On the origin of the spiral morphology in the Elias 2-27 circumstellar disc

TL;DR

This study investigates the origin of spiral structures in Elias 2-27's circumstellar disc, suggesting they may result from gravitational instabilities or an external massive planetary companion, based on simulations and observations.

Contribution

It provides the first detailed simulation-based analysis of spiral formation mechanisms in Elias 2-27's disc, considering both gravitational instability and external companions.

Findings

Disc may be gravitationally unstable or have an external companion.

External companion could be a massive planet (~10-13 Jupiter masses).

Companion likely located at 300-700 au from the star.

Abstract

The young star Elias 2-27 has recently been observed to posses a massive circumstellar disc with two prominent large-scale spiral arms. In this Letter we perform three-dimensional Smoothed Particle Hydrodynamics simulations, radiative transfer modelling, synthetic ALMA imaging and an unsharped masking technique to explore three possibilities for the origin of the observed structures -- an undetected companion either internal or external to the spirals, and a self-gravitating disc. We find that a gravitationally unstable disc and a disc with an external companion can produce morphology that is consistent with the observations. In addition, for the latter, we find that the companion could be a relatively massive planetary mass companion (less than approximately 10 - 13 MJup) and located at large radial distances (between approximately 300 - 700 au). We therefore suggest that Elias 2-27 may be one of the first detections of a disc undergoing gravitational instabilities, or a disc that has recently undergone fragmentation to produce a massive companion.

Equations

$$T(R)=13.4\mathrm{K}{\left(\frac{R}{200\mathrm{au}}\right)}^{-q}.$$

$$\Sigma (R)={\Sigma }_{\mathrm{c}}{\left(\frac{R}{R_{\mathrm{c}}}\right)}^{-p}\exp \left(-{\left(\frac{R}{R_{\mathrm{c}}}\right)}^{2-p}\right),$$

Full text

1. Introduction

With the advent of the Atacama Large Millimetre Array (ALMA), it has for the first time become possible to spatially resolve, and thus directly observe, the midplane structure of protoplanetary discs where planet formation processes occur. Such an extreme increase in observational capability has given rise to several surprising results, examples of which include the symmetric ring structures in HL Tau (ALMA Partnership et al., 2015), TW Hydrae (Andrews et al., 2016) and HD 163296 (Isella et al., 2016), the horseshoe shaped dust traps in HD 142527 (Casassus et al., 2013), and the birth of a ternary system via disc fragmentation in L1448 IRS3B (Tobin et al., 2016). Observations such as these are extremely powerful, as sub-structure within protoplanetary discs can be a signpost of dynamical or chemical effects occurring within the star-disc system. Therefore, a proper understanding of their cause is essential to determine which of these processes are important during the star and planet formation process.

A recent example of such a spatially-resolved observation was presented by Pérez et al. (2016) in which Elias 2-27 (catalog ) was targeted with ALMA. Elias 2-27 is a low mass young star (M${}_{\star}=0.5$ – $0.6$ ${\rm M_{\odot}}$, tage $\sim 1$ Myr; Luhman & Rieke 1999; Natta et al. 2006). Based on its spectral energy distribution (SED), the system is thought to belong to the Class II phase (Andrews et al., 2009; Evans et al., 2009), yet at the same time, observations have suggested an unusually large disc mass, ranging from 0.04 – 0.14 ${\rm M_{\odot}}$ (Andrews et al., 2009; Isella et al., 2009; Ricci et al., 2010).

The Elias 2-27 disc posseses two large-scale symmetric spiral arms (Figure 1, right). Additionally when the raw ALMA observations are processed with an unsharp masking filter, two dark crescents interior to the spirals and a bright inner ellipse are revealed (Figure 1, left). The origin of these is unclear. With such a large disc-to-star mass ratio, could the disc be self-gravitating? Or, could an as-yet-undetected companion be causing these features via dynamical interactions?

In this Letter we describe the results of hydrodynamical and radiative transfer modelling of the Elias 2-27 system. We produce synthetic ALMA observations to explore three possibilities that may give rise to the observed features — a companion internal to the spirals, a companion external to the spirals, or gravitational instabilities operating within the disc.

