# Large granulation cells on the surface of the giant star
π1 Gruis

C. Paladini, F. Baron, A. Jorissen, J.-B. Le Bouquin, B. Freytag, S. van Eck, M. Wittkowski, J. Hron, A. Chiavassa, J.-P. Berger, et al.

► To cite this version:

C. Paladini, F. Baron, A. Jorissen, J.-B. Le Bouquin, B. Freytag, et al. Large granulation cells on the surface of the giant star π1 Gruis. Nature, 2018, 553 (7688), pp.310-312. 10.1038/nature25001. hal-02307843

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<figure><img src="image_1.png" /></figure>

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# Large granulation cells on the surface of the giant star π<fnref n="1" /> Gruis

C. Paladini<fnref n="1" />,², F. Baron<fnref n="3" />, A. Jorissen<fnref n="1" />, J.-B. Le Bouquin⁴, B. Freytag⁵, S. Van Eck<fnref n="1" />, M. Wittkowski⁶, J. Hron<fnref n="7" />, A. Chiavassa⁸, J.-P. Berger⁴, C. Siopis<fnref n="1" />, A. Mayer<fnref n="7" />, G. Sadowski<fnref n="1" />, K. Kravchenko<fnref n="1" />, S. Shetye<fnref n="1" />, F. Kerschbaum<fnref n="7" />, J. Kluska⁹ & S. Ramstedt⁵

Convection plays a major part in many astrophysical processes, including energy transport, pulsation, dynamos and winds on evolved stars, in dust clouds and on brown dwarfs<fnref n="1" />,². Most of our knowledge about stellar convection has come from studying the Sun: about two million convective cells with typical sizes of around 2,000 kilometres across are present on the surface of the Sun<fnref n="3" />—a phenomenon known as granulation. But on the surfaces of giant and supergiant stars there should be only a few large (several tens of thousands of times larger than those on the Sun) convective cells<fnref n="3" />, owing to low surface gravity. Deriving the characteristic properties of convection (such as granule size and contrast) for the most evolved giant and supergiant stars is challenging because their photospheres are obscured by dust, which partially masks the convective patterns⁴. These properties can be inferred from geometric model fitting⁵⁻<fnref n="7" />, but this indirect method does not provide information about the physical origin of the convective cells⁵⁻<fnref n="7" />. Here we report interferometric images of the surface of the evolved giant star π<fnref n="1" /> Gruis, of spectral type⁸,⁹ S5.7. Our images show a nearly circular, dust-free atmosphere, which is very compact and only weakly affected by molecular opacity. We find that the stellar surface has a complex convective pattern with an average intensity contrast of 12 per cent, which increases towards shorter wavelengths. We derive a characteristic horizontal granule size of about 1.2 × 10¹<fnref n="1" /> metres, which corresponds to 27 per cent of the diameter of the star.

Our measurements fall along the scaling relations between granule size, effective temperature and surface gravity that are predicted by simulations of stellar surface convection¹⁰⁻¹².

The giant star π<fnref n="1" /> Gruis was observed with the four-telescope H-band beam combiner PIONIER¹³ mounted at the Very Large Telescope Interferometer (VLTI; Cerro Paranal, Chile) during the nights of 2014 September 25 and 29. The observations (see also Methods section 'Data') cover three spectral channels across the near-infrared H band (central wavelengths, 1.625 µm, 1.678 µm and 1.730 µm; width of the filters, 0.0483 µm, corresponding to a spectral resolution of 35). Owing to the excellent Fourier plane coverage acquired and to the good signal-to-noise ratio (Extended Data Fig. 1), we are able to reconstruct model-independent images in each spectral channel (Fig. 1). For this purpose, we use the image reconstruction software SQUEEZE¹⁴, which is based on a Markov chain Monte Carlo (MCMC) approach to the regularized maximum likelihood problem. To assess the reliability of the image we also use a different image reconstruction algorithm, MiRa¹⁵. The images from SQUEEZE and MiRa have very similar characteristics (Fig. 1; see also Methods section 'Image reconstruction'). The dusty envelope that enshrouds the star is transparent in the wavelength range of our observations. The major molecular contributions in this wavelength range are CO and CN; this molecular contribution is the weakest in the longest-wavelength filter, which can be considered as probing the continuum. The images show a stellar disk with the diameter weakly

