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A&A
Volume 620, December 2018
Article Number A141
Number of page(s) 17
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201834261
Published online 11 December 2018

© ESO 2018

1. Introduction

AM CVn stars occupy the extreme short period tail of stellar binaries, with observed orbital periods in the range ∼5−65 min. They consist of white dwarfs accreting material from Roche lobe-filling companion stars, typically a lower mass white dwarf or a semi-degenerate helium-rich star. The mass transfer in these binaries is driven by gravitational wave radiation and they are expected to be strong sources of low frequency gravitational waves (Nelemans et al. 2004). In particular, the fact that their binary properties such as orbital period and mass ratio can be measured from electromagnetic observations makes them useful as “verification sources” for the Laser Interferometer Space Antenna (LISA) mission. In a separate paper, we predict the gravitational wave strain of the 16 currently-known LISA verification binaries, 11 of which are AM CVn stars (Kupfer et al. 2018).

There are three proposed channels for the formation of AM CVn stars, but their relative importance is not yet clear. The population synthesis models of Nelemans et al. (2001a) suggest that the majority of AM CVn stars form from double white dwarf binaries that evolve closer together as a result of gravitational wave radiation, and start mass transfer at orbital periods of ∼2–3 min (Paczyński 1967). Given these small orbital separations, the initial mass transfer occurs as direct impact, which will lead to unstable mass transfer and hence merger in the majority of cases. The fraction of double white dwarfs which survive to become stable mass transferring AM CVn stars is highly uncertain, and depends on the efficiency with which the spin of the accretor can be tidally coupled to the binary orbit to stabilise the mass transfer (Marsh et al. 2004). There has also been a suggestion by Shen (2015) that due to increased friction from ejected material in nova eruptions earlier in the evolution of the binary, all double white dwarf binaries will merge, and that no AM CVn stars should form in this way.

The alternative is that the companion is a core helium-burning star instead of another white dwarf (Savonije et al. 1986; Iben & Tutukov 1987). Such a binary will reach a minimum period of ∼10 min before mass transfer starts and the helium star will get increasingly degenerate as it evolves to longer periods.

A third channel involves a hydrogen-rich cataclysmic variable with a donor that is already partially evolved at the onset of mass transfer. The binary then loses its hydrogen through evolution and accretion to become an AM CVn star with a period at the long end of the range. It is considered an unimportant channel compared to the white dwarf and helium star scenarios given the long evolutionary timescales involved, but potential progenitor binaries for this channel have been identified (Breedt et al. 2012; Carter et al. 2013b).

Only the two eclipsing AM CVn stars, YZ LMi (SDSS J0926+3624) and Gaia14aae, have parameters measured to high enough precision to discriminate between these models. YZ LMi is likely to be of helium star origin, although the white dwarf route cannot be ruled out completely (Copperwheat et al. 2011). Gaia14aae on the other hand, is inconsistent with a white dwarf donor scenario, but it is also not straightforwardly compatible with either of the other models (Green et al. 2018b). A detailed discussion of the three formation channels and a review of the observed properties of the AM CVn population is given by Solheim (2010).

A well-defined sample of AM CVn stars from the Sloan Digital Sky Survey (SDSS) made it possible to compare the observed space density of these binaries, ρ = (5 ± 3)×10−7 pc−3, to population synthesis predictions (Carter et al. 2013a). Even though the models take into account a range of efficiencies for the spin-orbit coupling and the subsequent AM CVn survival rate, the models overpredict the space density by an order of magnitude. The reason for the discrepancy is not clear, but may be related to the uncertainty of the distribution of these binaries in the Galaxy (Nissanke et al. 2012). Most surveys where AM CVn stars have been found have covered only high Galactic latitudes, and it is possible that a substantial fraction reside in the Galactic plane.

One of the main limitations in modelling the spatial distribution of the AM CVn population and calibrating models of space density and luminosity is the lack of accurate distances. Only five systems have a parallax determined using the Hubble Space Telescope Fine Guidance Sensor (HST FGS; Roelofs et al. 2007b) with distances to others are generally estimated by comparing model fluxes with observations. With reliable distances we can determine the mass transfer rate, Ṁ, which in conjunction with an orbital period, can constrain which of the three formation channels the binary formed. In turn, this can provide a more reliable value for their space density.

The Gaia Data Release 2 (DR2) on 25 April 2018 provided the parallaxes of 1.3 billion stars down to G ∼ 21 (Gaia Collaboration 2018a) and has allowed us to determine the distances to 41 of the 56 known AM CVn stars. The first Gaia data release (DR1; Gaia Collaboration 2016b) in September 2016 relied on a combined Tycho-Gaia astrometric solution (TGAS; Gaia Collaboration 2016a), and did not include any AM CVn stars. However, it included parallaxes of 16 hydrogen cataclysmic variables (CVs; Ramsay et al. 2017), which provided a validation of the Disc Instability Model which is widely used to model accreting binaries, including AM CVn stars (Osaki 1989; Kotko et al. 2012; Cannizzo & Nelemans 2015). Another key result from this work was the comparison between the HST FGS, Very Large Array radio data and Gaia DR1 parallax measurements of the CV SS Cyg, which resolved a long-standing discrepancy in the distance to (and hence luminosity of) this system, and showed that the HST parallaxes may be unreliable.

In this paper, we use the GDR2 parallax measurements to determine the absolute magnitudes of AM CVn stars and their mass accretion rates. We then use these results to infer the space density of these binaries.

2. The known AM CVn stars

Observationally, AM CVn stars are characterised by their hydrogen deficient optical spectra and blue colour, so surveys for AM CVn stars have typically focussed on these properties to identify new members of the class. The past decade has seen a rapid increase in the number of known AM CVn stars. Firstly because of a dedicated spectroscopic survey of colour-selected targets from SDSS (Carter et al. 2013a, and references therein) and secondly from photometric and spectroscopic follow-up of transient events in large area photometric surveys, such as the Catalina Real-time Transient Survey (CRTS; Breedt et al. 2014), the Palomar Transient Factory (PTF; Levitan et al. 2015) and the All-Sky Automated Survey for Supernovae (ASASSN; Breedt 2015).

Since the data compilation by Levitan et al. (2015), a number of additional AM CVn systems have been discovered. Some of the more recent discoveries include Gaia14aae, the first in which the white dwarf is fully eclipsed (Campbell et al. 2015; Green et al. 2018b), ASASSN-15fp, the longest period AM CVn system to have been observed in outburst so far (Cartier et al. 2017; Marsh et al. 2017), and SDSS J1351-0643, the first system with a period shorter than 17 min to be discovered in ∼15 years (Green et al. 2018c). In Table 1, we list the 56 AM CVn stars known at present, ordered by increasing orbital period. We provide a full table, including J2000.0 and J2015.5 sky coordinates and multi-wavelength photometry at the CDS. The column description of the full table is shown in Appendix A.

Table 1.

Currently known AM CVn stars ordered by increasing period, either the orbital period (most reliably determined from spectroscopic observations) or the superhump period (sh) which is typically within a few percent longer than the orbital period.