2. METHODOLOGY

2.1. Hydrodynamics

Our simulations are performed using a three-dimensional Smoothed Particle Hydrodynamics code (sph) which includes the heating due to work done and the radiative transfer of energy in the flux-limited diffusion limit (Whitehouse et al., 2005; Whitehouse & Bate, 2006). A detailed description of the code can be found in Meru (2015), however for this work we employ two differences. Firstly, boundary particles are located at every timestep, allowing the vertical location between the optically thick and thin region to be regularly re-evaluated, leading to more accurate boundary temperatures. Secondly, we employ the Morris & Monaghan (1997) artificial viscosity with the sph parameter, $\alpha_{\rm SPH}$, varying between 0.1 – 1.0 and $\beta_{\rm SPH}=2\alpha_{\rm SPH}$, to model shocks within the disc.

We perform 72 hydrodynamical simulations varying a number of disc properties as well as orbit properties for the companion simulations. We first describe our reference disc setup: we model a $0.5{\rm M_{\odot}}$ star surrounded by a disc whose temperature follows

[TABLE]

The disc surface density follows

[TABLE]

where $\Sigma_{\rm c}$ is the surface mass density of gas at the cut-off radius, $R_{\rm c}$. We model this disc between $R_{\rm in}=10$ au and $R_{\rm out}=400$ au using the parameters determined by Pérez et al. (2016), namely $\Sigma_{\rm c}=5$ g cm*-2*, R${}_{\rm c}=200$ au, $q=0.45$ and $p=0.7$.

We then perform a suite of simulations with a wide range of parameters to test the internal companion, external companion and gravitational instability hypotheses. Due to the computational expense of each simulation, our aim is not to fit the exact parameters, but to test whether each hypothesis can reproduce the observed morphology. We vary the disc mass, surface mass density profile, temperature profile, cut-off radius, and outer disc radius. We also model pure power surface density profiles, i.e. without the exponential term in equation 2, so that, once evolved, the disc has a much steeper profile in the outer regions. In addition, for the companion simulations, we vary the companion mass, the pericentre distance, eccentricity and inclination.

Each disc is modelled using 250,000 sph gas particles. The ratio of the smoothing length to the disc scale-height is $<0.5$ outside $40$ – $60$ au, giving sufficient resolution to probe dynamical effects on the disc. The discs are modelled with radiation hydrodynamics using flux-limited diffusion, and the surface temperature (representing irradiation from the central star) is held at the profile given by Eqn. 1. For the parameters studied here, the disc is optically thick to stellar irradiation, and remains vertically isothermal at the boundary temperature beyond a radius of 20 and 30 au in the companion and self-gravitating disc simulations, respectively. This implies that the thermodynamics are mainly set by external irradiation.

We assume that the gas and dust are well mixed. For our self-gravitating simulations the Stokes numbers of millimeter particles are $\mathcal{O}(0.01)$, and thus dust trapping in the spirals is expected to be marginal (Booth & Clarke, 2016; Shi & Chiang, 2014). In our simulations with a companion the Stokes numbers are $\mathcal{O}(0.1)$. For a spiral to trap dust, however, it is also necessary that the timescale for it to concentrate towards the pressure maximum (Clarke & Lodato, 2009) is less than the crossing timescale of a spiral feature. Although this condition is readily met in the case of self-gravitating discs where the spirals nearly co-rotate with the Keplerian flow, this is not true in the case of a planet generated spiral which co-rotates with the planet (e.g. Paardekooper & Mellema, 2006; Zhu et al., 2012; Birnstiel et al., 2013)