<figure><img src="image_2.png" /></figure>

**Figure 1** | The stellar surface of π<fnref n="1" /> Gruis.

*a–c*, Images of the stellar surface of π<fnref n="1" /> Gruis reconstructed from the interferometric data using the SQUEEZE¹⁴ algorithm (upper panels) or the MiRa¹⁵ algorithm (lower panels). Images are shown in the spectral channels centred on 1.625 µm (a), 1.678 µm (b) and 1.730 µm (c). The angular resolution of the observations is $\lambda/(2B) \approx 2$ mas, where $\lambda$ is the wavelength and B is the baseline, that is, the distance between two apertures, and is represented by the circle at the bottom right of the top panel in a. In each image, one pixel corresponds to 0.45 mas.

<footnote n="1">¹Institut d'Astronomie et d'Astrophysique, Université libre de Bruxelles, CP 226, 1050 Bruxelles, Belgium. ²European Southern Observatory, Alonso de Cordova 3107, Vitacura, Santiago, Chile.</footnote>

<footnote n="3">³Department of Physics and Astronomy, Georgia State University, PO Box 5060 Atlanta, Georgia 30302-5060, USA. ⁴Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France. ⁵Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden. ⁶European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany.</footnote>

<footnote n="7">⁷Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria. ⁸Laboratoire Lagrange, UMR 7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France. ⁹University of Exeter, Department of Physics and Astronomy, Stocker Road, Exeter EX4 4QL, UK.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 2 | Power spectral density.** *a*, The resulting power spectrum (multiplied by ξ, where ξ is the number of wavelengths per unit of distance) from the SQUEEZE images in three different PIONIER spectral channels (see legend). The granule size is derived by averaging the maximum of the three curves after smoothing. *b*, Comparison between the power spectrum of the SQUEEZE and MiRa images corresponding to</figcaption></figure>

the first spectral channel of PIONIER (1.625 µm). The peak of the MiRa images corresponds to a granule size consistent (within error bars) with that derived from the SQUEEZE image. In *a* and *b*, the grey shaded area on the left marks the limit of the box of the image and the grey shaded area on the right marks the limit of the angular resolution of our observations ($\lambda/(2B)$, as indicated in Fig. 1).

dependent on the wavelength, indicating that the molecular envelope is very shallow and that we are probing the stellar surface continuum. There are patchy structures, all well within the nearly circular stellar surface (in contrast to, for instance, the situation for the well studied$^{7,16}$ supergiant Betelgeuse). For all of these reasons, we infer that the patterns seen on the stellar surface are the actual convective granules. Arguably, this is the most detailed model-independent (see Methods section 'Image reconstruction') image of convective patterns on the surface of a giant star obtained so far.

We estimate the intensity contrast$^{17}$ $\Delta I_{rms}/\langle I \rangle$ after correcting the intensity profile for the limb-darkening effect (see Methods section 'Power spectrum'). This correction ensures that the contrast is sensitive only to the convective pattern. We obtain $13.1\% \pm 0.2\%$, $12.3\% \pm 0.4\%$ and $11.9\% \pm 0.4\%$ in the three spectral channels (ordered by increasing wavelength), where the (statistical) uncertainty corresponds to the standard deviation of the contrast on the various images produced by the MCMC approach used within the SQUEEZE code (see Methods section 'Image reconstruction'). The contrast measurements show a trend towards higher values at shorter wavelengths, indicative of a stronger molecular contamination. Three-dimensional models$^{18,19}$ of red giants are still at an exploratory stage and do not cover the parameter space of $\pi^1$ Gruis. Such models predict a bolometric intensity contrast for the surface convective motions of around 20%; contrasts in the H band, as observed here, may be expected to be lower. Systematic errors (resulting from seeing, limited resolution, and so on) that are difficult to assess quantitatively are also expected to make the observed contrast lower. The above effects (and others) have been discussed in the context of direct imaging of solar granulation$^{11,17}$, but they are likely to reduce the contrast in the interferometric context considered here as well.