Time series spectroscopy remains the most reliable method to measure the orbital periods of AM CVn stars, but it is a challenging task due to the faintness of many systems and the short exposures which are needed to phase resolve the short orbital period. For systems which display outbursts (see Table 1) the superhump period may be used as a proxy. These are flux variations observed during superoutbursts, resulting from the interaction between the precessing accretion disc and the donor star (e.g. Wood et al. 2011). It is typically a few per cent longer than the orbital period. Other proxies include the relationship between the equivalent width of emission lines and the orbital period (Carter et al. 2013a), and the recurrence time between outbursts (Levitan et al. 2015).

The orbital periods of the known AM CVn stars range from 5.4 min to 65.6 min. Eight of the known systems do not have an estimate of their orbital period yet. AM CVn stars at the short period end (Porb <  20 min), are akin to novalike CVs, with hot, high state accretion discs. The accretion rate drops as the binary evolves to longer periods, and at the longest periods in the range (i.e. lowest accretion rates) the discs are in a low, stable state. At intermediate periods, 20 <  Porb ≲ 44−52 min, the discs display ∼1−5 mag outbursts similar to the dwarf nova outbursts observed in the hydrogen cataclysmic variables (Levitan et al. 2011, 2015; Ramsay et al. 2012). The long period boundary below which outbursts are observed is not sharp. For example, Gaia14aae and ASASSN-15fp, with periods of 49.7 and 51.0 min respectively, were discovered as a result of their outbursts, but the long-known system GP Com with Porb = 46.6 min, has never been observed in outburst. Cannizzo & Nelemans (2015) show that this is a result of the dependence of the mass transfer rate on the accretor mass, in the sense that systems with a more massive accretor have a higher mass transfer rate at a given orbital period. This dependence is stronger at the long period edge than at the short period edge, resulting in a mix of outbursting and stable systems near Porb ∼ 44−52 min.

3. Parallaxes and distances of AM CVns in Gaia DR2

In Table 1 we show the parallaxes for all AM CVn stars included in the Gaia DR2: out of the 56 known systems 41 have parallax measurements. The closest system is the long known GP Com with a parallax of 13.73 ± 0.06 mas, with the most distant being V407 Vul which has a parallax consistent with zero (0.10 ± 0.33 mas). In Table 2 we compare the parallaxes for three sources which have both Gaia and HST parallaxes (V803 Cen and CR Boo have no parallax in Gaia DR2). There is reasonable agreement for GP Com. However, HP Lib is significantly more distant and AM CVn significantly closer compared to the results of HST. Indeed the HST parallax derived for AM CVn implied a greater distance than other estimates and therefore implied a high luminosity and mass accretion rate, all of which were problematic in explaining.

Table 2.

Gaia DR2 and HST parallaxes of the five AM CVn stars which were measured using the HST Fine Guidance Sensor.

We convert parallaxes from the Gaia DR2 into distances following the guidelines from Bailer-Jones (2015), Astraatmadja & Bailer-Jones (2016) and Gaia Collaboration (2018c). Given the measured parallax ϖ with the uncertainty σϖ, the probability density of possible values for the distance can be found by using Bayes’ theorem:

P ( r | ϖ , σ ϖ ) = 1 Z P ( ϖ | r , σ ϖ ) P ( r ) , $$ \begin{aligned} P(r|\varpi ,\sigma _{\varpi })= \frac{1}{Z}\ P(\varpi |r,\sigma _{\varpi })\ P(r), \end{aligned} $$(1)

where r is the distance, P(ϖ|r, σϖ) is the likelihood function, that can be assumed Gaussian (Gaia Collaboration 2018b). P(r) is the prior and Z is a normalisation constant. The prior is an arbitrary function that expresses our knowledge on the distribution of the distances of AM CVn stars and allows us to introduce assumptions in the inference procedure that are not related to the measurement of the parallax itself. The properties of various priors and their performance on the data from the Gaia DR1 have been investigated in Astraatmadja & Bailer-Jones (2016). For this work we adopt the exponentially decreasing space density prior:

P ( r ) = { r 2 2 L 3 exp ( − r / L ) if r > 0 , 0 otherwise , $$ \begin{aligned} P(r) = {\left\{ \begin{array}{ll}\frac{ r^2}{2L^3} \exp (-r/L)&\text{ if} \ r > 0,\\ 0&\text{ otherwise}, \end{array}\right.} \end{aligned} $$(2)

where L is the scale length. This prior implies a constant space density of AM CVn stars for r ≪ L and an exponential drop for r ≫ 2L, where 2L corresponds to the peak of the distribution. The choice of the value for L needs to be fine-tuned to reproduce the distribution of AM CVn stars with the distance. We adopt L = 400 pc calibrated on the mock population of double white dwarf binaries (progenitor systems of AM CVns) from Korol et al. (2017). For more detailed argumentation we refer the reader to Kupfer et al. (2018). In Table 1 we show the inferred distance and uncertainty (which covers the 90 percent confidence interval) for those AM CVn systems which have parallax measurements in the Gaia DR2. The distances range from 73 pc (GP Com) to 1.8 kpc (V407 Vul), although the latter is rather uncertain. The median distance is 580 pc. For sources closer than 340 pc the mean uncertainty on the distance is 9 pc, and for those between 500–1000 pc it is 380 pc.

4. Galactic distribution

For the 41 systems with parallax and proper motions from Gaia DR2 (shown in Table B.1), we calculate 3D kinematics and put constraints on their population membership: thin disc, thick disc, and halo. Only AM CVn, SDSSJ 1908+3940, CP Eri, SDSS J1730+5545 and SDSS J1240-0159 have measured systemic velocities based on radial velocity curves of their accretion disc lines. Seven additional systems have a strong central spike feature which can be used to measure the radial velocity. These central spike lines are believed to originate close to the photosphere of the accretor and are shifted with the gravitational redshift of the accretor. Assuming an accretor with M = 0.8 M⊙ and a radius of R = 0.01 R⊙ leads to a gravitational redshift of 50 km s−1, so we correct the measured velocity from the central spike by 50 km s−1. For the remaining systems with no measured radial velocity, we assume 0 km s−1 with an error of ±50 km s−1.

Combined with right ascension and declination, we calculate velocity in the direction of the Galactic Centre (Vρ) and the Galactic rotation direction (Vϕ), the Galactic orbital eccentricity (e), and the angular momentum in the Galactic z direction (Jz). The Galactic radial velocity Vρ is negative towards the Galactic centre, while stars that are revolving on retrograde orbits around the Galactic Centre have negative Vϕ. Stars on retrograde orbits have positive Jz. Thin disc stars generally have very low eccentricities e. Population membership can be derived from the position in the Vρ − Vϕ diagram and the Jz − e diagram following the description in Pauli et al. (2003, 2006).

