Hamza Khassali

Alex Baumel

Frédéric Mahé

Estelle Tournier

Pierre Tisseyre

Yves Prin

Lahcen Ouahmane

Hervé Sanguin

The belowground bacterial and fungal communities differed in their significance as microbial indicator of Moroccan carob habitats

Keywords: Biodiversity, Belowground microbiota, Ceratonia siliqua, Microbial indicator, Metabarcoding

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

INTRODUCTION

Carob trees (Ceratonia siliqua L., Leguminosae), an important component of Mediterranean thermophilous woodlands and traditional rural landscapes, are characterized by declining population levels [START_REF] Rankou | Ceratonia siliqua. The IUCN Red List of Threatened Species[END_REF]. The major causes are the high urbanization affecting the Mediterranean coasts where most carob populations are localized, and an abandon of traditional carob orchards in favor of other fruit sectors [START_REF] Rankou | Ceratonia siliqua. The IUCN Red List of Threatened Species[END_REF][START_REF] Talhouk | Status and prospects for the conservation of remnant semi-natural carob Ceratonia siliqua L. populations in Lebanon[END_REF]. A phytosociological study of Mediterranean carob habitats highlighted their high floristic diversity, notably in the Western basin where the carob tree meets its maximum ecological gradient [START_REF] Baumel | Assessment of plant species diversity associated with the carob tree (Ceratonia siliqua, Fabaceae) at the Mediterranean scale[END_REF]. In addition to its ecological importance, carob habitat conservation could be of great importance for the future since carob tree is known for its tolerance to marginal soils [START_REF] Correia | The use of macronutrients and water in marginal Mediterranean areas: the case of carob-tree[END_REF][START_REF] Ozturk | Ecophysiological responses of some maquis (Ceratonia siliqua L., Olea oleaster Hoffm. & Link, Pistacia lentiscus and Quercus coccifera L.) plant species to drought in the east Mediterranean ecosystem[END_REF] and for the nutritional quality of its fruits as functional food [START_REF] Papaefstathiou | Nutritional characterization of carobs and traditional carob products[END_REF][START_REF] Stavrou | Polyphenols in carobs: A review on their composition, antioxidant capacity and cytotoxic effects, and health impact[END_REF].

The development of efficient habitat conservation policies and actions needs an integrative view of the biodiversity that sustains ecosystem functioning. However, shortfalls in knowledge are observed for belowground biodiversity in the Mediterranean basin [START_REF] Cameron | Global mismatches in aboveground and belowground biodiversity[END_REF], whereas it constitutes, notably soil microbiota, the bedrock on which soil nutrient cycling, plant productivity and ecological succession are built [START_REF] Bardgett | Belowground biodiversity and ecosystem functioning[END_REF][START_REF] Van Der Heijden | The unseen majority: soil microbes as drivers of plant diversity and productivity in terrestrial ecosystems[END_REF][START_REF] Wagg | Soil biodiversity and soil community composition determine ecosystem multifunctionality[END_REF]. Moroccan semi-natural and traditional agrosystems have a pivotal role for the conservation of carob genetic ressources by sheltering the main evolutionary lineages found in this tree (Viruel et al., 2020). Moreover, Moroccan carob habitats are divided into two main floristic groups related to distinct edaphic parameters, climatic conditions and biogeographic history. The North group is close to South Iberian and North African vegetations and the South group is at the margin of the carob geographic range with a vegetation composed of species found nowhere else on carob habitats [START_REF] Baumel | Assessment of plant species diversity associated with the carob tree (Ceratonia siliqua, Fabaceae) at the Mediterranean scale[END_REF].

