Joel Sanchez-Bermudez

Gerd Weigelt

Joachim M Bestenlehner

Pierre Kervella

Wolfgang Brandner

Thomas Henning

André Müller

Guy Perrin

Jorg-Uwe Pott

Markus Schöller

J.-U Pott

R Van Boekel

R Abuter

M Accardo

A Amorim

N Anugu

G Ávila

M Benisty

J P Berger

N Blind

H Bonnet

P Bourget

R Brast

A Buron

F Cantalloube

A Caratti O Garatti

F Cassaing

F Chapron

E Choquet

Y Clénet

C Collin

V Coudé Du Foresto

W De Wit

T De Zeeuw

C Deen

F Delplancke-Ströbele

R Dembet

F Derie

J Dexter

G Duvert

M Ebert

A Eckart

F Eisenhauer

M Esselborn

P Fédou

P J V Garcia

C E Garcia Dabo

R Garcia Lopez

F Gao

E Gendron

R Genzel

S Gillessen

X Haubois

M Haug

F Haussmann

S Hippler

M Horrobin

A Huber

Z Hubert

N Hubin

C A Hummel

G Jakob

L Jochum

L Jocou

M Karl

A Kaufer

S Kellner

S Kendrew

L Kern

M Kiekebusch

R Klein

J Kolb

M Kulas

S Lacour

V Lapeyrère

B Lazareff

J.-B Le Bouquin

P Léna

R Lenzen

S Lévêque

M Lippa

Y Magnard

L Mehrgan

M Mellein

A Mérand

J Moreno-Ventas

T Moulin

E Müller

F Müller

U Neumann

S Oberti

T Ott

L Pallanca

J Panduro

L Pasquini

T Paumard

I Percheron

K Perraut

P.-O Petrucci

A Pflüger

O Pfuhl

T P Duc

P M Plewa

D Popovic

S Rabien

A Ramirez

J Ramos

C Rau

M Riquelme

G Rodríguez-Coira

R.-R Rohloff

A Rosales

G Rousset

S Scheithauer

N Schuhler

J Spyromilio

O Straub

C Straubmeier

E Sturm

M Suarez

K R W Tristram

N Ventura

F Vincent

I Waisberg

I Wank

F Widmann

E Wieprecht

M Wiest

E Wiezorrek

M Wittkowski

J Woillez

B Wolff

S Yazici

D Ziegler

G Zins

GRAVITY chromatic imaging of η Car's core. Milliarcsecond resolution imaging of the wind-wind collision

Keywords:

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A&A proofs: manuscript no. GRAVITY_EtaCar Fig. 1. Homunculus Nebula and the binary orbit projected in the plane of the sky (left panel; Front view) and in a plane formed by the observer's LOS and the sky plane (right panel; Side view). The 3D Homunculus model was obtained from the online resources of Steffen et al. (2014). Meynet et al. 2011). One of the evolutionary stages of high-mass stars that exhibit sporadic but violent mass-loss episodes is the luminous blue variable phase (LBV; Humphreys & Davidson 1994). The importance of LBVs to stellar evolution models relies on the possibility of them to directly explode as SN without being a Wolf-Rayet (WR) star [START_REF] Smith | Supernova 1987A: 20 Years After: Supernovae and Gamma-Ray Bursters[END_REF]Smith et al. 2011;Trundle et al. 2008). Therefore, detailed studies of LBVs are crucial to understand the mass-loss processes in high-mass stars (see e.g., Pastorello et al. 2010;Smith et al. 2011).

The source, η Car, is one of the most intriguing LBVs in the Galaxy. Located at the core of the Homunculus Nebula in the Trumpler 16 cluster at a distance of 2.3 ± 0.1 kpc (Walborn 1973;Allen & Hillier 1993;Smith 2006), it has been identified as a luminous (L tot ≥ 5x10 6 L [START_REF] Davidson | [END_REF]Smith et al. 2003) colliding-wind binary (Damineli et al. 1997;Hillier et al. 2001;Damineli et al. 2008b,a;Corcoran et al. 2010) in a highly eccentric orbit (e ∼ 0.9; Corcoran 2005) with a period of 2022.7 ± 1.3 d (Damineli et al. 2008a).

The primary, η A , is a very massive star with an estimated M ∼ 100 M , a mass-loss rate Ṁ ∼ 8.5 x 10 -4 M yr -1 and a wind terminal speed v ∞ ∼ 420 km s -1 (Hillier et al. 2001(Hillier et al. , 2006;;Groh et al. 2012a,b). Evidence suggests that η A is near the Eddington limit [START_REF] Conti | Observational Tests of the Stellar Evolution Theory[END_REF]Humphreys & Davidson 1994). Therefore, it loses substantial mass in violent episodes such as the "Great Eruption" where ∼15 M , possibly more than 40 M [START_REF] Gomez | [END_REF]Morris et al. 2017), were ejected over a period of ∼10 yr. Mass-loss events dominate the evolutionary tracks of the most massive stars (Langer 1998;Smith 2006). In binary star systems, like η Car, the presence of a companion affects wind-driven mass loss, providing alternative evolutionary pathways compared to single stars. Therefore, understanding in detail their mass-loss processes is particularly important.

The nature of the secondary, η B , is even less constrained since it has not been directly observed (it is, at least, of the order of 100 times fainter than η A ; Weigelt et al. 2007) because it is embedded in the dense wind of the primary. Models of the Xray emission (kT ∼ 4-5 keV) predict a wind terminal velocity v ∞ ∼ 3000 km s -1 , a mass-loss rate Ṁ ∼ 10 -5 M yr -1 (Pittard & Corcoran 2002;Okazaki et al. 2008;Parkin et al. 2011), and a T eff ∼ 36000-41000 K (Teodoro et al. 2008).

Models of the mutual motion of the stars suggest an inclination i ∼ 130-145 • , an argument of periastron ω ∼ 240-285 • , and a sky projected PA ∼ 302-327 • for the best-fit orbital solution (Damineli et al. 1997;Okazaki et al. 2008;Parkin et al. 2009Parkin et al. , 2011;;Groh et al. 2010c;Gull et al. 2011;Madura & Groh 2012;Madura et al. 2012;Teodoro et al. 2016). This suggests that the orbital plane of the binary is almost perpendicular to the Homunculus axis ( i ∼ 49 • with respect to the sky plane; PA∼132 • ; [START_REF] Davidson | P Cygni 2000: 400 Years of Progress[END_REF]Smith 2006). These orbital parameters also imply that the secondary remains in front of the primary (in the line-of-sight -LOS-of the observer) most of the time during the orbital motion, except close to the periastron, where η B goes behind η A and it is obscured by the dense primary wind.

Figure 1 displays the inclination and PA of the Homunculus Nebula and of the orbit of η B around η A , according to the orbital solution reported by Teodoro et al. (2016). The left panel displays the nebula projected in the plane of the sky. The PA (east to the north) of the semi-major axis is labeled in the image. The right panel displays the position of the nebula and of the orbit of the binary in a plane parallel to the observer's line-of-sight and the sky plane. The inclination angles (relative to the sky plane) of the nebula (i HN ) and of the binary's orbital plane (i Binary ) are labeled.

The secondary, η B , photoionizes part of the primary wind, changing the strength of lines such as Hα, He i, [Fe ii], and [Ne ii] (Hillier et al. 2001;Nielsen et al. 2007;Mehner et al. 2010Mehner et al. , 2012;;Madura et al. 2012;Davidson et al. 2015). Additionally, it ionizes the inner 1" circumstellar ejecta (Weigelt & Ebersberger 1986;Hofmann & Weigelt 1988;Weigelt et al. 1995). 2D radiative transfer models and 3D hydrodynamical simulations of the wind-wind collision scenario suggest that the high-velocity secondary wind penetrates the slower and denser primary wind creating a low-density cavity in it, with thin and dense walls where the two winds interact (Okazaki et al. 2008;Groh et al. 2012a;Madura et al. 2012Madura et al. , 2013;;Clementel et al. 2015b,a). This windwind collision scenario produces the shock-heated gas responsible for the X-ray variability, and the ionization effects observed in the optical, infrared, and ultraviolet spectra. These aforementioned models also show that during the periastron passage (phase φ ∼ 0.98-1.02) the acceleration zone of the post-shock wind of η B is affected by η A . The hot wind of η B pushes the primary wind outward and it ends up trapped inside the cavity walls. The material in the walls is accelerated to velocities larger than η A 's wind terminal velocity, creating a layer of dense trapped primary wind. These layers have been observed as concentric fossil wind arcs in [Fe ii] and [Ni ii] images at the inner 1" obtained with the HST/STIS camera (Teodoro et al. 2013;Gull et al. 2016).

To explain the wind-wind phenomenology at 2-10 mas (∼5-25 au) scales, several attempts have been made to characterize the core of η Car. Particularly, long-baseline infrared interfer-ometry has been a decisive technique for such studies. [START_REF] Kervella | Exotic Stars as Challenges to Evolution[END_REF] and van Boekel et al. (2003) resolved an elongated optically thick region using the K-band (2.0-2.4 µm) beamcombiner VINCI [START_REF] Kervella | terferometry in Optical Astronomy[END_REF] at the Very Large Telescope Interferometer (VLTI; [START_REF] Glindemann | Interferometry for Optical Astronomy II[END_REF]. Those authors measured a size of 5-7 mas (11-15 au) for η Car's core, with a major to minor axis ratio = 1.25 ± 0.05, and a PA = 134 ± 7 • . Using a Non-Local Thermal Equilibrium (non-LTE) model, a mass-loss rate of 1.6 ± 0.3 × 10 -3 M yr -1 was estimated.

