­16. 6 2 7 5 0 8 0 7 3 19. 19. 18. 20. 19. 19. 18. 19. 16. 31 30 89 35 31 62 54 58 22 0. 1. 1. 0. 1. 0. 0. 0. 0. 52 33 34 18 31 17 30 09 05 13.51 15.00 17.68 0.02 1.00 1.19 16.66 0.09 LT Range g (mag) LT mean g (mag) LT rms g (mag) Outbursting System? N N N N N N Y Y Y Y Y Y Y Y Y Y Y N N N N N N N N N Y Reference [1] [2] [3] [4] [5] [6] [7] [8] 25] [9] 10] 11] 12] 13] 16] 17] 18] 14] 19] 20] 21] 22] 23] 20] 20] 20] 24]

[ [ [ [ [ [14, 15, [16, [ [ [ [ [ [ [ [ [ [ [

Table 1. The currently known AM CVn binaries. We show their period which is either the orbital period (most reliably determined from spectroscopic observations) or the dominant photometric period which is typically within a few percent of the orbital period. A colon implies the period is approximate, while the lower five systems do not have known periods. We show by means of a tick or a cross whether the source is included our Liverpool Telescope survey and the observed range, the mean mag and the rms of the light curve in the g band magnitude. We also show through a `Y' or a `No' whether the source has been seen in outburst, either in these LT observations or through previous work. References: [1] Ramsay, Cropper & Hakala (2002), [2] Ramsay et al. (2000), [3] Espaillat et al. (2005), [4] Fontaine et al. (2011), [5] Nelemans, Steeghs & Groot (2001), [6] O'Donoghue et al. (1994) [7] Wood et al. (1987), [8] Wood et al. (2002), [9] Kato et al. (2004), [10] Copperwheat et al. (2011), [11] Abbott et al. (1992), [12] Wood-Vasey et al. (2003), [13] Woudt, Warner & Rykoff (2005), [14] Anderson et al (2005), [15] Barclay et al. (2009), [16] Shears et al. (2011), [17] Roelofs et al. (2005), [18] Roelofs et al. (2009), [19] Nather, Robinson & Stover (1981), [20] Rau et al. (2010), [21] Roelofs et al. (2007a), [22] Ruiz et al. (2001), [23] Anderson et al. (2008), [24] Prieto et al. (2006), [25] Levitan et al. (2011).

(40 min < Porb < 70 min) lie in the cool stable region and therefore do not show large optical photometric variations. Little is known ab out the long-term photometric b ehaviour of most AM CVn systems, in particular the fainter half of the sample which has b een discovered in recent years. These systems are generally b eyond the reach of amateur variable star networks (although see Shears et al. 2011), and coverage on larger telescop es has b een patchy. To b etter characterise the prop erties of AM CVn systems and obtain a b etter understanding of the physics of the outbursts, we b egan a monitoring programme using the Liverp ool Telescop e in Feb 2009 and ended in June 2011.

2

LIVERPOOL TELESCOPE OBSERVATIONS

Our target list (see Table 1) include 18 out of the 27 known AM CVn systems. Exp osure times ranged from 5 sec in the brightest source (GP Com) to 140 sec in the faintest (eg SDSS J0129). Observations were made in a range of transparencies, lunar brightness and airmass. Images were typically downloaded within a few days of them b eing taken and have already b een bias subtracted and flat-fielded in an automatic way. We selected two comparison stars and used the photometry analysis tool autophotom which is incorp orated in the package Gaia to determine the relative brightness of our source with resp ect to the comparisons1 . Some fields have low stellar density which meant that the comparison stars were as faint as g 19. We derived a differential light curve b etween the comparison stars used for each AM CVn system. The mean rms of these light curves was 0.04 mag when b oth

The Liverp ool Telescop e is a 2m rob otic telescop e sited on the island of La Palma in the Canaries and has a suite of instruments including the RATCAM imager (Steele 2004). Our goal was to obtain one g band image p er source once p er week for the first year and once every 5 days thereafter.