The prospect offered by the granule size in that respect is much better. Although in previous studies$^{5-7}$ this quantity was obtained via model fitting, often unconvincingly because of the high values of the resulting reduced $\chi^2$, our interferometric model-independent images allow us to derive the granule size directly from a spatial power-spectrum density (PSD) analysis. This technique is applied routinely on theoretical model predictions$^{10-12}$ and is used here to derive the wavenumber ($k = 2\pi\xi$; where $\xi = 1/\lambda$ is the number of wavelengths per unit of distance, not to be confused with the wavelengths $\lambda$ of the observations) that carries the maximum power, that is, the characteristic granule size. In Fig. 2a we show the PSD as a function of spatial frequency for the three spectral channels of the PIONIER SQUEEZE image cube. After smoothing the PSD of the three spectral channels to remove the 'wiggles', we derive the maximum of the PSD by averaging the position of the three peaks. The error is calculated as the standard deviation of these three maximum values. The resulting granule size is

$5.3 \pm 0.5$ mas. The PSD from the MiRa images gives very similar results (Fig. 2b), and the granule size agrees within the error with that derived from the SQUEEZE images. It is not possible to compare this observed value directly with a global model atmosphere that matches $\pi^1$ Gruis because such a model does not exist. Clearly, stellar surface convection does not look the same across the entire Hertzsprung-Russell diagram in terms of, for instance, granule size. However, if stellar convection is governed by the same (magneto-)radiation-hydrodynamic processes across the Hertzsprung-Russell diagram, then the parametric formulae that relate the characteristic granule size to the stellar parameters, which are based on predictions from the mixing-length theory of convection$^{20}$ and from models for less-evolved stars$^{10-12}$, might be applicable to $\pi^1$ Gruis as well.

To perform this comparison between the spatial structure detected at the surface of $\pi^1$ Gruis and these parametric relations, we convert the typical angular size of the granules observed at the surface of $\pi^1$ Gruis into a linear size. Using the $\pi^1$ Gruis parallax of $6.13 \pm 0.76$ mas (ref. 21), we obtain a characteristic linear granule size of $x_g = (1.2 \pm 0.2) \times 10^{11}$ m. The comparison also requires knowledge of the atmospheric

<figure><img src="image_4.png" /><figcaption>**Figure 3 | The characteristic horizontal scale of granulation of $\pi^1$ Gruis versus theoretical predictions.** The characteristic granule size $x_g$ obtained from the PIONIER images of $\pi^1$ Gruis (triangle; $\log(g) = -0.44$) is quite different from the solar value (circle; $\log(g) = 4.4$). Even though theoretical predictions (dotted line$^{10}$, dashed line$^{11}$ and solid line$^{12}$) had to be extrapolated to lower effective temperatures to match the stellar parameters of $\pi^1$ Gruis ($T_{eff} = 3,200$ K, $\log(g) = -0.44$), they are in good agreement with the observations.</figcaption></figure>
parameters of $\pi^1$ Gruis (see Methods section 'Stellar parameters'): effective temperature $T_{\text{eff}} = 3,200$ K, surface gravity $\log(g) = -0.4$, solar metallicity and mean molecular weight $\mu = 1.3 \text{ g mol}^{-1}$ for a non-ionized solar mixture with 75% hydrogen and 25% helium in mass.

The mixing-length theory of convection predicts that the characteristic granule size $x_g$ scales linearly with the pressure scale height $H_p$ (ref. 10):

$$x_g = 10H_p \quad (1)$$

where $H_p = T_{\text{eff}}R_{\text{gas}}/(\mu g)$ and $R_{\text{gas}} = 8.314 \times 10^7 \text{ erg K}^{-1} \text{ mol}^{-1}$ is the gas constant. The proportionality factor of 10 ensures that the formula correctly predicts the granulation at the surface of the Sun (ref. 11 and Fig. 3). Expressing $x_g$ in units of $10^6 \text{ m}$, $g$ in cm s$^{-2}$ and $T_{\text{eff}}$ in K, equation (1) becomes$^{10}$

$$\log(x_{g, \text{Freytag}}) = \log(T_{\text{eff}}) - \log(g) - \log(\mu) + 0.92 \quad (2)$$

or $x_{g, \text{Freytag}} = 5.1 \times 10^{10} \text{ m}$ using the atmospheric parameters for $\pi^1$ Gruis.