We show the results in Fig. 1. We find that the most of the systems show a Galactic orbit typical for a thin disc population (see Table B.1). About 10 systems have a typical thick disc orbit. None of the systems show a halo orbit. In a small number of AM CVn stars, the extreme depletion of heavy elements have been taken as evidence that these stars were halo objects (GP Com: Marsh et al. 1991; V396 Hya: Nagel et al. 2009 and PTF1 J0719+4858: Gehron et al. 2014). Our study has shown that these AM CVn stars are likely thin or thick disc objects and not halo objects. It is of interest to understand how disc objects can have such low abundances of heavy elements.

thumbnail Fig. 1.

AM CVn stars in the plane of the velocity in the direction of Galactic rotation (Vϕ) and the Galactic centre(Vρ) (left hand panel) and the orbital eccentricity (e) and the angular momentum in the Galactic z direction(Jz) (right hand panel). The solid and dotted ellipses render the 3σ thin and thick disc contours in the Vϕ–Vρ diagram, while the solid box in the e–Jz marks the thick disc region as specified by Pauli et al. (2006).

5. Determining the line of sight extinction

To determine the absolute magnitude of AM CVn stars we need to subtract the effects of interstellar extinction. Although 47 of the 56 AM CVn stars shown in Table 1 lie at Galactic latitudes |b| > 20° (implying the extinction is likely to be low), we have determined the line-of-sight extinction to our sources using 3D-dust maps derived from Pan-STARRS1 data (Green et al. 2018a). For each AM CVn star, we derived the extinction, EB−V, for the sky co-ordinates and distance of that star given in Table 1 (the uncertainty is typically EB−V∼0.02). To determine the reddening, we use AV = R × EB−V, where we assume the standard value of R =3.2. To obtain the reddening in the g band, we assume Ag = 1.1 × AV (Cardelli et al. 1989). For those AM CVn stars at declinations too south to feature in the Pan-STARRS1 catalogue we use the dustmaps of Schlafly & Finkbeiner (2011) which give the extinction to the edge of the Galaxy in that line of sight (this step was required for only two stars and given that the upper limits are only 0.2 mag, we do not expect that this uncertainty will significantly effect their place on the period – absolute magnitude relationship).

We show the reddening to those AM CVn stars with parallaxes in Table 3. The median reddening of our sample is Ag = 0.14 mag, with 90 percent of sources having Ag <  0.35 mag. Therefore for the majority of our targets the effects of interstellar absorption has a small effect on the resulting absolute magnitudes. The only source with a high extinction, V407 Vul, was previously known to have a high degree of reddening (Motch et al. 1996).

Table 3.

Reddening in the g band (Ag), which have been determined using Pan-STARRS1 data (Green et al. 2018a).

6. The absolute magnitudes of AM CVn stars

Using the distances shown in Table 1, we show in Fig. 2 the absolute magnitude, MG, against the BP-RP (the “Blue Photometer” and “Red Photometer” colour derived from Gaia data) of AM CVn stars and a sample of Galactic stars with accurate parallax measurements. The single white dwarf track can be seen in the lower left of the figure. High state AM CVn stars are significantly brighter than the isolated white dwarfs, being MG ∼ 6. The majority of quiescent AM CVn stars appear 1–2 mag brighter than the white dwarfs, being MG ∼ 8−12, though a minority lie on the white dwarf track.

thumbnail Fig. 2.

An HR diagram made using Gaia DR2 data. In red we show the absolute G magnitude, MG, as a function of the blue-red colour, BP-RP, for AM CVns with known parallaxes. No reddening or extinction corrections have been applied to this figure. For comparison, in grey points we show a sample of essentially randomly selected main sequence stars which have a parallax better than 1 percent. For single white dwarfs shown as slightly larger grey points) we have used the sample of white dwarfs within 20 pc (Hollands et al. 2018). The majority of AM CVns appear to be brighter than the single white dwarf track, though some long-period systems lie on the track. A clear outlier is V407 Vul, which has BP-RP ≈ 1.5 through a combination of severe reddening and contamination from an unresolved nearby G-star.

As the wavelength range of the GaiaG band filter is very broad, it is not the optimal filter with which to test evolutionary models which usually predict the absolute magnitude in the V or g bands. We have therefore collated all the available multi-filter photometry of the AM CVn stars from the Pan-STARSS1, Skymapper, GALEX and SDSS surveys and we show these in Appendices A.4–A.7 and associated tables. Since most surveys release mean or median values for each source and filter, the effects of outbursts are generally smoothed out and usually they reflect the quiescent brightness for outbursting systems. In Table 3 we show the mean quiescent g mag which we derive for these systems. For most systems this magnitude is found from analysis of the g-band data shown in the appendix. In the case of ASASSN-14cc, a short-period system which is in outburst for around 60 percent of the time, the magnitude measured by Skymapper is representative of its outburst magnitude. We therefore take its quiescent magnitude from Kato et al. (2015).

Based on these quiescent magnitudes, we calculate the absolute magnitudes shown in Table 3. In Fig. 3 we plot the absolute magnitudes of AM CVn binaries as a function of orbital period, for the 37 systems in which both magnitude and orbital period are known. For those systems which outburst we also plot an approximate outburst magnitude. For comparison, we show the predicted magnitudes of the central white dwarf and the accretion disc, both of which vary in magnitude as a function of orbital period. We show two cooling tracks for a 0.65 M⊙ central white dwarf, both taken from Bildsten et al. (2006): one assumes a low mass transfer rate (as would be seen for a cool, low-mass white dwarf donor) and one assumes a high mass transfer rate (as would be seen in a hot, high-mass dwarf donor). The donor masses assumed span the range of white dwarf donor masses predicted by Deloye et al. (2005), but we note that higher-mass donors are possible through other evolutionary channels. The accretion disc magnitudes are calculated by Nelemans et al. (2004).

thumbnail Fig. 3.

Extinction-corrected absolute magnitudes (Mg) of AM CVn binaries as a function of orbital period. For known outbursting systems, we plot the quiescent magnitude, and show the magnitude change during outburst as a dotted line. The dashed line is the predicted MV of the accretion disc as originally taken from Nelemans et al. (2004) while the solid line shows the evolution of a 0.65M⊙ accreting white dwarf with a high-entropy white dwarf donor, including accretion heating, from Bildsten et al. (2006). Most systems appear somewhat brighter than an isolated white dwarf model during quiescence, and close to the duty-cycle-scaled disc magnitude during outburst.

As Fig. 3 shows, a strong decrease in AM CVn absolute magnitude with increasing orbital period is seen. High-state systems (Porb ≲ 20min) lie close to the predicted accretion disc magnitudes, as expected for these disc-dominated systems. Quiescent systems lie a little above the white dwarf cooling track, with an excess that generally decreases with increasing period, though there is considerable scatter between systems. For outbursting systems, the outburst magnitude in most cases is far in excess of the mean disc magnitude.

All AM CVn systems shown in Fig. 3 are brighter than the predicted white dwarf cooling track for a high-mass white dwarf donor, and significantly brighter than the cooling track for a low-mass white dwarf donor. For systems at Porb > 50 min, which are dominated by their white dwarf magnitudes, this is particularly interesting. It may suggest that AM CVn donors have a systematically higher mass than predicted. Measurements of AM CVn mass ratios imply a similar trend (Green et al. 2018c). If true, this would imply either that white dwarf donors have higher temperatures (and hence higher masses for a given orbital period) than predicted, or that the majority of systems have non-white dwarf donors.

