S Boissier
email: samuel.boissier@lam.fr

O Cucciati

A Boselli

S Mei

L Ferrarese

The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). VII.: BCG UV upturn and the FUV-NUV color up to redshift 0.35 ⋆

Keywords: ultraviolet:galaxies, galaxies: ellipticals and lenticulars, cD, galaxies:stellar content

Context. At low redshift, early-type galaxies often exhibit a rising flux with decreasing wavelength in the 1000-2500 Å range, called "UV upturn". The origin of this phenomenon is debated, and its evolution with redshift is poorly constrained. The observed GALEX FUV-NUV color can be used to probe the UV upturn approximately to redshift 0.5. Aims. We provide constraints on the existence of the UV upturn up to redshift ∼ 0.4 in the brightest cluster galaxies (BCG) located behind the Virgo cluster, using data from the GUViCS survey. Methods. We estimate the GALEX far-UV (FUV) and near-UV (NUV) observed magnitudes for BCGs from the maxBCG catalog in the GUViCS fields. We increase the number of nonlocal galaxies identified as BCGs with GALEX photometry from a few tens of galaxies to 166 (64 when restricting this sample to relatively small error bars). We also estimate a central color within a 20 arcsec aperture. By using the r-band luminosity from the maxBCG catalog, we can separate blue FUV-NUV due to recent star formation and candidate upturn cases. We use Lick indices to verify their similarity to redshift 0 upturn cases. Results. We clearly detect a population of blue FUV-NUV BCGs in the redshift range 0.10-0.35, vastly improving the existing constraints at these epochs by increasing the number of galaxies studied, and by exploring a redshift range with no previous data (beyond 0.2), spanning one more Gyr in the past. These galaxies bring new constraints that can help distinguish between assumptions concerning the stellar populations causing the UV upturn phenomenon. The existence of a large number of UV upturns around redshift 0.25 favors the existence of a binary channel among the sources proposed in the literature.

Introduction

Code (1969) presented for the first time evidence of an excess of far-ultraviolet (FUV) light in the bulge of M31. The International Ultraviolet Explorer (IUE) observations of Ellipticals allowed astronomers to characterize this as "UV upturn", i.e., a rising flux with decreasing wavelengths from about 2500 Å to 1000 Å (e.g., Bertola et al. 1982). The UV upturn was found in the nearby universe in quiescent gas depleted ellipticals and has been associated to old stars (O'Connell 1999;Ferguson 1999). This feature has also been found in other old stellar systems such as M32 (Brown 2004) or open clusters (Buson et al. 2006;Buzzoni et al. 2012). Empirical work to find the actual source of the upturn included the analysis of color-magnitude diagrams (Brown et al. 1998), the detection of individual horizontal branch stars (Brown et al. 2000), or surface brightness fluctuations (Buzzoni & González-Lópezlira 2008).

⋆ Tables 2 to 5 are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ Since the UV upturn is found in early-type galaxies characterized by old stellar populations, an effect of age can be expected. Observed correlations also suggest a role of metallicity (Faber 1983;Burstein et al. 1988). However, these results have been extensively discussed (see the conflicting results in Deharveng et al. 2002;Rich et al. 2005;Boselli et al. 2005;Donas et al. 2007).

The recent work on absorption indices revealing old and young populations by Le Cras et al. (2016) has showed that there is still a strong interest to understand the nature of UV upturn sources and their contribution to stellar populations as a whole. From the point of view of the evolution of galaxies and the role of the environment, it is important to understand the UV emission associated with old stellar populations in early-type galaxies and to determine whether it is related to the environment (see Boselli et al. 2014). Hills (1971) suggested that the UV emission in M31 could be related to the presence of very hot stars. [START_REF] Renzini | Spectral Evolution of Galaxies[END_REF] discussed the possible candidates in the context of stellar population evolution. This included young stars, hot horizontal A&A proofs: manuscript no. sambcg branch stars, post-AGB stars, and binaries. Several theoretical works studied the UV emission of various types of stars during their advanced evolution phases (e.g., Greggio & Renzini 1990;Dorman et al. 1993Dorman et al. , 1995;;D'Cruz et al. 1996). These works showed that their UV output is very sensitive to small differences in the assumptions made. Greggio & Renzini (1990) suggested that stellar evolution theory alone could not provide the explanation of the UV upturn.

It is still generally believed that the UV upturn is related to extreme horizontal branch stars (Brown 2004, and references therein). These stars could be low mass helium burning stars having lost their hydrogen-rich envelope (e.g., Han et al. 2007, and references within). However, the precise stellar evolution producing hot low mass stars is still debated. Recent models include single-star evolution with both metal-poor and metal-rich populations (e.g., Park & Lee 1997;Yi et al. 1998) or models including the effect of binarity, with stars losing their hydrogen envelopes during binary interactions (Han et al. 2007).

The various models proposed for the UV upturn sources predict drastic differences concerning the evolution of galaxy colors with redshift. [START_REF] Renzini | Spectral Evolution of Galaxies[END_REF] and Greggio & Renzini (1990) already suggested that observations at a look-back time of a few Gyr should allow us to distinguish between possible sources. In the case of single-star origin, the UV upturn is expected to occur late because it is produced by evolved stars. If it is related to binaries, its apparition can be more progressive. Higher redshift observations are needed to distinguish these different evolutionary scenarios.

From the observational point of view, Rich et al. (2005) found little evolution up to redshift 0.2 in a sample of 172 red quiescent galaxies (not restricted to the most massive or to central clusters) obtained by cross-matching SDSS and GALEX results. Lee et al. (2005) and Ree et al. (2007) compared the observed FUV-V color of nearby ellipticals to the brightest ellipticals in 12 remote clusters up to redshift 0.2, and also compared this color to a few previous works (see Brown 2004) up to redshift 0.6. These results suggest that the FUV-V restframe color is bluer by about 0.8 mag around redshift 0.2 with respect to redshift 0, with a large dispersion at all redshifts. The color of the few galaxies at redshifts higher than 0.2 is close to the average color at lower redshifts. Donahue et al. (2010) presented the evolution of the FUV-R color with redshift in 11 brightest cluster galaxies (BCGs) in the redshift range 0.05-0.2, detected in FUV, with little evolution. Direct studies of the evolution of the UV upturn with redshift are still limited to small samples and include only a few tens of objects when limited to BCGs. Table 1 list the samples of early-type galaxies with FUV and near-ultraviolet (NUV) magnitudes from GALEX.

Several colors or other quantities have been used to detect and study the UV upturn. One of them is simply the FUV-NUV GALEX color that is easily accessible from GALEX data. It has been used by, e.g., Boselli et al. (2005); Donas et al. (2007); Loubser & Sánchez-Blázquez (2011). This color probes the slope of the UV spectrum, and can be used to this end up to moderate redshift. In Fig. 1 we show the spectrum of NGC1399, a Fornax elliptical with a strong UV upturn at redshift 0. We also show the spectrum shifted for a few redshifts, and the evolution of the corresponding FUV-NUV color as a function of redshift. The FUV (around 1500 Å) and NUV (around 2300 Å) filters from GALEX are also indicated, showing that the FUV-NUV color probes the UV slope. The FUV-NUV color can thus be an indicator of the presence of an upturn, and of the value of the slope of the spectrum. As a visual reference, we also show the evolution for a flat UV spectrum. Any upturn will be by defini-Fig. 1. Top: Arbitrarily scaled spectrum of NGC1399 (solid line). The spectrum was taken from the database of UV-Optical Spectra of Nearby Quiescent and Active Galaxies (http://www.stsci.edu/science/sed/sed.htm), the original UV data are from Burstein et al. (1988). The spectrum was smoothed for visualization, and extrapolated at low wavelength (between 912 and 1170 Å) to match a typical upturn galaxy spectra (Yi et al. 1998). This spectrum is also shown after redshifting to z=0.3, 0.6, 0.9. A "flat" version is also shown (i.e., removing the upturn) for reference purposes (see text in the introduction). The GALEX FUV and NUV passbands are respectively indicated as a blue and red shaded area. Middle: Evolution with redshift of the FUV-NUV color for the upturn and flat spectra as the solid and dashed curve, respectively. The dotted horizontal lines corresponds to FUV-NUV=0.9, the limiting color for an upturn as defined by Yi et al. (2011). Bottom: Evolution with redshift of the FUV-V color of the upturn and flat spectra as the solid and dashed curve, respectively. tion bluer than this reference (at redshift 0, it corresponds to a color close to the 0.9 limit, proposed by Yi et al. 2011, to characterize the presence of an upturn). On the contrary, old stellar populations without upturn are redder than this reference. The upturn FUV-NUV color is distinguishable from a flat spectrum up to approximately redshift 0.5. Beyond this redshift, no more flux is found in the observed FUV band, and the color can no longer be used to detect a UV upturn. The figure illustrates that the presence of a UV upturn can clearly be detected as a blue Notes. (a) Number of FUV detections. (b) Sample with low uncertainty on the central color (sum of uncertainties on each side lower than 1.2 mag) and excluding galaxies flagged as contaminated. (c) Red global NUV-r color and blue central FUV-NUV color (see Sect. 3.1).

observed FUV-NUV color at the redshifts considered in this paper (below redshift 0.4). In the nearby universe, the UV upturn is often studied on the basis of a color rather similar to FUV-V.

Figure 1 shows differences between the flat and upturn cases that are similar to those for the FUV-NUV color. For this color, however, we find a greater evolution of the observed FUV-V color (in AB magnitudes) with redshift. This makes it impossible to adopt a single color threshold for the detection of an upturn over the same redshift range. The two bottom panels of this figure can still help the reader compare our study to this color choice. We note that this is very close to the classical (1550-V) Burstein from Burstein et al. (1988) with FUV-V (in the AB system) ∼ (1550-V) Burstein + 2.78 (Buzzoni et al. 2012).

The Virgo area was extensively studied in the FUV and NUV bands of GALEX in the context of the GUViCS project (Boselli et al. 2011). The photometry collected by GUViCS provides a deeper coverage than in most large areas over the sky. The UV properties of early-type galaxies inside the Virgo cluster were studied in Boselli et al. (2005). In the present paper, we take advantage of these data to extract FUV and NUV photometry for massive galaxies in the background of the cluster, up to a redshift of about 0.35.

We select a sample of BCG galaxies from the maxBCG catalog (Koester et al. 2007), extract FUV and NUV data for 177 of these galaxies from GUViCS, and perform a visual inspection to ensure the quality and noncontamination of these fluxes. Considering the small statistics of existing BCG samples with FUV data (e.g., only 36 galaxies in Loubser et al. 2011 at redshift 0;12 in Rhee et al. 2007 up to redshift 0.2), even after removing the galaxies with possible contamination or large error bars, our sample brings new constraints for future models of the UV upturn population. We provide all our data in the form of easyto-use tables for this purpose.