Follow-up observations (Weigelt et al. 2007) with the Kband beam combiner VLTI-AMBER (Petrov et al. 2007) using medium (R = 1500) and high (R = 12000) spectral resolutions of the He i 2s-2p (2.0587 µm) and Brγ (2.1661 µm) lines, resolved η Car's wind structure at angular scales as small as ∼ 6 mas (∼ 13 au). These authors measured a (50% encircled energy) diameter of 3. 74-4.23 mas (8.6-9.7 au) for the continuum at 2.04 µm and 2.17 µm; a diameter of 9.6 mas (22.6 au) at the peak of the Brγ line; and 6.5 mas (15.3 au) at the emission peak of the He i 2s-2p line. They also confirmed the presence of an elongated optically thick continuum core with a measured axis ratio = 1.18 ± 0.10 and a projected PA = 120 • ± 15 • .

The observed non-zero differential phases and closure phases indicate a complex extended structure across the emission lines. To explain the Brγ-line profile and the signatures observed in the differential and closure phases, Weigelt et al. (2007) developed a "rugby-ball" model for an optically thick, latitude dependent wind, which includes three components: (a) a continuum spherical component; (b) a spherical primary wind; (c) and a surrounding aspherical wind component inclined 41 • from the observer's LOS.

New high-resolution AMBER observations in 2014 allowed Weigelt et al. (2016) to reconstruct the first aperture-synthesis images across the Brγ line. These images revealed an asymmetric and elongated structure, particularly in the blue wing of the line. At velocities between -140 and -380 km s -1 , the intensity distribution of the reconstructed maps shows a fan-shaped structure with an 8.0 mas (18.8 au) extension to the southeast and 5.8 mas (13.6 au) to the northwest. The symmetry axis of this elongation is at a PA = 126 • , which coincides with that of the Homunculus axis. This fan-shaped morphology is consistent with the wind-wind collision cavity scenario described by Okazaki et al. (2008), Madura et al. (2012, 2013), and Teodoro et al. (2013, 2016), with the observed emission originating mainly from the material flowing along the cavity in a LOS preferential toward the southeast wall.

Additionally to the wind-wind collision cavity, several other wind structures were discovered in the images reported by Weigelt et al. (2016). At velocities between -430 and -340 km s -1 , a bar-like feature appears to be located southwest of the continuum. This bar has the same PA as the more extended fossil wind structure reported by [START_REF] Falcke | [END_REF] and Gull et al. (2011Gull et al. ( , 2016)), that may correspond to an equatorial disk and/or toroidal material that obscures the primary star in the LOS. At positive velocities, the emission appears not to be as extended as in the blue-shifted part of the line. This may be because we are looking at the back (red-shifted) part of the primary wind that is less extended because it is not as deformed by the wind collision zone. Finally, the wind lacks any strong emission line features at velocities lower than -430 km s -1 or larger than +400 km s -1 .

This work presents VLTI-GRAVITY chromatic imaging of η Car's core across two spectral lines in the infrared K-band: He i 2s-2p and Brγ. The paper is outlined as follows: Sect. 2 presents our GRAVITY observations and data reduction. In Sect. 3 the analyses of the interferometric observables, and the details of the imaging procedure are described. In Sect. 4 our results are discussed and, finally, in Sect. 5 the conclusions are presented.

Observations and Data reduction

Observations

The milliarcsecond resolution of GRAVITY [START_REF] Eisenhauer | SPIE Conference Series -Optical and Infrared Interferometry[END_REF](Eisenhauer et al. , 2011;;Gravity Collaboration et al. 2017) enables spectrally resolved interferometric imaging of the central wind region of η Car. At an apparent magnitude of m K = 0.94 mag, the target is bright enough for observations with the 1.8-meter Auxiliary Telescopes (ATs). η Car was observed during the nights of February 24th and 27th, 2016, as part of the commissioning phase of the instrument, and during the nights of May 30th and July 1st 2017, as part of the GRAVITY Guaranteed Time Observations (GTO). The observations were carried out using the highest spectral resolution (R = 4000) of the GRAVITY beam combiner, together with the split-polarization and single-field modes of the instrument. With this configuration, GRAVITY splits the incoming light of the science target equally between the fringe tracker and science beam combiner to simultaneously produce interference fringes in both. While the science beam combiner disperses the light at the desired spectral resolution, the fringe tracker works with a low-spectral resolution of R∼22 (Gillessen et al. 2010) but at a high temporal sampling (∼1 kHz). This allows to correct for the atmospheric piston, and to stabilize the fringes of the science beam combiner.

For the 2016 observations, ten data sets were recorded with the A0-G1-J2-K0 array plus four more with the A0-G2-J2-J3 configuration. The uv coverage obtained (Fig. 2) provides a maximum projected baseline of ∼130 m (J2-A0) that corresponds to a maximum angular resolution (θ=λ/2B; where B is the maximum baseline) of θ = 1.75 mas, at a central wavelength of λ 0 = 2.2 µm. The 2017 observations comprise three data sets with the D0-B2-J3-K0 array plus seven data sets with the A0-G1-J2-K0 array. For this second epoch the maximum baseline length (J2-A0) was around 122 m (θ = 1.85 mas). However, since most of the longest baselines for both imaging epochs are of 100 m, we adopted a mean maximum angular resolution θ = 2.26 mas for our imaging program. Tables A.1 and A.2 list individual data sets and observing conditions.

Data reduction

The interferometric observables (squared visibilities, closure phases, and differential phases) as well as the source's spectrum were obtained using versions 0.9.0 and 1.0.7 of the GRAVITY data reduction software1 [START_REF] Lapeyrere | SPIE Conference Series -Optical and Infrared Interferometry IV[END_REF]. More details on the data reduction procedure are provided in Sanchez-Bermudez et al. (2017). To calibrate the interferometric observables, interleaved observations of the science target and a point-like source were performed. We used the K3 II star HD 89682 (K-band Uniform Disk diameter d UD = 2.88 mas) as interferometric calibrator for both epochs. Before analyzing the data, all the squared visibility (V 2 ) points with a signal-to-noise ratio (S/N) ≤ 5 and closure phases with σ cp ≥ 40 • were excluded from the analysis.

Calibration of η Car's integrated spectrum

For each one of the data sets, four samples of η Car's integrated spectrum were obtained with GRAVITY. The data reduction software delivers the spectrum flattened by the instrumental transfer function obtained from the Pixel to Visibility Matrix (P2VM; Petrov et al. 2007). Additionally, GRAVITY uses the internal calibration unit [START_REF] Blind | Optical and Infrared Interferometry IV[END_REF]) to obtain the fiber wavelength scale, producing a wavelength map with a precision of ∆ λ = 2 nm. Apart from this preliminary calibrations, we had to correct the η Car spectrum for the atmospheric transfer function together with a more precise wavelength calibration. For this purpose, we used the following method:

1. A weighted average science and calibrator spectra were computed from the different samples obtained with GRAVITY. 2. To refine the wavelength calibration, we used a series of telluric lines across the spectrum of our interferometric calibrator. A Gaussian was fitted to each one of the lines profiles recording their peak positions. The high-resolution (R = 40000) telluric spectrum at the Kitt Peak observatory was then used as reference to re-calibrate the GRAVITY wavelength map. For this, we first degraded the reference spectrum to the GRAVITY resolution and then, we identified a mean wavelength shift of the calibrator's tellurics from the Kitt Peak ones. Finally, the GRAVITY wavelength map was corrected. With this method, we reached a 1σ wavelength calibration error relative to the reference spectrum of 1.23 Å (∆ν = 16.8 km s -1 at λ 0 = 2.2 µm) for the 2016 data, and 0.67 Å (∆ν = 9.1 km s -1 ) for the 2017 data, respectively. A similar calibration method was used by Weigelt et al. (2007Weigelt et al. ( , 2016) ) on the previously reported η Car AMBER data . 3. Once the wavelength calibration was performed, we remove the atmospheric transfer function from the η Car spectrum by obtaining the ratio of the science target and of the interferometric calibrator spectra. Since the interferometric calibrator, HD 89682, is a K3 II star, we have to correct for its intrinsic photospheric lines (e.g., the CO bands seen in absorption from 2.29 µm onward). For this purpose, we used a theoretical BT-Settl 2 model (see Allard et al. 2012) of a star with a T eff = 4200 K, a log(g) = 1.5, and Z= -0.5. Figure 3 displays the normalized η Car spectrum with all the lines, between 2.0-2.2 µm, with interferometric signals different from the 2 http://svo2.cab.inta-csic.es/theory/newov2/ continuum labeled. Although the 2016 spectrum appears to be slightly noisier than the 2017 one, no significant differences were found between the two GRAVITY epochs. This work focuses on the interferometric imaging of η Car across He i 2s-2p and Brγ. Figure 4 displays the normalized η Car spectrum at these wavelengths, together with the differential visibilities and phases of one of our interferometric data sets. Notice the strong changes of the observables between the continuum and the lines.

Ancillary FEROS spectrum

To complement the analysis of the η Car GRAVITY spectrum, we obtained four optical high-resolution spectra of the source using the Fiber-fed Extended Range Optical Spectrograph (FEROS; [START_REF] Kaufer | Optical Astronomical Instrumentation[END_REF] at the MPG 2.2m telescope at La Silla Observatory in Chile. FEROS covers the entire optical spectral range from 3600 Å to 9200 Å and provides a spectral resolution of R = 48 000. All spectra were obtained using the object-sky mode where one of the two fibers is positioned on the target star and the other fiber is simultaneously fed with the sky background. The exposure time was 15 s and 30 s for every two spectra. The reduction and calibration of the raw data were performed using the CERES pipeline (Brahm et al. Article number, page 5 of 32

A&A proofs: manuscript no. GRAVITY_EtaCar

Data Analysis

Geometric model to the GRAVITY Fringe Tracker data

To obtain an angular measurement of the continuum size, a geometrical model was applied to the V 2 Fringe Tracker data. The model consists of two Gaussian disks with different angular sizes tracing the compact and extended brightness distribution of the source. The expression used to estimate the complex visibilities, V(u, v), is the following one:

V(u, v) = G(θ 1 , u, v) + F 2 /F 1 G(θ 2 , u, v) 1 + F 2 /F 1 (1) with G(θ, u, v) = exp        -πθ (u 2 + v 2 ) 4ln(2)        , (2)
where F 2 /F 1 is the flux ratio between the two Gaussian disks, (u, v) are components of the spatial frequency sampled per each observed visibility point (u=B x /λ and v=B y /λ), and θ is the fitted full-width-at-half-maximum (FWHM) angular size for each one of the components.