Several individual systems are worthy of note:

  • V407 Vul appears unusually bright due to the G star which is co-aligned on the sky. Barros et al. (2007) estimated that the G star contributes 92% of the light in the g-band, giving a magnitude difference of 2.7.

  • SDSS J1351-0643 has an unexpectedly low magnitude for a high-state system, though its uncertainties are large. This low magnitude could be explained if the system is at a high inclination, such that the disc is viewed close to edge-on. Its broad double-peaked spectrum and photometrically-visible disc precession also support a high inclination.

  • ASASSN-14ei, SDSS J0804+1616, Gaia14aae, and SDSS J1642+1934 seem to be unusually bright for their orbital period. For some of these systems there is evidence they may have a high mass transfer rate: SDSS J0804+1616 is unusually variable (Ramsay et al. 2012), while Gaia14aae is among the longest-period outbursting AM CVns and has an unexpectedly high-mass donor star (Campbell et al. 2015; Green et al. 2018b). As discussed in Sect. 7, the elevated magnitude of Gaia14aae is almost entirely due to its hot central white dwarf.

  • Several systems have outburst magnitudes that are lower than the general trend, including PTF1 J1919+4815, YZ LMi, and SDSS J1240-0159. The first two of these systems are partial eclipsers and therefore high-inclination, which will reduce the observed outburst magnitude. The reason for the weak outburst of SDSS J1240-0159, reported by Roelofs (2007), is uncertain.

7. Component magnitudes of eclipsing AM CVns

Three AM CVns are currently known which undergo eclipses. In Gaia14aae and YZ LMi, the central white dwarf is eclipsed, while in PTFJ 1919+4815, only the edge of the disc is eclipsed. The first two systems present an opportunity to measure the flux contributions from, and hence absolute magnitudes of, their central white dwarfs. We can additionally measure the flux contribution from the ‘bright spot’ component of these systems, this being a bright region located at the point of collision between the accretion disc and the stream of infalling matter from the donor.

Photometry of YZ LMi in Sloan ugr bands and of Gaia14aae in ugri bands were presented in Copperwheat et al. (2011) and Green et al. (2018b) respectively. Both papers quote the measured white dwarf fluxes, from which we calculate the absolute magnitudes. To calculate the bright spot contributions, we obtained the best-fit models presented in both papers and measured the bright spot contribution directly. Uncertainties were calculated from the 1-σ spread of the MCMC results created for those papers when converging on the data. The absolute magnitudes we calculate for these components are presented in Table 4. In the case of YZ LMi, large uncertainties result from the poorly constrained Gaia parallax of the system. The i-band Gaia14aae magnitudes are poorly constrained due to the small number of eclipses observed in that band.

Table 4.

Absolute magnitudes of the central white dwarfs and bright spots in two eclipsing systems: YZ LMi and Gaia14aae.

7.1. Central white dwarfs

These central white dwarf magnitudes may be compared with the predicted white dwarf magnitude track shown in Fig. 3, for corresponding orbital periods. It should be noted that both white dwarfs are somewhat higher mass (≈0.85 M⊙) than the mass assumed in that model (0.65 M⊙). A larger mass effects the magnitude in two ways: the reduction in size of the white dwarf causes it to appear fainter, but the smaller surface area increases the effect of accretion heating on temperature. With this caveat, the central white dwarf g magnitude of YZ LMi agrees reasonably well with the predicted value of 10.6. For Gaia14aae, the central white dwarf magnitude of 11.66(9) is considerably brighter than the predicted magnitude of 12.4. As shown in Bildsten et al. (2006), the white dwarf mass is less significant than accretion rate for long-period systems like Gaia14aae. It therefore seems likely that the elevation of the central white dwarf magnitude of Gaia14aae above the model track is due to a higher accretion rate than predicted, resulting in a hotter white dwarf.

Given the tightly constrained absolute magnitudes of Gaia14aae, the temperature of the central white dwarf can be estimated. From DB atmosphere models (Bergeron et al. 2011; Tremblay et al. 2011; Kowalski & Saumon 2006; Holberg & Bergeron 2006), for a surface gravity log(g) ≈ 8.5 as measured by Green et al. (2018b), these magnitudes in all four colour bands predict a temperature of ≈17 000 ± 1000 K. This temperature disagrees with the previously established temperature of 12 900 ± 200 K established from UV flux (Campbell et al. 2015). The discrepancy may be the result of metals accreted from the donor star, in particular nitrogen, which are expected given the evolved nature of the donor (Nelemans et al. 2010). Such metals would cause absorption in the UV not present in a pure DB atmosphere, making the UV-derived temperature unreliable. We therefore interpret 17 000 K as the most likely temperature of the white dwarf.

7.2. Bright spots

The magnitudes of the bright spots in these systems allow for their instantaneous mass transfer rates, Ṁ, to be estimated. If the luminosity of the bright spot is equal to the kinetic energy released by the infalling matter as it slows to match the disc velocity, the luminosity can be described as

L = 1 2 M ˙ | V stream − V disc | 2 $$ \begin{aligned} L = \frac{1}{2} \dot{M} |\boldsymbol{V}_\mathrm{stream} - \boldsymbol{V}_\mathrm{disc} |^2 \end{aligned} $$(3)

where Vstream and Vdisc are vectors describing the velocities of material in the stream and disc at the point of intersection between the two. Assuming that the disc material follows a Keplerian orbit and that the stream trajectory is ballistic, these can be calculated based on the measured stellar masses of the system. The luminosity found by Eq. (3) can then be converted to a magnitude using an assumed spectral response for the bright spot. We assume the spectral response of a 12000 K black-body, as was observed for the cataclysmic variable IP Peg (Marsh 1988). To account for our uncertainty in this choice of spectral response, we increase the uncertainties on the predicted magnitude by 0.2 mag, and propagate this through to the uncertainties on Ṁ. We find log(Ṁ/M⊙ yr−1) = −10.6 ± 0.4 for YZ LMi and −10.74 ± 0.07 for Gaia14aae.

For comparison we calculate theoretical values of Ṁ based on the photometrically measured masses, using the relations in Deloye et al. (2007). It is necessary to assume a value for the donor star’s response to mass loss, dlog(R)/dlog(M). For this we assume 0.2, which approximates the tracks in Deloye et al. (2007) for donors evolving isothermally. For YZ LMi, the predicted log(Ṁ/M⊙ yr−1) = 10.0 is within 1.5-σ of our measured value. Given that these uncertainties are likely to be non-Gaussian, we do not consider this discrepancy to be significant. In the case of Gaia14aae, an assumed donor response of 0.2 implies log(Ṁ/M⊙ yr−1) = 10.77, in good agreement with our measured mass transfer rate.