1

Both packages are part of suite of software which can be http://starlink.jach.hawaii.edu/starlink

the STARLINK downloaded from

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The long term behaviour of AM CVn systems

3

Figure 1. The light curves of AM CVn systems obtained using the Liverpool Telescope which showed an outburst. We show the start date of the observations in the top right of each panel and the orbital period of each system towards the right.

comparison stars were brighter than g =18, and 0.11 mag when b oth stars were fainter than g =18. Since our aim is to detect variations greater than 1 mag, this is sufficient for our purp oses. To place our results on to the standard g band system, we used SDSS photometry of stars in the immediate field when available. For other sources we obtained images of the field (along with standard star fields) using the INT on La Palma. We show the light curve of each system in Figure 1 (for those showing outbursts) and in Figure 2 (for those which did not). The mean magnitude and range in brightness of our sources as derived using LT data is shown in Table 1, along with the rms of the light curve (see also Figure 3).

3 3.1

RESULTS Overview

Outbursts from hydrogen accreting cataclysmic variables (CVs) show amplitudes of at least one mag (eg Koto, Lasota & Dubus 2010). We therefore define an AM CVn system in outburst as that which shows light curve variations greater than 1 mag. Of the 18 AM CVn systems in our LT survey,
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seven were found to show at least one outburst (CR Boo, KL Dra, SDSS J0926, CP Eri, V406 Hya, SDSS J0129 and SDSS J0804). The LT data of SDSS J0129 were the first to show this system in outburst (Barclay et al. 2009). The other sources all had rms variations less than 0.2 mag (Figure 3). Two systems which have previously b een seen in outburst, (2QZ J1427 and SDSS J1240) were not seen in outburst in our LT data (although it is p ossible we have detected a decline from outburst in SDSS J1240 at MJD55170). Combining our results with those in the literature, we find that out of the 27 AM CVn systems currently known, 10 show outbursts, and they fall into a narrow range of orbital p eriods, covering 24.5­44.5 min. To get an overview of the outburst characteristics of each source we show in Figure 4 the outburst profile of each source (with the exception of CR Boo and SDSS J0804 which show erratic outbursts). For sources which have shown more than one outburst we over-lay data from different outbursts. The shap e of the outburst light curves can b e split into three broad classes: relatively long duration events such as those seen in V406 Hya and SDSS J0129; shorter duration bursts such as SDSS J0926, CP Eri and KL Dra (Ramsay et al. 2010), and rapid transitions from bright to faint states as seen in CR Boo and SDSS J0804. We show the typical dura-


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Figure 3. Using our LT data we show the mean g band brightness of our sources as a function of the root mean squared of the light curve.

Source CR Bo o K L Dr a J0929 CP Er i V406 Hya J0129 J0804 Figure 2. The light curves obtained using the Liverpool scope of those systems which did not show an outburst. We the orbital period of each system towards the right hand si each panel. The orbital period is not known for the lower systems. Teleshow de of four

Orbital Period (mins) 24.5 25.0 28.3 28.4 33.8 :37 44.5

Duration (days) 10 10 15 50 50

Amplitude (mag) 2. 3. 2. 4. 5. 4. 1. 3 3 6 0 2 2 2

Duty Cycle 70% 15% 8% 27% 27% 22% 8%

Table 2. The typical duration, amplitude and duty cycle (the percentage of observations for which the source was seen in outburst) of those AM CVn systems seen in outburst in our LT data. CR Boo and SDSS J0804 showed erratic rather than regular outbursts.

tion, amplitude and duty cycle (the fraction of observations which showed the source in outburst) of each source in Table 2. For systems with orbital p eriods b etween 33­37 mins, there is a tendancy for the outbursts to have longer durations and higher amplitude than the shorter p eriod systems. 3.2 Likelihood of missing outbursts

We have carried out simulations in order to estimate characteristic probabilities for missing an outburst given the typical data sampling. In particular, we have created synthetic light curves with a range of outburst lenghts and separation intervals. This was done by assuming an exp onential distribution for inter-outburst times and a uniform distibution for outburst lengths. A range of different means were used for the inter-outburst exp onential distributions. Figure 5 shows two representative cases. We have plotted a 2D probability distribution of missing outbursts from GP Com (top) and J2047 (b ottom) as a function of mean inter-outburst duration versus the outburst length. GP Com and J2047 represent two cases where we did not detect an outburst.