More recent three-dimensional models$^{12}$ have extended the early analysis to FGK dwarfs and K giants, and predict that the size of the convective granules depends on the stellar parameters in a manner very similar to equation (2) (using the same units):

$$\log(x_{g, \text{Trampedach}}) = (1.321 \pm 0.004)\log(T_{\text{eff}}) - (1.0970 \pm 0.0003)\log(g) + (0.031 \pm 0.036)$$

This relation yields $x_{g, \text{Trampedach}} = 1.2 \times 10^{11} \text{ m}$ for $\pi^1$ Gruis. Finally, the CIFIST grid$^{11,22}$, which also covers M-type stars and sub-solar metallicities (expressed as $[\text{Fe/H}] = \log[N(\text{Fe})/N(H)]_{\text{star}} - \log[N(\text{Fe})/N(H)]_{\text{Sun}}$, where $N(\text{A})$ is the number density of element A), follows$^{11}$

$$\log(x_{g, \text{Tremblay}}) = 1.75\log[T_{\text{eff}} - 300\log(g)] - \log(g) + 0.05[\text{Fe/H}] - 1.87$$

This relation yields $x_{g, \text{Tremblay}} = 4.9 \times 10^{10} \text{ m}$ for $\pi^1$ Gruis.

Despite the fact that none of the above relations is derived from stellar models that match the atmospheric parameters of $\pi^1$ Gruis (a very evolved late-type giant star), the predictions are in fairly good agreement (Fig. 3). This result suggests that predictions from current models of stellar surface convection may be extrapolated to the region of the Hertzsprung-Russell diagram where luminous red giants are located. In future studies, securing time-series images will enable the lifetime of the observed convective structures to be determined, providing another way of comparing observations with model predictions.

**Online Content** Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

**Received 9 March; accepted 24 October 2017.**

**Published online 20 December 2017.**

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**Acknowledgements** C.P. acknowledges the support of the Fonds National de la Recherche Scientifique (F.R.S.-FNRS), Belgium. C.S., G.S. are supported by the PRODEX office, Belgium. This research has been funded by the Belgian Science Policy Office under contract BR/143/A2/STARLAB (S.S., A.J., S.V.E.). K.K. is supported by a FRIA grant (Belgium). F.B. acknowledges funding by the National Science Foundation, NSF-AST numbers 1445935 and 1616483. J.K. acknowledges the Philip Leverhulme Prize (PLP-2013-110). S.V.E. thanks the Fondation ULB for its support. The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement 730890 (OPTICON) and from the Austrian Science Fund (FWF) under project AP23006-N16. We thank all the ESO/VLTI staff for supporting our observations.

**Author Contributions** This project was initiated by C.P. A.M. carried out the observations. J.B.L.B. performed the data reduction, F.B. and J.B.L.B. performed the image reconstruction. The contrast and the PSD analysis was carried on by C.P., B.F. and F.B. The stellar parameter determination was made by C.P., S.V.E., S.S., and K.K. A.J. gave crucial help through all the scientific analysis. The text was written by C.P., F.B. and A.J., and edited by the other authors that contributed to the scientific discussion.

**Author Information** Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Correspondence and requests for materials should be addressed to C.P. (cpcaladin@eso.org).

**Reviewer Information** Nature thanks P. Kervella, J. Young and the other anonymous reviewer(s) for their contribution to the peer review of this work.
METHODS

**Data.** The target of this study was observed with the PIONIER¹³ instrument mounted at the Very Large Telescope Interferometer (VLTI; Cerro Paranal). The light from the four auxiliary telescopes, with 1.8-m apertures, was combined to obtain 303 spectrally dispersed visibilities and 201 closure phases (Extended Data Fig. 1). The maximum baseline used to collect the observations is 90 m, which corresponds to an array angular resolution $\lambda/(2B)$ of approximately 2 mas. The data reduction was performed using the *pndrs* package¹³. Following the standard procedure of PIONIER data reduction, the calibrated data are the average of five consecutive files of each observing block. A systematic relative uncertainty of 5% is added on the data. The stars HD 209688 (diameter²³, 2.62 ± 0.03 mas) and HD 215104 (diameter²⁴, 1.7 ± 0.1 mas) were used as calibrators. These objects were selected by using the SearchCal tool developed by the Jean-Marie Mariotti Center (JMMC).