2.2. Radiative Transfer & Synthetic Imaging

To calculate synthetic observations of our models, we use the 3D radiative transfer code radmc-3d111http://www.ita.uni-heidelberg.de/~dullemond/software/radmc-3d/. The dust opacity is calculated from the optical constants for astronomical silicates (Weingartner & Draine, 2001) using Mie-theory, assuming a power-law grain size distribution between 0.005 – 1000 $\mu$m with a power exponent of $-3.5$. Outside 80 au we obtain the dust temperature and density on the spherical mesh by interpolating the gas density and temperature from the hydrodynamic simulations using an sph interpolation with a cubic spline smoothing kernel (Monaghan, 1992) and assume a uniform gas-to-dust ratio of 100. Due to the accretion of sph particles on the central star, we extrapolate the density inwards of 80 au using a radial power-law with an exponent chosen to give a smooth transition from the results of the hydrodynamic modelling. We assume a vertical Gaussian density distribution, whose scaleheight is calculated from the temperature given by Eq. 1. The dust and gas temperatures are assumed to be identical. Using these temperatures and densities on a spherical mesh, we calculate images at $\lambda=1.3$ mm using the raytracer in radmc-3d.

Synthetic observations for ALMA are calculated using the Common Astronomy Software Application v4.5 (CASA, McMullin et al., 2007). Visibilities are calculated with the simobserve task while imaging is performed with the clean task. Since our goal is not to fit the observations exactly, but merely to show the morphological similarities between our models and the observations, we do not use exactly the same $(u,v)$ co-ordinates as the observations to calculate our visibilities. Instead, we choose an antenna configuration in CASA (alma.out13) which results in a very similar synthesised beam to that of the real data: 0.27″$\times$0.25″  with PA = $86\arcdeg$. To ensure our synthetic observations are as close to the real data as possible, we use a bandwidth of 6.8 GHz, assume a precipitable water vapour column of 2.7 mm, and a total integration time of 725 seconds.

We then apply an unsharp masking filter to the images in a similar manner to Pérez et al. (2016). This involves convolving the image with a Gaussian kernel with a full width half maximum (FWHM) of 0.33″  and subtracting a scaled version of the result from the original image. This acts to remove large scale emission and boost the contrast of small scale structures.

2.3. Observational constraints

We describe various observational constraints that apply to the Elias 2-27 system, which we use when testing the three possible scenarios.

2.3.1 Constraints on the total system mass

The 12CO $J=2-1$ emission toward Elias 2-27 seems to be undergoing Keplerian rotation out to $\sim 630$ au, and according to kinematic modelling, the enclosed mass interior to the emission is $0.5\pm 0.2{\rm M_{\odot}}$ (Pérez et al., 2016). However, absorption by the surrounding molecular cloud significantly obscures the red-shifted component of the emission, leading to some uncertainty in these derived masses.

2.3.2 Constraints on the mass of a potential companion

A volume-limited multiplicity survey of the $\rho$-Ophiuci molecular cloud was performed by Ratzka et al. (2005). Elias 2-27 was found to be a single star with an upper limit on the K-band contrast of 2.5 mag between 0.13–$6.4\arcsec$. Additionally, the area around Elias 2-27 has been targeted by the UKIRT Infrared Deep Sky Survey (UKIDSS, e.g. Lawrence et al. 2007). The closest point source is located approximately $14\arcsec$ to the South ($16^{\rm h}26^{\rm m}44.95^{\rm s}$, $-24\arcdeg 23^{\prime}21.88^{\prime\prime}$) with a K-band magnitude of 15.9 mag, giving a K-band contrast of 7.5 mag with Elias 2-27. The limiting magnitude of the survey in the K-band (17.8 mag) suggests a maximum contrast with Elias 2-27 of 9.4 mag for any undetected sources.

Using the NextGen atmosphere models (Allard et al., 1997; Baraffe et al., 1998; Hauschildt et al., 1999), we convert these K-band contrasts to upper limits for the mass of any potential companion, $M_{\rm comp}$, for various orbital distances from Elias 2-27. Assuming all objects lie at the same distance as Elias 2-27 (139 pc), the UKIDSS data excludes any unseen companions $>0.01{\rm M_{\odot}}$ beyond 420au (with the exception of the closest source mentioned above, which would translate to $M_{\rm comp}\approx 0.02{\rm M_{\odot}}$ at 2000 au). Inside 420au a companion up to $0.08{\rm M_{\odot}}$ could be present based on Ratzka et al. (2005).