For b oth systems, the probability of us missing an outburst is less than 10 p ercent when the burst is interval is less than 150 days. For longer burst intervals the probability of us missing a burst reaches 30 p ercent in the case of J2047 when the burst length is shorter than 2 weeks. We also examined the light curve of J0926 which shows two outbursts although we may well have missed additional bursts. We p erformed a similar set of simulations although on this occasion we define the outburst length as b eing 10 days. We find the numb er of missed outbursts does not dep end on the outburst frequency - we exp ect to miss 47 p ercent of outbursts if the outburst frequency is b etween 60 and 400 days. Our data of J0926 unevenly cover 800 days and our similations predict three outbursts over this timescale where we detected two. We now proceed and discuss individual outbursting systems in more detail.
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The long term behaviour of AM CVn systems

5

Figure 5. We show the probability of missing an outburst as a function of mean outburst interval and outburst length. In the top panel we derive the probability for GP Com and in the lower panel J2047. Figure 4. We show typical outburst profile of outbursting AM CVn systems. Different symbols have been used for different outbursts. The UV data from KL Dra has been obtained using the Swift satellite.

3.3

CR Bo o

CR Boo shows marked changes in its intensity with an amplitude of 3 mag. It is either brighter than g =14.5, or fainter than g =16.5 for 90 p ercent of time and is brighter than g =14.5 for 70 p ercent of the ep ochs it was observed using the LT. However, our sampling is not frequent enough to determine if there is an underlying p eriodic or quasi-p eriodic signal. However, observations covering a timescale of 3 years show evidence for a quasi p eriodic transition b etween bright and faint states of 46.3 days (Kato et al. 2001). On the other hand, Patterson et al. (1997) found a prominent modulation (1 mag) on a p eriod of 19­22 hrs (which our data are unable to sample).

3.4

KL Dra

The first nine months of our LT observations of KL Dra have b een rep orted in Ramsay et al. (2010). They showed an outburst every 60 days (or roughly six p er year), making KL Dra the b est example of a helium accreting dwarf nova. Since then KL Dra has continued to show regular outc 0000 RAS, MNRAS 000, 000­000

bursts. We have determined the recurrence time b etween successive outbursts and their p eak brightness. Although there is some uncertainty in determining b oth parameters since the cadence of our observations is variable, it is clear that the recurrence time shortened from 60 days at the b eginning of our observations, to 45 days after a further five outbursts (Figure 6). When KL Dra b ecame visible again the recurrence time had increased to 65 days. There is a hint that the p eak brightness in the optical band followed the trend seen in the recurrence time. Although our coverage is such that the duration of the outbursts is not well defined, the outburst with the b est coverage rep orted by Ramsay et al. (2010) lasted 17 days. However, for the cycle which had a recurrence time of 44 days, the duration of the outburst prior to this lasted only 9 days. The typical duty cycle for the system b eing in the outburst state is 15 p ercent. The fact that there is a significant spread in the outburst recurrence time is entirely consistent with that seen in the hydrogen accreting dwarf novae, which can show a spread of up to a factor of 4 (cf Cannizzo, Shafter & Wheeler 1988). We note that the Kepler observations of the dwarf nova V344 Lyr shows a shortening in the recurrence time of the outbursts immediately after a sup er-outburst, which then app ears to lengthen and shorten in the lead up to the next sup er-outburst (Cannizzo et al. 2010).


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than on the POSS images and Abb ot et al. (1992) observed it at one ep och when it was brighter still.

3.7

V406 Hya

Figure 6. KL Dra: In the left hand panel we show the delay between the burst peaking at the date shown on the y-axis (MJD55000) and the previous one. In the middle panel we show the g mag peak brightness of the burst, while in the right hand panel we show the duration of the burst.

V406 Hya was originally thought to b e a sup ernova (2003aw) but subsequent sp ectroscopic observations showed it was an AM CVn system. Followup photometric observations showed that V406 Hya exhibits outbursts which can b e up to 5 mag in amplitude and have durations lasting two or three months (Woudt & Warner 2003, Nogami et al 2004). Our observations using the LT showed one long duration outburst, which lasted more than 60 days and had an amplitude of 4 mag. We also observed an increase in brightness at MJD56170 which could b e the decline from an outburst which was not detected (Figure 1). Although our observations did not have high cadence, they indicate that the rise to maximum took place on a timescale <12 days, and showed a very rapid initial decline from maximum (4 days) followed by a lengthy decline phase. Our data show V406 Hya was brighter than g =18.5 mag for 27 p ercent of our observations. The characteristics of this outburst are very similar to that found in Nogami et al. (2004). Our observations also show a very short duration (less than 10 days), high amplitude outburst (maximum at MJD=54920).