In Sect. 2, we present our sample and methods. The selection of galaxies showing upturn signs is discussed in Sect. 3. In Sect. 4, we show the dependences of the FUV-NUV color on luminosity and redshift in our sample, and discuss their implications. A summary is given in Sect. 5.

Throughout the paper, we use a flat cosmology (H 0 =70, Ω m =0.3) to convert between look-back time τ and redshift (z). In our redshift range, the relation is linear with τ ∼ 11.5 × z.

Samples and data

BCG sample

In order to obtain a sample of galaxies that are as evolved as possible in the background of the Virgo cluster area, we ex-tracted a sample of BCGs using the maxBCG catalog that was computed from the Sloan Digital Sky Survey photometric data (Koester et al. 2007). We selected all galaxies with right ascension (RA) in the 180-195 degrees range and with declination (DEC) in the 0-20 degrees range, and with available GALEX images in the FUV and the NUV bands, from the GUViCS survey of this area (Boselli et al. 2011). This sample consists of 177 galaxies listed in Table 2. Koester et al. (2007) provided a number of properties of each BCG galaxy (position, redshift, luminosity) and of its cluster (e.g., number of members, luminosity of the members). We also performed a query to the DR13 SDSS release (Albareti et al. 2016) to obtain the latest spectroscopic information. We checked that the spectroscopic redshifts are in agreement with the Koester et al. (2007) values for the 71 galaxies for which it was provided, and we increased the number of spectroscopic redshifts in this way up to 150 objects, i.e., the vast majority of our sample. We also obtained the SDSS spectroscopic class ("GALAXY" for the 150 objects) and subclass based on line properties that result, in our sample, in one active galactic nucleus (AGN), three "BROAD-LINE" objects, one "STAR-FORMING" object. Finally, SDSS also provides measurements of the Mg2 and Hβ Lick indices often used in the literature to study the origin of the upturn in galaxies (e.g., Faber 1983;Burstein et al. 1988;Boselli et al. 2005;Buzzoni et al. 2012).

Table 2 compiles RA, DEC, photometric redshift, r-and iband luminosity from the maxBCG catalog, while Table 3 provides the spectroscopic information obtained by querying the DR13 database: spectroscopic redshift, subclass, and Lick Mg2 and Hβ indices when available.

UV images

The early-type distant galaxies are often very faint in the ultraviolet bands, and a blind search can easily be affected by nearby objects (especially considering the ∼5 arcsec resolution of GALEX) or low signal-to-noise ratio. Due to the nature of the GUViCS survey and the GALEX circular field of view, the survey is not homogeneous, and many galaxies were observed on several occurrences. We constructed stamps around the position of the BCGs by coadding any available UV images around our sources. This was done using the Montage sofware [START_REF] Jacob | Montage: An Astronomical Image Mosaicking Toolkit[END_REF] following the procedure described in Boissier et al. (2015), which allows the deepest possible UV exposure for each target. The UV original pixel is 1.5 arcsec wide, but since we reconstructed images from a variety of sources with arbitrary position shifts, we used Montage to project the UV im-A&A proofs: manuscript no. sambcg ages on a finer pixel grid. For practical reasons, we adopted the same pixel scale (0.187 arcsec per pixel) as the optical data that we obtained from the NGVS survey (Ferrarese et al. 2012), as discussed in Sect. 2.4.

UV photometry

Since we are targeting relatively small and faint galaxies whose shape in the UV is not known a priori, we computed photometry systematically in a number of circular rings around the BCG galaxies, with apertures of radii 20,30,50,70,90,110,130 pixels (with a size of 0.187 arcsecs), chosen to cover the range of sizes found in our sample. We note that the first aperture is only slightly larger than the GALEX PSF. We use it nevertheless because early-type galaxies are often very compact in the UV, and this allows us to have an estimate of the color even when a nearby galaxy could contaminate a larger aperture. The magnitude obtained is by definition partial. Aperture corrections for a point source at this size are 0.23 mag in both filters1 , thus the color is unchanged. This central aperture has the advantage that it often presents a higher S/N, and may be more sensible to UV upturn if the stellar populations giving rise to it are concentrated. NGC1399, which we use to illustrate a typical upturn as seen in the nearby universe, clearly shows a FUV-NUV color gradient in the inner 30 arcsec, with the maximum upturn at the center as can be seen in Fig. 3 of Gil de Paz et al. (2007). The UV spectrum shown in Fig. 1 was obtained in the IUE aperture. For our distant objects, we certainly probe a larger physical size, thus this NGC1399 reference is likely to be the bluest color we can expect for a galaxy with a central upturn.

The sky value was measured in many independent regions around the galaxy and is void of obvious sources. The photometry and associated uncertainties were then computed as in Gil de Paz et al. (2007). The photometry was corrected for the Galactic extinction, using the Schlegel et al. (1998) values for the visual extinction and R FUV =8.24, R NUV =8.20 (Wyder et al. 2007).

Optical images

For all these galaxies, we fetched optical images from the NGVS survey (Ferrarese et al. 2012). Because the UV area we started from is larger than the NGVS area, we obtained these observations for about half of our sample (84 out of 177 galaxies). For the others, we fetched SDSS images. The optical images are not crucial for the analysis in this work, but were used for visual inspection allowing for instance to flag for possible contamination by nearby galaxies, or signs of star formation in the form of spiral arms (Sect. 2.5) or other morphological peculiarities. In order to have homogeneous data; however, we use the SDSS photometry from the Koester et al. (2007) catalog for all our galaxies in the i and r band (in order to test the relations found in early-type galaxies and to test for the presence of a young stellar population). We do not perform photometry measurements in the optical images in this work.

Visual inspection

A visual inspection of our images was performed. This step was important for this work for several reasons:

• We identified four BCGs with strong signs of star formation (spiral arms, prominent and spread out UV emission) that would obviously pollute any signal from the UV upturn; • We identified objects for which the UV photometry was polluted by a nearby companion. In optical images, it is easy to spot small companions that are unimportant in optical bands, but that can be the dominant source in the UV images if they are star-forming. Considering the GALEX PSF, in these cases the flux in the BCG region could be due to these companions and not to the BCG. Comparing the images, we can easily say when the UV emission is centered on a companion rather than on the BCG; • We chose the best circular aperture for this work. Having measurements in a collection of apertures, we could see in the image the surface covered by each aperture. We then selected the best one according to the following rules: 1) if possible the aperture including all the emission observed in the UV image (when not possible, our magnitude was flagged as partial) and 2) in any case, an aperture not polluted by a nearby companion (when not the case, we used another flag to indicate contamination).

The inspection was performed independently by two people (O.C. and S.B.). A small discrepancy occurred for 25 % of the galaxies (in most of the cases a different optimal aperture was chosen with a different flag). The discrepancies were resolved through discussion (usually adopting the smaller aperture to avoid possible pollution by a companion).

Table 4 provides our results concerning the photometry, including the exposure time, the chosen aperture, the FUV and NUV magnitudes and their 1 σ uncertainties. We have 11 galaxies without FUV measurements (measured flux below the sky level). In this case the table indicates a -99.9 magnitude and the -1 σ column is replaced by the limiting magnitude as deduced from the sky noise measurement.

Table 5 provides the flags. For both FUV and NUV, a flag can be "ok" (the aperture encompasses all the observed emission in the image and there is no contamination), "part." (we had to use a smaller aperture than the full observed emission to avoid contamination), or "contam." (the flux is likely to be contaminated by a nearby source, usually a star-forming galaxy). When possible, we preferred to have a part. flag, with a meaningful color in a small aperture, but in some cases, it was impossible to avoid a contamination. We also added some notes that indicates clear signs of star formation and spiral arms ("spiral structure"), presence of arcs ("arc"), or presence of other signs that might be related to a merger or interactions ("shells/tails/asymetric/mergers"). These flags allow the identification of objects that may be affected for example by a recent merger or by star formation. It may be useful to distinguish them since, e.g., Using GALEX imaging, Rampazzo et al. (2011) found signs of star formation in their sample of 40 nearby early-type galaxies in low density environments that can produce rings or arm-like structures. At high redshift (0.2 to 0.9), Donahue et al. (2015) found in their CLASH BCG sample that BCGs with star formation activity indeed show perturbed morphology, while quiet BCGs have a smooth aspect.

We found similar percentages of the various flags on the subsamples with deep NGVS or SDSS optical images. Our flags are thus not affected by the source of the optical image that was examined together with our UV images. The only exception is the arc flag. We visually recognized four arcs, all of them in the NGVS images. Deep high quality exposures are necessary to recognize this feature. In our figures, we identify the galaxies 4 and text for details). In blue: obvious spiral structure (crosses); arcs (circles); strong asymmetries, shells, tails, or signs of merger (squares). The red circles indicate galaxies with the SDSS spectral subclass BROADLINE.

The dashed lines indicates 0 (no color gradient) and the dotted line is a LOWESS fit to the dark blue points.

flagged for these different categories so that it is possible to see if the one where they are found present differences in a systematic manner with respect to the global sample or not.

Aperture issues

We also provide in Table 4 the central color, i.e., the color of the innermost aperture. It provides an idea of the central upturn in the case of an extended object, where the population responsible for the upturn might be more concentrated (see Sect. 2.3). When it was not possible to measure a FUV-NUV color in this aperture, the table indicates -99.9 color. We found that the central color correlates quite well with the total color. Figure 2 shows the difference between the central and global color as a function of redshift. Over the range of redshift considered, for an intrinsic constant size, the observed size may change by a factor of about 2 with redshift. The difference in the selected optimal size compensates for this effect. For galaxies with ok flags, we selected mostly the 30-or 50-pixel apertures. We chose 50 pixels for most of the nearby galaxies (z <0.15), and 30 pixels for all the distant ones (z >0.25). Figure 2 shows that we do not introduce a color trend by adopting the central color with respect to the global one. The central color has in general smaller error bars than the global color. The uncertainty is on average reduced by a factor of 3 when using the 20 arcsec aperture with respect to the total aperture. For this reason, in the following we perform an analysis of the UV upturn in this smallest aperture. This has two main advantages. First, by definition, our color does not correspond to the total galaxy, but when we can have a total galaxy, they correlate. We are thus not limited to galaxies without contamination in the outer part (i.e., we can use galaxies having only a partial magnitude). Second, the error bar is smaller, which allows us to better distinguish trends. For the same adopted limit on the error bar size, we obtain larger statistics. Of course, this is not adequate for all analysis, thus Table 5 also provides the total magnitude measured as described above. This allows us to obtain what we call the "best sample", i.e., 64 BCGs with a central FUV-NUV color with global uncertainty (sum of the error bars on each side) lower than 1.2 magnitudes, and not contaminated.

