Coplanar circumbinary debris discs

Abstract

We present resolved Herschel images of circumbinary debris discs in the α CrB (HD 139006) and β Tri (HD13161) systems. By modelling their structure, we find that both discs are consistent with being aligned with the binary orbital planes. Though secular perturbations from the binary can bring the disc into alignment, in both cases the alignment time at the distances at which the disc is resolved is greater than the stellar age, so we conclude that the coplanarity was primordial. Neither disc can be modelled as a narrow ring, requiring extended radial distributions. To satisfy both the Herschel and mid-infrared images of the α CrB disc, we construct a model that extends from 1 to 300 au, whose radial profile is broadly consistent with a picture where planetesimal collisions are excited by secular perturbations from the binary. However, this model is also consistent with stirring by other mechanisms, such as the formation of Pluto-sized objects. The β Tri disc is modelled as a disc that extends from 50 to 400 au. A model with depleted (rather than empty) inner regions also reproduces the observations and is consistent with binary and other stirring mechanisms. As part of the modelling process, we find that the Herschel PACS (Photodetector and Array Camera & Spectrometer) beam varies by as much as 10 per cent at 70 μm and a few per cent at 100 μm. The 70 μm variation can therefore hinder image interpretation, particularly for poorly resolved objects. The number of systems in which circumbinary debris disc orientations have been compared with the binary plane is now 4. More systems are needed, but a picture in which discs around very close binaries (α CrB, β Tri and HD 98800, with periods of a few weeks to a year) are aligned, and discs around wider binaries (99 Her, with a period of 50 yr) are misaligned, may be emerging. This picture is qualitatively consistent with the expectation that the protoplanetary discs from which the debris emerged are more likely to be aligned if their binaries have shorter periods.

binaries: general, circumstellar matter, stars: formation, stars: individual: β Trianguli, stars: individual: α Coronae Borealis, stars: individual: 99 Herculis, HD 98800

1 Introduction

The Herschel key programme DEBRIS (Dust Emission via a Bias free Reconnaissance in the Infrared/Submillimetre) has observed a large sample of nearby stars to discover and characterize extrasolar analogues to the Solar system's asteroid and Edgeworth–Kuiper belts, collectively known as ‘debris discs’. The 3.5 m Herschel mirror diameter provides 6–7 arcsec resolution at 70–100 μm (Pilbratt et al. 2010), and as a consequence our survey has resolved many discs around stars in the Solar neighbourhood for the first time (Matthews et al. 2010; Churcher et al. 2011; Kennedy et al. 2012; Wyatt et al. 2012).¹

Here we present resolved images of circumbinary discs in the α CrB and β Tri systems. These systems are interesting because unlike most debris disc+binary systems, the binary orbits are well characterized. The combination of a known orbit and a resolved disc means we can compare their relative inclination.

Our observations of a disc around the binary 99 Her (Kennedy et al. 2012) were a step towards building on the binary debris disc study of Trilling et al. (2007). Their Spitzer study found that debris discs are generally as common in binary systems as in single systems, but are less likely to reside in systems with binary separations in the 3–30 au range (see also Rodriguez & Zuckerman 2012). However, only some of their systems had detections at multiple wavelengths to constrain the disc location and none were reported as resolved, making the true dust location uncertain. Even in the case of dust detection at multiple wavelengths, the true dust location is unknown because grains of different compositions and sizes can have the same temperature at different stellocentric distances. In addition to uncertainty in the dust location, only the projected sky separation of the binary (not the binary semi-major axis) was generally known, adding further uncertainty.

Systems with resolved discs and well-characterized binary orbits, such as 99 Her, α CrB, β Tri and HD 98800 (Andrews et al. 2010) remove these ambiguities. The dust location and structure can be inferred within the context of the binary orbit, leading to robust conclusions about whether the dust resides on stable orbits. One can also consider whether perturbations from the binary play an important role in setting the dust dynamics. For example, in the 99 Her system the disc position angle (PA) appears misaligned with the binary line of nodes. This misalignment is best explained with particles on polar orbits because these are stable for the stellar lifetime (Kennedy et al. 2012). Another question is whether binary perturbations can ‘stir’ the disc particles by increasing their inclinations and eccentricities, eventually resulting in high enough relative velocities that collisions are destructive. This process is analogous to the planet stirring model proposed by Mustill & Wyatt (2009), though may rely on vertical (inclination) stirring because companions of comparable mass induce lower forced eccentricities than companions that are much less massive than the star (Moriwaki & Nakagawa 2004; Kennedy et al. 2012).

An additional link can be made to star and planet formation. Young binary systems with small to medium (≲100 au) separations are thought to form coplanar with their protoplanetary discs, because the disc torque aligns the binary orbit on time-scales short relative to the disc lifetime (e.g. Bate et al. 2007). Testing this prediction is difficult because it is difficult to ascertain disc and binary orientations at the distances of the nearest star-forming regions (e.g. Monin et al. 2007). Because debris discs around older main-sequence binaries should retain the same orientation as the protoplanetary discs from which they emerged, these discs yield information on the outcome of star formation. The advantage is that compared to star-forming regions, these systems are much closer to Earth and hence larger on the sky and brighter, making disc and binary characterization much easier.

Though planet formation may be hindered to some degree by high collision velocities induced by binary perturbations (e.g. Moriwaki & Nakagawa 2004; Scholl, Marzari & Thébault 2007), the discovery of several circumbinary planets shows that planets do indeed form around binary stars (e.g. Doyle et al. 2011; Welsh et al. 2012). Few such systems are known because binaries are generally avoided by radial velocity surveys (see Konacki 2005; Konacki et al. 2009). However, the very existence of circumbinary debris discs provides evidence that planet formation around binaries can proceed to form at least 10–100 km sized objects, which must exist to feed the observed dust through collisions (e.g. Wyatt 2009; Krivov 2010). Further, circumbinary discs are relatively common (Trilling et al. 2007), suggesting that circumbinary planets may be no less unusual than their circumstellar equivalents.

This paper is laid out as follows. We first consider the stellar and orbital properties, along with previous infrared (IR) observations of the α CrB and β Tri systems (Section 2). We then show the Herschel data (Section 3) and simple models (Section 4), and then interpret these within the context of the expected dynamics (5). We discuss the results and conclude in Sections 6 and 7.

2 The binary systems

2.1 Coronae Borealis

Among the ‘alpha’ stars, α CrB (HD 139006, HIP 76267) is the only known eclipsing binary (Stebbins 1914; Tomkin & Popper 1986). Though some properties of this binary have been known for over a century (e.g. Jordan 1910), only recently has the orientation of the orbit on the sky been constrained by the Hipparcos mission (which also provides a system distance of 23 pc; Perryman 1997; van Leeuwen 2007). The orbital elements are given in Table 1. The primary is an A0 dwarf, orbited by a G5 secondary (Tomkin & Popper 1986). The age of the system is about 350 Myr (Song et al. 2001; Rieke et al. 2005; Vican 2012).

Table 1.