3.5

SDSS J0926

3.8

SDSS J0129

Observations made using the Catalina Real-Time Transient Survey showed five outbursts (of amplitude 3 mag) of SDSS J0926 over nearly 6 years of observations (Copp erwheat et al. 2011). (Our simulations suggest that roughly eight outbursts would b e exp ected over 6 years). The sampling is such that the source was observed, at b est, once every 20 days or so. Our observations made using the LT show one clear outburst with an amplitude of 2.5 mag and a duration 16 days, with a second outburst for which we caught the decline phase (at MJD55192, cf Figure 1). Our data show SDSS J0926 was brighter than g =18.4 mag for 8 p ercent of our observations. We note the presence of a brightening 8 days after the initial outburst ­ this mayb e related to the dip seen in b oth CP Eri and KL Dra (Figure 4. We will discuss these dips further in §4.

SDSS J0129 was seen in outburst on Dec 3rd 2009 when it was seen 3 mag brighter than it was 14 days earlier. It went on to reach maximum brightness after a further two days when it was 5 mag brighter than found in quiescence (Barclay et al. 2009). The shap e of the light curve is very similar to V406 Hya, showing a very rapid initial decline from maximum brightness (less than a day) and an extended tail. Our data show SDSS J0129 was brighter than g =18.5 mag for 22 p ercent of our observations. Shears et al. (2011) have recently rep orted the detection of the same outburst as rep orted here. Moreover they detected sup er-humps during the outburst which had a p eriod of 38 min. Since the sup er-hump p eriod is typically longer than the orbital p eriod by a few p ercent at most, the likely orbital p eriod is 37­38 min.

3.6

CP Eri 3.9 SDSS J0804 Of all our `outbursting' AM CVn systems, SDSS J0804 shows the lowest amplitude variations (1.2 mag) and has the longest orbital p eriod. It does not show obvious outbursts such as KL Dra or SDSS J0129, but shows a light curve more similar to CR Boo (which has the shortest orbital p eriod of our outbursting systems). However, in contrast to CR Boo there are no clear low/high states, with 90 p ercent of our datap oints in the range 18.2< g <18.8 and only 8 p ercent brighter than g =18.2. It is therefore not clear whether SDSS J0804 shows genuine outbursts but rather is just more active than systems which do not show outbursts.
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We have detected CP Eri in outburst on three occasions (although in the first there is only one data p oint where our sampling was rather sparse). The amplitude of the outbursts is 4 mag, while the rise time from the faint state to the high state was less than 5 days in the second outburst and less than 10 in the third. Our data show CP Eri was brighter than g =18.0 mag for 27 p ercent of our observations. We note a short duration drop in the intensity of CP Eri 2 days after the on-set of the second burst (cf Figure 4 and §4). The third outburst took place 114 days after the second. The only other recorded instances of CP Eri showing outbursts is Luyten & Haro (1959) who found it 2.5 mag brighter


The long term behaviour of AM CVn systems
4 THE 'DIP' FEATURE

7

Ramsay et al. (2010) found clear evidence for a short duration decrease in the optical flux of KL Dra around five days after the start of the outburst. With our more extended dataset, we have identified a total of five such dips in KL Dra suggesting they are not transient. Moreover, similar dips are seen in our LT optical light curves of SDSS J0926 and CP Eri (Figure 4) and in the recently discovered system PTF1 J0719+4858 (Levitan et al. 2011). We show in Figure 4 the outburst light curve of KL Dra in the optical and UV bands. Given the relatively sparse cadence of our data, this is accurate only to within a few days. However, the dip lasts 2­3 days and has a depth of a factor of 5 compared to the pre-dip light curve. Although the UV data are more scattered compared to the optical data, the UV flux tends to b e weaker at the time of the optical dip. (We have included Swift UV data which were taken in April 2010 ­ after the pap er by Ramsay et al. 2010 was accepted). Our data do not have high enough cadence to determine whether a dip is seen in every outburst of KL Dra. A dip-like feature has also b een rep orted in the AM CVn system V803 Cen by Kato et al. (2004) who noted its similarity to the 2001 sup er-outburst of WZ Sge. This dip has b een interpreted as a re-brightening due to a recurring thermal instability (eg Osaki et al. 2001). However, compared to KL Dra the dip occurs much longer after the on-set of the outburst. We note that dips have also b een seen in some hydrogen accreting CVs, eg T Leo, (Kato 1997), which are thought to due to a normal outburst triggering a sup eroutburst (van der Woerd & van Paradijs 1987).