Sample of local galaxies in GUViCS

A previous work on UV upturn in elliptical galaxies inside the Virgo cluster, based on GALEX data, was performed by Boselli et al. (2005). We refer the reader to this work for a detailed analysis of local galaxies. We consider here a similar comparison sample of local galaxies in the Virgo cluster, using the most recent set of data (Boselli et al. 2014). For all galaxies, the UV data have been taken from the GUViCS catalog of UV sources published in Voyer et al. (2014). The optical data in the SDSS photometric bands (Abazajian et al. 2009) have been taken, in order of preference, from the SDSS imaging of the Herschel Reference Survey (Boselli et al. 2010), published in Cortese et al. (2012), or from Consolandi et al. (2016). Given the extended nature of all these nearby sources, all magnitudes have been taken from imaging photometry of extended sources and thus are total magnitudes.

Among this sample, we identify the seven galaxies being central to subgroups in Virgo (Boselli et al. 2014) that are probably more similar to our BCGs than the other early-type galaxies in the local sample.

Confirmed upturn sample

Using optical photometry to exclude recent star formation

Brightest cluster galaxies are not systematically quiescent systems: 10 % to 30 % of BCGs in optically selected samples show star formation or AGN activity (Donahue et al. 2015, and references therein). A blue FUV-NUV is thus not necessarily the result of an evolved upturn population and can be the result of star formation activity. BCGs with star formation tend to have morphological signs such as filaments, elongated clumps, or knots (Donahue et al. 2015). From our visual inspection, we have identified a few obvious cases that can be excluded when focusing on the upturn phenomenon. Fortunately, Yi et al. (2011) and Han et al. (2007) showed that combining the FUV-NUV and NUV-r (or FUV-r) colors allows the separation of upturns, compared to galaxies that are simply blue as a result of young populations. Donahue et al. (2010) also showed that UV-optical colors are sensitive to even modest amounts of recent star formation. We thus present in Fig. 3 a FUV-NUV versus NUV-r color diagram for our sample. The NUV-r color is sensitive to young populations even if it does not probe exactly the same restframe waveband at all redshifts: blue colors indicate the presence of young stellar populations. We adopt the qualitative limits of Yi et al. (2011) to confirm the detection of rising UV flux when FUV-NUV is lower than 0.9; and the detection of a young population component when NUV-r is bluer than 5.4 mag. The galaxies that were flagged for spiral structures all fall on the young population side of the NUV-r=5.4 limit, three of them being even among the bluest objects in our galaxies. The figure clearly shows that we have a number of BCGs in the best sample at all redshifts falling in the upturn/old stellar population part of this diagram. We consider that these 27 BCGs are likely to present a UV upturn.

Another possible contribution to blue FUV-NUV color would be the presence of an AGN. O'Connell (1999) however discusses the contribution of known bright nuclei in elliptical galaxies (M87, NGC4278). Only 10 % of the FUV luminosity is related to the nuclei. While it could affect the FUV-NUV color, this is marginal with respect to our observational uncertainties. Moreover, the subclass from SDSS indicates one AGN and a few BROADLINE objects in our sample. Only three of them pass our UV photometry criteria (uncertainties, noncontamination). These few objects do not distinguish themselves from the rest of our sample, as can be seen in the figures where we marked them. In summary, our results should not be affected by AGNs.

Spectroscopic confirmation

We show in Fig. 4 the SDSS Mg2 and Hβ Lick indices of the "confirmed upturn" sample (and of the full sample for comparison). These features have been used in the context of UV upturn studies since Faber (1983) and Burstein et al. (1988). SDSS provides values for many of our galaxies and the majority of our upturn sample (24 out of 27). In local galaxies, a trend between the Mg2 index and the strength of the upturn was found, with stronger upturns in more metallic galaxies. With our sample of BCG galaxies, we probe only the most massive of the galaxies with respect to the local sample. We thus do not find a trend with the Mg2 index as in the redshift 0 sample from Boselli et al. (2005). Our confirmed upturn sample behaves as the local "centrals". As can be expected from color evolution of Fig. 1, the BCGs are slightly bluer at higher redshift, but present similar Mg2 values to the more massive of the local early-type galaxies showing upturns.

In the nearby universe, the Hβ index has been used to distinguish galaxies with real upturn and those presenting residual star formation. The bottom panel of Fig. 4 shows its value for our full sample and confirmed upturns. We find a very mild trend of bluer UV colors for smaller Hβ indices. This pattern is typical of upturns (Buzzoni et al. 2012). Blue UV colors related to star formation are instead found with higher values of the Hβ index (above 2 Å). Most of our BCGs are found with values between 1 and 2 Å, typical of the passive galaxies with UV upturns.

From this section, we conclude that even if our selection of confirmed upturn were based on photometry alone, the spectroscopic information would confirm the status of these galaxies as quiescent with a real UV upturn, similar to that observed in the Local Universe and not polluted by residual star formation. The central galaxies of the various subgroups in Virgo are indicated by larger symbols than the rest of the sample. These centrals are repeated in the other panels (squares). In the middle panel, we show our full and best sample (colored circles). We use the central FUV-NUV color (smaller error bar, larger statistics). Galaxies with contamination or very large error bars (1 σ interval larger than 1.2 mag) are indicated by a pale green circle. For the other galaxies, the color corresponds to the redshift, as indicated in the color bar. Peculiarities found in our visual inspection (blue) or in the SDSS spectral subclass (red) are marked as in Fig. 2. The dotted line is a LOWESS fit to our sample. In the right panel, the colored circles are used only for the galaxies with confirmed upturn.

Results

FUV-NUV color vs. luminosity

We compare in Fig. 5 the FUV-NUV color and i-band luminosity of the local sample, our BCG sample, and the upturn sample. While some works have found an evolution with luminosity (Boselli et al. 2005), the color in our BCG sample varies little with luminosity. However, the sample covers a small range of i-band luminosity, since BCG have by definition higher masses (well traced by the i-band luminosity) than the general population of galaxies. The dispersion is reduced, however, when we restrict the sample to galaxies with confirmed upturn with a very mild trend.

The central galaxies in subgroups of Virgo are found in the same range of luminosities as our BCGs. In this range, the upturn sample is slightly bluer on average than the local sample, in agreement with the K-correction that can be deduced from Fig. 1. Loubser & Sánchez-Blázquez (2011) studied a sample of 36 nearby BCGs. Their FUV-NUV color (0.79 ± 0.055) is bluer than normal ellipticals of the same mass, but they do not find a strong dependence on mass or other parameters within BCGs. This is similar to what we find at higher redshift on average.

FUV-NUV color vs. redshift

As seen in the Introduction, the evolution with redshift of the UV upturn can bring direct constraints on the nature of stars producing it. Rich et al. (2005) did not find any evolution of the UV upturn up to redshift 0.2. Brown (2004) suggested that the UV upturn fades progressively with redshift up to redshift 0.6. Ree et al. (2007) compared the observed FUV-V color of nearby ellipticals to the ellipticals in 12 remote clusters up to redshift 0.2, and also compared this color to six objects in two clusters at redshifts around 0.3 and 0.5, suggesting a weak evolution of this color (they did not show the evolution of the FUV-NUV color, but provided the corresponding data in their table). Le Cras et al. (2016) has suggested that the UV upturn appears at redshift 1 in massive galaxies and becomes more frequent at lower redshift.

Their work is based on the fitting of line indices in synthesis population models where they can include a UV upturn component. They found that the rate of galaxies better fitted with models including an upturn is of 40 % at redshift 0.6 and 25 % at redshift 1. A weak evolution could be consistent with the binary model of Han et al. (2007), but the constraints are still scarce, and our sample can bring new information.

Figure 6 shows our measurement of the observed FUV-NUV color as a function of redshift for the BCG sample. Here, we use the best sample, i.e., all the galaxies with good constraints on the FUV-NUV color, which can be directly compared to published works with similar data. In the next section, we focus instead on the confirmed upturn that can be defined using optical photometry. Our galaxies are compared to the other samples of BCGs with published FUV-NUV colors: the 36 local BCGs of Loubser & Sánchez-Blázquez (2011) for which we indicate the average value and observed range of color, and at intermediate redshifts the BCG samples of Ree et al. (2007) and Donahue et al. (2010). Our sample adds new points at redshift lower than 0.2, and brings unique measurements in the redshifts 0.2 to 0.3, namely a significant increment in look-back time. When a FUV-NUV color could be measured with a global range of uncertainty lower than 1.2 magnitude (this is an arbitrary value that we chose in order to balance precision and statistics), we do obtain relatively blue colors. Most of these galaxies are bluer than the flat spectrum that we used as an artificial reference, as expected in the case of an upturn. A LOcally WEighted Scatterplot Smoothing (LOWESS) fit (implemented in Python by Cleveland 1979) performed on our BCGs combined with the two intermediate redshift samples stresses the trend of obtaining bluer colors at higher redshifts. However, this blue color is not necessarily a sign of a UV upturn, as discussed above. We thus study the FUV-NUV color as a function of redshift for confirmed upturn in the next section.

Detected UV upturn up to look-back times of 3.5 Gyr

In Fig. 7, we finally show the FUV-NUV color as a function of redshift for our BCGs, this time indicating only the BCGs for which a UV upturn is considered very likely based on the colorcolor diagram and the spectroscopic confirmation discussed in section 3.

We include in the figure the evolution predicted by different models. At all our redshifts, we selected very massive passive galaxies. It is likely that their stellar mass or i luminosity does not evolve much over the considered period since their star formation must have occurred at much earlier times in such galaxies (Thomas et al. 2005). The FUV-NUV evolution with redshift may thus be close to the actual color evolution of passively aging very massive galaxies. However, we cannot be sure that we select the precursors of redshift 0 upturn galaxies when we select upturns at higher redshift. Thus, the evolution with redshift that we present is not necessarily the redshift occurring in any individual galaxy. Even so, our results bring a new constraint for the stellar evolution models producing a UV upturn since models should at least predict the possibility of an upturn at the redshift when it is observed, which is not necessarily the case for all models. Fig. 7. FUV-NUV color as a function of redshift as in Fig. 6, but keeping only our BCG galaxies with old populations and UV upturn, as defined by the bottom right part of Fig. 3 (confirmed upturn sample). In the top panel, we show the rest-frame color. We corrected the observed points assuming the NGC1399 spectrum since we selected upturn galaxies. In the bottom panel we show the observed color. In each panel our points are compared to model predictions. The shaded area indicates the evolution of the rest-frame color for a SSP model of Han et al. (2007) including binaries (assuming a redshift 5 formation). The dot-dashed lines indicate the observed colors in typical models of Yi et al. (1998) based on single stars, for infall histories from Tantalo et al. (1996) for two galaxy masses (10 12 and 5 10 11 M ⊙ ), and two mass-loss efficiency parameter (0.7 for the two lower and 1 for the two upper curves). The dotted curve is a LOWESS fit to our data.