The agreement in the case of Gaia14aae is, to some extent, surprising. Deloye et al. (2007) predict dlog(R)/dlog(M) = 0.2 for AM CVn donors during their short-period evolution. However, once they evolve to periods ≳40 min, a change of state in the donor is expected that would result in this value decreasing. The fact that 0.2 still appears to hold for Gaia14aae agrees with our suggestion in Green et al. (2018b) that the donor has not yet undergone this change of state.

Recent work by Piersanti et al. (2015) predict the mass accretion rate for systems with periods shorter than 22 min. However, we use the work of Bildsten et al. (2006) who give a relation between the mass transfer rate and the temperature of the accretion-heated central white dwarf in AM CVn systems for the entire orbital period seen in AM CVn stars. Bildsten et al. (2006) predict that, for long-period (P ≳ 30 min) and hence low-Ṁ systems, energy radiated from the white dwarf core will heat the surface more than energy from accretion. The surface temperature will then be higher than would be predicted from Ṁ alone. This can be seen in Gaia14aae, where the Ṁ measured above would suggest a black-body white dwarf temperature of 5500 K. The difference between this and our measured temperature of 17 000 K implies, as predicted, that the temperature has decoupled from Ṁ.

8. Mass transfer rate as a function of orbital period

One of the reasons that determining the theoretical space density of AM CVn stars has so many uncertainties, is that although there are three likely formation channels, the relative importance of each channel is not well determined. The formation channels largely differ in the nature of the mass donating star. A white dwarf donor would start mass transfer at short orbital periods, whilst the helium star, or highly evolved CV donor, would initially evolve to short orbital periods before evolving to long periods as the mass donating star becomes fully degenerate (see Solheim 2010 for a detailed overview).

If we were able to accurately determine the mass transfer rate for many sources with a range of orbital period we would make progress in understanding the relative importance of the formation channels since they follow different tracks on the P orb − Ṁ plane. Determining reliable values for Ṁ requires photometric information across a wide range of the spectrum, including the UV, where much of the accretion luminosity is emitted (especially for short period systems, for instance, Ramsay et al. 2005, 2006).

For AM CVn stars which have a parallax accurate to within 20 percent, we converted the multi-band photometric data outlined in the appendix to flux units (Jy) (we also included SDSS J1351 since it has a short orbital period – 15.7 min – and is therefore interesting from an evolutionary point of view). Some systems, such as KL Dra and AM CVn show a large scatter between the multi-filter flux measurements (possibly due to outbursts in the case of KL Dra, and perhaps significant flickering in the case of AM CVn) and were therefore not suited to determining their mass transfer rate by this means. There were 15 systems which had suitable data and we show their spectral energy distributions in Fig. B.1. For the shortest orbital period systems, the energy distribution is generally still increasing at our bluest flux point (GALEX FUV). For long period systems we can locate the wavelength which the flux appears to peak.

To determine the mass transfer rate we sum up the contribution of flux emitted from the white dwarf and accretion disc. Although the cooling models of Bildsten et al. (2006) assume that the primary star has a mass of 0.65 M⊙, the primary in both of the eclipsing systems is M1=0.8 M⊙. We therefore set M1 = 0.8 ± 0.1 M⊙ for the non-eclipsing systems. We calculate the radius of the primary using the formula of Eggleton’s quoted in Verbunt & Rappaport (1988). We also assume that the disc is accreting at a steady state and has a number of annuli (40) which we compute the temperature assuming a black-body. Again apart from Gaia14aae the system inclination is not well determined and therefore we fix cos(i) = 0.5 (apart from Gaia14aae where i = 86.3°). An additional parameter was the radius of the accretion disc, rout. There will be some trade-off between rout and cos(i) which we did not explore in detail.

We use modules readily available in python modules including astropy. To determine the mass transfer rate and its uncertainty we randomly select values for distance, mass and extinction within the assigned errors with the other parameters kept fixed and repeat this 50 times. From these solutions we determine the mean value and standard uncertainty. Although this is a fairly simple approach the mass transfer rate it is robust enough to make general conclusions from the results as a whole. In Table 5 we show the derived mass transfer rates. In Fig. 4 we show the mass transfer rate as a function of orbital period along with two predicted tracks from Bildsten et al. (2006) and we show the fit to the SED’s in Fig. B.1.

Table 5.

Mass transfer rates determined by fitting the SED of each system using a model consisting of a white dwarf plus steady-state accretion disc model.

thumbnail Fig. 4.

Predicted mass accretion rate, Ṁ, of Bildsten et al. (2006) as a function of orbital period, where the accretor is a 0.65 M⊙ white dwarf and the blue track has a cool donor star and the red track a hot donor star. We show the mass transfer rate derived using a white dwarf plus accretion disc model, GDR2 parallax data and multi-wavelength photometric measurements.

In Fig. 4 we can see that some systems appear to lie close to the predicted evolutionary track of a M1=0.65 M⊙-pagination and hot donor star. However, there is a tendency for sources to lie above this track. In two cases, SDSS J1908 and ASASSN-14mv, their mass transfer rate is several orders of magnitude greater than the hot donor track. SDSS J1908 lies above the predicted absolute magnitude for its orbital period by ∼1 mag (Fig. 3), which is consistent with a higher mass transfer rate. On the other hand, ASASSN-14mv has an absolute magnitude consistent with expectations, which seems to be at odds with the high mass transfer rate. For the eclipsing system Gaia14aae, we predict a mass transfer rate of log10 = −10.48, which is within 3σ of the prediction (log10 = −10.74) based on using the absolute magnitude of the bright spot (Sect. 7.2). Despite these caveats, our results show evidence that the mass transfer rate for the majority of systems is higher than predicted from the models – and in some cases perhaps by an order of magnitude or more.

The most obvious reason for this result is that the donor star is larger – with a correspondingly higher mass transfer rate – than predicted. Indeed, recent observational work has shown that the donor star is larger than expected from white dwarfs models and in some cases larger than helium star models (Green et al. 2018a). Moreover, a detailed study of the eclipsing system Gaia14aae (Green et al. 2018c) were able to determine system parameters (M1, M2, R1, R2) to high accuracy. This suggests that this system is likely to have originated via the hydrogen CV evolutionary track. However, no hydrogen is observed in its spectrum as would be expected. These results taken with our findings should provide an impetus to revisiting the formation models.

9. Space density of AM CVn stars

The AM CVn stars are at the very shortest period end of the binary star orbital period distribution and their space density is a sensitive test for binary evolutionary models. Together with the non-interacting double white dwarf binary, their number largely sets the astrophysical background for gravitational wave detectors such as LISA. Nelemans et al. (2001a) found that the space density of AM CVn stars was very uncertain and subject to uncertainties due to selection effects but determined a range of 0.4–1.7×10−4 pc−3 (limits being termed “pessimistic” and “optimistic” respectively).