Since previous studies suggest an elongation of η Car's core along the projected PA of the Homunculus semi-major axis, we applied our geometrical model to V 2 at two orientations. To cover PAs perpendicular and parallel to the semi-major axis of the nebula, we used all the V 2 points at PA ⊥ = 40 • ± 20 • and at PA = 130 • ± 20 • , respectively. The model optimization was done using a dedicated Markov-Chain Monte-Carlo (MCMC) routine based on the python software pymc (Patil et al. 2010). To account for the standard deviations and correlations of the model parameters, we explore the solution space over 10000 different models, considering the first 5000 iterations as part of the burnin phase and accepting only one every three draws of the Monte Carlo. Initial linear distributions were assumed for all the parameters. To avoid an underestimation of the error-bars, the waist of the posterior Gaussian likelihood distribution was also marginalized for each one of the fitted parameters. Figure 5 shows the best-fit model and its uncertainties. Table 1 displays tion. Therefore, SQUEEZE applies a regularized minimization of the form:

x ML = argmin x [1/2χ 2 (x) + n i µ i R(x) i ] , (3)
where χ 2 (x) is the likelihood of our data to a given imaging model, R(x) i are the (prior) regularization functions used and µ i the weighting factors that trade-off between the likelihood and priors. For η Car, we used a combination of the following three different SQUEEZE regularizers: 1. To avoid spurious point-like sources in the field-of-view (FOV), we applied a spatial L0-norm.

2. To enhance the extended structure expected in some of the mapped spectral channels, a Laplacian was used.

3. To ensure spectral continuity all over the mapped emission lines, a spectral L2-norm was applied.

For the minimization, SQUEEZE uses a Simulated Annealing Monte-Carlo algorithm as the engine for the reconstruction. We created 15 chains with 250 iterations each to find the most probable image that best-fit our interferometric data. We used a 67×67 pixel grid with a scale of 0.6 mas/pixel. As initial point for the reconstruction, we chose a Gaussian with a FWHM of 2 mas centered in the pixel grid, and containing 50% of the total flux. We simultaneously fitted the V 2 , closure phases, and wavelength- differential phases. The differential phase is defined in SQUEEZE of the following form:

φ(λ i ) = φ 0 (λ i ) -φ ref .
(4) where φ 0 (λ i ) is the measured phase at channel i, and φ ref is the reference phase. The SQUEEZE implementation of φ(λ i ) uses the REFMAP table, of the OI_VIS extension in the OIFITS v2 files (Pauls et al. 2005;Duvert et al. 2015), to determine which channels are used to define the reference phase φ ref .

In our case, we defined φ ref as the average of the measured phases over the full spectral bandpass used for the reconstruction, with exception of the working channel itself, in the following way:

φ ref = φ 0 (λ k ) λ k λ i (5)
With this definition, the reference phase varies from channel to channel but avoids quadratic bias terms (a similar definition of φ(λ i ) has been used before to analyze AMBER data; see e.g., [START_REF] Millour | EAS Publications Series[END_REF]Millour et al. , 2007;;Petrov et al. 2007). While the V 2 data measure the flux contribution at different spatial scales and the closure phases the asymmetry of the source, the wavelength-differential phases give information about the relative flux-centroid displacement between a given wavelength and the reference one.

For Brγ, 35 channels between 2.160 µm and 2.171 µm were imaged, while for He i, 34 channels between 2.054 µm and 2.063 µm were used. The final mean images were created through the following procedure:

1. We ranked the converged chains, assigning the highest score to the one with the global χ 2 closest to unity. From the ranked chains, we select the best five of them to create the final images. 2. To align the selected cubes of images to a common reference pixel position, a mean centroid position of the continuum was estimated. For this purpose, the first and last five channels of each cube of images were used. The individual centroid positions were computed using a mask of 5 pixels around the maxima of the images at every channel used as continuum reference. Then, their mean value was computed. All the images in the cube were shifted, with sub-pixel accuracy (∼ 0.1 pixels), from this mean centroid position to the center of the image defined at position [34,34] in the pixel grid. 3. From the aligned cubes, we compute a mean image per wavelength. Finally, since most of the spatial frequencies in the uv coverages correspond to 100 m baselines, each image was smoothed with a 2D Gaussian with a FWHM equivalent to λ 0 / 2B max = 2.26 mas.

Article number, page 9 of 32

For both lines, reconstruction tests with the s-and ppolarization data were done independently, however, no significant morphological changes were observed. The images here presented correspond to the p-polarization data. 3.2.2. Effects of the uv coverage on the reconstructed images Due to the interacting winds of the eccentric binary at the core of η Car, we expect changes in the spatial distribution of the flux at different orbital phases. This condition could explain the differences in the observed morphologies between our two imaging epochs. However, while the uv coverage of the 2016 data is homogeneous, the 2017 uv coverage is more sparse. The sparseness of the 2017 uv coverage was caused, partially, because the target was observable above 35 • over the horizon only for a few hours at the beginning of the night.

Therefore, the long baselines of our interferometric array could not properly sample north-south orientations of the uv space. This sparseness in the uv coverage produced a clumpy fine structure and a cross-like shape, superimposed on the source's emission, on the reconstructed images. This crosslike structure is caused by the strong secondary lobes and the elongation of the primary beam (see Fig. C.1). This effect could mimic or mask real changes in the morphology associated with the physics of the wind-wind interactions with the synthesized beam and/or artifacts in the reconstruction process.

To detect the morphological changes between two epochs associated to the physical conditions of the source and not caused by the uv coverage, we searched for coincidental baselines (in size and position angle) at both epochs, to compare the differential phases and visibilities between them. This test allows us to monitor the flux centroid evolution between the continuum and the lines together with the changes observed in the flux distribution. Three baselines, tracing the small, intermediate and large angular scales were selected. Additionally, we compute the differential observables from the reconstructed images to monitor the goodness of the images recovering the possible morphological changes.

Figure 8 displays, as an example, the results of this comparison for Brγ. For the short (θ = 5.7 mas; 13.4 au) and intermediate (θ = 3.8 mas; 8.4 au) baselines, the overall signatures of the centroid and of the flux distribution are similar at both epochs, with more prominent centroid changes at blue-shifted velocities than at the red-shifted side. The long (θ =1.9 mas; 4.46 au) baseline shows more drastic differences at blue-shifted velocities between the two epochs. For example, while the differential phases of the 2017 data exhibit an upside-down double-peak profile at velocities between -420 km s -1 and -170 km s -1 , the 2016 shows a single and less prominent peak.

These changes in the observables for coincidental baselines provide evidence of modifications in the brightness distribution between the two epochs. However, despite the good fit of the 2017 images to the observables (see Figs. E.3, E.4, E.7, and E.8), it is clear that the sparse uv coverage of the second epoch strongly detriments the quality of the reconstructed images. Therefore, they cannot be used for a proper (direct) comparison of the global morphology observed in the 2016 data.

Thus, the 2017 images were excluded for the following analysis and discussion.

Discussion

He I 2s-2p

Fe

Spectroscopic analysis of η Car's primary wind

To characterize the properties of η A 's wind, we fitted the integrated spectrum of our GRAVITY observations (Sect. 2.3) with model spectra. The synthetic spectra were computed with the 1D spherical non-LTE stellar atmosphere and radiative transfer code CMFGEN (Hillier & Miller 1998). Our atomic model includes a large number of ionization stages to cover a wide temperature range in our stellar atmosphere grid without changing the atomic model. The following ions were taken into account:

H i, He i-ii, C i-iv, N i-iv, O i-iv, Ne i-iv, Na i-iv, Mg i-iv, Ca i-iv, Al i-iv, Si i- iv, P ii-v, S i-v, Ar i-iv, Fe i-v,
and Ni ii-v; and the metallicity was set to solar according to Asplund et al. (2005). For comparison, we computed a reference spectrum with the stellar parameters derived by Groh et al. (2012a) for the primary, which in turn is based on previous estimates by Hillier et al. (2001Hillier et al. ( , 2006)). The terminal velocity ( ∞ ), beta-type velocity law (β) and volumefilling factor ( f v ) were taken from Groh et al. (2012a) and were not varied for the grid computation. The luminosity was scaled to match the K-band flux of the reference spectrum. The stellar parameters of our best-fit model and the reference spectrum are listed in Table 2.

While our best-fit model reproduces the spectral lines in the GRAVITY spectrum between 2.0 µm and 2.2 µm, the reference spectrum fails to reproduce the He i lines (Figure 9). Our best-fit model is about 4 000 K hotter than the reference spectrum, but the mass-loss rate is decreased by a factor of two. There is a large debate in the literature whether η A 's mass-loss rate has decreased by a factor between two to four over the last two decades (see e.g., Corcoran et al. 2010;Mehner et al. 2010Mehner et al. , 2012Mehner et al. , 2014)). This could explain the change in the mass-loss estimate from the 2000 HST data used by Groh et al. (2012a) and our 2016-2017 GRAVITY observations, but not the increased temperature.