The rest-frame FUV-NUV colors for the SSP models of Han et al. (2007) are shown in the top panel. We computed restframe colors for our galaxies assuming the NGC1399 spectrum. In future model computations, it should be straightforward to obtain the observed color to compare it directly to the values provided in our tables to avoid this step. The weak evolution they propose is quite consistent with the lack of evolution found in our sample and the colors are globally consistent with these galaxies; we recall that they do not represent the full population of BCGs, but those presenting a UV upturn, which is a significant fraction (27 out of the 64 galaxies in the best sample).

We also show in the figure four typical models among those presented in Yi et al. (1998) for two infall accretion histories and for two values of their mass-loss efficiency parameters. We refer to their paper for a more detailed description of their models. In this case, we reproduce their prediction for the observed color m(1500)-m(2500), which are not the GALEX bands but probe the UV slope in a similar wavelength range. These models tend to be characterized by more ample and rapid variations than the Han et al. (2007) model is. Such large variation is not favored by our data (at least for a fraction of the BCG population).

We note that the models were basically constructed on the basis of redshift 0 constraints, with large uncertainties on the population responsible for the UV upturn. The inclusion of binary evolutions by Han et al. (2007) seems to help reproduce the observed upturn at look-back times of around 3 Gyr that we find in many of our galaxies. Ciocca et al. (2017) recently found at redshift 1.4 blue color gradients in ellipticals in one cluster, with bluer UV-U colors in their center that may indicate the existence of a UV upturn population at even higher redshift.

Environment influence on the UV upturn?

We verified whether there is a correlation between the FUV-NUV color and other parameters in the maxBCG catalog. We could not find any significant trend, especially with those parameters related to the environment (e.g., number of cluster members). This is consistent with the findings of Yi et al. (2011) andLoubser &Sánchez-Blázquez (2011), suggesting that the UV upturn is intrinsic to galaxies and not directly related to their environment.

Conclusions

This work extends by a factor of several the size of BCG samples and provides constraints on their UV color. For the first time, we bring constraints on this subject to the redshift range 0.2-0.35, almost multiplying by 2 the look-back time with respect to previous studies.

We took advantage of the GUViCS survey to study the FUV-NUV color (probing the UV slope) of 177 massive galaxies of the maxBCG catalog. Even if it is poorly constrained for many of them (due to their intrinsic faintness, and low exposure time in part of the GUViCS survey), we measured the FUV magnitude for 166 objects in this sample. Removing from this sample the galaxies with relatively large uncertainties and those with contamination, we obtained an interesting constraint (sufficient to distinguish different models) on the (central) FUV-NUV color of 64 BCGs at redshift 0.05 to 0.35.

Our most important result is that 27 out of the 64 BCGs with good photometry at these redshifts present the characteristic of a UV upturn. They are selected on the basis of their blue FUV-NUV color, and of red optical colors suggesting an old underlying stellar population. The quiescent nature of these galaxies is confirmed by spectroscopic information. They bring important constraints for models of the stellar populations responsible for the UV upturn phenomenon in very massive early-type galaxies. The comparison of our new data set with models from the literature favors a mild evolution with redshift like that obtained by models taking into account the effect of binaries on stellar evolution (Han et al. 2007). In conclusion, our data favors the existence of a binary channel to produce very hot stars that can produce a UV upturn, even up to redshift 0.35. This empirical work cannot give a definitive answer, however. Our tabulated data should offer a new constraint for future models of stellar evolution.

From the empirical point of view, follow-up work could be done to increase the statistics on the basis of extensive UV and optical data sets. Especially, a search for all massive galaxies, ellipticals, and BCGs in the NGVS optical catalog, and a similar systematic measurement of the UV color, but also of the UVoptical colors would be useful. In the long term, future large UV facilities (e.g., LUVOIR) could allow us to directly probe the UV spectrum of massive galaxies, providing more direct constraints on this still enigmatic phenomenon.

Table 2. BCG galaxies in our sample.They are selected from the reference catalog of Koester et al. (2007), from which we list here RA, DEC, photometric redshift, r and i band luminosities.

Fig. 2 .

 2 Fig. 2. Difference between the central and global FUV-NUV color. Galaxies with contamination or very large error bars (1 σ interval on the central or global color larger than 1.2 mag) are indicated by a pale green circle. The dark blue symbols with error bars are all our other points, including indications from the visual inspection results (see Table4and text for details). In blue: obvious spiral structure (crosses); arcs (circles); strong asymmetries, shells, tails, or signs of merger (squares). The red circles indicate galaxies with the SDSS spectral subclass BROADLINE. The dashed lines indicates 0 (no color gradient) and the dotted line is a LOWESS fit to the dark blue points.

Fig. 3 .

 3 Fig. 3. Central FUV-NUV vs. global NUV-r color-color diagram in the best sample (colored by redshift). For comparison, pale green dots show the location of the other BCGs. The vertical line indicates NUV-r=5.4,above which there should be no contamination from young stars, and the horizontal line indicates FUV-NUV=0.9, below which the UV slope is consistent with a UV upturn(Yi et al. 2011). Peculiarities found in our visual inspection (blue) or in the SDSS spectral subclass (red) are marked as in Fig.2.

Fig. 4 .

 4 Fig. 4. FUV-NUV color as a function of the Mg2 and Hβ Lick indices.Galaxies not pertaining to our upturn sample are shown as pale green dots. For the confirmed upturn galaxies, the symbols are colored according to their redshift. Peculiarities found in our visual inspection (blue) or in the SDSS spectral subclass (red) are marked as in Fig.2. In the top panel, the squares show the relation found in the local sample (larger squares for centrals).

Fig. 5 .

 5 Fig.5. FUV-NUV color as a function of the i-band luminosity. The left panel shows the relation for the redshift 0 early-type galaxies (Sect. 2.7). The central galaxies of the various subgroups in Virgo are indicated by larger symbols than the rest of the sample. These centrals are repeated in the other panels (squares). In the middle panel, we show our full and best sample (colored circles). We use the central FUV-NUV color (smaller error bar, larger statistics). Galaxies with contamination or very large error bars (1 σ interval larger than 1.2 mag) are indicated by a pale green circle. For the other galaxies, the color corresponds to the redshift, as indicated in the color bar. Peculiarities found in our visual inspection (blue) or in the SDSS spectral subclass (red) are marked as in Fig.2. The dotted line is a LOWESS fit to our sample. In the right panel, the colored circles are used only for the galaxies with confirmed upturn.

Fig. 6 .

 6 Fig.6. Observed FUV-NUV color as a function of redshift. The gray squares are the redshift 0 centrals of Virgo subgroups (Sect. 2.7). The diamond is the average value ofLoubser & Sánchez-Blázquez (2011), the error bar corresponding to the range of values they found for local BCGs. Intermediate redshift BCGs ofRee et al. (2007) andDonahue et al. (2010) are shown as orange triangles and magenta pentagons, respectively. The circles correspond to our sample for which we use the central FUV-NUV color (smaller error bar, larger statistics). Galaxies with contamination or very large error bars (1 σ interval larger than 1.2 mag) are indicated by pale green circles, others by dark blue circles with corresponding error bars. Peculiarities are marked as in Fig.2(noted in our visual inspection in blue; noted in the SDSS spectral subclass in red). The solid (dashed) curve show the FUV-NUV color for the upturn spectrum of NGC1399 (for a flat spectrum) as a function of redshift. A LOWESS fit to our sample combined with the points ofDonahue et al. (2010) andRee et al. (2007) is indicated as the dotted line.

Table 1 .

 1 Boissier et al.: The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). VII.: UV upturn in early-type galaxy FUV-NUV samples

	Reference Rich et al. (2005) Boselli et al. (2005) Boselli et al. (2014) Ree et al. (2007) Donahue et al. (2010) Loubser et al. (2011) This work (all, FUV measurements) 0.05-0.35 redshift range Galaxies 0-0.2 early types 0 Virgo early types 264 Statistics 172 0 Virgo centrals 7 0-0.2 BCGs 12 0.06-0.18 BCGs 10 a 0 BCGs 36 BCGs 166
	This work (best sample b ) This work (confirmed upturn c )	0.05-0.35 0.05-0.35	BCGs BCGs	64 27

S.

Table 2 .

 2 ID RA (deg) DEC (deg) phot. redshift L r (10 10 L ⊙ ) L i (10 10 L ⊙ ) continued. ID RA (deg) DEC (deg) phot. redshift L r (10 10 L ⊙ ) L i (10 10 L ⊙ )