The current study aims at identifying the belowground microbiota associated with carob trees and major plant components of Moroccan carob habitats. Indicator plant taxa associated with both the North and South habitats (Pistacia lentiscus), or mainly with North (Cistus albidus)

or South (Vachellia gummifera, Globularia alypum) [START_REF] Baumel | Assessment of plant species diversity associated with the carob tree (Ceratonia siliqua, Fabaceae) at the Mediterranean scale[END_REF] were selected. In addition, Lavandula dentata and Retama monosperma were selected for their known beneficial properties on soil mycorrhizal potential [START_REF] Hafidi | Managing Mediterranean nurse plants-mediated effects on soil microbial functions to improve rock phosphate solubilization processes and early growth of Cupressus atlantica[END_REF][START_REF] Manaut | Valorisation de la microflore symbiotique endémique des sols marocains pour améliorer la domestication du Caroubier[END_REF]Ouahmane et al., 2006b).

MATERIALS AND METHODS

Study sites and soil sampling

Two carob habitats representative of the floristic group 1 (Asparago albi-Rhamnion oleoidis) and 4 (Senecio anteuphorbii-Arganion spinosae) as defined in [START_REF] Baumel | Assessment of plant species diversity associated with the carob tree (Ceratonia siliqua, Fabaceae) at the Mediterranean scale[END_REF] S1).

DNA extraction, gene amplification and sequencing

Total DNA was extracted from 500 mg of soil using the FastDNA SPIN kit for soil (MP Biomedicals Europe, Illkirch, France) according to manufacturer's instructions. DNA purity was improved by adding 40 mg Polyvinylpolypyrrolidon (PVPP) during the first step of DNA extraction, and an additional washing step with 5.5 M guanidine thiocyanate before the use of the washing buffer SEWS-M. DNA extractions were done in duplicate and stored at -20°C for further analysis. Amplification of a 16S rRNA gene sub-region and the internal transcribed spacer ITS2 were performed for bacterial and fungal communities, respectively. All amplification products were analyzed using paired-end Illumina MiSeq sequencing (2×300 bp) performed by Get-PlaGe (Genotoul, Castanet-Tolosan, France). The 16S was amplified by polymerase chain reaction (PCR) using the primers V3F (5'-TACGGRAGGCAGCAG-3') and V4R (5'-GGACTACCAGGGTATCTAAT-3') [START_REF] Alm | The oligonucleotide probe database[END_REF] , and ITS2 with the primers ITS86F

(5'-GTGAATCATCGAATCTTTGAA-3') [START_REF] Turenne | Rapid identification of fungi by using the ITS2 genetic region and an automated fluorescent capillary electrophoresis system[END_REF] and ITS4 (5'-TCCTCCGCTTATTGATATGC-3') [START_REF] White | Amplification and direct sequencing of fungal ribosomal rna genes for phylogenetics[END_REF]. Details of the amplification and sequencing steps are provided in Appendix S1.

Data processing

Illumina sequencing, base calling and demultiplexing were carried out using RTA v1.18.54, MCS 2.6 and bcl2fastq2.17. Paired reads were assembled with vsearch v2.11.0 [START_REF] Rognes | VSEARCH: a versatile open source tool for metagenomics[END_REF], and primer clipping was performed with cutadapt v1.9 (Martin 2011). Clustering with swarm v2.2.2 [START_REF] Mahé | Swarm v2: highlyscalable and high-resolution amplicon clustering[END_REF], chimera detection and taxonomic assigment were performed as detailed in [START_REF] Maghnia | Habitat-and soil-related drivers of the root-associated fungal community of Quercus suber in the Northern Moroccan forest[END_REF]. The ribosomal database SILVA v132 [START_REF] Quast | The SILVA ribosomal RNA gene database project: improved data processing and web-based tools[END_REF] and a custom version of the ITS database UNITE v7 (Koljalg et al., 2013) were used for the bacteria and fungi, respectively. Details of data processing steps are provided in Appendix S1. The raw data are available under the bioproject PRJEB36517

(https://www.ebi.ac.uk/ena/data/view/PRJEB36517).