α CrB system properties and 1σ uncertainties (Tomkin & Popper 1986; Perryman 1997). The ascending node Ω is measured anti-clockwise from North. The longitude of pericentre is measured anti-clockwise from the ascending node. The semi-major axis is calculated from the period, masses and system distance. The luminosities are derived from our spectral energy distribution (SED) fitting to the AB pair (Sections 4.1), with the individual values found by scaling the Tomkin & Popper (1986) values of 74 and 0.8 L_⊙. They derive a slightly greater system distance (26 pc), which accounts for their larger luminosities. The uncertainty in L_A is set by the SED fitting, and for L_B we use the 25 per cent uncertainty from Tomkin & Popper (1986) to account for the uncertainty in the flux ratio

This system was discovered to have an IR excess with IRAS (Aumann 1985), and the disc has subsequently been detected with the Spitzer MIPS² and IRS³ instruments (Rieke et al. 2005; Chen et al. 2006; Su et al. 2006). The proximity and brightness mean that this system has also been the target of high resolution mid-IR imaging campaigns, with resolution of the disc at 11 μm (Moerchen, Telesco & Packham 2010). They may have resolved the disc at 18 μm, but ambiguity arising from artefacts of the observing procedure meant that the results at this wavelength were unclear. The PA of the extension in the 11 μm and first 18 μm images is roughly 350°, so consistent with the (rather uncertain) binary line of nodes. The images also suggest that the disc is edge on, so the inner part of the disc appears to be aligned with the binary orbital plane.

2.2 Trianguli

The β Tri (HD 13161, HIP 10064) system was first recognized as a double-lined spectroscopic binary over a century ago (Mitchell 1909). The orbital period was then found to be 37 d, based on 12 radial velocity measurements. Further study has refined the orbit (Struve & Pogo 1928; Ebbighausen 1960) and modern instruments have since resolved the pair allowing a visual orbit to be derived (Hummel et al. 1995). The orbit is now well characterized,⁴ with the orbital elements given in Table 2. The primary star has an A5IV spectral type (Gray et al. 2003), and as class IV indicates has probably reached the end of the main sequence. The spectral type of the secondary is not known, but the mass suggests a mid-F-type. There remain uncertainties in this system; as discussed by Hummel et al. (1995), the A5 spectral type is at odds with the 3.5 M_⊙ mass, and the mass ratio is inconsistent with the luminosity ratio. The system is simply classed as ‘Old’ by Trilling et al. (2007); Vican (2012) derived an isochrone age of 730 Myr, though this figure is systematically uncertain both due to a relatively small luminosity ratio (so the age may be overestimated) and because β Tri lies outside the range encompassed by some isochrone models. The exact age is not particularly important for our purposes here, so we assume it is 730 Myr.

Table 2.

β Tri system properties and 1σ uncertainties (Pourbaix 2000). The ascending node Ω is measured anti-clockwise from North. The longitude of pericentre is measured anti-clockwise from the ascending node. The total binary luminosity is derived from the SED in Sections 4.1.

Like α CrB, this system was first discovered to have an IR excess with IRAS (Sadakane & Nishida 1986). It was observed with Spitzer MIPS as part of a sample of main-sequence binaries (Trilling et al. 2007), and also observed with IRS in the two longer wavelength modules (14–38 μm).

3 Observations

3.1 Herschel

Herschel Photodetector and Array Camera & Spectrometer (PACS; Poglitsch et al. 2010) data were taken for both α CrB and β Tri at 100 and 160 μm during routine DEBRIS observations (Table 3). Subsequently, a Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010) observation of β Tri was triggered by the large PACS excess indicating a likely sub-mm detection. For both targets, we also obtained 70 μm PACS images to better resolve the discs. Because every PACS observation includes the 160 μm band, we have two images at this wavelength for each target. All observations were taken in the standard scan-map modes for our survey: mini-scan-maps for PACS data and small maps for SPIRE. Data were reduced using a near-standard pipeline with the Herschel Interactive Processing Environment (hipe, Version 7.0; Ott 2010). We decrease the noise slightly by including some ‘turn-around’ data taken as the telescope is accelerating and decelerating at the start and end of each scan leg.

Fig. 1 shows the Herschel PACS images of α CrB. The disc is not obviously resolved, so the inset shows the residuals from a point spread function (PSF) fit to the 100 μm data (an observation of Herschel calibrator γ Dra generated using the same data reduction method was used as a PSF; see below). The residual emission in the inset is symmetric about the stellar position along a PA of about 350°, showing that the disc is most likely resolved with a near edge-on geometry. The emission extends to around 10 arcsec (∼230 au from either side of the stellar position), suggesting a disc diameter of several hundred au. The disc does not appear to be resolved along the minor axis, so is consistent with the disc being edge on and aligned with the (eclipsing) binary plane. A PSF fit to the 70 μm image shows similar results, while the 160 μm image is unresolved.

Table 3.

Herschel observations of α CrB and β Tri

Figure1.

Resolved PACS images of α CrB at 70 (left) and 100 μm (right). North is up and East is left, and the arrow shows the spacecraft ‘Z’ direction. The colour scale is in mJy arcsec⁻². The overlaid contours show the corresponding 160 μm images in five linear steps from 5 to 13σ. Similar contours correspond to 30–200σ for the 70 μm image, and 10–75σ for the 100 μm image. The hatched circles show the average PACS beam FWHM of 5.75 arcsec (70 μm) and 6.87 arcsec (100 μm; see the text). The inset (25 × 25 arcsec) shows residuals of the 100 μm α CrB image after PSF fitting, and the lobes show that the disc is clearly resolved.

Because the α CrB disc is not well resolved, it is possible that this extension is affected by variation in the PACS PSF (or beam). Further, a key difference between our method and that used for beam characterization by the PACS team is that because they are much fainter than the calibration stars our data cannot be re-centred on a frame-by-frame basis, resulting in a slightly larger beam size. Thus, comparison of the Gaussian size in our images with those reported by the PACS team could lead to the conclusion that the disc is slightly more extended than it really is. To characterize the beam variation, we have obtained two observations each of the five PACS calibration stars at both 70 and 100 μm. These observations were nearly all taken using the same mini-scan-map mode used by DEBRIS. These data are reduced in the same way as all DEBRIS data, so allow a realistic comparison. The expectation is that each calibration PSF will be slightly different, with the differences across all 10 being representative of the uncertainty in the PSF specific to a given science observation.

The 70 μm calibration observations are shown in Fig. 2, where each image shows the residuals when the average of all 10 observations is subtracted (after the peak is scaled to the same as the observation). All images have been rotated so that spacecraft ‘Z’ is up (spacecraft ‘Y’ is to the right). Each panel shows the observation number (ObsID), star name, and Gaussian major and minor full width at half-maximum (FWHM). The ellipse shows the Gaussian FWHM and the line shows the major axis orientation. Because the expectation is that each observation is independent, the panels are ordered chronologically (i.e. by ObsID). It is clear that the beam width varies at about the 10 per cent level along the minor axis, between 5.28 arcsec for α Boo and 5.79 arcsec for α Cet. The variation along the major axis is much smaller at about 2 per cent. The beam variation appears to be systematically different for two stars; both the α Boo and α Tau images show similarly small minor FWHM despite being observed about 6 months apart. This variation cannot be attributed to the circumstellar material because none of the calibration stars have IR excesses. It may be difficult to confirm this possible systematic effect, for example, as a function of Solar elongation or declination, as there are only five PACS calibration stars.