However, this scenario is not fully consistent with all the observational evidence and theoretical predictions. The hydrodynamic simulations of the wind-wind collision zone, created by Madura et al. (2013), suggest that, instead of an extreme decrease of the η A mass-loss rate, changes in η Car's ultra-violet, optical, and X-ray light curves, as well as of the spectral features, are due to slight changes in the wind-wind collision cavity opening angle in combination with a moderate change in the mass-loss rate.

Moreover, when comparing our CMFGEN model with our complementary FEROS optical spectrum (λ4 200-7 100 Å), we noticed that it is not able to reproduce the metallic [Fe ii] and Si ii lines, while the cooler Groh model reproduces them (see Fig. F.1). Similar behavior is observed for other previous models that include low primary mass-loss rates close to ∼10 -4 M yr -1 (see e.g., Fig. 12 in Madura et al. 2013). This speaks against the strong decrement in the mass-loss rate obtained by our CMFGEN model, and highlights that η B plays a major role in the formation of the observed lines in the GRAVITY spectrum. The effects of the secondary and the wind-wind collision zone on the formation of Brγ and He i cannot be reflected by our 1D non-LTE single star model. Nevertheless, they can be investigated with aperturesynthesis images.

For a better understanding of the system's geometry and how η B could change the parameters derived by our CMFGEN model, we show in Fig. 10 the line-forming regions of our best-fit model and of the reference one as a function of radius for He i 2s-2p (top panel) and Brγ (lower panel). The vertical black lines indicate the following reference points: (a) the red-dotted line shows the location of photosphere of η A , which is not equal to the hydrostatic radius (because of its optically thick wind) but to the point where the optical depth τ = 2/3; (b) the black-solid line shows the mean angular resolution limit of the GRAVITY observations (∼ 2 mas); (c) and the black-dashed line marks the expected projected position of η B at the time of apastron.

With our CMFGEN model, the wind of η A could form the peak of the Brγ emission only at 3 mas (7 au), which is clearly closer than the extended emission observed in the reconstructed images. Furthermore, it can be seen that, with a single star, the peak of the He i 2s-2p line is formed at an angular scale close the resolution of our observations (in the reference model, the He i line-formation region is at a scale smaller than the resolution of GRAVITY). Therefore, the extended emission in the He i 2s-2p images should be related to the UV ionization of η B on the wind-wind collision zone. Any modification to He i as a consequence of the wind-wind interaction would require that (i) η B 's wind penetrates deeply into the denser regions of the primary wind and/or (ii) that η B ionizes part of the pre-and post-shock primary wind near the apex of the wind-wind collision zone. In this scenario, it is expected that the modification of the ionization structure caused by the secondary largely changes the intensity of Helium and Hydrogen lines depending on the orbital phase, particularly at periastron (see e.g., Groh et al. 2010a;Richardson et al. 2015Richardson et al. , 2016)).

We do not detect any significant differences in the line profiles between the 2016 and 2017 GRAVITY spectra. However, when comparing the 2016 GRAVITY data and the 2004 AM-BER data reported by Weigelt et al. (2007) (both of them obtained at a similar orbital phase), we noticed that the He i 2s-2p shows the P-Cygni profile, but the amplitudes of the valley and peak are different for both data sets. This observation suggests the presence of a dynamical wind-wind collision environment with possible changes in the wind parameters over time (see e.g., Fig. 3 in Richardson et al. 2016, where the P-Cygni profile of He i λ5876 is observed close to several periastron passages but the profile of the line varies with time even for similar phases). Therefore, this highlights the importance of monitoring the lines' morphological changes through the reconstructed interferometric images.

The size of η Car's continuum emission

The observed quiescent continuum emission in η Car is caused by extended free-free and bound-free emission (Hillier et al. 2001), and it traces the dense, optically thick primary wind. From our geometrical model to the Fringe Tracker data, we estimated that ∼50% of the K-band total flux corresponds to θ FWHM = 2 mas (∼ 5 au) core (compact emission), with the rest of the flux arising from a surrounding halo of at least θ FWHM = 10 mas (∼ 24 au; see Table 1). The size derived for the continuum η A wind is consistent with the size of the extended primary photosphere, according with our CMFGEN model and previous spectroscopic and interferometric estimates (Hillier et al. 2001(Hillier et al. , 2006;;[START_REF] Kervella | Exotic Stars as Challenges to Evolution[END_REF]van Boekel et al. 2003;Weigelt et al. 2007Weigelt et al. , 2016)).

Previous interferometric studies suggested an elongated continuum primary wind along the PA of the Homunculus. From our data modeling, we derived an elongation ratio of = 1.06 ± 0.05, a value that is consistent with the most recent interferometric measurements with AMBER, but it is 4-σ smaller than the first VINCI estimate in 2003 (see Table . 3). It has been hypothesized that the origin of this elongation could be (i) a latitudedependent wind caused by a rapid rotation of the primary and/or (ii) a consequence of the wind-wind collision cavity. For example, Mehner et al. (2014) suggest that the angular momentum transfer between η A and η B at periastron could be affected by tidal acceleration, resulting in a change of the rotation period of η A , which in turn may affect the shape of the continuum emission.

Additionally, Groh et al. (2010b) used radiative transfer models applied to the VINCI and AMBER data to explore the changes in the continuum associated with modifications in the rotational velocity and with a "bore-hole" effect due to the presence of the wind-wind collision zone. These authors found that both prolate or oblate rotational models reproduce the interferometric signatures. Nevertheless, those models required large inclination angles in which η A 's rotational axis is not aligned with that of the Homunculus. Inclinations where the rotational axis is aligned with the Homunculus would require a decrement in the rotational velocity (and of the size) of η A with time. However, the cavity could also mimic the effects of the observed elongation. Therefore, new radiative transfer models of interferometric data (including GRAVITY and other wavelengths like PIONIER in the H-band) are necessary to test these scenarios. Such models are beyond the scope of the present work and are left for future analysis.

The Brγ interferometric images in the context of the η

Car wind-wind collision cavity

Our 2016 GRAVITY Brγ aperture-synthesis images reveal the morphology of η Car's wind-wind collision cavity. Here, we discuss the principal wind components and their interpretation with previous theoretical models and simulations. The Brγ maps reveal the following general structure as function of the radial velocity:

(1) Continuum wind region. For radial velocities smaller than -510 km s -1 and larger than +368 km s -1 , the maps show a compact emission where the optically thick continuum wind region is dominant. For velocities between -510 km s -1 and +368 km s -1 , additional wind components are observed in the images, however, the continuum emission is always present.

(2) Wind-wind collision region. 3D smoothed particle hydrodynamic models (Okazaki et al. 2008;Gull et al. 2009;Madura et al. 2012Madura et al. , 2013;;Teodoro et al. 2013Teodoro et al. , 2016) ) of η Car's windwind interaction suggest a density distribution that extends far beyond the size of the primary wind. This wind-wind collision zone is identified with a cavity created by the fast wind of η B that penetrates deep into the dense but slow wind of η A as the secondary changes its orbital phase. Following the orbital solution of Teodoro et al. (2016) presented in Fig. 1, η B was close to apastron (in front of η A ) at the time of our GRAVITY observations. Figure 11 displays a schematic view of this wind-wind scenario according to Madura et al. (2013). The diagram represents the position of the system at apastron in a plane defined by the LOS and the sky plane (i.e., called the xz plane in Madura et al. 2013). The cavity opens with a LOS oriented preferably toward the southern wall, along its walls the hot (T ∼ 10 6 K) post-shock η B wind is moving, and, in between, the cold (T ∼ 10 4 K) pre-shock η B wind is observed.

In the Brγ GRAVITY images at radial velocities > -364 km s -1 , we observe an extended asymmetric emission increasing in size and brightness as we approach the systemic velocity, and then it decreases toward positive ones. At velocities be- tween -364 km s -1 and -71 km s -1 , the wind-wind collision cavity presents an elongated and asymmetric cone-like morphology with a bright arc-like feature in the southeast direction. The extended and bright southeast asymmetric emission was first observed in the AMBER images reported by Weigelt et al. (2016). In particular, for velocities between -140 km s -1 and -380 km s -1 , those authors identified a SE fan-shaped morphology. However, there are some changes between the AMBER images and the maps recovered with GRAVITY. We infer that some of those changes are associated with the dynamics of the wind-wind collision zone (i.e., different orbital phases), however, some others are caused by the different spatial frequencies sampled with the two observations. The majority of the longest baselines of the AMBER data are of 80 m, which limits the angular resolution up to λ /2B max = 3 mas, in contrast our GRAVITY data provide a mean maximum angular resolution of 2.26 mas. However, the AMBER data include a better sampling of low spatial frequencies with baselines as small as 10 m. In this respect, our GRAVITY data present a clear limitation since most of our short baselines are above 40

Article number, page 13 of 32 m. Those constraints allowed us to recover images of the smallscale structure of η Car, at the cost of restricting the imaging capabilities to map the most extended emission observed in the AMBER images. Madura et al. (2013) suggested that the time-dependent changes in the spectral lines are a consequence of changes in the line-of-sight morphology of the wind-wind collision cavity. Their hydrodynamical simulations predict that, at apastron, the cavity maintains an axisymmetric conical shape with the leading and trailing arms clearly visible in the orbital plane4 . The half-opening angle of the cavity depends on the ratio of the wind momenta, which can be expressed in terms of mass-loss rate and wind velocity (β = Ṁη A ν η A / Ṁη B ν η B ), of the two interacting stars. Therefore, any modification to the mass-loss rates and/or wind velocities would change the opening angle of the cavity. For example, Ṁη A = 8.5×10 -4 M yr -1 would produce a half-opening angle close to 55 • . On the other hand, Ṁη A = 1.6×10 -4 M yr -1 would create a half-opening angle close to 80 • .