Statistics

Tables were transformed using the R tidyverse package version 1.2.1 (Wickham, 2017) and the plots were generated using the R ggplot2 package version 3.0.0 (Wickham, 2016). Global rarefaction (based on the samples with the smallest sizes), diversity (Shannon, inverse

Simpson [1/D]) and richness (number of OTUs) analyses of microbiota were performed with the R vegan package version 2.5-2 [START_REF] Oksanen | vegan: Community Ecology Package. R package version 2[END_REF]. Microbiota structure analysis was performed either by hierarchical clustering (HC) with the stat package (R Core Team, 2017) or nonmetric multi-dimensional scaling (NMDS) with the R package vegan, and significance of differences was assessed using PERMANOVA and HOMOVA from the R package vegan.

The variability of soil properties, the correlation between them and with the components of principal component analysis (PCA) were estimated with the R package ade4 [START_REF] Chessel | The ade4 package -I : One-table methods[END_REF]. The best subset of soil properties with maximum (rank) correlation with the microbiota structure was estimated with the R vegan package. Community membership among plant species and between habitats were assessed with the R package VennDiagram version 1.6.20 [START_REF] Chen | VennDiagram: Generate High-Resolution Venn and Euler Plots[END_REF], and because of their importance in plant ecology, the specificity of interactions between Glomeromycota taxa and plant species was evaluated and visualized using the R package bipartite version 2.11 [START_REF] Dormann | Indices, graphs and null models: analyzing bipartite ecological networks[END_REF]. The significance of microbial taxa association with respect to habitat types (North and South), defined as microbial indicator, was based on the indicator value (IndVal) index from the R package indicspecies version 1.7.6 (De Cáceres and Legendre, 2009). Details of R functions used for statistics are provided in Appendix S1.

RESULTS

Global composition of belowground microbiota

Higher ranges of bacterial community richness (2,080 ± 188 OTUs) and diversity (shannon index 6.7 ± 0.2) were observed compared to the fungal community (richness 647 ± 209

OTUs; shannon index 4.1 ± 0.9) (Table S1). Lower levels were obtained for the fungal community in the South (richness 557 ± 169 OTUs; shannon diversity 3.7 ± 0.3) compared to the North (richness 760 ± 218 OTUs; shannon diversity 4.8 ± 1.0), but not for the bacteria (Table S1). The bacterial community was dominated by Actinobacteria (52 % of sequences)

and Proteobacteria (32 %) (Figure 1A; Table S2), and the fungal community by Ascomycota (71 %), except for C. albidus (Basidiomycota, 69 %) (Figure 1B; Table S3). Only 1 % of microbial OTUs were found in all samples, and 60 % only in one sample.

The most dominant bacterial OTUs (top 10 % of most abundant; present in 2/3 of samples) belonged for 62 % to Actinobacteria and 28 % to Proteobacteria (Table S2) whereas the remaining 10 % were split among seven other phyla. The most dominant fungal OTUs belonged mostly to Ascomycota (89 %), then Mortierellomycota (8 %) and Basidiomycota (2 %) (Table S3). The top genera (> 5 %) were Rubrobacter and Microvirga for bacteria and Mortierella, Alternaria and Fusarium for fungi, but a large part of sequences were not identified, 36 % and 54 %, respectively.

Habitat-related microbiota taxa

Microbiota structure analysis revealed a significant North / South pattern for the bacterial (Figure 2B, P < 0.0202) and fungal (Figure 2D, P < 0.0345) communities, with only 3 % of bacterial OTUs and 20 % of fungal OTUs shared between both habitats (Figure S1).

However, HC and NMDS analyses revealed a higher similarity of bacterial community associated with C. albidus in the North (Figure 2A,B) with those associated with plant species in the South. In a lesser extent, the fungal community of P. lentiscus in the South was strongly dissimilar from those associated with the other plant species of the same habitat (Figure 2C,D). Indicator species analyses revealed significant contrasted results between the North / South habitats and bacterial / fungal microbial taxa (Table 1). The North was characterized by 17 fungal indicator taxa, notably Pestalotiopsis, Pleurostoma, Spirosphaera, and one bacterial taxa, whereas the South was characterized by 11 bacterial indicator taxa, notably Kocuria and Naasia, and no fungal indicator taxa (Table 1). The functional assignment of the microbial indicators also showed functionnal divergences with a predominance of fungal pathogens in the North and stress-tolerant plant-beneficial bacteria in the South.