Figure 2.

PACS 70 μm beam comparison. Each panel shows the beam after the average beam has been subtracted, with labels noting ObsID, star name and Gaussian major and minor FWHM. The ellipse shows the FWHM, with the line along the major axis. The colour scale shows the fractional difference (in per cent) relative to the peak. In these images, the spacecraft ‘Z’ direction is up and ‘Y’ is to the right, and the two scan directions that make a mini-scan-map are ±20° from horizontal.

The major and minor FWHM of the average 70 μm PACS beam are 5.91 and 5.59 arcsec, so similar to, but slightly larger than, the values of 5.76 and 5.46 arcsec found by the PACS team (for a scan speed of 20 arcsec s⁻¹).⁵ Based on the variation seen in Fig. 2, the uncertainties on these values are about 0.05 arcsec in the major axis (approximately along the spacecraft ‘Y’ direction) and 0.2 arcsec in the minor axis (approximately along the spacecraft ‘Z’ direction).

A similar analysis for the 100 μm beam is shown in Fig. 3. The panels are again in chronological order, so the order of the stars is not the same as at 70 μm. The variation is smaller at this wavelength (2–4 per cent), but some systematic difference for α Tau and α Boo is still seen. The average major and minor beam FWHM are 6.95 and 6.78 arcsec (compared to 6.89 and 6.69 arcsec found by the PACS team), with uncertainties of about 0.1 arcsec in both axes. The lower left-hand panel (α Cet, ObsID:1342203033) shows rather different residuals compared to all others, arising because the observation comprises only one scan direction. This difference shows that aside from variation, the beam is also a function of the observing strategy, and that the strategy should be the same when using calibration stars to analyse science data (e.g. for PSF fitting and image modelling).

Figure 3.

PACS 100 μm beam comparison. The layout is as described in Fig. 2

Having quantified the beam characteristics specific to our data, we now compare them to the α CrB observations. A Gaussian fit to the star-subtracted 70 μm image finds a PA of 348° ± 3°, which is consistent with the ascending node of 330 ± 20° for the binary. The major and minor FWHM are 7.3 ± 0.1 arcsec and 6.1 ± 0.1 arcsec. Fig. 2 shows that the major axis of the beam is typically perpendicular to the spacecraft Z axis, so the disc PA is between the major and minor axes, where the beam has a FWHM of about 5.75 ± 0.1 arcsec. Therefore, the disc is clearly resolved along the direction of the PA, but at only about 2σ significance in the perpendicular direction. Simple deconvolution suggests a disc diameter of about 100 au. This size is much smaller than suggested by the residuals in the inset in Fig. 1, indicating that the bulk of the emission is poorly resolved. This structure is perhaps consistent with the mid-IR imaging if α CrB hosts warm and cold components that both contribute to the Herschel fluxes but only the cold component is resolved with Herschel. Though the minor Gaussian FWHM is slightly larger than expected, variation in the 70 μm beam means that the disc is consistent with being edge-on, and therefore aligned with the (eclipsing) binary orbital plane. This analysis also shows that the outer component resolved by Herschel is consistent with being aligned with the inner component resolved in the mid-IR (Moerchen et al. 2010). At 100 μm, the major and minor FWHM are 8.2 ± 0.16 arcsec and 6.9 ± 0.13 arcsec, yielding a size of about 100 au and a PA of 347 ± 4°. Therefore, at this wavelength, the disc is resolved along the disc PA, but not in the perpendicular direction, so is again consistent with being edge-on, and aligned with the binary plane. We return to the issue of beam variation when creating resolved models of the α CrB disc in Section 4.2.

The β Tri images are shown in Fig. 4. Compared to the beam size, the disc around β Tri is clearly resolved at 70 and 100 μm. The disc is also resolved at 160 μm, but not at the SPIRE wavelengths of 250–500 μm. A Gaussian fit to the star-subtracted image at 70 μm finds major and minor FWHM of 9.1 ± 0.13 arcsec and 7.5 ± 0.1 arcsec at a PA of 66 ± 3°. Simple Gaussian deconvolution suggest a disc size of about 270 au, and an inclination of about 46 ± 3°. At 100 μm the FWHM are 10.4 ± 0.13 arcsec and 8.6 ± 0.1 arcsec at a PA of 68 ± 3°, suggesting a size of about 300 au and inclination of 48 ± 3°. At 160 μm the FWHM are 14.4 ± 0.12 arcsec and 12.3 ± 0.1 arcsec at a PA of 68 ± 2° (the 160 μm beam is elongated and is about 10.7 arcsec by 12.1 arcsec). The 160 μm image is therefore poorly resolved, but suggests an approximate size of 300–370 au. Taken together, these angles mean that in this system the disc is again consistent with being aligned with the binary plane. The increasing disc size with wavelength suggests that the disc may be extended.

Figure 4.

Resolved PACS images of β Tri at 70 (left) and 100 μm (right). North is up and East is left. The colour scale is in mJy arcsec². The overlaid contours show the corresponding 160 μm images in five linear steps from 5σ to 30σ. Similar contours correspond to 5–75σ for the 70 μm image, and 5–70σ for the 100 μm image. The hatched circles show the average PACS beam FWHM of 5.75 and 6.87 arcsec (see the text). The inset (25 × 25 arcsec) shows residuals of the 100 μm β Tri image after PSF fitting, and the elliptic residual emission shows that the disc is probably resolved.

The flux density in the PACS images for both α CrB and β Tri is measured using apertures and the SPIRE fluxes with PSF fitting. The measurements are given in Table 4. The uncertainties include both statistical and systematic uncertainties due to repeatability and calibration (see Kennedy et al. 2012, for further comments on calibration).

Table 4.

Herschel photometry and 1σ uncertainties of α CrB and β Tri. The 160 μm measurements from each observation are given separately

3.2 Spitzer

As noted above, both systems were observed by Spitzer with the MIPS and IRS instruments. The MIPS photometry is taken from Phillips (2011), and the IRS spectra retrieved from the Cornell Atlas of Spitzer/Infrared Spectrograph Sources (CASSIS; Lebouteiller et al. 2011). The PACS and MIPS 70 μm measurements are consistent (460 ± 47 mJy for α CrB and 677 ± 62 mJy for β Tri). Though we instead use the PACS images, β Tri is clearly resolved at 70 μm with Spitzer.

4 Models

4.1 Spectral energy distributions

We first model the stellar and disc photometry to derive approximate disc temperatures and fractional luminosities. This photometry is collected from numerous catalogues (Morel & Magnenat 1978; Moshir et al. 1993; Hauck & Mermilliod 1997; Perryman 1997; Høg et al. 2000; Mermilliod 2006; Skrutskie et al. 2006; Ishihara et al. 2010; Phillips 2011; Lebouteiller et al. 2011). Photometry and colours at wavelengths up to 9 μm are used to model the stellar photosphere, using the phoenix Gaia grid (Brott & Hauschildt 2005). The best-fitting model is found by least-squares minimization. At wavelengths longer than 9 μm we model the excess emission above the photosphere with a simple modified blackbody function; at wavelengths beyond λ₀ the blackbody is multiplied by (λ/λ₀)^−β.