	BCG24 188.57278 BCG129 186.45179 BCG271 191.04632 14.482497 9.766238 7.971470 BCG304 182.92986 8.018963 BCG485 188.94962 15.555812 BCG671 183.13768 6.076853 BCG692 187.03522 8.945062 BCG933 181.14637 11.095937 BCG1076 188.90784 13.177456 BCG1123 190.82471 19.013533 BCG1140 184.92495 0.840782 BCG1152 182.95640 8.439066 BCG1187 183.29939 14.229333 BCG1251 183.28358 12.019687 BCG1355 185.43028 0.329512 BCG1383 185.24322 11.528934 BCG1408 187.79463 11.786205 BCG1520 187.29306 14.728700 BCG1529 191.95320 10.648070 BCG1574 185.60712 6.502490 BCG1635 187.69004 9.170359 BCG1684 186.82361 2.601625 BCG1805 188.03874 13.302351 BCG1934 183.24882 7.898145 BCG1961 184.82473 11.279270 BCG2196 192.43198 1.746452 BCG2199 193.94356 1.980950 BCG2255 190.47262 10.902658 BCG2296 186.72384 12.365892 BCG2322 182.88571 10.805757 BCG2395 180.60957 10.562301 BCG2410 192.83481 10.812324 BCG2566 188.37254 8.835154 BCG2801 183.64345 0.791082 BCG2833 187.20573 8.314187 BCG2907 183.38725 7.421361 BCG3098 186.99976 13.942666 BCG3137 181.02868 1.779234 BCG3194 193.99197 9.706866 BCG3299 187.46419 14.412767 BCG3332 192.11267 12.143343 BCG3571 180.92705 1.031848 BCG3728 189.20382 8.853715 BCG3786 188.77550 19.269088 BCG3809 183.87004 1.840244 BCG3858 180.26887 15.209924 BCG4032 194.52230 5.328463 BCG4048 181.62656 1.820709 BCG4106 181.03875 13.664575 BCG4120 189.24367 14.695208 BCG4189 185.44575 7.806539 BCG4259 185.50020 15.793529 BCG4262 180.89012 11.101584 BCG4264 181.29986 10.435014 BCG4391 185.94397 16.155459 BCG4674 183.69782 0.515216 BCG4702 188.48709 8.626259 BCG4810 180.86246 11.157377 BCG4909 192.35491 6.410631 BCG4919 189.03059 9.055363	0.243050 0.248450 0.275450 0.264650 0.267350 0.132350 0.267350 0.237650 0.261950 0.116150 0.299750 0.135050 0.299750 0.153950 0.156650 0.261950 0.172850 0.275450 0.243050 0.102650 0.291650 0.229550 0.278150 0.132350 0.253850 0.207950 0.288950 0.113450 0.164750 0.229550 0.232250 0.121550 0.248450 0.240350 0.218750 0.148550 0.253850 0.243050 0.240350 0.288950 0.270050 0.259250 0.170150 0.237650 0.256550 0.108050 0.286250 0.288950 0.207950 0.264650 0.135050 0.216050 0.256550 0.253850 0.248450 0.202550 0.251150 0.221450 0.221450 0.167450	17.90260 9.48259 11.28250 18.48990 7.44125 8.40151 16.49510 11.01730 9.87069 9.03394 14.13630 7.61520 10.18440 10.31280 8.38778 11.40520 11.27210 9.69912 10.15970 7.37734 6.05027 7.50154 8.07326 7.24300 9.85226 6.77548 7.68495 5.97685 8.30567 8.58161 8.10823 6.90917 8.20927 7.34158 7.47353 8.42181 5.43397 6.02762 5.82393 6.20903 6.84018 6.88905 6.51664 6.90189 6.56095 4.72527 4.46252 5.12966 6.80957 7.04354 5.56824 6.42034 4.67782 6.57431 6.41880 7.41103 5.73425 7.27635 6.31448 6.52211	21.94700 11.81850 14.54510 24.32040 9.18799 10.62250 19.86410 13.09370 12.29600 10.88040 18.22730 9.68125 12.66650 13.23270 10.61470 13.99760 13.43390 12.29420 12.65270 9.44810 7.71484 9.51897 10.13060 9.11284 11.54580 8.75636 9.16246 7.83891 10.67860 10.37810 9.51045 8.73994 10.14310 8.89927 9.13566 10.39250 6.64345 7.36433 6.94385 7.80151 8.07318 8.58642 8.38270 8.42570 7.96016 5.94890 5.58348 6.41988 8.51718 8.58972 6.99704 7.65803 5.85087 8.10770 7.84344 9.13500 6.95224 8.66375 7.76555 7.90281

Table 2 .

 2 continued. ID RA (deg) DEC (deg) phot. redshift L r (10 10 L ⊙ ) L i (10 10 L ⊙ )

	BCG9130 183.79112 BCG9161 191.99719 BCG9375 188.01972 BCG9402 190.47755 16.107645 1.164337 8.624872 1.465264 BCG9419 187.17228 13.676487 BCG9455 194.07920 18.619761 BCG9478 188.50546 11.973708 BCG9512 189.25606 7.631371 BCG9514 186.97122 16.030243 BCG9686 186.11951 2.465236 BCG9693 186.04074 8.730912 BCG9737 184.80382 14.395416 BCG9799 193.64689 10.002305 BCG10141 185.55197 14.590736 BCG10151 193.53080 3.804609 BCG10217 194.28821 14.722016 BCG10326 191.03480 8.069578 BCG10339 183.42129 1.628454 BCG10372 187.08285 14.608728 BCG10430 180.91580 1.204584 BCG10452 192.03184 11.352027 BCG10815 192.97780 11.842069 BCG11017 185.16711 1.404918 BCG11239 188.99457 13.207563 BCG11241 189.62273 5.904392 BCG11369 189.41545 7.794008 BCG11442 186.81470 9.169160 BCG11482 180.85448 10.811054 BCG11484 185.86695 15.655224 BCG11518 189.07718 15.494217 BCG11534 183.49782 1.602452 BCG11547 187.59676 14.259085 BCG11551 192.94604 3.879207 BCG11571 187.65542 9.283149 BCG11683 187.13218 2.635468 BCG11703 187.70206 2.218458 BCG11762 182.74433 1.192858 BCG11787 187.53217 2.836198 BCG11965 187.10510 13.898171 BCG12016 186.49359 16.200333 BCG12019 186.24668 11.836638 BCG12122 188.76065 15.269065 BCG12155 180.76919 10.410552 BCG12463 185.14656 6.376248 BCG12522 185.62052 14.471922 BCG12632 182.74434 1.612938 BCG12703 184.97424 7.512982 BCG12990 192.18827 1.647833 BCG13101 189.35622 10.383818 BCG13175 193.80410 10.232985 BCG13480 187.03828 8.954130 BCG13497 188.38020 0.190788 BCG13609 189.60870 15.768887 BCG13639 192.86621 2.883622 BCG13672 180.13584 0.336242 BCG13790 185.21390 11.476087	0.272750 0.256550 0.240350 0.288950 0.256550 0.183650 0.178250 0.299750 0.283550 0.207950 0.167450 0.259250 0.191750 0.224150 0.224150 0.221450 0.164750 0.234950 0.286250 0.102650 0.256550 0.175550 0.172850 0.170150 0.240350 0.178250 0.275450 0.210650 0.286250 0.256550 0.207950 0.256550 0.205250 0.240350 0.213350 0.248450 0.275450 0.137750 0.229550 0.221450 0.102650 0.245750 0.232250 0.118850 0.234950 0.297050 0.280850 0.183650 0.264650 0.164750 0.229550 0.183650 0.226850 0.218750 0.253850 0.229550	5.33444 3.76567 3.78301 4.12880 4.65006 4.18043 4.55322 3.55800 3.33753 4.63002 3.74240 4.47137 3.62893 3.88453 3.64730 3.98609 3.84886 4.38894 2.72270 2.99825 3.62367 4.07066 3.62870 3.04897 3.41960 3.78488 3.32945 3.73503 2.89435 3.53120 3.29541 3.39592 3.80870 3.26598 3.38850 4.11068 3.50309 3.34340 2.88396 2.73968 2.16607 2.48031 2.92582 2.53692 2.33325 3.12973 2.18398 2.89727 2.53288 2.35196 1.90207 1.92044 1.95320 1.92269 1.52157 1.16904	6.41501 4.60629 4.68663 4.94586 5.57512 5.33622 5.92121 4.34681 4.15719 5.94480 4.74735 5.52323 4.58484 4.72299 4.39979 4.88795 4.77938 5.31973 3.44370 3.73585 4.52326 5.10382 4.53496 3.80921 4.25677 4.57201 4.23054 4.63222 3.63280 4.22659 4.02701 4.05598 4.80651 4.09370 4.19167 5.11039 4.27821 4.21592 3.54409 3.33520 2.74446 2.99305 3.67983 3.09705 2.75455 3.70466 2.71403 3.58857 3.13100 2.94989 2.18253 2.40199 2.37338 2.40750 1.85562 1.43750

Table 3 .

 3 Galaxies in our sample with spectroscopic information provided by SDSS: redshift, sub-class (AGN, STARFORMING, or BROADLINE), Mg2 and Hβ Lick indices and their uncertainty.

	ID spec. redshift	sub-class	Mg2	±	Hβ	±
	BCG24 BCG129 BCG271 BCG304 BCG485 BCG671 BCG692 BCG933 BCG1076 BCG1123 BCG1140 BCG1152 BCG1187 BCG1251 BCG1355 BCG1383 BCG1408 BCG1520 BCG1529 BCG1574 BCG1635 BCG1684 BCG1805 BCG1934 BCG1961 BCG2196 BCG2255 BCG2296 BCG2322 BCG2395 BCG2410 BCG2566 BCG2801 BCG2833 BCG2907 BCG3137 BCG3194 BCG3299 BCG3332 BCG3571 BCG3728 BCG3786 BCG3809 BCG3858 BCG4032 BCG4048 BCG4106 BCG4120 BCG4189 BCG4259 BCG4262 BCG4264 BCG4391 BCG4674 BCG4702 BCG4810 BCG4909 BCG4919 BCG4920 BCG4944	0.230558 0.252744 0.272047 0.248118 0.284612 0.137062 0.231012 0.225683 0.251505 0.113173 0.324538 0.144250 0.316567 0.146893 0.158895 0.254507 0.171116 0.285424 0.245753 0.075471 0.321950 0.218690 0.283662 0.137488 0.225744 0.201966 0.116928 0.163604 0.225985 0.229071 0.125230 0.251963 0.251029 0.214718 0.137207 0.240821 0.227791 0.290972 0.263462 0.255169 0.165497 0.225821 0.241753 0.109187 0.324959 0.295877 0.205980 0.230859 0.137094 0.209841 0.288793 0.277109 0.233642 0.183824 0.250176 0.202245 0.225047 0.165049 0.235314 0.242670	0.313916 0.024135 1.624143 0.842013 0.254789 0.018935 0.947647 0.611584 0.274995 0.017862 2.101470 0.584695 0.293060 0.016535 1.441411 0.571690 0.272066 0.026296 1.362648 0.921333 0.288143 0.015167 2.183753 0.400882 0.256044 0.019307 0.602522 0.693763 0.276631 0.017347 2.785665 0.501516 0.271697 0.009468 1.914185 0.278490 0.221946 0.021216 1.258562 0.626185 0.297741 0.011613 1.711954 0.344826 0.285260 0.016848 1.749445 0.504575 0.292536 0.014081 2.338836 0.493430 0.280844 0.009324 1.602184 0.295529 0.273814 0.016362 2.003437 0.512988 0.301538 0.017347 1.501519 0.558158 0.249108 0.021581 2.431830 0.765589 0.262535 0.016176 1.070567 0.548029 BROADLINE 0.278830 0.010293 1.364787 0.294204 0.273304 0.023427 -0.048969 0.706194 0.317027 0.012773 0.914725 0.590046 0.252599 0.018863 0.840112 0.627715 0.311870 0.010023 1.219293 0.280608 0.264401 0.017479 1.400491 0.636460 0.290880 0.020839 1.298720 0.715578 BROADLINE 0.277711 0.016368 1.565580 0.522218 0.285680 0.016465 1.087216 0.615393 0.227800 0.016382 0.740022 0.596499 0.290743 0.010008 1.168643 0.283420 0.275614 0.020150 1.001811 0.694451 0.261442 0.015082 0.970654 0.514771 0.262154 0.022697 1.579777 1.061491 0.239093 0.015403 1.684279 0.348206 0.279896 0.018839 1.752254 0.681716 0.280011 0.017548 1.264112 0.645362 0.287693 0.022433 1.620180 0.707405 0.241738 0.024016 2.952008 0.707217 0.288372 0.016482 1.510066 0.529413 0.270516 0.014891 1.181187 0.518753 0.235692 0.019025 1.411908 0.689607 0.311572 0.010663 1.377183 0.292759 0.203827 0.030595 1.650039 0.828820 0.261821 0.020166 2.665730 0.712405 0.294526 0.016561 1.060984 0.675914 0.254494 0.021146 1.600741 0.790321 0.274778 0.014361 1.429085 0.397715 0.271855 0.017336 2.728652 0.734529 0.309794 0.029587 0.596318 1.027418 0.268839 0.022987 1.420293 0.846605 0.260215 0.027254 1.726228 1.030619 0.265723 0.019309 0.534590 0.642284 0.286761 0.016784 2.222454 0.548012 0.290797 0.026173 2.369166 0.947302 0.264383 0.017178 2.231198 0.752067 0.295891 0.020710 1.875535 0.641725 0.260306 0.022286 1.717322 0.848310 0.255257 0.014690 2.228167 0.508443

Table 3 .