As η B moves from apastron (lower-left panel in Fig. 12) toward the periastron, the wind-wind cavity is distorted, creating a spiral (lower-middle panel in Fig. 12). Interesting is the phenomenology after the periastron passage, where the leading arm of the cavity collides with the "old" trailing arm, forming a dense, cold, and compressed "shell" of η A 's wind (lower-right panel in Fig. 12). Since the secondary wind is providing pressure from the direction of the binary, but because of the very high velocity, the shell is expanding outward through the lowdensity region on the far (apastron) side, the expansion velocity could reach values larger than the terminal velocity of η A 's wind (ν ∞ =420 km s -1 ). The stability and size of the compressed η A shells are also dependent on the adopted Ṁη A . Bordering the compressed shell of primary wind, there is the hot post-shock η B wind. Due to the increment of orbital speed of η B as it approaches the periastron, the post-shock η B wind is heated to higher temperatures ( T ∼ 10 6 K) than the gas in the trailing arm (T ∼ 10 4 K), producing an asymmetric hot shock. After the periastron, photo-ablation of the post shock η A wind could stop the η B wind from heating the primary wind, enhancing the asymmetric temperature in the inter-cavity between the secondary and (bordering) the compressed shell of primary wind.

In this framework, the 2016 GRAVITY images reveal the structure of the cavity at an orbital phase φ ∼ 1.35 (upper-left panel in Figure 12), where the arc-like feature could be interpreted as the inner-most hot post-shock gas flowing along the cavity walls that border the compressed η A wind shell in our lineof-sight. The fact that we observe material preferentially along the SE cavity walls, suggests that the half-opening angle is quite similar to the inclination angle of the system. Madura et al. (2013) shows detailed model snap-shots that illustrate the dependence of the opening angle on the mass-loss rate. However, a straight-forward estimate following the twowind interaction solution of Canto et al. (1996), keeping constant the secondary mass-loss rate and wind velocities, suggests that a primary mass-loss rate between 5.8 × 10 -4 and 1.2 × 10 -3 M yr -1 is necessary to produce a half-opening angle in the cavity of 40 • -60 • . Smaller mass-loss rates would produce bigger angles, which would prevent the wall of the wind-wind collision cavity from intercepting the LOS. The orientation of the extended emission is also consistent with a prograde motion of the secondary (i.e., i > 90 • , ω > 180 • ), with a leading arm projected motion from east to west.

Our analysis of the Brγ arc-like feature's peak in the 2016 images suggests that not all the material is moving at the same speed, Figure 13 displays the centroid position (flux centroid of the 90% emission peak) of the arc-like feature versus radial velocity. As it is observed, the centroid distribution varies between 3.0 and 4.0 mas (7 to 9 au) and between -1.5 and -3.0 mas (3.5 to 7 au) in R.A. and Dec., respectively. This indicates that the observed material has a clumpy structure that is not expanding at the same speed. It is also consistent with the hydrodynamic simulations which suggest that the stability of the shells depends on the shock thickness and that fragmentation begins later the higher the value of the primary's mass-loss rate.

Furthermore, it also provides a plausible explanation for the structures observed in the 2014 AMBER images (Weigelt et al. 2016), which correspond to a later orbital phase previous to the periastron passage (upper-right panel in Fig. 12), where the shells are disrupted and the hot η B wind has already mixed with some portions of the compressed η A wind. In this scenario the bar, observed in the AMBER data between -414 and -352 km s -1 , could be part of the highest velocity component of the hot gas around the distorted shell, while the two antennas of the fan-like structure (from -339 to -227 km s -1 ) could trace portions of the shell that are not yet fragmented. The SE extended emission at lower negative velocities could be interpreted as part of the material bordering the disrupted shell. The observed extended SW emission at positive velocities could be identified as the material flowing along the leading arm's wall which is moving away from the observer at the orbital phase of the AMBER images.

This scenario agrees with observations of the fossil shells on larger spatial scales. Teodoro et al. (2013) observed three progressive shells using HST [Fe ii] and [Ni ii] spectroimages. Since the emission of the forbidden lines is optically thin, the observed shells in the [Fe ii] and [Ni ii] images support a future radio mapping with ALMA in H α lines at an angular resolution better than 0.1" to properly constrain their emmitting regions. The positions of the arcs are consistent with the SE extended emission observed in the interferometric images, but the HST arcs extend up to 0.5". Those authors derived a time difference between the arcs of the order of the orbital period (∼5.54 years), suggesting that each one was created during a periastron passage. Assuming a constant shell velocity, Teodoro et al. (2013) derived a traveling speed of the fossil shells of +475 km s -1 , with the closest arc to η A located, in projection, at ∼0.1" (235 au). Notice that the innermost arc presented in Fig. 2 of Teodoro et al. (2013) resembles the fan-like structure observed in the AMBER images.

It is important to highlight that, while the HST images are tracing the compressed η A wind in the fossil shells, our Brγ images are tracing the hot gas, bordering them, along the cavity walls. A monitoring of the arc-like features with GRAVITY (using short baselines) will be fundamental to characterize the primary's mass-los rate and the effect of η B over the primary wind shells over future orbital phases. He i lines (Damineli 1996;Damineli et al. 1997). Since then, several authors have studied the variations in the helium profiles as a consequence of a binary signature (Groh & Damineli 2004;Nielsen et al. 2007;Humphreys et al. 2008;Damineli et al. 2008b;Mehner et al. 2010Mehner et al. , 2012)). The different CMFGEN models support that the helium lines could be originated in the densest wind of η A . Depending on the Ṁ used, the line-emitting region could be extended from a few au to several hundred au (Hillier et al. 2001(Hillier et al. , 2006;;Groh et al. 2012a, see also Sec.,4.1). However, these models do not fully reproduce the observed evolution of the He i lines without considering the role of η B (see e.g., Nielsen et al. 2007;Damineli et al. 2008b). It is still not clear where and how the Helium lines are formed in the wind-wind collision scenario. Humphreys et al. (2008), based on HST observations, suggested that the He i lines originate at spatial scales smaller than 100-200 au (∼40-80 mas), but still the structure of the line-formation region was not indicated. The recent 3D hydrodynamic simulations of Clementel et al. (2015b,a) presented maps of the different ionization regions (He 0+ , He + , He 2+ ) at the innermost 155 au of η Car's core. These simulations take into account the ionization structure of η A 's wind and the effect of η B 's wind on the collision region for the three different mass-loss rates studied in Madura et al. (2013). These models show that there are several regions composed by He + that might be responsible for the changes observed in the He i profiles.

The GRAVITY observations presented in this study allowed us to obtain the first milliarcsecond resolution images of the inner 20 mas (50 au) He i 2s-2p line-emitting region. In contrast to Brγ, which is observed purely in emission, He i 2s-2p shows a P-Cygni profile with the absorption side blue-shifted. This profile is similar to the helium lines observed at other wavelengths (see e.g., Nielsen et al. 2007). In our images, at velocities between -403 and -326 km s -1 , which correspond to the valley of the line, the extended emission is brighter than at other wavelengths. As we move from the valley to the peak of the line, the brightness of the extended emission decreases, slightly increasing again at velocities around the line's peak (between -95 and -18 km s -1 ). At the red-shifted velocities, the continuum is dominant and the extended component is marginally observed at low-velocities. At the valley of the line, the 2016 images show an elongated emission that is oriented at a PA ∼ 130 • and it extends on both sides of the continuum, with the southeast side slightly more extended.

To compare the morphological changes observed in the images with the model developed by Clementel et al. (2015a,b), we use an adapted version of the helium distribution presented in Fig. 8 by Clementel et al. (2015b). The schematic diagram, in Fig. 14 displays the distribution of helium, in the inner 155 au of η Car. Region 1 corresponds to the zone in the primary wind that is composed mostly by He 0+ . Region 2 shows the hot post-shock η B 's wind composed mostly by fully ionized He 2+ . Regions 3, 4, 5, and 6 correspond to the zones composed by He + and region 7 displays the borders of the cavity walls where compressed postshock η A 's wind is found.

From the distribution of He + , four main regions are observed at different morphological scales. The first of them (region 3) corresponds to the pre-shock primary wind that is partially ionized only by η A . The second zone (region 4) is created by the He 0+ -ionizing photons from η B 's wind that penetrate the preshock primary wind. This region varies in size, being more compact along the azimuthal plane than in the orbital one. Clementel et al. (2015b) argued as possible cause for these differences the Article number, page 15 of 32 A&A proofs: manuscript no. GRAVITY_EtaCar less turbulent nature of the wind-wind interaction region in the azimuthal plane. Region 5 shows the He + , of the post-shock wind of η A , trapped in the walls of the cavity. Finally, region 6 displays the section of the pre-shock η B wind with He + . It is important to highlight that regions 3, 4, and 5 are expected to be around three orders of magnitude denser than region 6.

The fact that we observe the absorption side of the He i 2s-2p blue-shifted implies that it is formed by material in front of η A . It means that regions 4, 5, and 6 are in the LOS. Therefore, the He i 2s-2p structure observed in the GRAVITY images is formed by the different contribution of those regions. By analyzing the images, we hypothesized that the elongated structure, at velocity channels near the valley of the line, appears to be formed by the emission coming mainly from regions 4 and 5. This idea is consistent with the flow of the He + pre-shock primary wind, coming toward us at a velocity of ∼ -400 km s -1 , near the apex of the wind-wind collision zone.

This effect could explain why we observe the most prominent emission at large velocity channels between -403 and -326 km s -1 . Given the PA of the observer's LOS and the orbital plane, we expect to observe emission coming from region 4 at the top and bottom of the continuum. This scenario is also consistent with the emission observed in the GRAVITY images. Since the system near apastron is preferentially oriented toward the material in region 4 that borders the lower wall of the cavity, we also expect to observe an asymmetric emission as the one detected in the images.