With the advent of the large scale Sloan Digital Sky Survey (SDSS) it was possible to obtain optical spectra of stars which had colours consistent with the known AM CVn stars and therefore identify new systems in a systematic manner. Based on SDSS data (Roelofs et al. 2007a) found a space density of 1 − 3 × 10−6 pc−3 – more than an order of magnitude lower than the pessimistic model of Nelemans et al. (2001b). Using a significantly expanded SDSS sample, Carter et al. (2013a) derived an observed space density of 5 ± 3 × 10−7 pc−3, a value which is even lower than that of Roelofs et al. (2007a), and is currently the most reliable estimate.

Perhaps the greatest source of uncertainty in predicting the space density lies in the relative importance of the formation channels. As we summarise in Sect. 1, there are three predicted channels – detached double white dwarfs that start mass transfer at very short orbital periods; systems in which a non-degenerate core helium burning star starts mass transfer and binaries in which a white dwarf is accreting from a semi-degenerate star (the hydrogen CV channel). The very low observed space density is compatible with only the double white dwarf contribution to the formation. So either there are many fewer systems coming from the helium star channel (and the CV channel) or we do not sufficiently understand which detached binaries turn into stable mass-transfer systems.

The main challenge in obtaining a space density estimate from the full sample of known AM CVn stars shown in Table 1 is that it contains systems discovered by a variety of different methods and surveys. For example, variability, the presence of emission lines and unusual colours have all been used to detect AM CVn stars. As a result, the sample in Table 1 is neither flux- nor volume-limited, but is instead affected by complex and often poorly understood selection effects. Determining completeness corrections for the entire sample with confidence is therefore impossible.

Nevertheless, the Gaia DR2 distances for the known AM CVn stars do contain crucial information. First, we can test if the sample is complete out to some limiting distance. If so, then a space density estimate can be derived immediately from this volume-limited subsample. Second, even if completeness cannot be established out to any distance, the sample can at least be used to set a firm lower limit on the space density.

Figure 5 shows the results of implementing these ideas. The top panel shows the cumulative distribution of AM CVn stars as a function of distance, compared to the expected distributions for stellar populations associated with the Galactic disc. It is immediately obvious that completeness cannot be established with confidence out to any distance. Based on this data set alone, it is quite possible that there is a significant population of undiscovered AM CVn stars, with systems waiting to be discovered even within ≃100 pc.

thumbnail Fig. 5.

Top panel: observed and predicted cumulative distribution of AM CVn stars as a function of distance. Predicted distributions are shown for Galactic disc models with three different exponential vertical scale heights: 100 pc (green), 300 pc (red) and 500 pc (blue). Given that AM CVn stars are thought to be preferentially old systems, the two larger scale heights are likely to be more appropriate for this population. All models have been normalised to the data at 100 pc. The clear discrepancy between models and data – which increases with distance – points to serious incompleteness in the observational sample. Bottom panel: space density (and 1σ error bands) as a function of distance, as estimated from the number of AM CVn stars and the effective volume contained within this distance. Effective volumes have been calculated for the same three Galactic disc models as shown in the top panel, thus providing three different space density estimates.

The bottom panel of Fig. 5 shows the space density one would estimate from the number of AM CVn stars as a function of distance, d. This is given by N/Veff(d), where N is the number of systems found at distances smaller than d and Veff is the effective volume contained within d in a given Galactic model. Since our sample is likely to be incomplete everywhere, these estimates must be treated as lower limits. The lower limit suggested by our highest space density estimate would be ρ0 > 3 × 10−7 pc−3. However, allowing for the Poisson errors affecting our small sample, our best 2σ limit is substantially weaker, ρ0 >  7 × 10−8 pc−3.

10. Searching for companion stars to the AM CVn stars

We performed a search to identify companions to those AM CVn stars which have a Gaia DR2 parallax determined to better than 20 percent. For each AM CVn star, we obtained the Gaia DR2 data for all sources within 20′, and then searched for stars which had a parallax and proper motion in RA and DEC within 3σ. Two AM CVn stars, KL Dra and SDSS J1525+3600, had nearby stars which fulfilled these criteria: their positions and properties are shown in Table 6.

Table 6.

Results of searching for physically nearby stars to AM CVn stars.

We determined the physical separation between the candidate companion stars and show these in the final column of Table 6. The candidate companion star to KL Dra is 12.4′ distant (=3.5 pc), whilst for SDSSJ1525+3600 they are 8.4′ and 6.1″ (=1.4 pc and 0.06 pc or 1.25 × 105 AU). The more distant candidate companions are too distant to have any effect on the dynamics of the AM CVn binary, although they may have been much closer in the distant past. However, the candidate companion to SDSSJ1525+3600 is only 6.1″ distant providing powerful impetus to obtain a radial velocity measurement to determine whether it is physically associated with the AM CVn binary. If they do show similar velocities then they will be interesting from a binary formation and evolutionary point of view.

11. Conclusions

For the first time we have reliable distances to more than a few AM CVn stars. Using these distances we determine the expected cumulative distribution of AM CVn stars and compare it with the distribution of a Galactic disc population. We find that there is likely to be a significant number of AM CVn stars awaiting to be discovered. Since we find that the location of AM CVn stars are in a distinctive region of the HR diagram (Fig. 2) the Gaia DR2 dataset will be a useful tool for identifying candidate systems based on their colour and absolute magnitude.

One of the great uncertainties in predicting the space density of AM CVn stars has been in determining the relative importance of the three formation channels. There is now mounting evidence that the majority donor stars in AM CVn stars are not fully degenerate. We were able to determine the mass transfer rate in 15 AM CVn stars and find that most have rates which are greater than predicted by standard tracks. The donors appear to be larger than expected.

We also find that none of the AM CVn stars which have proper motion and parallax data are likely to be halo objects. Those objects which have very low heavy element abundances are therefore not likely to be due to their age. Coupled with the findings that the parameters of the eclipsing AM CVn star, Gaia14aae, does not readily fit with the models should serve as impetus to revisit these models and the nature of the donor star in particular.

Acknowledgments

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. We extracted GALEX data from Multi-Mission archive at the Space Telescope Science Institute (MAST). The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Centre for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation. The national facility capability for SkyMapper has been funded through ARC LIEF grant LE130100104 from the Australian Research Council, awarded to the University of Sydney, the Australian National University, Swinburne University of Technology, the University of Queensland, the University of Western Australia, the University of Melbourne, Curtin University of Technology, Monash University and the Australian Astronomical Observatory. SkyMapper is owned and operated by The Australian National University’s Research School of Astronomy and Astrophysics. The survey data were processed and provided by the SkyMapper Team at ANU. The SkyMapper node of the All-Sky Virtual Observatory (ASVO) is hosted at the National Computational Infrastructure (NCI). Development and support the SkyMapper node of the ASVO has been funded in part by Astronomy Australia Limited (AAL) and the Australian Government through the Commonwealth’s Education Investment Fund (EIF) and National Collaborative Research Infrastructure Strategy (NCRIS), particularly the National eResearch Collaboration Tools and Resources (NeCTAR) and the Australian National Data Service Projects (ANDS). This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration 2018). Armagh Observatory and Planetarium is core funded by the Northern Ireland Executive through the Dept for Communities. MJG acknowledges funding from an STFC studentship via grant number ST/N504506/1. A.A. acknowledges the support of the National Research Council of Thailand (grant number R2561B087).