Pérez et al. (2016) present ${}^{12}{\rm CO}$, $\rm C^{18}O$ and ${}^{13}{\rm CO}$ observations which combined, show the presence of gas out to $\approx 630$ au. Based on their channel maps and the PV diagram of ${}^{12}{\rm CO}$, there is no strong indication of a gap in the gas (though we note that the signal-to-noise is low). In order to not open up a gap in the gas a planet must satisfy the viscosity and pressure conditions for gap-opening (Equations 68 and 69 of Lin & Papaloizou, 1993; see also Crida et al., 2006). Between $300-420$ au (i.e. from the spirals to where the UKIDSS observations become relevant), the pressure condition is more stringent for $\alpha\lesssim 0.015$ providing a gap-opening mass of $\approx 13M_{\rm Jup}$ (though this mass limit is likely to be higher for migrating planets; Malik et al., 2015). Beyond 420au the UKIDSS limit is more stringent than any realistic gap-opening mass. Figure 2 shows a schematic diagram illustrating the observational and theoretical constraints.

3. Results

We require the unsharp masked synthetic observations of the simulated discs to display morphology that is consistent with the observations. This constitutes three main features — i) two large-scale symmetric spiral arms, ii) two dark crescents interior to the spirals, and iii) a bright inner ellipse along the major axis of the disc (see Figure 1, left). The spiral arms are visible in the unsharped masking and deprojected images while the dark crescents and bright inner ellipse are only present in the unsharped masking image. The discs presented in Figure 3 employ a steep outer disc edge rather than an exponentially tapered disc.

3.1. Internal companion

Figure 3 (left) shows the simulated observation for one of our internal companion simulations. The disc is a $0.08{\rm M_{\odot}}$ disc with $\Sigma\propto R^{-0.75}$ and $T\propto R^{-0.75}$, and includes a $0.01{\rm M_{\odot}}$ companion at 140 au that is allowed to accrete from the disc and grow to approximately $0.03{\rm M_{\odot}}$. The companion clears a large gap in the disc, forming the required central elliptical feature, but without the dark crescents or two armed spiral as in the original unsharped masking observations. A lower companion mass does not generate the large-scale spirals, while higher mass companions remove large amounts of material from the disc. We therefore suggest that the morphology in Elias 2-27 is unlikely to be due to an undetected companion internal to the spirals.

3.2. External companion

Figure 3 (centre) shows the simulated observations for one of our external companion simulations. This disc is the same as that in Section 3.1 but includes a $\approx 10M_{\rm Jup}$ companion at $\approx 425$ au. The simulated unsharped masking observation reproduces the large-scale spiral arms, the dark crescents and the bright inner ellipse, while the deprojected image shows two large-scale spirals analogous to Figure 1 (right). We also note that simulations with companions located much beyond the gas disc ($\gtrsim 700$ au) can only reproduce the observed morphology by violating the companion mass limits in Section 2.3.2.

3.3. Gravitationally unstable disc

Figure 3 (right) shows the simulated observation for a gravitationally unstable disc with $\Sigma\propto R^{-0.5}$ and $T\propto R^{-0.75}$. The disc mass is 0.24 ${\rm M_{\odot}}$, leading to a disc-to-star mass ratio of 0.49. Even with this relatively massive disc, the combined system mass lies within the limits discussed in Section 2.3.1. The simulated unsharp masking observation reproduces the large-scale spiral arms, the dark crescents and the bright inner ellipse, while the deprojected image shows two large-scale spirals analogous to Figure 1 (right).

4. Discussion

The combination of our hydrodynamic modelling and simulated observations allows us to put strong constraints on the disc structure from which the sub-millimetre continuum emission originates. Throughout all of our models, we find that a steeply declining surface mass density beyond $\approx$ 300 au is key to producing a close match to the masked image. Figure 4 shows the scaled radial intensity profile of our successful self-gravitating disc and the radial intensity profile of the successful companion simulations compared to the observational data from Pérez et al. (2016) and the model of Andrews et al. (2009). The steep decline beyond $\approx$ 300 au in our simulation manifests itself in the form of a steep emission profile at large radii that turns over at approximately the right radius, matching the observed profile well. The modest scaling factor for the self-gravitating disc ($\sim 1.5$) is well within uncertainties associated with dust-to-gas ratios and/or grain opacities for circumstellar discs.