As we move toward the systemic velocity of the line, we notice that the extended emission decreases in brightness and size, but it increases again at velocity channels near the emission peak. We suspect that this effect is caused by the material in region 5. The post-shock primary wind in the thin walls of the cavity experiences a turbulent environment, particularly at the apex, that causes some of the material to have zero or positive radial velocities. Notice, however, that for velocities larger than +98 km s -1 , the main source of the emission is within the size of the primary beam. This suggests that the origin of large redshifted velocities is the pre-shock ionized wind from η A (region 3). Hence, similar to Brγ, the observed spatial distribution of He i is in agreement with Clementel et al. (2015a) models with Ṁη A close to 10 -3 M yr -1 . However, future, new hydrodynamic models of the He i 2s-2p line in addition to a GRAVITY monitoring of the line's morphology are necessary to provide solid constraints on the mass-loss rate of the system.

Conclusions

-We present GRAVITY interferometric data of η Car's core.

Our observations trace the inner 20 mas (50 au) of the source at a resolution of 2.26 mas. The spectro-interferometric capabilities of GRAVITY allowed us to chromatically image Brγ and He i 2s-2p emission regions with a spectral resolution of R = 4000, while the analysis of the Fringe Tracker data allowed us to measure the size of the continuum emission, and the integrated spectrum to characterize the parameters of the primary star. -From our geometrical model of the Fringe Tracker squared visibilities, we constrained the size of the continuum emission. We derived a mean FWHM angular scale of 2 mas (∼ 5 au) and an elongation ratio = 1.06 ± 0.5 for the compact continuum emission of η A , together with an extended over-resolved emission with an angular size of at least 10 mas. These estimates are in agreement with previous interferometric measurements. Some of the plausible hypotheses to explain the observed elongation of the continuum compact emission are the fast rotation of the primary and/or the effect of the wind-wind collision cavity. A future monitoring of the continuum size and elongation with GRAVITY and other interferometric facilities at different wavelengths, in combination with radiative transfer models, would serve to test these scenarios. -To characterize the properties of η A 's wind, we applied a CMFGEN 1D non-LTE model to the GRAVITY spectrum. Our model reproduces the He i 2s-2p and He i 3p-4s lines, which could not be formed with the parameters used in previous models in the literature. However, the line-emitting regions of the best-fit model are quite small compared to the structure observed in the reconstructed images. These results imply that single-star models are not enough to reproduce all the observational data. Therefore, the role of η B should be taken into account when modeling the η Car spectrum. Furthermore, when comparing our model with the η Car spectrum in the visible, we could not reproduce the observed metallic features. We suspect that this is caused because many of the metallic lines are forbidden lines with critical electron densities of 10 7-8 cm -3 . With the FEROS aperture, this emission is originating in the fossil wind shells and hence not reproduced in the stellar model. -Our aperture-synthesis images allowed us to observe the inner wind-wind collision structure of η Car. Previous AM-BER interferometric images of Brγ revealed the wind-wind collision cavity produced by the shock of the fast η B 's wind with the slow and dense η A 's wind. Our new 2016 GRAV-ITY Brγ images show the structure of such cavity at a different orbital phase with a 2.26 mas resolution. The observed morphologies in the images are (qualitatively) in agreement with the theoretical hydrodynamical models of Madura et al. (2013). Particularly interesting is the bright SE arc-like feature, which could be interpreted as the hot post-shock gas flowing along the cavity wall (oriented toward the observer) that border the innermost shell of compressed primary wind, which is formed by the shock of the cavity's trailing arm with the leading arm after the most recent periastron passage. -Due to the sparseness of the 2017 GRAVITY data the quality of the reconstructed images from this epoch is clearly affected. Therefore, those images could not be used for a direct comparison with the 2016 ones. Nevertheless, our analysis of the interferometric observables, in coincidental baselines, reveals changes in the cavity structure. The ulterior characterization of those changes is subject to future imaging epochs with a less limited uv coverage than the 2017 data. -We presented, the first images of the He i 2s-2p line. They were qualitatively interpreted using the model of Clementel et al. (2015a,b). We hypothesized that the observed emission is coming mainly from the He + at the cavity walls and from a portion of the pre-shock primary wind ionized by the secondary. From the size of the observed emission and the theoretical models, we suspect that the mass-loss rate of the primary is close to 10 -3 M yr -1 . The emission observed require an active role of η B to ionize the material near the apex of the wind-wind collision cavity. -Spectro-interferometric imaging cubes offer us unique information to constrain the wind parameters of η Car, not accessible by other techniques. In this study, we have shown the imaging capabilities of GRAVITY to carry out this task. A future monitoring of η Car over the orbital period (particularly at the periastron passage), in combination with dedicated hydrodynamical models of the imaged K-band lines, will provide a unique opportunity to constrain the stellar and wind parameters of the target, and, ultimately, to predict its evolution and fate.

Fig. 2 .

 2 Fig. 2. η Car's uv coverages obtained during the GRAVITY runs in February 2016 (top) and May-June 2017 (bottom). Different quadruplets are indicated with different colors.

Fig. 4 .

 4 Fig. 4. Normalized GRAVITY spectrum at the position of the He i 2s-2p and Brγ lines. The calibrated differential visibilities (middle) and phases (bottom) of one of the GRAVITY data sets (MJD: 57903.9840) are also shown. In the middle and bottom panels, different colors correspond to each one of the baselines in the data set (see label on the plots). The dashed-red vertical lines indicate the reference wavelength of the emission feature, and the dashed-horizontal lines show the reference value of the continuum baseline.

Fig. 5 .

 5 Fig. 5. The left panels show the best-fit geometrical model to the Fringe Tracker V 2 data. The model is plotted with a black line, the data are shown with blue dots and the model parameters (with their uncertainties) are indicated on each panel. The right panels display the visibility points used for each model fitting at two different position angles, PA ⊥ = 40 • ± 20 • and PA = 130 • ± 20 • .

  the best-fit parameters of our geometrical model and Figure B.1 shows the 2D posterior distributions of the fitted parameters.

3. 2 .Fig. 6 .

 26 Fig. 6. Brγ interferometric aperture synthesis images from the Feb. 2016 data. The Doppler velocity of each frame is labeled in the images. For all the panels, east is to the left and north to the top. The displayed FOV corresponds to 36×36 mas. The small white ellipse shown in the lowermostleft panel corresponds to the synthesized primary beam (the detailed PSF is shown in Fig. D.1). Above all the images, the GRAVITY spectrum is shown and the different positions where the images are reconstructed across the line are labeled with a colored square, which is also plotted in the images for an easy identification.

Fig. 7 .

 7 Fig. 7. He i interferometric aperture synthesis images from the Feb. 2016 data. The maps are as described in Figure 6.

Fig. 8 .

 8 Fig.8. Differential phases (left) and differential visibilities (right) between the continuum and the line emission for the 2016 (blue line) and 2017 data (purple line). The (reference) continuum phase and visibility were estimated using the first and last five channels in the imaged bandpass. Each one of the rows corresponds to a similar baseline in both epochs, tracing large (top), intermediate (middle) and small (bottom) spatial scales. The baseline lengths and position angles are labeled on the left panels, while the baseline stations are labeled on the right ones. The black-dashed lines correspond to the differential quantities extracted from the unconvolved reconstructed images. The vertical red-dotted line marks the systemic velocity of Brγ. The horizontal red-dotted lines show the continuum baselines.

  Figures 6 and 7 show the mean-reconstructed 2016 Brγ and He i images, respectively. The 2017 images are shown in Figures D.1 and D.2 in the Appendix. To inspect the quality of the reconstruction, Figures between E.1 and E.8 in the Appendix E display the V 2 and closure phases from the recovered images together with the data.

Fig. 9 .

 9 Fig. 9. Lower panel: GRAVITY spectrum from 2.0 µm to 2.2 µm (bluesolid line) with a vertical scale that displays the complete line profiles. Upper panel: magnification of the GRAVITY spectrum, where the fine details of our best-fit CMFGEN model (red-dashed line) and of the reference spectrum derived with the stellar parameters from Groh et al. (2012a) (black-dashed line) are appreciated. Notice that the He i 2s-2p and He i 3p-4s are only matched by our hotter red model.

Fig. 10 .

 10 Fig.10. CMFGEN normalized line equivalent width (EW) as a function of radius for our best-fit model and the reference one. Top and bottom panels: line-forming region as a function of radius for He i 2s-2p and Brγ, respectively. The red/blue dotted line corresponds the location of the η A 's photosphere. The black-solid line indicates the spatial resolution limit of GRAVITY and the black-dashed line shows the projected position of η B at apastron, according with the mean orbital solution presented byTeodoro et al. (2016).

  L/L ) is scaled to match the K-Band flux b Helium abundance in mass fraction c Exponent of the wind-velocity law d Volume filling factor e Stellar wind's terminal velocity * Note: β, f v , and ∞ were fixed parameters in our grid of models. The used values were taken from Groh et al. (2012a)

Fig. 11 .

 11 Fig. 11. Schematic of η Car's wind-wind collision scenario reported byMadura et al. (2013). The wind-wind collision cavity carved by the secondary (green star) in the primary wind is depicted, with the different elements of the primary (blue star) and secondary winds labeled. Notice how the LOS lies preferentially toward the lower cavity wall. The angular scales (centered around η A ) traced with the shortest baselines of the GRAVITY (∼40 m) and AMBER (∼10 m) data are shown with a yellow-dashed and red-dotted rectangles, respectively.

Fig. 12 .