The SEDs are shown in Fig. 5. The best-fitting stellar model for α CrB has T_eff = 9280 ± 100 K, R_⋆ = 3.06 ± 0.03 R_⊙ and L_⋆ = 60 ± 1 L_⊙, and for β Tri has T_eff = 8000 ± 100 K, R_⋆ = 4.6 ± 0.05 R_⊙ and L_⋆ = 74 ± 2 L_⊙. Because no photometry resolves either binary, these parameters simply describe what the total stellar emission spectra look like and are not physical. The α CrB disc model has temperature T_disc = 124 K, fractional luminosity ƒ = 1.7 × 10⁻⁵, corresponding to a total grain surface area σ_tot = 0.34 au² for blackbody grains, and m and β = 1.6. The β Tri model has temperature T_disc = 84 K, ƒ = 3.0 × 10⁻⁵, total grain surface area σ_tot = 3.3 au² for blackbody grains and m and β = 1.25.

Figure 5.

SEDs for α CrB (left) and β Tri (right). Photometry is shown as black dots or black triangles for upper limits. Disc (i.e. photosphere-subtracted) fluxes and upper limits are shown as grey dots, open triangles and small green dots for IRS. The stellar spectrum is shown as a blue line and the blackbody disc model as a red line, with the total shown as a black line.

Despite the suggestion of warm dust by mid-IR imaging (Moerchen et al. 2010), the α CrB disc SED, most notably the IRS spectrum, does not require dust at multiple temperatures. The inferred disc radius assuming blackbody properties for the single component fit to the SED is 40 au, well beyond the few au scale of the mid-IR emission. The SED does not strongly preclude the existence of warm dust however, because it is limited by the ∼2 per cent level that is achievable with typical photometric calibration, and a similar uncertainty for the IRS spectrum. Therefore, at 10–20 μm an excess of ≲100 mJy could be present yet not confidently detected. How this limit converts into a limit on the fractional luminosity depends on the dust temperature (e.g. Wyatt 2009). In the case of 300 K dust, the limit on the fractional luminosity is about 10⁻⁵, so only about a factor of 2 lower than derived from the 124 K disc SED above.

For β Tri the blackbody radius is larger at around 95 au. This size is somewhat smaller than the 150 au derived from the Gaussian fitting, but as noted above the disc could be extended. Aside from being marginally resolved with MIPS, there are no constraints on the structure from other observations.

4.2 Images

The main goal of modelling the resolved images is to derive the orientation of the disc in space, for comparison with the orientation of the binary orbital plane. Though alignment is already suggested by Gaussian fitting in both cases, the PACS beam is not azimuthally symmetric so resolved modelling provides a worthwhile check. To achieve this goal, we must find a spatial structure that reproduces the images satisfactorily. The models are generated using the method described in Wyatt et al. (2012) (see also Kennedy et al. 2012). Basically, a high resolution model of the structure is generated and multiplied by the grain emission properties at each wavelength. The structure is the spatial distribution of dust, implemented as the cross-sectional area as a function of radial distance from the star. The distribution is disc like with a small range of particle inclinations and the dust's face-on optical depth (τ) is parametrized as a function of radius by one or more power laws. The grain emission properties are simply described with a modified blackbody whose temperature decreases with radial stellocentric distance as a power law. The high resolution models are then created with some spatial orientation and convolved with the instrument beam for comparison with the observed images. The large number of model parameters, as well as different possible configurations (e.g. extended discs versus multiple rings) means that we do not undertake a grid search of possible parameter spaces. The final models are found by a combination of by-eye fitting and least-squares minimization.

Our general approach to modelling is to use the simplest model possible to explain the data in hand, increasing the model complexity as required. Here, we find that the simplest model, a narrow ring, is not sufficient to reproduce the PACS images for either system. As a second step, we use extended dust distributions, though two discrete narrow rings are also a possibility (e.g. Wyatt et al. 2012), as is the inclusion of an unresolved component. Because we do not use a grid approach, estimating uncertainties on model parameters, many of which are highly degenerate, is made more difficult. However, we find that multiple different configurations can reasonably reproduce the data, which gives an idea of how well the data constrain the disc structure given the relatively poor resolution compared to the disc sizes. Similarly, we find no requirement for the temperature distribution to deviate from a simple blackbody relation ( K, where L_⋆ is the binary luminosity in Solar units, and r is the disc radius in au). We do not claim this is the true temperature distribution, given that grain temperatures are expected to be somewhat different (hotter) than the blackbody relation suggests, but that there is insufficient information to quantify this difference.

4.2.1 α CrB

We first model α CrB, for which about half to two-thirds of the Herschel emission is unresolved, with the remainder more distant from the stellar position and resolved (see Fig. 6). This large level of unresolved flux means that different models of the system can satisfy the observations, with the main constraint being that mid-IR emission must be detected only within a few au of the star. Because this detection could be the Wein side of the emission, it does not preclude the existence of material just beyond a few au. That is, the mid-IR emission does not indicate that no dust exists where it was not detected, because it could be cool enough to evade detection.

Figure 6.

Residuals after the resolved model of α CrB is subtracted from the observations at 70 μm (left) 100 μm (middle) and 160 μm (right). The colour scale is in units of the pixel to pixel uncertainty, and contours are shown at ±3σ, 4σ and 5σ. The white contour shows the 3σ contour from the observed images.

The size of the 11 μm images (described in Section 2.1; Moerchen et al. 2010) compared to the reference PSF suggests a disc radius of about 2.3 au. Given that this warm emission cannot be resolved by Herschel, there must either be (at least) two separate disc components (i.e. inner and outer components) or a continuous disc that extends from a few to a few hundred au, whose structure appears different at different wavelengths due to the changing temperature with radial distance.

As an example, the Herschel data and SED can be modelled with an outer disc that extends from 45 to 195 au with a decreasing face-on optical depth τ = 2.1 × 10⁻⁵r^−2.9, and an unresolved inner component at a temperature of 120 K. The outer component has a PA of 345° and is edge-on, so consistent with being aligned with the binary orbital plane. The interpretation of this model is that the unresolved emission is distributed such that some dust is close enough to the star to provide the mid-IR emission and structure, while most of it lies distant enough from the star so that overall it appears to have a temperature of 120 K. However, the distance inferred for a blackbody at 120 K around α CrB is 40 au, or 1.8 arcsec, which is relatively large given the 6–7 arcsec FWHM PACS beam at 70–100 μm, and should be detectable in the images.