 3 continued.

	ID spec. redshift	sub-class	Mg2	±	Hβ	±
	BCG5015 BCG5041 BCG5189 BCG5232 BCG5349 BCG5498 BCG5642 BCG5758 BCG5853 BCG5856 BCG5866 BCG5908 BCG6008 BCG6133 BCG6141 BCG6336 BCG6351 BCG6414 BCG6449 BCG6452 BCG6511 BCG6591 BCG6606 BCG6654 BCG6824 BCG6963 BCG7149 BCG7211 BCG7356 BCG7528 BCG7607 BCG7665 BCG7815 BCG7849 BCG7925 BCG7990 BCG7992 BCG8059 BCG8085 BCG8201 BCG8239 BCG8300 BCG8338 BCG8395 BCG8511 BCG8535 BCG8603 BCG8617 BCG8643 BCG8658 BCG8692 BCG8767 BCG8918 BCG8934 BCG9065 BCG9088 BCG9130 BCG9161 BCG9419 BCG9455 BCG9478	0.285776 0.227974 0.132145 0.264033 0.223418 0.242627 0.235521 0.255011 0.296180 0.254792 0.193292 0.231782 0.284115 0.296098 0.190765 0.268462 0.323224 0.231156 STARFORMING 0.242674 0.017245 0.142032 0.657410 0.271097 0.023992 2.314066 0.813229 0.266843 0.016595 1.377062 0.551542 BROADLINE 0.286807 0.010781 1.367809 0.313986 0.252630 0.021272 1.902738 0.689642 0.214403 0.029562 2.294126 1.067352 0.269739 0.021343 1.229566 0.783294 0.260319 0.020424 3.442233 0.696234 0.276979 0.026336 1.460787 0.903020 0.287312 0.030376 1.137156 1.062628 0.280112 0.021290 2.649512 0.642271 0.274434 0.016210 1.366956 0.556039 0.283237 0.020836 0.349850 0.789100 0.327230 0.022497 1.443567 0.754465 0.261117 0.023851 0.710391 0.838279 0.279060 0.024338 2.091054 0.758165 0.241370 0.021738 1.564736 0.736708 0.258681 0.254429 2.003296 0.699393 0.164279 0.279094 0.013334 1.413066 0.426180 0.225377 0.224416 0.019607 2.907984 0.636684 0.135480 0.297471 0.012751 1.132342 0.343998 0.246205 0.199980 0.023050 1.667743 0.839960 0.267358 0.211951 0.024373 0.817268 0.777089 0.163213 0.258033 0.147835 0.271783 0.012884 2.711296 0.432613 0.237128 0.247838 0.022450 0.491749 0.860989 0.238646 0.254240 0.019507 2.450907 0.670883 0.185485 0.314032 0.018754 0.523212 0.619710 0.188359 0.250326 0.019063 1.907109 0.610453 0.156296 0.290713 0.016277 1.703787 0.488739 0.297713 0.288204 0.319072 0.032785 1.828393 1.146880 0.110779 0.260042 0.010400 1.710873 0.299358 0.297880 0.138473 0.238749 0.025068 0.793702 0.696294 0.157149 0.264521 0.020285 1.181411 0.645111 0.246665 0.226726 0.231797 0.020208 2.718560 0.744617 0.268376 0.297682 0.182181 0.291955 0.014758 0.979427 0.477231 0.282993 0.136322 0.249261 0.017110 1.604781 0.410299 0.134509 0.246746 0.018423 1.434693 0.441388 0.164692 0.273411 0.016561 1.824647 0.522287 0.247998 0.260107 0.258923 0.284193 0.266323 0.157578 0.278197 0.018817 2.075243 0.562048 0.293149 0.143465 AGN 0.241417 0.272666 0.255641 0.168573 0.227542 0.021991 2.536526 0.711398 0.151029 0.235051 0.016479 2.477687 0.594636

Table 3 .

 3 continued.

	ID spec. redshift	sub-class	Mg2	±	Hβ	±
	BCG9512 BCG9514 BCG9686 BCG9693 BCG9799 BCG10141 BCG10151 BCG10217 BCG10326 BCG10339 BCG10372 BCG10430 BCG10452 BCG10815 BCG11017 BCG11239 BCG11369 BCG11442 BCG11482 BCG11547 BCG11551 BCG11571 BCG11683 BCG11703 BCG11787 BCG12019 BCG12463 BCG12990 BCG13175	0.310271 0.292013 0.221717 0.176730 0.199863 0.225204 0.208103 0.224653 0.161365 0.221089 0.284212 0.077954 0.254391 0.180769 0.159263 0.178699 0.176449 0.288675 0.230001 0.255540 0.219413 0.260091 0.217616 0.247557 0.134161 0.100942 0.121134 0.199584 0.153552		0.284064 0.021264 2.206975 0.748415 0.268354 0.018521 1.542066 0.608530 0.257792 0.017475 0.461349 0.614137 0.253260 0.022747 1.615399 0.890202 0.246809 0.032352 2.047414 1.186051 0.192641 0.018991 3.032758 0.647151 0.275198 0.016163 1.633791 0.488293 0.282606 0.023190 0.000000 -1.000000 0.254954 0.014284 1.656597 0.381681 0.246739 0.019481 0.005139 0.654559 0.303790 0.018146 1.295591 0.555865 0.224435 0.026502 1.138037 0.841920 0.236906 0.016402 2.130898 0.570206 0.195462 0.025990 2.273386 0.970192 0.246214 0.029532 1.130792 1.433648 0.261489 0.019548 1.456438 0.520110 0.260534 0.015678 1.443693 0.437083 0.242750 0.029549 1.733223 1.099187 0.212377 0.019158 0.353287 0.683562

Table 4 .

 4 UV photometry measurements (see Sect. 2.3).

	Table 4. continued.
	ID BCG11442 BCG11482 BCG11484 BCG11518 BCG11534 14669 13644 FUV NUV Aperture exp.(s) exp.(s) (pixels) 5227 6713 30 -16.88 0.18 FUV +1σ (AB) 1295 1194 30 -17.49 0.12 6583 8691 30 -17.63 0.06 1746 1609 30 -16.73 0.32 30 -15.70 0.18 BCG11547 1651 1540 30 -99.90 0.00 -15.77 -16.75 0.36 -1σ NUV +1σ (AB) 0.21 -16.42 0.36 0.14 -18.54 0.08 0.06 -17.60 0.14 0.47 -18.20 0.12 0.21 -16.55 0.09 BCG11551 1523 1584 70 -19.51 0.25 0.32 -19.76 0.20 BCG11571 3196 6403 30 -16.04 0.39 0.63 -16.83 0.16 BCG11683 29672 45423 50 -15.95 0.31 0.43 -16.80 0.17 BCG11703 32676 48586 30 -16.31 0.10 0.12 -17.03 0.05 BCG11762 14920 15286 30 -16.76 0.15 0.18 -17.47 0.08 BCG11787 29675 45494 50 -15.58 0.18 0.21 -16.13 0.08 BCG11965 3350 4658 30 -15.64 0.63 1.64 -15.81 0.36 BCG12016 4617 4269 30 -15.92 0.26 0.34 -17.54 0.09 BCG12019 7934 9315 50 -15.62 0.24 0.31 -17.00 0.08 BCG12122 1769 3130 30 -15.86 0.52 1.05 -15.56 0.52 BCG12155 1406 1296 30 -16.91 0.32 0.46 -17.12 0.21 BCG12463 29943 32240 50 -15.28 0.17 0.20 -16.23 0.07 BCG12522 1657 4605 30 -99.90 0.00 -15.41 -16.40 0.32 BCG12632 14920 15286 30 -15.90 0.32 0.45 -16.68 0.20 BCG12703 3232 7435 30 -16.57 0.24 0.31 -16.67 0.23 BCG12990 1390 1264 50 -18.56 0.13 0.15 -18.92 0.09 BCG13101 1810 1721 30 -99.90 0.00 -15.21 -16.56 0.45 BCG13175 166 1756 30 -16.00 0.46 0.82 -16.85 0.13 BCG13480 4801 6313 30 -15.54 0.43 0.72 -18.34 0.04 BCG13497 4641 10557 30 -13.89 0.97 113.79 -15.45 0.29 BCG13609 1746 3064 30 -15.77 0.51 1.00 -16.13 0.44 BCG13639 1340 1209 30 -14.08 1.72 113.98 -15.40 0.92 115.30 -1σ FUV-NUV center 0.54 -0.24 0.08 1.13 0.16 -0.31 0.13 1.15 0.10 0.82 0.53 -99.90 0.25 -0.12 0.19 1.00 0.20 0.91 0.05 0.55 0.09 0.79 0.08 0.45 0.53 -0.02 0.10 1.48 0.09 1.39 1.02 -0.21 0.26 0.24 0.08 0.85 0.46 1.39 0.25 0.34 0.29 0.15 0.09 0.34 0.78 -0.16 115.23 +1σ 0.37 0.14 0.14 0.29 0.20 0.00 0.18 0.46 0.22 0.09 0.21 0.11 0.85 0.22 0.14 0.70 0.53 0.10 1.44 114.35 -1σ 0.33 0.15 0.13 0.33 0.21 0.00 0.18 0.60 0.24 0.10 0.22 0.11 1.07 0.25 0.15 0.72 0.60 0.10 0.40 0.40 0.43 0.44 0.08 0.08 1.60 0.14 1.45 0.65 1.26 0.05 3.34 0.53 0.98 0.40 1.81 1.20 113.21 0.75 -0.51 0.91 0.72 2.48 2.69 113.39 BCG13672 1858 1711 30 -17.42 0.16 0.19 -16.49 0.53 1.08 -1.37 1.08 0.62 BCG13790 5591 6627 30 -14.81 0.64 1.79 -15.23 0.61 1.49 -0.05 2.03 1.45

Table 5 .