 12 Fig.12. Upper-middle panel: projected orbit of η B around η A , with the position of the periastron, apastron, and two imaging epochs labeled on it. Upper-right panel: AMBER map at -277 km s -1 , where the fan-shaped SE morphology is observed at φ ∼ 0.91. Upper-left panel: GRAVITY image at -291 km s -1 , the SE arc-like feature is observed at φ ∼ 1.28. The FOV of the images is of 36 mas, and they are oriented with the east pointing toward the left and the north toward the top of frames. Lowermost panels: three orbital phases, φ=0.5 (lower-left), φ=1.0 (lower-middle) and φ=1.1 (lower-right), of the wind-wind collision model created byMadura et al. (2013). The panels show the structure of the wind-wind cavity in the orbital plane. The red lines indicate the contour where the density is 10 -16 g/cm 3 and they highlight the changes in the leading and trailing arms of the wind-wind cavity. The positions of the primary and secondary for each phase are marked on the panels with blue and green dots, respectively. The green, magenta, and yellow areas trace the hot (T ∼ 10 6 -10 8 K) post-shock secondary wind bordering the cavity shells. The vector of the observer's line-of-sight is labeled on each panel, and it corresponds to ω =243 • and Ω =47 • . The principal components of the windwind cavity are also indicated in the panels. The lowermost panels were taken fromMadura et al. (2013) and adapted to the discussion presented in Sect. 4.3.

4. 4 .

 4 Ionization effect of η B 's wind observed through the He i 2s-2p line Helium lines are one of the most intriguing spectral features in η Car's spectrum. For example, the discovery of the binary was in part based on spectroscopic variations of the H-band Article number, page 14 of 32 GRAVITY Collaboration: J. Sanchez-Bermudez et al.: η Car Chromatic Imaging

Fig. 13 .

 13 Fig. 13. The image displays the centroid position of the 2016 arc-like feature vs velocity. Left panel: centroid changes in R.A vs velocity. Middle panel: centroid changes in Dec. vs velocity. Right panel: 2D centroid position relative to the η A 's continuum marked at origin with a blue star.

Fig. 14 .

 14 Fig. 14. Different He ionized regions: He 0+ (blue), He + (purple), He 2+ (yellow). The sketch is oriented in a plane parallel to the line-of-sight and the sky plane. Different regions in the wind-wind collision scenario are labeled. Region 1 represents the He 0+ zone in the primary wind. Region 2 shows the hot post-shock secondary wind composed by He 2+ . Regions 3, 4, 5, and 6 correspond to the zones composed by He + in the primary and secondary winds. Region 7 displays the borders of the cavity walls.

Fig. B. 1 .

 1 Fig. B.1. Posterior distributions of the best-fit parameters of the geometrical model presented in Sec. 3.1. The left panel shows the posterior distributions for the model applied to the V 2 data at PA ⊥ = 40 • ± 20 • , while the right panel displays the posterior distributions for the model at PA = 130 • ± 20 • . The 2D distributions show 1 and 2 standard deviations encircled with a black contour. The mean of each distribution is displayed with a blue square. The 1D histograms show the expected value (mean) and ±1σ with vertical dashed lines, together with their corresponding values at the top.

  Fig. 3. 2016 (blue straight line) and 2017 (black straight line) η Car normalized spectra in the 2.0-2.2 µm bandpass. The vertical red-dashed lines indicate the spectral features identified in the spectrum.

		3.5 4.0		HeI 2s-2p		Car GRAVITY spectrum FeII [FeII] [FeII] HeI 3p-4s	MgII	MgII	Br	2016 2017
		3.0
	Normalized flux	2.0 2.5
		1.5
		1.0
		2.000 0.5	2.025	2.050	2.075	2.100 Wavelength [meters]	2.125	2.150	2.175	1e 6 2.200

Table 1 .

 1 Best-fit parameters of the geometrical model

	PA 40 • ± 20 • 130 • ± 20 • θ 1 [mas] Parameter Value 1-σ θ 1 [mas] 2.09 0.03 θ 2 [mas] 10.17 0.13 F 2 / F 1 1.00 0.02 2.21 0.09 θ 2 [mas] 9.51 F 2 / F 1 1.19 0.15 0.79	2s-2p lines. For this purpose, we used SQUEEZE 3 (Baron & Klop-penborg 2010), an interferometry imaging software that allows simultaneous fitting of the visibility amplitudes, squared visibili-ties, closure phases, and chromatic differential phases (or combi-nations of them). At infrared wavelengths, image reconstruction from interferometric data is constrained mainly by the (i) sparse baseline coverage and (ii) the lack of absolute phase informa-

  Article number, page 8 of 32 GRAVITY Collaboration: J. Sanchez-Bermudez et al.: η Car Chromatic Imaging

						Car Br Diff. Phases and Visibilities
			-567.84 -290.85 Velocity [km/s] -13.85	263.15	540.14			-567.84 -290.85 Velocity [km/s] -13.85	263.15	540.14
					BL (2016): 40.6 m; 179.0 BL (2017): 40.3 m; 189.0
										K0-J2 (2016) K0-J2 (2017)
			2.162	2.164	2.166 BL (2016): 54.9 m; 241.0 2.168 2.170 BL (2017): 59.3 m; 240.0			2.162	2.164	2.166	2.168	2.170
	Diff. Phases [degrees]	60 40 20 0 20 40	2.162	2.164 Wavelength [meters] 2.166 BL (2016): 118.9 m; 231.0 2.168 2.170 1e 6 BL (2017): 115.3 m; 230.0	Diff. Visibilities	1.2 0.4 0.6 0.8 1.0 0.0 0.2	2.162	2.164 Wavelength [meters] 2.166	J2-G1 (2016) K0-G1 (2017) 2.168 1e 6 2.170 J2-A0 (2016) J3-B2 (2017)

Table 2 .

 2 Stellar parameters of the CMFGEN models.

	Parameter T eff log(L/L ) a Y b log( Ṁ/M /year)	Groh et al. (2012) This work 9.4 kK 13.5 kK 6.7 7.1 0.55% 0.50% -3.1 -3.

Article number, page 11 of 32 A&A proofs: manuscript no. GRAVITY_EtaCar

Table 3 .

 3 Values of η Car's continuum elongation ratio from different interferometric observations

	Article number, page 12 of 32

http://www.eso.org/sci/software/pipelines/gravity/gravity-piperecipes.html

https://github.com/fabienbaron/squeeze Article number, page 7 of 32 A&A proofs: manuscript no. GRAVITY_EtaCar

For a complete description of the changes in the wind-wind collision cavity and their 3D orientation at scales relevant to the interferometric images, we refer the reader to Fig.1, 2, B1, B2, B3 and B4 inMadura et al. (2013).

Here, we adopted the 2009 periastron passage, T 0 =2454851.7 JD, as reference for the orbital phases labeled on the reconstructed images and diagrams of the wind-wind cavity structure.

Acknowledgements. We thank the anonymous referee for his/her comments to improve this work. J.S.B acknowledges the support from the Alexander von Humboldt Foundation Fellowship program (Grant number ESP 1188300 HFST-P) and to the ESO Fellowship program. The work of A.M. is supported by the Deutsche Forschungsgemeinschaft priority program 1992. A.A., N.A. and P.J.V.G. acknowledge funding from Fundação para a Ciência e a Tecnologia (FCT) (SFRH/BD/52066/2012; PTDC/CTE-AST/116561/2010; UID/FIS/00099/2013) and the European Commission (Grant Agreement 312430, OPTICON).

GRAVITY is

ii lines. The absorption component of the P-Cygni profiles are filled in and the He i emission lines are not reproduced by the model, which has been already observed and discussed in detail by Hillier et al. (2001). The hotter red model can hardly fit the spectral lines observed at FEROS' wavelengths.

Article number, page 32 of 32


Théo Baumard
email: theo.baumard@mines-albi.fr

Olivier De Almeida

Gary Menary

Yannick Le Maoult

Fabrice Schmidt

Jérôme Bikard

Determination of Thermal Contact Conductance in Vacuum-Bagged Thermoplastic Prepreg Stacks Using Infrared Thermography

The infrared heating of a vacuum-bagged, thermoplastic prepreg stack of glass/PA66 was studied to investigate the influence of vacuum level on thermal contact resistance between plies. A higher vacuum level was shown experimentally to decrease the transverse heat transfer efficiency, indicating that considering only the effect of heat conduction at the plies interfaces is not sufficient to predict the temperature distribution. An inverse analysis was used to retrieve the contact resistance coefficients as a function of vacuum pressure.

INTRODUCTION

The use of thermoplastic composites has seen an important growth in the transportation sector in the past few years, partly thanks to shorter manufacturing time achievable compared to thermosetting composites. In order to reach the production rates required by the automotive industry, the processing techniques used such as thermoforming [START_REF] Throne | Understanding Thermoforming -2 nd Edition[END_REF] must be optimized, for example by forming directly a non-consolidated stack. It is therefore critical to predict accurately the heat-up time and temperature distribution of the stack, given the effect on the mechanical properties of the final part [START_REF] Wakeman | Stamp forming of carbon fibre/PA12 composites -A comparison of a reactive impregnation process and a commingled yarn system[END_REF]. The thermal contact resistances that exist in this case between the plies lower the heating efficiency and have to be carefully characterized.

Thermal contact resistance between composite prepreg stacks has been studied mainly in the frame of thermoplastic tape placement [START_REF] Barasinski | An improvement in thermal modelling of automated tape placement process[END_REF][START_REF] Levy | Inter-layer thermal contact resistance evolution with the degree of intimate contact in the processing of thermoplastic composite laminates[END_REF], or in an environment at ambient pressure [START_REF] Cassidy | Effect of contact resistances on the thermal conductivity of an unconsolidated fibre-reinforced thermoplastic prepreg stack[END_REF]; it has been shown that an increase in compaction pressure leads to better heat transfer along the stack thanks to a better intimate contact between plies. Analytical models exist that allow the determination of thermal contact resistance as a function of applied pressure, for example through Hertzian contact theory [START_REF] Mikic | Thermal contact conductance; theoretical considerations[END_REF]. However, the case in which the compaction pressure is generated by mean of a vacuum bag has not been investigated.