5

OUTBURSTING SYSTEMS AS A FUNCTION OF ORBITAL PERIOD

One of the main motivations for our study was to test the prediction of Smak (1983), and later elab orated by Tsugawa & Osaki (1997), who suggested that systems with orbital p eriods in the range 20­40 min would exp erience outbursts. For AM CVn systems with Porb >40 mins, the accretion disc is predicted to b e cooler than the ionisation state of helium. For binaries with Porb <20 mins, the disc is predicted to b e hotter than the ionisation state of helium. Since these discs were exp ected to b e stable it was predicted that systems would not show photometric outbursts. Tsugawa & Osaki (1997) indicated (their Figure 3) the predicted location of these thermally stable and unstable regions in the Porb , M plane for AM CVn binaries. Dep ending on whether the donor star is fully or partially degenerate may shift a particular source to the stable or unstable region. We have taken Figure 3 of Tsugawa & Osaki (1997) as a starting p oint, but employed the predicted relationship b etween Porb and M from Deloye et al. (2007) which is more physical than that of the earlier work. In the top of Figure 7 we place a `Y' or a `N' indicating whether a source shows outbursts or not (Table 1). We find that all the systems with orbital p eriods b etween 24­44 mins show outbursts and are located in the unstable region (Figure 7). However, taking into account the p eriod of the systems which do not show outbursts, the unstable
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Figure 7. We show the stable and unstable regions for AM CVn systems as a function of orbital period and mass transfer rate where we have taken the general outline from Tsugawa & Osaki (1997) as a starting point but annotated and updated it. Unstable accretion disks are predicted to lie between the hot and the cool stable regions (top and bottom). The horizontal dashed-dotted lines give the location of the cool stable region depending on the mass of the accreting star. The lines travelling from the lower right to the upper left are the predicted mass-transfer rate as a function of orbital period (taken from Figure 15 of Deloye et al. 2007). We have added a 'Y' or a 'N' at the appropriate orbital period depending on whether the AM CVn binary goes into outbursts or not.

region p otentially extends b etween 19­46 mins (cf Table 1). At the lower end of the unstable range, CR Boo (which is thought to have a semi-degenerate donor star Roelofs et al. 2007b) is just inside the unstable regime. In the case of KL Dra, which has a virtually identical orbital p eriod, it is unknown whether its donor star is semi or fully degenerate. At the shortest orbital p eriods, these systems would b e stable whether their donor star was fully or semi degenerate. At longer p eriods ( J0804, GP Com, J1411) these stars would b e more likely to b e unstable if their donor star was semi-degenerate and/or their accreting white dwarf was relatively low mass. This result indicates a remarkable agreement b etween the prediction of Smak (1983), Tsugawa & Osaki (1997) and observation.