 5 Flags and notes for galaxies in our sample (see Sect. 2.5). number, page 18 of 21 S.Boissier et al.: The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). VII.:

	ID Flag FUV Flag NUV Note
	BCG24 ok BCG129 ok BCG271 part. BCG304 ok BCG485 ok BCG671 ok BCG692 ok BCG933 ok BCG1076 ok BCG1123 ok BCG1140 ok BCG1152 ok BCG1187 contam. BCG1251 ok BCG1355 ok BCG1383 ok BCG1408 contam. BCG1520 ok BCG1529 contam. BCG1574 ok BCG1635 ok BCG1684 ok BCG1805 ok BCG1934 ok BCG1961 contam. BCG2196 contam.	ok ok part. ok ok ok ok ok ok ok ok ok contam. ok ok ok contam. ok contam. ok ok ok ok ok contam. contam.	Arcs Arcs shells/tails/asymetric/mergers shells/tails/asymetric/mergers

Article

Table 5 .

 5 continued.Boissier et al.: The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). VII.:

	ID Flag FUV Flag NUV Note
	BCG6824 ok BCG6963 contam. BCG7149 contam. BCG7211 part. BCG7356 contam. BCG7528 ok BCG7607 ok BCG7665 ok BCG7815 contam. BCG7849 ok BCG7925 ok BCG7970 ok BCG7990 ok BCG7992 ok BCG8059 ok BCG8085 contam. BCG8201 contam. BCG8239 ok BCG8300 ok BCG8338 contam. BCG8395 ok BCG8511 ok BCG8535 ok BCG8603 contam. BCG8617 ok BCG8643 contam. BCG8658 ok BCG8692 contam. BCG8767 contam. BCG8918 part. BCG8934 ok BCG9065 contam. BCG9088 contam. BCG9106 contam. BCG9130 ok BCG9161 ok BCG9375 ok BCG9402 ok BCG9419 ok BCG9455 ok BCG9478 contam. BCG9512 contam. BCG9514 contam. BCG9686 ok BCG9693 contam. BCG9737 ok BCG9799 contam. BCG10141 ok BCG10151 ok BCG10217 ok BCG10326 ok BCG10339 contam. BCG10372 ok BCG10430 ok BCG10452 ok BCG10815 ok BCG11017 ok BCG11239 ok BCG11241 ok BCG11369 contam. BCG11442 ok	ok contam. ok part. contam. ok ok ok contam. ok ok ok ok ok ok contam. contam. ok ok contam. ok ok ok contam. ok contam. ok contam. contam. part. ok contam. contam. contam. ok ok ok ok ok ok contam. contam. contam. ok contam. ok contam. ok ok ok ok contam. ok ok ok ok ok ok ok contam. ok	Spiral structure Spiral structure shells/tails/asymetric/mergers shells/tails/asymetric/mergers Arcs Spiral structure shells/tails/asymetric/mergers shells/tails/asymetric/mergers shells/tails/asymetric/mergers
	Article number, page 20 of 21

http://www.galex.caltech.edu/researcher/techdoc-ch5.html

Article number, page 21 of 21

Acknowledgements. This research is based on observations made with the NASA Galaxy Evolution Explorer. GALEX is operated for NASA by the California Institute of Technology under NASA contract NAS5-98034. We wish to thank the GALEX Time Allocation Committee for the generous allocation of time devoted to GUViCS. This research made use of Montage, funded by the National Aeronautics and Space Administration's Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. Montage is maintained by the NASA/IPAC Infrared Science Archive.


Sylvain Chateau
email: sylvain.chateau@usherbrooke.ca&sebastien.poncet@usherbrooke.ca

Sébastien Poncet

Julien Favier
email: julien.favier@univ-amu.fr&umberto.d-ortona@univ-amu.fr

Umberto D'ortona

Metachronal

Metachronal wave formation in 3D cilia arrays immersed in a two-phase flow

Keywords: Lattice-Boltzmann method, Immersed Boundary, Metachronal waves, Mucociliary clearance

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

Introduction

Ciliary propulsion is a universal phenomenon developed by nature as a way to propel fluids. It can be found in almost every living organisms, going from the prokaryotic bacteria to mammals. In the particular case of the mucociliary clearance, cilia are found in tufts and serve to propel the mucus, a complex fluid whose purpose is to protect the bronchial epithelium against foreign particles. This epithelium is covered by a fluid layer called the Airways Surface Liquid (ASL), usually considered to be the superposition of two layers : the periciliary liquid (PCL) and the mucus just above it. The PCL is generally considered to be a Newtonian fluid similar to water. In normal epithelium, its depth is around 6 µm, which allows the tips of the cilia (length of 7 µm) to emerge into the mucus layer. The mucus is a highly non-Newtonian fluid which possesses characteristics such as visco-elasticity and thixotropy [START_REF] Lai | Micro-and macrorheology of mucus[END_REF]. Its height varies between 5 to 100 µm [START_REF] Widdicombe | Regulation of human airway surface liquid[END_REF]. The main purpose of the mucus is to act as a barrier against the foreign particles that may enter the human body (dust, pollutants, bacteria) by catching them. The cilia protrude on the epithelial surface and serve to transport the mucus up to the stomach, where it can be digested. Their motion can be decomposed into two steps : the stroke and the recovery phases, which take around 1/3 and 2/3 of the beating period respectively. Their beating frequency varies between 10 and 20 Hz. Note that in creeping flows, only the spatial asymmetry is essential for the cilia to generate propulsion [START_REF] Khaderi | Breaking of symmetry in microfluidic propulsion driven by artificial cilia[END_REF]. Defects in the mucociliary process usually lead to stagnant mucus, which induces breathing difficulties. Infections that may cause death also develop. It is then of prime importance to understand the hidden mechanisms behind the mucociliary clearance which allow thousands of cilia to act together for transporting mucus. Indeed, early experimental observations [START_REF] Sleigh | The biology of Cilia and Flagella[END_REF] have shown that cilia do not usually beat randomly, but instead adapt their beatings accordingly to their neighbors, giving birth to metachronal waves (MCW). If the phase lag ∆Φ between two cilia is positive (0 < ∆Φ < π), then the waves are called antipleptic MCW and move in the same direction as the fluid. On the contrary, if the phase lag ∆Φ between two cilia is negative (-π < ∆Φ < 0), then the waves are called symplectic MCW and move in the opposite direction. For the particular case where ∆Φ = 0, the cilia beat synchronously, and for ∆Φ = π a standing wave appears.

In this work, the formation of MCW is studied in a two-layer environment. To the best of our knowledge, the present study is the first one where both antipleptic and symplectic MCW are seen to emerge using a simple feedback law, while usually only one type of wave is observed, as in [START_REF] Gueron | Energetic considerations of ciliary beating and the advantage of metachronal coordination[END_REF]. Moreover, while many studies considered single-layer fluid [START_REF] Elgeti | Emergence of metachronal waves in cilia arrays[END_REF], only few had considered two-layer environments when studying MCW [START_REF] Mitran | Metachronal wave formation in a model of pulmonary cilia[END_REF]. A parametric study where the metachrony is imposed is also performed. A particular value of phase lag ∆Φ = π/4, corresponding to an antipleptic MCW, is shown to be the more suitable for transporting and mixing the fluids. Finally, the numerical method possesses the following advantages : (i) viscosity ratios up to O(10 2 ) can be achieved [START_REF] Porter | Multicomponent interparticlepotential lattice Boltzmann model for fluids with large viscosity ratios[END_REF], and (ii) the mucus-PCL interface emerges intrinsically from the model. This solver is the only one that combines all these capabilities.

Numerical method

Geometrical modeling

The computational domain is a box composed of N x × N y × N z points regularly spaced. The cilia are hair-like structures modeled by a set of 20 Lagrangian points, such that their base point is located at z = 0 along the wall. The spacing between two neighbouring cilia is a in the x and y-directions, and their length L is set to 15 lattice unit (lu). Their motion is imposed to be in the (x,z) plane, and the MCW propagate in the x-direction only. Thus, cilia located at the same value of x beat in phase with each other. The ratio h/H between the PCL thickness and the height of the domain is set to 0.27 for all simulations. The equations of motion for the cilia are inspired from [START_REF] Chatelin | Méthodes numériques pour l'écoulement de Stokes 3D : fluides à viscosité variable en géométrie complexe mobile ; application aux fluides biologiques[END_REF] and reproduce the beating pattern by resolving a 1D transport equation along a parametric curve. With such a beating pattern, the essential ingredients of the beating are captured, such as the angular amplitude between the beginning and the end of a stroke phase (θ = 2π

3 ), which agrees well with experimental data [START_REF] Sleigh | The Propulsion of Mucus by Cilia[END_REF]. Figure 1(a) gives a schematic view of the geometry, and figure 1(b) an insight of the stroke and recovery phases as modeled in the present work.

In the simulations, the PCL thickness h varies between 0.6L to 0.9L. Thus, the cilia tips enter the mucus phase when the cilia are in the stroke phase, as observed in real epithelium configurations. Both the PCL and the mucus are considered Newtonian fluids. The kinematic viscosity of the mucus is ν m = 10 -3 m 2 /s, and the viscosity ratio r ν = ν m /ν P CL between the mucus and PCL is set to 20.

A recent study [START_REF] Chatelin | A parametric study of mucociliary transport by numerical simulations of 3D non-homogeneous mucus[END_REF] has indeed shown that mucus transport was maximized for such viscosity ratios when considering a stiff transition between the mucus and PCL. The beating period of the cilia is N it × dt (with dt = 1 using the classical LBM normalization), N it being the number of iterations for a cilium to perform a complete beating cycle.

Algorithm

The numerical model is described in [START_REF] Li | An improved explicit immersed boundary method to couple with Lattice Boltzmann model for single-and multi-component fluid flows[END_REF], and validated on several configurations involving flexible and moving boundaries in multiphase flows, with a 2 nd order accuracy.

The fluid part is first solved on a Cartesian grid with LBM using the Bhatnagar-Gross-Krook (BGK) model and a D3Q19 scheme. The collision and streaming steps proper to the LBM method are first performed. The model of [START_REF] Porter | Multicomponent interparticlepotential lattice Boltzmann model for fluids with large viscosity ratios[END_REF] is used to simulate the two-phase flow as it allows to minimize the magnitude of spurious currents near the fluid-fluid interface. More importantly, it also enables to consider higher density or viscosity ratios. Then, values for the fluid velocity are interpolated at the Lagrangian points. It allows to compute an IB force to be spread onto the neighbouring Eulerian fluid nodes in order to ensure the no-slip condition along the cilia. The macroscopic fluid velocity is then updated.