We therefore use a more complex two-power-law model, in which the disc extends continuously from very near the star to several hundred au. The surface density increases from the inner edge to some break radius, beyond which it decreases to the outer edge. This model has the advantage that it is extended near the binary, so may be able to explain the mid-IR emission without invoking a separate warm component. Such a surface density structure may be expected, because debris disc decay (and stirring in some models) is an inside-out process (e.g. Kenyon & Bromley 2004; Wyatt et al. 2007a; Mustill & Wyatt 2009; Kennedy & Wyatt 2010).

Fig. 6 shows the results of implementing this model, where the dust extends from 1 to 300 au, with the break radius at 50 au. The inner edge of 1 au corresponds to the inner limit of stability for particles orbiting the α CrB binary (e.g. Holman & Wiegert 1999). The optical depth of the inner component is τ = 6.4 × 10⁻⁸r^1.7. For the outer component, τ = 3.3 × 10⁻³r^−1.6. The disc temperature has a blackbody dependence, with T_disc = 775r^−0.5 K. As can be seen from the SED (Fig. 5), some modification of the blackbody function is needed, with m and β = 1.3 for the inner component and m and β = 2.2 for the outer component. The poor resolution relative to the disc size means that these parameters are poorly constrained with strong degeneracies. There is a factor of 8 drop in surface density at the break radius; attempts to keep the dust distribution continuous within the two-power-law model were unsuccessful because the outer component is fairly extended but with low surface brightness. Joining the outer component smoothly to the inner component results in too much flux just beyond the break radius. Such a drop is an expected feature of some disc evolution models (e.g. Kennedy & Wyatt 2010), a point we return to in Section 6. The extent of the outer component is not very well constrained because the surface brightness decreases strongly with radius. The disc model has a PA of 345° so is consistent with the binary line of nodes. The disc is edge on, so again consistent with being coplanar with the binary orbit. The images show significant residuals for changes of 10–20° in both inclination and PA, giving an indication of their uncertainties.

The two models considered above show a similar residual structure when the model is subtracted from the observations. The only sizeable (>3σ) residual related to the star+disc is located on one side of the stellar position at 70 μm. With the simple models considered here, similar residuals remain for a range of PSFs (i.e. those shown in Fig. 2), even if the opening angle of the inner disc component is allowed to vary (as might be expected if this component was misaligned with the outer component; see Section 5). Our inability to construct a model that accounts for these residuals leads us to conclude that they are likely due to the beam variations discussed in Section 3. Alternatively, there may be additional structure unaccounted for by our model, which would have a scale of a few arcseconds to leave such small residuals. While the mid-IR images suggest that our coplanar configuration is representative, these observations should be repeated, specifically at 18 μm, as a further test of disc coplanarity and structure near the star.

To compare the extended model with the resolved structure seen in the mid-IR by Moerchen et al. (2010), Fig. 7 shows synthetic images at 11 and 18 μm, where we have convolved the star+disc models with appropriately sized Gaussian PSFs, added noise and then subtracted the PSFs scaled to the image peak (i.e. the same method used by Moerchen et al. 2010, to detect extension). The background noise level is calculated from the photometric uncertainties of 2 and 15 mJy at 11 and 18 μm, respectively, assuming aperture radii of 2.0 arcsec. In these images, we have multiplied our model by a factor of 2 at 11 μm, and 5 at 18 μm to make them appear similar to the mid-IR observations, and show how the observed mid-IR structure could arise from an extended disc. A factor of 2 at 11 μm results in a disc flux of 65 mJy, so is reasonable given the uncertainty in the disc flux at this wavelength, which is limited by the calibration of the photosphere and IRS spectrum. The factor 5 at 18 μm results in a disc flux of 1000 mJy, which is less reasonable and would make the disc flux inconsistent with the IRS and AKARI measurements. Our disc model is therefore fainter at 18 μm than could be detected with the mid-IR imaging. That the 18 μm observations suffer from artefacts due to the observing procedure is the likely explanation, providing further motivation for repeating these observations.

Figure 7.

Simulated 11 μm (left) and 18 μm (right) peak-subtracted mid-IR observations of the α CrB model for comparison with Moerchen et al. (2010). The pixel scale is 0.1 arcsec pixel⁻¹, and the scales are in mJy pixel⁻¹. Contours are drawn at three, six and nine times the background noise level. Our model has been multiplied by a factor of 2 at 11 μm, and 5 at 18 μm (see the text).

4.2.2 β Tri

The simplest β Tri model is shown in the top row of Fig. 8. We found that the images could not be modelled as a single narrow ring, so first allowed the inner and outer disc edges to vary with a power-law surface density profile in between. This model extends from 50 to 400 au with an optical depth of τ = 6.7 × 10⁻⁵r^−0.9. The temperature dependence is again that for a blackbody (T_disc = 819r^−0.5 K), with m and β = 1.5. The disc outer edge is not well constrained by the PACS images, but is constrained to some degree by not being resolved with SPIRE at 250 μm. The PA and inclination are 67° and 46°, respectively. The variation of the inclination by 10° leaves significant residuals compared to the data, as does a similar change in the PA. The PA of the binary plane is 65° so is easily consistent with that found for the disc. The inclination of the binary plane is 40°, so not significantly different to that found for the disc. While the inclination is fairly well constrained, the disc opening angle is not, with values between 0° and 50° giving similarly good fits (though lower disc opening angles are preferred). As we discuss in detail below in Section 5, this ambiguity can be resolved by considering circumbinary particle dynamics.

Figure 8.

Residuals after the resolved model of β Tri is subtracted from the observations at 70 μm (left) 100 μm (middle) and 160 μm (right). The top row shows results from the extended (50–400 au) model, and the bottom row shows results from the continuous (1–400 au) model. The colour scale is in units of the pixel to pixel uncertainty, and contours are shown at ±3σ. The white contour shows the 3σ contour from the observed images.

As with α CrB, we also tried a continuous surface density profile by adding an inner component to the first model. This continuous model extends from the innermost stable orbit at about 4 au (Holman & Wiegert 1999) out to 500 au with the surface density peaking at 100 au and is equally successful at reproducing the Herschel images (bottom row of Fig. 8). In this model, we restricted the inner component to join smoothly to the outer component; without this restriction the inner component can be arbitrarily small and the model no different to the extended one above. The inner component has an optical depth of τ = 2 × 10⁻⁸r^1.7, and the outer component decreases with an index of −1.7. The temperature is for a blackbody as above, with m and β = 1 for the inner component and m and β = 1.5 for the outer component. As with α CrB, these parameters are poorly constrained and highly degenerate.

While these two models show that the radial and vertical disc structure is poorly constrained, both suggest that the disc optical depth decreases beyond a maximum that lies around 60–100 au. Interior regions may be depleted as in the continuous model, or completely empty. Despite these uncertainties, our main conclusion that the disc is consistent with being aligned with the binary orbital plane is robust.

5 Dynamics

The main result of the resolved modelling is that the discs are both consistent with being aligned with the orbital planes of the host binaries. Whether this alignment simply reflects the initial debris disc+binary configuration at the end of the protoplanetary disc phase, or subsequent evolution requires some study of the expected dynamics.