**Image reconstruction.** The image reconstruction was performed using two different algorithms, SQUEEZE¹⁴ and MiRa¹⁵, to assess the reliability of the image reconstruction process. Using regularized maximum likelihood, MiRa minimizes a joint criterion which is the sum of (1) a likelihood term that measures the compatibility with the data and (2) a regularization term that imposes priors on the image. The relative weight between these two terms is controlled by the 'hyper-parameter' factor $\mu$, and we use the so-called L-curve approach to estimate its optimal value for each regularizer²⁵. The output image is 64 × 64 pixels, with a pixel scale of 0.45 mas per pixel. After testing different priors and regularizations to identify possible spurious structures in the reconstructions, we concluded that a trustworthy image is obtained with the MiRa smoothness regularizer, without a prior image. SQUEEZE is based on an MCMC approach to the regularized maximum likelihood problem. It implements parallel simulated annealing and parallel tempering methods, enabling the use of non-convex or non-smooth regularizations that are not implemented in MiRa. SQUEEZE can also handle multi-wavelength datasets, again with the possibility of non-convex and non-smooth trans-spectral regularizations. The images of $\pi^1$ Gruis were reconstructed with the same pixel scale and field of view as used for the MiRA reconstruction.

We first ran 50 independent, parallel, simulated-annealing MCMC chains of 16 × 16-pixel reconstructions at a quarter of the final resolution (1.8 mas per pixel). We then ran 50 MCMC chains of 32 × 32-pixel images at half the final resolution (0.9 mas per pixel), initializing the chains using the mean image over the chains of the 16 × 16-pixel run. Finally, we ran 50 chains of 64 × 64-pixel reconstruction at full resolution (0.45 mas per pixel), initializing the chains with the mean image of the 32 × 32-pixel run. The final reconstruction is again the mean image over the 64 × 64-pixel chains. The whole procedure is designed to avoid falling into local minima, making sure the image is optimal at the lower resolutions before moving on to filling finer details.

Because selecting an adequate regularization is crucial for imaging quality, we determined an adequate combination of regularizers and regularizer weights by simulation. We generated 'ground truth' images of spotless and spotted limb-darkened disks, and using our code OIFITS-SIM (https://github.com/bkloppenborg/oifits-sim) we produced OIFITS data with the same (u, v) spatial frequency coverage and signal-to-noise ratio as the original $\pi^1$ Gruis dataset. We then followed the reconstruction procedure described above for several combinations of regularizers that are known to work for stellar surfaces (such as entropy, total variation, $l_0$ pseudo-norm, field-of-view centring and wavelets) and regularizer weights. We selected the 'optimal' combination and weights as those that minimized the absolute mean difference between the reconstructions and the ground-truth disks: the chosen combination and weights should not introduce features to the featureless disks and should recover existing spots well. We found that a combination of spot regularizer²⁶ and $l_0$ sparsity in the image plane give the best result.

The final SQUEEZE image has a reduced $\chi^2$ of approximately 1.3 and is remarkably similar to the image reconstructed with MiRa. Images at one MCMC standard deviation from the mean display the same features overall, although the details of the bright spots differ slightly (Extended Data Fig. 2). We note that our reconstructions were performed on the three PIONIER spectral channels independently.

For comparison, SQUEEZE was also used in polychromatic mode (using total variation as a trans-spectral regularizer), but we did not find any major differences between the polychromatic images and the channel-by-channel approach.

**Power spectrum.** The PSD is the integral over rings that comprise wavenumbers in a certain interval around $k = 2\pi\xi$, where $\xi = 1/\lambda$ is the number of wavelengths per unit of distance of the squared amplitude of the two-dimensional Fourier transform of the image¹⁷. The PSD analysis of the original images produces a dominant peak at the wavenumber that corresponds to the diameter of the star, followed by several lobes that contain information of higher order. To be able to separate the peak associated with the typical granule size from the one associated with the stellar diameter, we subtract the stellar disk from the image. To perform this step we designed two circular masks (one based on a Gaussian intensity profile and the other on the MARCS model that best fits the photometry) and a square mask fully enclosed on the stellar surface. The Gaussian and the MARCS intensity profiles both introduce some spurious signal in the final PSD, owing to the fact that the intensity profile does not match the reconstructed one well. In particular, the MARCS intensity profile is steeper than the observed one. The square mask provides a final image that is 24 × 24 pixels and is free of the limb effects. The square mask provides the cleanest PSD and is therefore the one discussed in the paper (Fig. 2).