We note that the resulting Toomre profile dips marginally below 1 for a limited radial range in our successful self-gravitating disc. However, this disc shows no sign of fragmentation even though we evolve it for many dynamical times for this radial range. On the other hand a companion beyond the spirals ($\gtrsim 300$ au) is unlikely to have formed by core accretion. This suggests that, should the companion hypothesis be correct, this would hint that the Elias 2-27 disc may have formed a fragment by gravitational instability in the past.

We also stress the importance of applying an unsharp mask to our simulated observations. While such a mask is primarily applied to increase the contrast of the image, subtle changes are introduced to the resulting image that allow us to remove models from consideration. Changes in the surface density profile affect the radial locations at which there is an excess or deficit with respect to a Gaussian mask. This is illustrated in Figure 5 which shows a disc modelled using the properties presented by Pérez et al. (2016) (see Section 2.1 for details) i.e. with an exponential surface mass density profile, which does not reproduce the observations well. Therefore while a range of models replicate the spirals seen in the unprocessed ALMA image (e.g. Tomida et al., 2017), comparison of masked images constrains the disc properties further.

However, special care must be taken when interpreting unsharp masked images. This is because some structures may not be real, but artificially created by the masking. For example, while Figure 1 (left) superficially suggests that a gap exists in the disc, similar structures in the masked images of the external companion and self-gravitating disc in Figure 3 are generated by the interaction of the mask with a smoothly declining emissivity profile. Masked images of observations therefore need to be interpreted via the type of forward modelling exercise undertaken here.

A two-armed spiral structure, as observed around Elias 2-27, is consistent with high disc-to-star mass ratios (e.g. Lodato & Rice, 2005). Indeed Tomida et al. (2017), who suggested that the Elias 2-27 disc is self-gravitating, obtained a high disc-to-star-mass ratio in their simulations. The shocks associated with spiral arms in self-gravitating discs have been shown to have an effect on the chemistry of the disc material (Ilee et al., 2011; Hincelin et al., 2013; Evans et al., 2015) leading to the prospect of detecting the features in line emission (Douglas et al., 2013). Future observations of the Elias 2-27 system, with sensitivities high enough to spatially resolve relevant molecular line transitions (e.g. CO, HCO*+*, OCS and H2CO) will be crucial in further evaluating the dynamics occurring within the star-disc system.

Finally, deep near infrared imaging should offer a first step towards deciding which scenario is at work in the system. If no companion is detected, gravitationally instability is likely. Otherwise further follow-up observations would be required to confirm any possible detected companion.

5. Conclusions

We present the results of a series of hydrodynamic and radiative transfer models to test three hypotheses regarding the origin of the disc morphology around Elias 2-27 — a companion internal or external to the spirals, and a gravitationally unstable disc. Our results show that a steep decline in surface mass density beyond $\approx 300$ au is required, and that the gravitational instability hypothesis or a $\lesssim 10-13M_{\rm Jup}$ companion between $\approx 300-700$ au can reproduce all components of the observed morphology. Given this, we suggest that Elias 2-27 may be one of the first examples of an observed self-gravitating disc or a disc that has recently fragmented forming a $\lesssim 10-13M_{\rm Jup}$ planet.

We thank Mike Irwin for obtaining UKIDSS photometry, and Jim Pringle and the referee for useful comments. We acknowledge support from the DISCSIM project, grant agreement 341137 under ERC-2013-ADG. FM acknowledges support from The Leverhulme Trust. This paper uses the following ALMA data: ADS/JAO.ALMA# 2013.1.00498.S. This work used the Darwin DiRAC HPC cluster at the University of Cambridge, and the Cambridge COSMOS SMP system funded by ST/J005673/1, ST/H008586/1 and ST/K00333X/1 grants.