Disc particles exterior to a pair of orbiting bodies (in our case a binary star system) are subject to secular perturbations that modify the particle orbits on long time-scales. How the particle orbits are modified depends on the properties of the binary, particularly the mass ratio and binary eccentricity, but also depends on the particle orbits themselves (Verrier & Evans 2009; Farago & Laskar 2010; Doolin & Blundell 2011). If the stars in the binary have similar masses, the effect on particle eccentricities is smaller than for larger mass ratios (Moriwaki & Nakagawa 2004; Kennedy et al. 2012). In contrast, the changes in particle inclinations and nodes can be significant. If the angle between the particle and binary orbital planes is small (i.e. particles have low inclinations with respect to the binary plane, we quantify ‘small’ and ‘large’ inclinations below), particle inclinations oscillate about the binary plane. Therefore, while a disc of such particles will have an opening angle double the initial misalignment, it will also appear to be aligned with the binary plane. The best example is the warp in the β Pictoris disc, which was proposed to be due to perturbations by a planet misaligned with the disc plane (Mouillet et al. 1997; Augereau et al. 2001) that was subsequently discovered (Lagrange et al. 2009, 2010). For large differences between the particle and binary planes (i.e. high inclinations with respect to the binary plane), particle inclinations are coupled to the evolution of their line of nodes, and oscillate around a polar orbit. In the context of a debris disc, these particles evolve into various structures depending on the degree of initial misalignment (Kennedy et al. 2012). Within the high-inclination family of orbits, only discs that are initially misaligned by about 90° and have their line of nodes perpendicular to the binary pericentre will not be strongly perturbed and continue to appear disc like.

The dividing line between ‘large’ and ‘small’ relative inclinations, and thus the different families of disc structures, was quantified by Farago & Laskar (2010). For α CrB with e = 0.37, the critical angle is 48°, and for β Tri with e = 0.433 the critical inclination is 43° (for an ascending node of ±90°). Thus, if the disc inclination relative to the binary plane was initially larger than 48° and 43° respectively for these systems, it could not become aligned with the binary plane.

While particles with initial inclinations lower than the critical angle can become aligned, the finite secular precession time means that they will only be aligned if they have been perturbed over a sufficiently long period. The time-scale for alignment is given by Farago & Laskar (2010), and is shown for an arbitrarily small initial disc–binary plane inclination, and for initial misalignments of 20° and 40° for α CrB and β Tri in Fig. 9. Particles with semi-major axes that lie to the left of where the curves intersect a given system age (i.e. less than r_align) have completed at least one cycle of secular evolution. The hatched region indicates the region where PACS cannot resolve the disc at 70 μm, so shows where the disc structure is poorly constrained by Herschel observations.

Figure 9.

Secular precession times for α CrB (left panel) and β Tri (right panel, solid lines, for misalignment angles of 0°, 20°, and 40° from bottom to top). The dot–dashed line shows the estimated stellar age, and the dotted lines disc radii (the break and outer radii for the continuous α CrB model, and the inner and outer radii for the extended β Tri model). The alignment radius is where the secular precession time equals the stellar age for low misalignment angles. The hatched region lies inside the PACS beam half-width at half-maximum at 70 μm, so the structure in this region is poorly constrained by PACS observations.

The α CrB system is about 350 Myr old, so the inclinations of particles within about 80 au will be symmetric about the binary orbital plane. Beyond this distance, however, particles have not yet had time to undergo a complete cycle of secular precession and will retain their original orbital inclinations. The transition between these regions is not sharp due to the finite secular precession time (see fig. 1 of Augereau et al. 2001). Fig. 9 also shows that the alignment distance is about the same as the inner extent of the PACS resolution at 70 μm. Thus, the disc structure that is constrained by the PACS images lies beyond r_align, and the alignment with the binary plane cannot arise due to secular perturbations. This conclusion is strengthened by the finding that the orientation as seen by Herschel is consistent with the inner disc as seen in the mid-IR.

In the β Tri disc, particles beyond r_align ≈ 140 au are too distant to be significantly affected by secular perturbations from the binary, assuming an age of 730 Myr. Because we find that the disc extends well beyond this distance, the alignment of the binary orbital and disc planes are again most likely primordial. Though we could not constrain the disc opening angle well, the assumption that it is small is reasonable based on (i) observations that edge-on debris discs typically have small opening angles (e.g. Krist et al. 2005; Golimowski et al. 2006), and (ii) that secular perturbations could not have increased the scale height at the distances resolved by the Herschel observations.

6 Discussion

By considering the resolved models and expected dynamics, we have shown that the circumbinary debris discs in both the α CrB and β Tri systems probably formed coplanar with their parent binaries. A corollary is that because the discs were primordially aligned, there should be little vertical structure inside the alignment radius. Both discs were successfully modelled as discs with a single plane of symmetry, but are too poorly resolved with Herschel to strongly verify this statement. However, for α CrB, the low-level contours from the 11 and 18 μm mid-IR imaging suggest that the inner disc has a similar PA to the binary and outer disc. Only one of the 18 μm images shows the same PA, though the fact that the other is actually narrower than the PSF in the same direction makes this extension questionable, as discussed by Moerchen et al. (2010).

While there appears to be no need or evidence for vertical disc structure induced by perturbations to disc particles’ inclinations, an indirect signature could exist from inclination and eccentricity variations imposed on disc particles. These variations ‘stir’ the disc, where we define ‘stirring’ to be any mechanism that increases relative velocities between particles sufficiently that collisions become catastrophically destructive, thus initiating a collisional cascade. In stirred regions, mass at the small end of the collisional cascade is removed by radiation forces, thus depleting the disc. In unstirred regions, the mass remains constant. The size distribution in stirred regions has many more small grains for a given mass in large objects, so is more easily detected due to the larger emitting surface area.⁶

Though the structure of the inner disc is not well constrained, we have shown that a plausible model that satisfies both the Herschel and mid-IR data for α CrB has a continuous optical depth profile that peaks around 50 au. Because the typical expectation from Solar system and protoplanetary disc studies is for the surface density to decrease with the distance from the star (e.g. Weidenschilling 1997; Andrews et al. 2009), this profile can be interpreted as a depletion of material inside 50 au. Such a depletion is expected in standard models of collisional evolution, where the disc decay rate is faster at smaller semi-major axes (e.g. Dominik & Decin 2003; Wyatt et al. 2007a). This 50 au turnover distance is similar to r_align shown in Fig. 9, so it is therefore plausible that the depletion inside here is due to increased velocities imposed by binary perturbations.