Before proceeding with the PSD analysis, we increased the number of padding points and rescaled the background of the image to the mean intensity of the stellar surface. The method was also applied to the MiRa image, yielding a PSD very similar to the one derived from the SQUEEZE image, as shown in Fig. 2.

**Stellar parameters.** The stellar parameters of $\pi^1$ Gruis available from the literature⁹ are the effective temperature $T_{\text{eff}}$ of 3,100 K, a luminosity⁹ of 7,200 times solar and a current mass⁹ of 1.5 solar masses. Taking advantage of the new grid²⁷ of MARCS models with S-type chemistry, we decided to perform a new parameter estimate. On the basis of the literature values, we calculated a small grid of models that cover the following parameter space: $2,000 K \le T_{\text{eff}} \le 3,200 K$, with steps of 200 K; $\log(g) = 0$ and $-0.44$; $1, 1.3$ and $2$ solar masses; $[\text{s/Fe}] = 1$ dex and $2$ dex; $C/O = 0.5, 0.752, 0.899, 0.925, 0.951, 0.971$ and $0.991$; and a micro-turbulence of $2 \text{ km s}^{-1}$. The parameters of the model that best reproduce the photometry (Extended Data Fig. 3), which are later used for the comparison with the theoretical equations of the granule size, are $T_{\text{eff}} = 3,200 \text{ K}, \log(g) = -0.44$, solar metallicity, s-process element abundances enhanced by $1$ dex and $C/O = 0.991$. These values are in agreement with the literature ones. The diameter of $\pi^1$ Gruis was derived by fitting the PIONIER visibility data with a uniform disk. This choice is justified because intensity profiles derived from the MARCS model atmospheres are very similar to a uniform disk in the first visibility lobe. For the fitting we used the LitPro program provided by the JMMC.

The equivalent uniform disk diameter that we derived is $18.37 \pm 0.18$ mas, which corresponds to about 658 solar radii for a parallax²¹ of 6.13 mas. Our diameter estimate is in agreement with literature values⁹,²⁸.

**Code availability.** The image reconstruction code SQUEEZE is publicly available at https://github.com/fabienbaron/squeeze. The image reconstruction code MiRa is publicly available at https://github.com/emmt/MiRA.

**Data availability.** The reduced PIONIER data sets are available in the http://oidb.jmmc.fr/repository.

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<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

**Extended Data Figure 1** | The PIONIER data. The upper left panel shows in black the PIONIER squared visibilities *V* and in blue the Fourier transform of the SQUEEZE image (first spectral channel) on a linear (main panel) and semi-logarithmic (inset) scale. The upper right panel is the same, but for the closure phase. The lower left panel shows the *u*-*v* coverage of the

<figure><img src="image_7.png" /></figure>

data. The blue data correspond to observations acquired with the short VLTI
array configuration (called 'A1-B2-C1-D0'). The red data correspond
to observations acquired with the intermediate array configuration
('D0-G1-H0-I1').
<figure><img src="image_8.png" /><figcaption>Extended Data Figure 2 | SQUEEZE images and error images. a–c, The first row of images corresponds to the adopted SQUEEZE images; the second row, labelled ‘+STD DEV’, corresponds to images one standard</figcaption></figure>

deviation above the average image; and the third row of images, labelled
‘-STD DEV’ shows images one standard deviation below the average
image.
<figure><img src="image_9.png" /><figcaption>**Extended Data Figure 3** | Spectral energy distribution. Comparison between the spectral energy distribution (yellow stars) and the best-fitting MARCS synthetic spectrum (black line). Note the presence of a moderate infrared excess longwards of 10µm (10⁵ Å) attributable to circumstellar dust.</figcaption></figure>