Soil properties-related microbial taxa

The North / South pattern observed for belowground microbiota is supported by the soil properties (Table S4), for which the main component of variance was organized between North and South (Figure 3A) (Axis 1, 61% of total inertia; Axis 2, 15 %). The differences was mainly explained by a higher global nutrient status in the North, with notably higher amount of organic matter and organic C (> 95% of relative contribution along axis 1). The South was, on the contrary, characterized by lower levels of all parameters measured, except for total K (> 80% of relative contribution along axis 1) (Figure 3B). High pH levels were observed in both habitats, but intra-habitat variability was observed (> 75 % of relative contribution along axis 2) (Figure 3B). The analysis of the best correlation between a subset of soil properties and the microbiota structure highlighted the C / N ratio (r = 0.61) for the bacterial community and the association of Total N, CaCO3, Olsen-P, K + and Total K (r = 0.52) for the fungal community.

Plant-related microbiota taxa

In the North, the belowground microbiota associated with P. lentiscus and L. dentata showed the strongest similarity with C. siliqua (Figure 2B,D). By contrast, the South was marked by divergences regarding the closest microbiota components between C. siliqua and the other plant species. The fungal community associated with R. monosperma in the South showed the strongest similarity with that of C. siliqua (Figure 2D), whereas the most similar bacterial community of that of C. siliqua were P. lentiscus and V. gummifera (Figure 2B). The C. siliqua -P. lentiscus association, one of the most frequent plant association in Moroccan carob habitats was more precisely analyzed, revealing a core microbiota of c.a. 25 % and 20 % of the total bacterial and fungal OTUs, respectively (Figure 4). The most dominant bacterial OTUs (top 10 % of most abundant; present in all samples) constituting the core microbiota belonged mainly to deep-branching actinobacterial taxa, Rubrobacter (Rubrobacteriales), Solirubrobacter (Solirubrobacter), and one alphaproteobacterial taxa, Microvirga (Rhizobiales) (Figure 4A). For the fungi, the most dominant OTUs were mainly assigned to Fusarium (Hypocreales), Mortierella (Mortierellales), Chrysosporium (Onygenales), Alternaria (Pleosporales), Chaetomium (Sordariales) (Figure 4B). Gaiellales and Capnodiales were composed of unidentified taxa at the genus level.

Characteristics of Glomeromycota community

The estimation of Glomeromycota abundance (read numbers) showed higher levels in the North (Figure 5), notably for L. dentata (> 250 sequences), but no significant North / South pattern (PERMANOVA, R 2 = 019362, P = 0.1217) was obverved Glomeromycota accounted for 0.03 % to 2.61 % of the total soil fungal community depending on the habitat. The analysis of potential mycorrhizal networks at the habitat level between Glomeromycota (genus level) and plant species (Figure 6) revealed a higher level of nestedness (weigthed NODF-based index) in the North (49.6) compared to the South (29.3), but low levels of specialisation (H2 index), 0.14 and 0.20, respectively. In the North, three genera were associated with only one plant species, Domonikia with P. lentiscus and Rhizophagus / Funnelifomis with L. dentata. In the South, Domonikia and Rhizophagus was not detected, and Funneliformis was associated with R. monosperma. Ceratonia siliqua was associated with the same Glomeromycota genera (i.e. Claroideoglomus, Diversispora, Glomus, and Septoglomus), except for Kamienskia only in the North.