Considering this binary stirring picture in more detail, vertical (inclination) stirring is probably more important than radial (eccentricity) stirring in circumbinary discs, particularly when the disc lies at large distances relative to the binary separation. As the binary mass ratio decreases (i.e. the stars’ masses become more similar), the eccentricities imposed on an exterior particle decrease. For example, using the expression derived by Moriwaki & Nakagawa (2004), the ‘forced’ eccentricity of particles at 50 au around α CrB is about 0.001, at least an order of magnitude lower than the eccentricities thought to exist in observed debris discs (e.g. Kenyon & Bromley 2004; Krivov et al. 2008). In contrast, for inclination stirring to be effective, the initial disc plane would only need to be a few degrees different from the binary plane (though some non-zero eccentricity is needed to ensure crossing orbits). For example, with an initial misalignment of 1°, collision velocities are stirred to about 0.02 times the Keplerian velocity (150 m s⁻¹ at 50 au), so objects with dispersal thresholds less than roughly 10⁴J kg⁻¹ (≲10 km) will be disrupted and dispersed in collisions with similar-sized objects. Therefore, the disc decays from the inside-out as secular perturbations increase the relative velocities in particle collisions by aligning the disc, and do so on a shorter time-scale closer to the central star(s). Assuming that the initial misalignment was large enough, collisions will be destructive inside some radius that will be close to r_align (but not exactly at r_align; Mustill & Wyatt 2009). Outside this radius, collisions are unaffected by the presence of the binary and therefore not destructive, providing a possible explanation for the drop in optical depth in our model beyond 50 au.

While the α CrB disc is consistent with being stirred by the binary, we also consider two alternative stirring mechanisms. The first is ‘pre-stirring’ in which objects are assumed to have been stirred at some very early time by an unspecified mechanism that does not necessarily still operate (e.g. a stellar flyby or the result of gas disc dispersal). A potential issue with such a scenario is that collisional damping may reduce the velocities sufficiently that collisions are not catastrophic for a significant fraction of the stellar main-sequence lifetime (e.g. Kenyon & Bromley 2002; Goldreich, Lithwick & Sari 2004). Whether collisional damping is important depends on the relative sizes of the objects and their destructive impactors, which in turn depends on the relative velocities. If pre-stirred objects can reach sufficiently high eccentricities (≳0.1, though the value depends on object strength and stellocentric distance), then the disc can remain stirred for the stellar lifetime (Shannon & Wu 2011). Such a disc is depleted radially from the inside-out, again because the depletion rate is a strong function of radius. The type of structure that is expected is therefore a radially increasing optical depth profile, which turns over and decreases where collisions have yet to deplete the disc significantly (e.g. Kennedy & Wyatt 2010). Using equation 6 from Kennedy & Wyatt (2010), we find for the best-fitting planetesimal properties from Wyatt et al. (2007b) that the α CrB disc would be depleted within 50 au if the disc was stirred from an arbitrarily early time (e.g. pre-stirred) and was about 5–15 times less massive than the solid component of the minimum-mass Solar nebula [MMSN (Weidenschilling 1977), when scaled linearly with the binary mass].⁷

The second mechanism is ‘self-stirring’, where random velocities are initially slow enough that collisions result in accretion and growth. Once the largest objects reach roughly Pluto size, they increase the velocities of smaller planetesimals and initiate a collisional cascade, and the production of visible levels of dust (Kenyon & Bromley 2004). Again, this process works in a radially inside-out fashion, so a self-stirred disc looks similar to a pre-stirred one, with one key difference. Because planetesimals have not been stirred outside where Pluto-sized objects have formed, collisions do not result in a collisional cascade and the disc should show a drop in optical depth beyond this distance (Kennedy & Wyatt 2010). Using equation 9 from Kennedy & Wyatt (2010), for Pluto-sized objects to stir the disc to only 50 au by 350 Myr, the disc would have to be 2000 times less massive than a scaled MMSN (see also Kenyon & Bromley 2010, from which the Pluto formation and stirring times were derived). A disc with such low mass would not be visible in a self-stirring scenario (e.g. Kenyon & Bromley 2010), which appears to disfavour this scenario. However, this calculation assumed that the planetesimals started out with 1 m to 1 km sizes. If the planetesimals were initially much larger, the time to form Pluto-sized objects would also be longer (e.g. Kenyon & Bromley 2010). This longer formation time would mean that a more massive disc, which would be correspondingly brighter and therefore more consistent with the observations, could form Pluto-sized objects and stir the disc only as far as 50 au by 350 Myr.

Therefore, all stirring models appear consistent with the observed peak in surface density at 50 au. However, the model derived in Section 4.2 required a drop in surface density beyond 50 au, a feature expected in self-stirred and binary-stirred discs, which would appear to disfavour a pre-stirred interpretation, but not discern between self- and binary stirring. A caveat on this conclusion is that the disc structure is poorly constrained by the low resolution of the observations, and the dust observed with Herschel may not trace the parent body locations, particularly in the outer regions. For example, the peak at 50 au may simply represent the outer edge of a parent body disc that is pre-stirred, and the (decreased) emission beyond 50 au could arise from small grains originating at 50 au forced on to larger eccentric orbits by radiation pressure (e.g. Thébault, Augereau & Beust 2003; Krivov, Löhne & Sremčević 2006).

Regardless of the stirring mechanism, we can compare the disc structures with those expected if they decayed from some arbitrarily large level. In this picture, the face-on geometrical optical depth (with the same assumptions used above) is

(1)

where M_⋆ is the stellar mass in Solar units and t is the system age in Myr (Kennedy & Wyatt 2010, equation 8). The r^7/3 dependence gives the expected radial profile of a disc whose planetesimal properties are the same everywhere. With these assumptions, for α CrB the expected optical depth at 350 Myr is 1.15 × 10⁻⁸ at 1 au, which is somewhat smaller than the model value of 6.4 × 10⁻⁸. Given that there is considerable uncertainty in the planetesimal properties and the true dust distribution, we do not consider this difference a cause for concern. The model does not increase as strongly with radius as equation (1), so is below the expected level outside a few au anyway. That the disc model has an r^1.7 dependence rather than r^7/3 could indicate that the planetesimal properties have a radial dependence, for example, that they become smaller or weaker at larger distances (the model parameters are very uncertain, however, so such a dependence is not required).

The β Tri data are consistent with a continuous optical depth profile that peaks around 100 au. Given that the secular precession time depends strongly on the semi-major axis, and that the stellar age is uncertain, this distance is not significantly inside r_align and the disc is therefore plausibly binary stirred. The expected optical depth at 730 Myr is 3.8 × 10⁻⁹ at 1 au, which is smaller than the model value of 2.0 × 10⁻⁸. Again, the discrepancy is not particularly large given the model assumptions and uncertainty. Using the same equations as above, the β Tri disc would be depleted out to 100 au by 730 Myr for a disc one to five times less massive than a scaled MMSN if it were stirred from the outset. Stirring by Pluto formation out to this distance only requires a disc 400 times less massive than a scaled MMSN (but again could be more massive if planetesimals are larger). Thus, the disc could be depleted out to 100 au by collisional evolution, but the stirring mechanism is unclear. Unlike α CrB, which has a mid-IR detection, there is no evidence for warm emission in the β Tri system. Such a detection could break the degeneracy in our models, which cannot tell whether the regions inside 50–100 au are devoid of debris (e.g. due to dynamical clearing by planets), or simply depleted by collisional evolution.