In the first part, an experimental campaign is conducted in order to investigate the effect of the partial vacuum pressure on the heating of a non-consolidated thermoplastic prepreg stack. Secondly, a numerical model is set up to determine a global thermal contact resistance coefficient through inverse analysis.

EXPERIMENTAL PROCEDURE

Material

The material used in this study is a commercially available 2/2 Twill glass/PA66 thermoplastic powderimpregnated prepreg, supplied by Rhodia -Solvay. The fabric has an areal density of 960g/m². Figure 1a shows the structure of the composite, i.e. glass fabric with high percentage coverage of polyamide droplets. The studied stack is composed of 6 plies, oriented in the same direction.

A surface roughness analysis was conducted using a confocal microscope profilometer. FIGURE 1. 1b shows the topography of a 48mmx5mm sample. Roughness parameters are presented in TABLE 1 1. They appear to be independent of the direction and the side of the fabric: the polyamide repartition can be considered homogeneous. The specific heat capacity of the fabric was carried out using a Perkin Elmer DSC. Optical properties of the material were measured using a Bruker Vertex 70 FTIR spectrometer. Transmission and reflection measurements were carried out on 30x30mm samples randomly cut from the prepreg roll. All samples were shown to be opaque on the considered bandwidth, so the measured reflectivity directly relates to the emissivity of the samples.

The measured material properties relevant to the study are summed up in TABLE 1 1; the thermal conductivity values were evaluated in [START_REF] Bakali | Simulation of IR heating for composite stamping[END_REF].

0.53 W.m -1 .K -1 Specific heat capacity C p 1.02 J.g -1 .K -1 (20°C), 1.11 J.g -1 .K -1 (50°C) Integrated emissivity ε 0.92 RMS roughness R q 0.112mm ± 0.016mm RMS slope of the roughness profile R dq 137° ± 13°

Experimental Set-up

The experimental setup used to study the influence of the vacuum pressure is presented in Figure 2. The prepreg stack is bagged with a Capran 518/HS8171-6 polyamide film, and vacuum drawn with a CompositVac E25 pump. The stack is held vertically and heated with a horizontal 30cm long, 1000W halogen lamp from Toshiba Lighting, whose properties have been determined in previous studies [START_REF] Nakouzi | Optimization of the incident heat flux upon a 3D geometry composite part (Carbon/Epoxy)[END_REF]. The effect of pressure on heating is tested for two levels of relative pressure (-400mbar and -990mbar), successively and in that order to avoid effects arising from the possible plastic deformation of microscopic contact areas. The pressure level is controlled by mean of a variable leak valve.

FIGURE 2. Experimental set-up

The temperature field is measured on the back face of the stack using a CS 325 FLIR infrared camera [7.5-13.5µm], and recorded during the first 4000 seconds of the heating phase. The stack is then allowed to cool down to room temperature before vacuum level is modified.

EXPERIMENTAL RESULTS

An example of a measured back face temperature distribution is shown in Figure 3a, after 4000s at -400mbar. The lamp is oriented along the horizontal profile 3, and symmetrical with regard to vertical profile 4. The thermogram is symmetrical with regard to profile 4 as expected, but does not present a horizontal axis of symmetry. This can be explained by non-homogeneous convective effects around the vertically held stack.

Figure 3b shows the temperature variation versus time at the central point of the back face of the stack, for the two different considered relative vacuum levels. The graphs (green and red curves) show that varying the relative pressure from -400mbar to -990mbar leads to a temperature difference of 2.5°C after 4000s of heating. This means that even though compaction pressure is increasing, the heat transfer efficiency along the out-of-plane direction of the prepreg stack is reduced.

This result seems in contradiction with previous studies. This may imply that considering only the change in contact area between the plies is not sufficient to explain the observed effect (since contact conductance should increase with increasing compaction pressure).

Two competing effects are thus to be taken into account during the heating of a vacuum bagged prepreg stack to predict the temperature distribution: the vacuum pressure affects on one hand the conductive heat transfer through the polyamide droplets, but also impacts the conductive and convective heat transfer through the interstitial air. A possible explanation of the observed trend is the change in thermal conductivity of the interstitial air. The pressure variation is inversely proportional to the mean free path of molecules [START_REF] Jennings | The mean free path in air[END_REF], which is related to thermal conductivity: the higher the distance between two molecular collisions, the lower the thermal conductivity.

Another possibility is the apparition of convective effects between the plies as the compaction pressure is decreased, considering that interstitial distance is large enough. The radiative transfer should also decrease with increasing compaction pressure, as the view factor depends on the effective contact area. However, given the range of temperatures reached inside the laminate, this mode of heat transfer should not be preponderant: the contribution of radiative transfer to thermal conductance is expected to be proportional to T 3 [START_REF] Donaldson | Effect of delamination on the transverse thermal conductivity of a SiC-fiber reinforced SiC-matrix composite[END_REF]. The Stark number [START_REF] Brewster | Thermal Radiative Transfer and Properties[END_REF] gives the ratio of conductive heat transfer over radiative heat transfer: it is computed to be 65 in our case at 50°C. This confirms the fact that inter-ply radiative transfer is almost negligible. An additional experiment is presented in Figure 4: the vacuum level is changed dynamically during the heating phase, from -900mbar to -400mbar and back, and the temperature evolution of the central point (blue curve) is plotted against the previous curves at -990mbar and -400mbar (in black, moving averaged for clarity purposes). The effect on temperature is reversible: the curve shows no hysteresis (the deformation of the contact points in this pressure range can be considered as purely elastic) and no dynamic effect once the pressure is stable: the temperature change is due to the pressure level, rather than pressure variation rate. This implies that the effect is due mostly to the change of the interstitial fluid thermal properties, rather than convective effects.

NUMERICAL SIMULATION

The experimental setup is implemented in commercially available finite elements software COMSOL Multiphysics®. The halogen lamp is modelled as in a previous paper [START_REF] Bakali | Simulation of IR heating for composite stamping[END_REF]: only the tungsten wire is considered as a cylindrical radiative source at a temperature T=1990 K (equivalent radius of the wire r=1.075mm), and the radiative heat transfer is treated as a view factor problem, using the hemicube method [START_REF] Cohen | A progressive refinement approach to fast radiosity generation[END_REF]. The stack is modelled as 6 plies with homogenized properties as defined in Tab. 1. As a first approach, the contact conductance is evaluated in steady state regime. It is assumed to be constant at each inter-ply interface. A classical inverse analysis procedure allows its determination: an optimization routine, using the Nelder-Mead algorithm [START_REF] Nelder | A simplex method for function minimization[END_REF], is used to minimize the squared difference between the simulated and measured temperature on the horizontal central profile. Figure 5a presents the Comsol meshed model. After a mesh sensitivity analysis, the mesh is reduced to 30x60 elements on the surface, with 4 elements per ply through the thickness. The simulated profile for the optimized contact conductance is presented in Figure 5b for the case -400mbar. The numerical results are shown in Table 2. The order of magnitude of the measured contact conductances is coherent with values from the literature. Cassidy and Monaghan [START_REF] Cassidy | Effect of contact resistances on the thermal conductivity of an unconsolidated fibre-reinforced thermoplastic prepreg stack[END_REF] reported thermal contact conductance ranging from 50 to 90W/(m².K), over a compaction pressure range of 0.2 to 0.8MPa for an APC/2 composite stack. Here, increasing the relative pressure from -990mbar to -400mbar leads to a 30% increase in contact thermal conductance.

CONCLUSIONS AND PERSPECTIVES

Thermal contact conductance in a vacuum-bagged, unconsolidated composite stack has been measured. Results presented show that the effect of decreasing the relative pressure inside the vacuum bag is to decrease the effective thermal conductivity of the stack, in apparent contradiction with previous results from the literature. The thermal contact conductance is decreased by 30%, over a relative pressure range of -990mbar to -400mbar. Two competing modes of heat transfer, namely conduction through surface asperities and conduction/convection from the interstitial air have to be taken into account to predict the temperature distribution in the stack. In terms of processing conditions, an optimum value of vacuum pressure can be found that maximizes the heat transfer along the stack. It is to be noted though that other parameters have to be taken into account (quality of impregnation …).

To further this work, a more comprehensive phenomenological model should be used in order to decouple the contributions of each mode of heat transfer at the plies interfaces. This study will be used as a part of a global, predictive simulation tool for the coupled heating and forming of thermoplastic composite parts.

FIGURE 1 .

 1 FIGURE 1. Surface analysis of the prepreg

FIGURE 3 .

 3 FIGURE 3. Results of the heating experiments

FIGURE 4 .

 4 FIGURE 4. Evolution of temperature with dynamically varying vacuum level at central point 5

FIGURE 5 .

 5 (a) Comsol meshed model (b) Simulated and experimental profile 3, -400mbar Numerical model and results

TABLE 1 .

 1 Material properties

	Properties	2/2 Twill Glass/PA66
	Density ρ	960 g/m²
	Transverse thermal conductivity κ Z

TABLE 2 .

 2 Contact conductance vs. relative pressure

	Relative pressure p	-990 mbar	-400 mbar
	Thermal contact conductance h global	78 W/(m².K)	102 W/(m².K)

ACKNOWLEDGMENTS

The work was conducted at Institut Clément Ader, Ecole des Mines d'Albi, France. The authors would like to thank Solvay for supporting this study and providing the testing materials.