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Appendix A: Photometry of AM CVn stars: online table

We provide an online table in fits format1 which includes data on all of the known AM CVn stars. The columns and caveats are described below.

A.1. Target names and coordinates

In the main body of the paper (e.g. Table 1), we use IAU Variable Star names or shortened survey IDs for each of the targets. The online table includes these IDs (Col. 1), as well as alternative names by which each target is known (Col. 2).

We give the J2015.5 coordinates from Gaia where available (Cols. 5, 6), as well as ICRS J2000.0 coordinates for all sources (Cols. 3, 4). The J2000.0 coordinates were derived from the Gaia 5-parameter astrometry where available, otherwise the table shows the most precise coordinates available for that target. We also computed the IAU 1958 Galactic latitude and longitude for each target. These are given in Cols. 7 and 8.

The Gaia DR2 source ID is shown in Col. 9.

A.2. Orbital period and brightness range

Columns 10 and 11 show the period of the binary in days and minutes respectively, with a flag/comment in Col. 12 to indicate whether the period is the orbital period (“orb”, most reliably measured from time series spectroscopy), the superhump period (“sh”, resulting from disc precession during the outburst and typically a few per cent longer than the orbital period), estimated from the outburst recurrence time (“est rec”, Levitan et al. 2015) or whether no period has been measured for the system so far (“unknown”). References for the discovery and the period measurements are indexed in Col. 15, corresponding to the following references:

[1] Ramsay et al. 2002a, [2] Ramsay et al. 2002b, [3] Espaillat et al. 2005, [4] Nelemans et al. 2001b, [5] Fontaine 2011, [6] Kupfer et al. 2015, [7] O’Donoghue et al. 1994, [8] Levitan et al. 2014, [9] Wevers et al. 2016, [10] Kato et al. 2015, [11] Wood et al. 1987, [12] Wood et al. 2002, [13] Kato et al. 2004, [14] Levitan et al. 2015, [15] Levitan et al. 2011, [16] ASASSN http://www.astronomy.ohio-state.edu/~assassin/transients.html, [17] AAVSO https://www.aavso.org, [18] Copperwheat et al. 2011, [19] Abbott et al. 1992, [20] Levitan et al. 2013, [21] Thorstensen & Skinner 2012, [22] Motsoaledi 2015, [23] Wood-Vasey et al. 2003, [24a] Carter et al. 2014a, [24b] Carter et al. 2014b, [25] Woudt et al. 2005, [26] Shears et al. 2012, [27] Roelofs et al. 2005, [28] Roelofs et al. 2009, [29] Anderson et al. 2005, [30] Ramsay et al. 2012, [31] Rau et al. 2010, [32] Nather et al. 1981, [33] Prieto et al. 2014, [34] Woudt et al. 2013, [35] Kato et al. 2014, [36] Campbell et al. 2015, [37] Marsh et al. 2017, [38] Anderson et al. 2008, [39] Kupfer et al. 2013, [40] Kepler et al. 2015, [41] Wagner et al. 2014, [42] Ruiz et al. 2001, [43] Green et al. 2018c, [44] Kato, vsnet-alert 18124, [45] Aungwerojwit et al. (in prep.), [46] Breedt et al. (in prep.), [47] Kupfer et al. (in prep.), [48] Maehara & Kojima, vsnet-alert 22174, [49] Green et al. 2018b, [50] Kong et al. 2018.

The Y/N flag in Col. 13 indicates whether the system has been observed in outburst, and the magnitude range (with filter information) is given in Col. 14.

A.3. Parallax, reddening and derived quantities

The calculation of the following quantities were discussed in detail in the main text:

Columns 16–17: parallax and error (mas), taken from Gaia DR2.

Columns 18–19: distance and error (pc) — calculated from an exponentially decreasing space density prior with L = 400 pc. See Sect. 3.

Columns 20–21: extinction and reddening parameters E(B − V) and Ag towards each system (mag), derived from the Pan-STARRS1 distance reddening maps (Green et al. 2018a) as discussed in Sect. 5. ASASSN-14cc, ASASSN-14ei, NSV1440 and Gaia16all have parallax measurements from Gaia, but are not in the Pan-STARRS1 footprint. For these four stars we show the maximum reddening from Schlafly & Finkbeiner (2011). A note has been added in Col. 66 of the table.

Column 22: g band quiescent magnitude taken from Pan-STARRS, used to calculated the absolute magnitude.

Columns 23–24: absolute magnitude Mg and its associated error (mag).

A.4. GALEX

Although Swift and XMM-Newton has been used to observe some AM CVn stars, GALEX provided the opportunity to take an unbiased snapshot survey of their near UV flux. GALEX was launched in April 2003 and had a lifetime of ten years and performed observations at UV wavelengths (Martin 2005). It had a primary mirror 50 cm in diameter and had a field of view of 1.25°. It had two UV channels, the Near UV (NUV, central wavelength 2271Å) and the Far UV (FUV, 1528 Å), the latter failing after 6 years. Whilst it could perform relatively short pointed observations, it also carried out a wide field survey and by its end it had sampled 3/4 of the sky in one UV band (Bianchi 2014). 41 of the known AM CVn stars are included in the catalogue of Bianchi (2014). We show the FUV and NUV fluxes in units of mJy in Cols. 25–26 (FUV) and Cols. 27–28 (NUV) of the online table.

A.5. SDSS

The Sloan Digital Sky Survey (SDSS) uses a 2.5m telescope at Apache Point Observatory in New Mexico, and has a field of view three degrees across (York 2000). Its Data Release 7 includes a photometric catalogue of northern-hemisphere targets (Abazajian et al. 2009).

We performed a cross-match of known AM CVn J2000.0 positions with all SDSS photometric objects, using a search radius of 2 arcsec. We identified 34 AM CVns which have SDSS photometry. All but two of these magnitudes are consistent with the faint end of the range shown in Table 1. The two outliers are SDSS J0804+1616, which is brighter by approximately 0.7 mag (perhaps consistent with the large-scale variability this system shows even in quiescence; Roelofs et al. 2009) and PU Aqr=SDSS J2047+0008, which is brighter by approximately 1.8 mag and may have been in outburst or in decline from outburst when the SDSS data were collected.

The SDSS ugriz magnitudes and their errors are shown in columns 29–38 of the online table.

A.6. Pan-STARRS1

Pan-STARRS1 is a 1.8m telescope with a field of view of seven square degrees, located on Halakala Observatory in Hawaii. There are five broad-band filters which are close to, but not exactly, the SDSS filters grizy (Chambers et al. 2016; Tonry 2012). It is performing an all-sky survey with declinations > −30°.

We performed a cross-match with Pan-STARRS1 DR1 using a 2 arcsec match radius to account for uncertainty in the recorded positions of the AM CVn stars. The mean AB PSF grizy magnitudes are shown in columns 39–48 of the online table for all systems which were found to have a match.