This ‘standard’ picture of debris disc stirring and evolution is not the only possibility. For example, catastrophic collisions may be caused due to crossing orbits in a disc where self-gravity is important, with the additional possibility that such discs may appear non-axisymmetric (Jalali & Tremaine 2012). It is also possible that some observed debris discs are not stirred to catastrophic collision velocities at all. Heng & Tremaine (2010) show that long-lived ‘warm’ planetesimal discs could exist, in which collisions are not typically disruptive. They suggest that a test for such a scenario is that the disc spectrum should look like a blackbody, because the disc particles required for such warm discs to survive are large enough that they act like blackbodies (i.e. absorb and emit light efficiently). For the two systems considered here, the disc spectra appear to rule out such a scenario because they lie significantly below pure blackbodies beyond wavelengths of about 100 μm (Fig. 5), suggesting that the particles emit inefficiently at long wavelengths and are predominantly smaller than ∼1 mm. However, we do not exclude the possibility that the discs are ‘warm’, because the small grains that are observed could have been created in erosive and bouncing collisions. Modelling the size distribution would make more quantitative predictions to test this possibility.

Though both discs have extended or continuous dust distributions as observed by Herschel, the parent bodies may (or may not) be more localized. All the models we considered find that the dust optical depth decreases with distance in the outer regions. Qualitatively, this structure is expected when the parent bodies occupy a narrow ‘birth’ ring and small grains are placed on eccentric and hyperbolic orbits (e.g. Strubbe & Chiang 2006; Müller, Löhne & Krivov 2010). However, it is also possible that the observed extent reflects the underlying parent body distribution, as might be argued for α CrB, which has dust detected both near and far from the star. Alternatively, the drop in optical depth beyond 50 au required by the continuous α CrB model may be a sign that the parent planetesimals lie relatively close to the star and that the more distant dust comprises small grains on eccentric and hyperbolic orbits.

Whether debris discs are typically rings or more extended structures is an open question (e.g. Kalas et al. 2006), in part because obtaining sufficiently high resolution sub-mm observations, those most sensitive to larger grains, is challenging. This ambiguity has only been overcome in a few nearby systems, where a parent body ring has been resolved at sub-mm wavelengths and is seen to be narrower than the radial extent of small grains (Kalas, Liu & Matthews 2004; Acke et al. 2012; Boley et al. 2012; Wilner et al. 2012). With the development of facilities such as the Atacama Large Millimeter Array (ALMA) and the Northern Extended Millimeter Array (NOEMA), the detection and resolution of larger parent body populations will become possible and will provide insight into the processes that set where planetesimals form and reside.

Looking at the issue of alignment from a wider perspective, coplanarity is the expected outcome for debris discs and planetary systems emerging from the protoplanetary disc phase for small to medium binary separations (e.g. Bate et al. 2007). However, only a few examples where the outcome can be tested actually exist. Three systems with transiting circumbinary planets, in which the stars are also eclipsing binaries, show that well-aligned systems are a possible outcome (Doyle et al. 2011; Welsh et al. 2012). Further, Welsh et al. (2012) find that the occurrence rate of aligned circumbinary planets is probably consistent with the rate for circumstellar planets with similar properties, suggesting that alignment is the typical outcome. However, they acknowledge that significant biases exist, and that further work is needed to understand the implications of these discoveries for circumbinary planetary system alignment and frequency.

In the case of circumbinary debris discs, only four systems where the disc and binary alignment can be tested exist: α CrB, β Tri, 99 Herculis (Kennedy et al. 2012) and HD 98800⁸ (Boden et al. 2005; Andrews et al. 2010). Of these, α CrB and β Tri are close binaries with periods of several weeks and HD 98800 has a period of 314 d, while 99 Her has a semi-major axis of 16.5 au and a 56 yr period. With only these systems, we cannot yet be sure of what trends will emerge. As hinted by the disc–binary alignment of α CrB, β Tri and HD 98800, and the misalignment for 99 Her, it may be that more widely separated systems are more likely to be misaligned. It will also be interesting to test whether stirring by secular perturbations from binaries is important for disc evolution. This hypothesis could be tested by comparing disc sizes (and structure where possible) with the radii at which secular perturbations could have reached within the system lifetime for a larger sample.

7 Summary

We have presented resolved images of debris discs around the nearby close binary systems α CrB and β Tri. These systems are relatively unusual among binaries because their orbital configurations are relatively well known, allowing a test for (mis)alignment between the disc and binary orbital planes. In both cases, we find that the disc and binary are most likely aligned. Though secular perturbations can align systems over time, the bulk of the resolved disc structure in these systems is too distant to be affected. Therefore, the alignment is most likely primordial, suggesting that the binary+protoplanetary disc system from which the debris disc emerged was also aligned. These initial conditions are consistent with expectations of alignment in protoplanetary disc+binary systems where the binary has a separation less than about 100 au (Bate et al. 2007).

Secular perturbations from the binary could provide the stirring mechanism in circumbinary discs, and both α CrB and β Tri are consistent with such a picture. However, they are also consistent with other stirring mechanisms. While binary stirring may happen, it cannot be the only mechanism because debris discs are observed with a similar frequency in both single and multiple star systems (Trilling et al. 2007).

These two systems bring the number in which debris disc–binary alignment can be tested to 4. Three of these (α CrB, β Tri and HD 98800) have orbital periods of several weeks to a year and appear to be aligned, while 99 Her has a period of 50 yr and is strongly misaligned. It is too early to draw conclusions about typical outcomes in such systems, but the results so far suggest that misalignment cannot be extremely rare, and may be preferred in systems with wider binary separations.

Acknowledgments

We thank Jonti Horner for his comments on a draft of this article, and the referee for comments that improved the discussion and overall clarity. This research has made use of the Washington Double Star Catalog maintained at the U.S. Naval Observatory. This work was supported by the European Union through ERC grant number 279973.

1

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

2

Multi-band Imaging Photometer for Spitzer (Rieke et al. 2004; Werner et al. 2004).

3

Infra-Red Spectrograph (Houck et al. 2004).

4

The Washington Double Star Catalogue (WDS; Mason et al. 2001) lists the orbit as ‘definitive’ (Grade 5).

5

See PACS Observer's Manual.

6

Once catastrophic collisions are occurring, the level of stirring is also important. An increase in stirring does not have a significant effect on the collision rate between particles of similar sizes because higher velocities are accompanied by a lower volume density of particles (e.g. the scale height and/or radial disc extent increases with the velocities). However, particles are typically destroyed in a collision with a much smaller particle, whose size is set by the collision velocity. Thus, higher levels of stirring mean that smaller particles are capable of destroying objects. In standard collisional size distributions (e.g. Dohnanyi 1969), the number of particles, and therefore the number of potential destructive impactors, increases strongly with decreasing size, so the disc depletion rate due to collisions increases with increased stirring.

7

We are not necessarily suggesting that the solid mass in the primordial protoplanetary disc was similarly depleted relative to the MMSN, as the mass could for example have gone into building planets. However, given the large observed dispersion in protoplanetary disc masses in star-forming regions, such a depletion is easily possible (e.g. Andrews & Williams 2005).

8

A weak accretion signature has recently been detected for ∼10 Myr old HD 98800 (Yang et al. 2012), suggesting that it lies somewhere between the protoplanetary and debris disc phases.