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6 A HELIUM-RICH DWARF-NOVA SEQUENCE? within the range 24­44 mins. This result is in excellent agreement with theoretical predictions. Moreover, we find tentative evidence for the characteristics of these outbursts to b e dep endent on orbital p eriod. Systems at the lower end of this p eriod range show outbursts which last a week or two and tend to show a characteristic dip a handful of days after the start of the outburst. At longer p eriods, the outbursts have greater amplitude and last for several months. Systems at the edge of this p eriod range, whether the disc is close to b eing in a stable hot state or a stable cool state, show rapid changes in brightness. This sequence can b e seen in the context of the rapidly diminishing mass transfer rate b etween 20­40 mins. At shorter p eriods the higher mass transfer rate enables the disc to achieve a critical mass on a shorter timescale than for longer p eriod systems where the mass transfer rate is significantly lower. Based on our survey we predict that J1427 will also exhibit large amplitude long duration outbursts. Indeed we encourage observations of J1427, V406 Hya and J0129 to detect further outbursts so that they can b e studied in much greater detail, and at different wavelengths, and determine how similar they are to the hydrogen accreting WZ Sge stars. Using the models of Nelemans et al. (2001, 2004), Roelofs, Nelemans & Groot (2007c) predict the p opulation surface density of AM CVn systems as a function of Galactic latitude. For |b| < 30 they predict that around half of all AM CVn binaries are exp ected to have orbital p eriods in the range 20­40 mins (irresp ective of whether one assumes `optimistic' or `p essimistic' assumptions for their space density), although this fraction is lower for higher Galactic latitudes. Although we find the duty cycle is quite variable from source to source (and indeed, not esp ecially well constrained), our results indicate that a duty cycle of 1/4 is not untypical, which may b e due to the small disks in AM CVn systems. Given this reasonably high duty cycle, surveys which followup blue transient systems may provide the b est method with which to discover AM CVn systems. The recent discovery of PTF1 J0719 using the Palomar Transient Factory confirms such a view (Levitan et al. 2011).

Our survey to characterise the long term b ehaviour of AM CVn binaries has found that 10 out of the 27 systems has shown at least one outburst. Moreover, the outbursting systems have p eriods b etween 24 and 44 mins ­ a result which is remarkably consistent with theoretical predictions. It app ears that systems with Porb <24 mins have an accretion disc which has a mean temp erature always ab ove the ionisation state of helium, while systems with Porb >44 mins have a disc with a mean temp erature b elow the ionisation state of helium. Of the seven systems which showed at least one outburst in our LT data, there is some evidence that the outbursts fall into three rather distinct characteristics, the nature of which may b e related (at least partly) to their orbital p eriod. KL Dra (25.0 min), J0926 (28.3 min) and CP Eri (28.4 min) all show outbursts lasting a week or two with a distinctive dip in the outburst profile. The recently discovered system PTF1 J0719 (26.8 min, Levitan et al. 2011) also shows outbursts lasting several weeks, but in addition exhibits bursts lasting several days (which is very similar to what we observe in KL Dra, although they are not well sampled). Given our low cadence it is p ossible that the 50­60 day outbursts seen in KL Dra are sup er-outbursts, and the short duration bursts are normal outbursts. CR Boo which has a p eriod just shorter than KL Dra (24.5 min) shows a rapid change b etween high and low states. In addition it has shown a p eculiar `cycling' state when it shows a prominent modulation (1 mag) on a p eriod of 19-22 hrs (Patterson et al. 1997). This photometric feature has also b een seen in V803 Cen (26.9 min) (Patterson et al. 2000). At the longer p eriod b oundary, SDSS J0804 (44.5 mins) also shows enhanced levels of activity, but not regular outbursts. This may hint that systems on the b oundary b etween having a stable or a non-stable accretion disc are likely to b e unstable. On the other hand, given KL Dra and CR Boo have practically identical p eriods it is likely that factors other than the orbital p eriod (for instance, the nature and metallicity of the donor star) affects the long term photometric b ehaviour. In complete contrast, V406 Hya (33.8 min) and J0129 (37 min) show outbursts which are up to 5­6 mag in amplitude and which last several months. Evidence exists that J1240 (37.4 mins) also shows high amplitude and long duration outbursts (Shears et al. 2011). The similar p eriod of these systems makes observations of J1427 (which has a photometric p eriod ­ probably a sup erhump ­ of 36.6 min, Shears et al 2011) particularly interesting. Does it also show similar long outbursts? In the case of SDSS J2047+0008, which currently does not have a known orbital p eriod, the fact that it has b een found to go into outburst, strongly suggests that it has an orbital p eriod b etween 24­44 mins.

8

ACKNOWLEDGEMENTS

The Liverp ool Telescop e is op erated on the island of La Palma by Liverp ool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial supp ort from the UK Science and Technology Facilities Council. TB and DS acknowledges STFC for a PhD Studentship and an Advanced Fellowship resp ectively. We thank the referee for useful comments on the original manuscript.

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Our survey of AM CVn binaries using the Liverp ool Telescop e coupled with existing published data shows that 1/3 of these helium accreting compact binaries undergo outbursts. These outbursting systems have orbital p eriods


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