For those AM CVn stars which do not show outbursts the mean g mag is consistent with the values shown in Table 1. For those systems which do show outburst, Pan-STARRS1 has a mean magnitude which is consistent with the source being in quiescent apart from three systems: CR Boo where g is more consistent with it being in quiescent and the other filters in outburst; SDSS J0804+1616 has range in magnitude in Table 1 between 17.8–19.0 and the mean Pan-STARRS1 mag appears in the middle of this range and CRTS J0744+3254 which has a Pan-STARRS1 g mag much fainter than r. The Pan-STARRS1 DR1 gives a mean magnitude of the source over the pointings covered. However, it also gives a range in magnitudes for the different filters. For the three sources which show evidence for being in different accretion states, we show in Table A.1 the range in these filters’ measurements.

Table A.1.

PanSTARRS1 measurements of these three AM CVn stars appears to have been taken in different accretion states in the different bands.

A.7. Skymapper

Skymapper is a telescope with a 1.35m primary mirror located Siding Spring Observatory, Australia, and has a camera which covers 2.4 × 2.3 degrees of the sky (Scalzo 2017). Its primary goal is to obtain a map of the southern sky in a number of filters, with periods of poor conditions being focussed on detecting transients. There are six filters, with the bluest u, v, being narrow band filters (FWHM = 42 and 28 nm respectively) which cover the SDSS u band. The filters griz differ compared to their SDSS equivalents by 40 nm in effective wavelength and width (Bessell et al. 2011).

We performed a 2 arcsec radius cross-match with the Skymapper DR1.1 release and find that six AM CVn stars have at least one detection in one filter. We show the magnitudes in the uvgrzi filters on the AB mag scale in columns 49–60 of the online table.

A.8. Kinematics

Columns 61–64 list the proper motions in RA and Dec (mas) from Gaia DR2. The population membership (thick/thin disc of the Galaxy), as computed in Sect. 4, is shown in Col. 65. For convenience, these data are also shown in Table B.1.

The final column in the online table, 66, is a text field for specific notes about the data for that target.

Appendix B: SEDs and kinematic data

thumbnail Fig. B.1.

Spectral energy distribution of AM CVn stars which have a parallax accurate to within 20 percent and have multi-colour survey data in more than two filter passbands. In the solid line we show the model spectral energy distribution where M1, EB−V and distance are restricted to the values shown in each panel and the mass transfer rate, Ṁ, is a free parameter.

thumbnail Fig. B.1.

continued.

Table B.1.

Kinematic information for the AM CVn stars with measured proper motions in Gaia DR2.

All Tables

Table 1.

Currently known AM CVn stars ordered by increasing period, either the orbital period (most reliably determined from spectroscopic observations) or the superhump period (sh) which is typically within a few percent longer than the orbital period.

In the text
Table 2.

Gaia DR2 and HST parallaxes of the five AM CVn stars which were measured using the HST Fine Guidance Sensor.

In the text
Table 3.

Reddening in the g band (Ag), which have been determined using Pan-STARRS1 data (Green et al. 2018a).

In the text
Table 4.

Absolute magnitudes of the central white dwarfs and bright spots in two eclipsing systems: YZ LMi and Gaia14aae.

In the text
Table 5.

Mass transfer rates determined by fitting the SED of each system using a model consisting of a white dwarf plus steady-state accretion disc model.

In the text
Table 6.

Results of searching for physically nearby stars to AM CVn stars.

In the text
Table A.1.

PanSTARRS1 measurements of these three AM CVn stars appears to have been taken in different accretion states in the different bands.

In the text
Table B.1.

Kinematic information for the AM CVn stars with measured proper motions in Gaia DR2.

In the text

All Figures

thumbnail Fig. 1.

AM CVn stars in the plane of the velocity in the direction of Galactic rotation (Vϕ) and the Galactic centre(Vρ) (left hand panel) and the orbital eccentricity (e) and the angular momentum in the Galactic z direction(Jz) (right hand panel). The solid and dotted ellipses render the 3σ thin and thick disc contours in the Vϕ–Vρ diagram, while the solid box in the e–Jz marks the thick disc region as specified by Pauli et al. (2006).
In the text
thumbnail Fig. 2.

An HR diagram made using Gaia DR2 data. In red we show the absolute G magnitude, MG, as a function of the blue-red colour, BP-RP, for AM CVns with known parallaxes. No reddening or extinction corrections have been applied to this figure. For comparison, in grey points we show a sample of essentially randomly selected main sequence stars which have a parallax better than 1 percent. For single white dwarfs shown as slightly larger grey points) we have used the sample of white dwarfs within 20 pc (Hollands et al. 2018). The majority of AM CVns appear to be brighter than the single white dwarf track, though some long-period systems lie on the track. A clear outlier is V407 Vul, which has BP-RP ≈ 1.5 through a combination of severe reddening and contamination from an unresolved nearby G-star.
In the text
thumbnail Fig. 3.

Extinction-corrected absolute magnitudes (Mg) of AM CVn binaries as a function of orbital period. For known outbursting systems, we plot the quiescent magnitude, and show the magnitude change during outburst as a dotted line. The dashed line is the predicted MV of the accretion disc as originally taken from Nelemans et al. (2004) while the solid line shows the evolution of a 0.65M⊙ accreting white dwarf with a high-entropy white dwarf donor, including accretion heating, from Bildsten et al. (2006). Most systems appear somewhat brighter than an isolated white dwarf model during quiescence, and close to the duty-cycle-scaled disc magnitude during outburst.
In the text
thumbnail Fig. 4.

Predicted mass accretion rate, Ṁ, of Bildsten et al. (2006) as a function of orbital period, where the accretor is a 0.65 M⊙ white dwarf and the blue track has a cool donor star and the red track a hot donor star. We show the mass transfer rate derived using a white dwarf plus accretion disc model, GDR2 parallax data and multi-wavelength photometric measurements.
In the text
thumbnail Fig. 5.

Top panel: observed and predicted cumulative distribution of AM CVn stars as a function of distance. Predicted distributions are shown for Galactic disc models with three different exponential vertical scale heights: 100 pc (green), 300 pc (red) and 500 pc (blue). Given that AM CVn stars are thought to be preferentially old systems, the two larger scale heights are likely to be more appropriate for this population. All models have been normalised to the data at 100 pc. The clear discrepancy between models and data – which increases with distance – points to serious incompleteness in the observational sample. Bottom panel: space density (and 1σ error bands) as a function of distance, as estimated from the number of AM CVn stars and the effective volume contained within this distance. Effective volumes have been calculated for the same three Galactic disc models as shown in the top panel, thus providing three different space density estimates.
In the text
thumbnail Fig. B.1.

Spectral energy distribution of AM CVn stars which have a parallax accurate to within 20 percent and have multi-colour survey data in more than two filter passbands. In the solid line we show the model spectral energy distribution where M1, EB−V and distance are restricted to the values shown in each panel and the mass transfer rate, Ṁ, is a free parameter.
In the text
thumbnail Fig. B.1.

continued.
In the text

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