Note that the geometric shape of the beating is fixed in all simulations. To save computing time, this shape is only computed once, decomposed into a finite number of steps (snapshots) during a beating period, and stored in memory. If necessary, an interpolation can be done in order to have the velocity values along the cilia in between two steps.

Since the model of [START_REF] Porter | Multicomponent interparticlepotential lattice Boltzmann model for fluids with large viscosity ratios[END_REF] uses a Shan-Chen (SC) repulsive force [START_REF] Shan | Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation[END_REF], surface tension effects emerge intrinsically at the PCL-mucus interface. m for the force imposed on the mucus phase and F i P CL for the force imposed on the PCL phase-, are projected on the velocity vector V s i corresponding to the s th Lagrangian point. The lever arm is

L p = X p ⊗ V s i / V s i .
Periodic boundary conditions are used in the x and y directions, while no-slip and free-slip boundary conditions are used at the bottom and top walls respectively. The size of the computational domain ranges from 50 lu to 400 lu depending on the configuration considered, except for the size along the z direction which is always set to 50 lu.

Taking advantage of the local character of the LBM algorithm, the code is parallelized using MPI libraries (Message Passing Interface), by splitting the full computational domain into 9 sub-domains of size (N x /3, N y /3, N z ). More details on the numerical model can be found in [START_REF] Li | An improved explicit immersed boundary method to couple with Lattice Boltzmann model for single-and multi-component fluid flows[END_REF].

Feedback law

The basic idea is to modulate the beating motion of the cilia as a function of the fluid motion. To do so, it is assumed that all cilia follow the same beating pattern, meanwhile a feedback of the fluids, which consists in accelerating or slowing down the motion of the cilia, is introduced.

Each cilium is discretized with N s = 20 Lagrangian points. Let s be the subscript corresponding to the s th Lagrangian point, starting from the base tip at s = 1, and V s i the velocity on the s th Lagrangian point of the i th cilium. For each cilium, we define the average velocity over all Lagrangian points V i , which is linked to the number of steps (snapshots) this cilium will skip during one iteration of the fluid solver. The fluid feedback onto the cilia thus consists in modifying the norm of the velocity vector V i , while its direction remains unchanged.

The feedback is computed in three steps. First, the IB forces corresponding to mucus and PCL are projected onto the corresponding velocity vectors for each Lagrangian point. Then, an estimate of the feedback is computed based on the torques of the forces for each Lagrangian point. Finally, the beating pattern of the cilia is adjusted at the beginning of the next time step. By doing so, only the norm of the velocity vector, but not its direction, is modified. A coupling parameter α is also introduced to control both the intensity of the fluid feedback and the direction of the wave propagation : V i = V i ± α dV i . Figure 2 gives a schematic view of the forces and variables considered. More details regarding the feedback law can be found in [START_REF] Chateau | Transport efficiency of metachronal waves in 3D cilia arrays immersed in a two-phase flow[END_REF].

Larger3.tif F 3 -Antipleptic MCW emerging from an initially random state of the cilia. 1024 cilia arranged in a 32 × 32 square are considered on a computational domain of size (N x = 161, N y = 161, N z = 32) with a cilia spacing a/L = 0.23. The mucus phase is in red and the PCL phase in blue. The color bar indicates the phase of a particular cilium within one beating period, which is represented by a circle at its base. Top : 3D view of the system. Bottom : 2D view of the same system in a (x,y) plane to highlight the 3D modulation in the z-direction.

Results

Emergence of MCW

Using the feedback law previously introduced, both antipleptic and symplectic MCW are seen to emerge. The parameter α plays a role in the emergence : it controls both the direction of the wave propagation and the time for synchronization to occur (higher absolute values of α reduce the time for MCW to emerge). Figure 3 shows an antipleptic MCW emerging from cilia beating initially randomly, using α = -3.5. In this figure the presence of two wavelengths can be noticed. The phase lag between neighbouring cilia is ∆Φ = π/8. Moreover, assuming a least effort behaviour of the cilia (meaning α < 0), antipleptic MCW are seen to emerge for small cilia spacings while symplectic MCW occur for higher cilia spacings (see figure 4). A tendency can also be observed (black line) and needs to be studied in more details. This result is important as it shows that natural cilia, who are usually highly packed, should adopt a least effort behaviour to organize in antipleptic MCW. However, with the present model, a least effort behaviour (α < 0) induces a stroke phase longer than the recovery phase. On the contrary, assuming that the cilia beat faster when encountering a resistance (meaning α > 0), the stroke phase becomes faster than the recovery phase as observed in real cilia configurations. While hydrodynamics interactions are sufficient to explain the synchronization of neighbouring cilia, they are not sufficient to explain the temporal asymmetry present in the beating pattern. Hence, the conclusion is that other biological parameters must also play a role. Note that the white space between the green and blue points (just above the black line) in figure 4 corresponds to simulations where no MCW emerged.

Transport efficiency of MCW

In order to quantify the efficiency of the MCW to transport fluids, a parametric study where the metachrony is imposed, has been performed. In the following, the stroke and recovery phases are fixed and take the same amount of time in order to study the influence of the spatial asymmetry only. Indeed, it is the only mechanism that is important for inducing motion in creeping flows [START_REF] Khaderi | Breaking of symmetry in microfluidic propulsion driven by artificial cilia[END_REF]. In order to save CPU time, the results presented here have been obtained using a Reynolds number of 20 larger than the one usually seen for such configurations (Re ≈ 10 -5 ). Thus, inertial effects are introduced in the model. However, it has been verified that such effects are small and do not modify the behaviour of MCW. The only notable quantitative differences are found for fully synchronized cilia : for such configurations, the inertial effects cancel the reversal of the flow that should occur during the recovery motion. More details regarding the effect of inertia can be found in [START_REF] Chateau | Transport efficiency of metachronal waves in 3D cilia arrays immersed in a two-phase flow[END_REF].

The total volume of fluid displaced during a beating cycle for the different phase lags is compared in figure 5. For a small cilia spacing (a/L = 1.67), the efficiency of the antipleptic metachrony is obvious. It agrees well with the results of [START_REF] Khaderi | Microfluidic propulsion by the metachronal beating of magnetic artificial cilia : a numerical analysis[END_REF] who observed a larger net flow produced by antipleptic metachrony for this value of cilia spacing. Symplectic waves appear to be less or at best equally efficient than antipleptic motion, except for ∆Φ = -7π/8 for a/L = 1.67 where there is a peak in the total displaced volume of flow. There are two neighbouring maxima at ∆Φ = π/4 and ∆Φ = π/2 for a/L = 1.67 and a/L = 2 respectively, indicating that specific phase lags are more able to generate a strong flow.

A displacement ratio that will quantify the capacity of a given system to transport particles, with respect to a given amount of power, is now introduced. In that context, η 1 is defined by the mean fluid displacement over the x-direction during one beating cycle, divided by the mean power P * that a cilium had to spend during this beating cycle. Since the main purpose of mucociliary clearance is to transport mucus, and since experimental data [START_REF] Winters | Roles of hydration, sodium, and chloride in regulation of canine mucociliary transport system[END_REF] report that the total thickness in the vertical direction of the mucus layer is in the range [1.4L; 10L], values for the displacement were taken on an arbitrary plane z/L = 3.2 near the extremity of the domain. To obtain a value for the displacement, the instantaneous average fluid velocity over the x-direction is computed, and the resulting value is then multiplied by the period of a full beating cycle, giving the mean displacement < d x > over one period on the (x,y,3.2L) plane. By dividing this mean displacement with appropriate quantities, a dimensionless expression of the displacement ratio is obtained :

η 1 = (< d x > N cil )/(λP * )
, where N cil is the number of cilia and λ the metachronal wavelength. For the synchronized case, i.e. ∆Φ = 0, λ is infinite and thus the size of the domain over the x direction was used and divided by the number of cilia.

On Figure 6, one can see the displacement ratio η 1 for different cilia spacings a/L and phase lags ∆Φ.

A clear peak exists for the smaller cilia spacing (a/L = 1.67) for a phase lag ∆Φ = π/4, showing that such antipleptic MCW are more able to transport fluids. On the other hand, symplectic MCW are often less, or at best equally efficient, than antipleptic MCW.

The mixing capacity of the systems has also been evaluated. To do so, the average stretching rate during a beating period has been computed. Figure 7 shows the corresponding results. One can see that the antipleptic MCW corresponding to ∆Φ = π/4 and a/L = 1.67 present the best capacity for stretching

Conclusion

Considering a simple feedback law, both antipleptic and symplectic MCW were observed to emerge spontaneously in a two-layer environment. Considering a least effort behaviour for cilia, antipleptic MCW were obtained for the smallest cilia spacing studied, while symplectic MCW were observed for larger ones. The resulting beating pattern consisted in a slow stroke phase and a fast recovery phase, which is the opposite of what is observed in nature. Hence, other biological parameters must play a role in the cilia beating pattern, and hydrodynamic interactions are not sufficient to fully explain their motion. A parametric study has also been performed and shows that the antipleptic MCW with ∆Φ = π/4 are the most efficient in transporting and mixing fluids.

  a) Schematic view of the computational domain. The present case corresponds to an antipleptic MCW. The domain is filled with PCL (in blue) and mucus (in red). (b) Beating pattern of a cilium with the parametric equation used. Steps 1 to 6 correspond to the recovery phase, and steps 7 to 9 to the stroke phase.

F 2 -

 2 Schematic view of a cilium with the corresponding forces exerted on the fluids. The interpolated IB forces applied by the i th cilium onto the fluids -respectively F i

F 4 -

 4 Emergence of MCW as a function of the cilia spacing a/L and number N of cilia in a row. Green : Antipleptic MCW ; Blue : Symplectic MCW. The markers respectively represent : (+) : 1 wavelength ; (•) : 2 wavelengths ; and ( ) : 3 wavelengths. The black line illustrates the presence of a "trend".

F 5 -

 5 Total dimensionless displaced flow volume generated by an array of cilia over a beating cycle for different phase lags and cilia spacings. + : a/L = 1.67 ; : a/L = 2 ; * : a/L = 2.53 ; : a/L = 3.33.

F 6 -

 6 Displacement ratio η 1 as a function of the phase lag ∆Φ for different cilia spacings a/L.

4 F 7 -

 47 Average stretching rate computed between 0 < z < 1.4L as a function of the phase lag ∆Φ for different cilia spacings a/L. the fluids. A more complete study is ongoing.

Acknowledgment

The authors would like to thank the Natural Sciences and Engineering Research Council of Canada for its financial support through a Discovery Grant (RGPIN-2015-06512). This work was granted access to the HPC resources of Compute Canada and Aix-Marseille University (project Equip@Meso ANR-10-EQPX-29-01).