DISCUSSION

Belowground microbiota is a major driver of plant diversity and ecosystem functioning [START_REF] Graham | Microbes as engines of ecosystem function: when does community structure enhance predictions of ecosystem processes?[END_REF][START_REF] Van Der Heijden | The unseen majority: soil microbes as drivers of plant diversity and productivity in terrestrial ecosystems[END_REF]. Recent worldwide surveys revealed their tremendous diversity [START_REF] Davison | Global assessment of arbuscular mycorrhizal fungus diversity reveals very low endemism[END_REF]Delgado-Baquerizo et al., 2018a;[START_REF] Egidi | A few Ascomycota taxa dominate soil fungal communities worldwide[END_REF][START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF], but also pinpointed the lack of data in some part of the world, e.g. Southern Mediterranean regions like Morocco. The current study focused on the belowground microbiota associated with several plant species representative of Mediterranean thermophilous carob woodlands in Morocco. The plant species investigated had been mainly assessed for their mycorrhizal community [START_REF] Alguacil | Plant type differently promote the arbuscular mycorrhizal fungi biodiversity in the rhizosphere after revegetation of a degraded, semiarid land[END_REF][START_REF] Azcon-Aguilar | Analysis of the mycorrhizal potential in the rhizosphere of representative plant species from desertification-threatened Mediterranean shrublands[END_REF][START_REF] Ferrol | Analysing arbuscular mycorrhizal fungal diversity in shrub-associated resource islands from a desertification-threatened semiarid Mediterranean ecosystem[END_REF][START_REF] Manaut | Potentialities of ecological engineering strategy based on native arbuscular mycorrhizal community for improving afforestation programs with carob trees in degraded environments[END_REF][START_REF] Ouahmane | Inoculation of Ceratonia siliqua L. with native arbuscular mycorrhizal fungi mixture improves seedling establishment under greenhouse conditions[END_REF][START_REF] Torrecillas | Modularity reveals the tendency of arbuscular mycorrhizal fungi to interact differently with generalist and specialist plant species in Gypsum Soils[END_REF][START_REF] Turrini | Arbuscular mycorrhizal fungi of a Mediterranean island (Pianosa), within a UNESCO Biosphere Reserve[END_REF] notably because of the role of mycorrhiza in ecosystem functioning [START_REF] Banerjee | Keystone taxa as drivers of microbiome structure and functioning[END_REF][START_REF] Gianinazzi | Agroecology: the key role of arbuscular mycorrhizas in ecosystem services[END_REF][START_REF] Qin | Arbuscular mycorrhizal fungi serve as keystone taxa for revegetation on the Tibetan Plateau[END_REF][START_REF] Rillig | Arbuscular mycorrhizae and terrestrial ecosystem processes[END_REF]. The Glomeromycota are more particularly well known for their benefits (i) on plant productivity, (ii) on tolerance to drought stress and resistance to pathogens, as well as (iii) in the process of plant succession [START_REF] Smith | Mycorrhizal symbiosis[END_REF]. In contrast, only fragmentary data were available for the other belowground microbiota compartments.

The global composition of belowground microbiota revealed in this study was congruent with worldwide surveys at the phylum levels (Delgado-Baquerizo et al., 2018a;[START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF], with Actinobacteria, Ascomycota, Basidiomycota, Proteobacteria and Mortierellomycota as the most dominant taxa. The rhizosphere of C. albidus was remarkably dominated by Basidiomycota compared to other plant rhizospheres, probably due to its preferential association with ectomycorrhizal basidiomycota [START_REF] Comandini | An overview of Cistus ectomycorrhizal fungi[END_REF].

Similarly to the patterns observed in worldwide surveys (Delgado-Baquerizo et al., 2018a;[START_REF] Egidi | A few Ascomycota taxa dominate soil fungal communities worldwide[END_REF], only few OTUs were dominant, mostly belonging to Ascomycota (Sordariomycetes and Dothideomycetes), Actinobacteria (Actinobacteria, Thermoleophilia and Rubrobacteria) and Proteobacteria (Alphaproteobacteria). Amongst the plant species investigated in the current study, the two trees (C. siliqua and P. lentiscus) the most frequently associated in Mediterranean thermophilous woodlands [START_REF] Baumel | Assessment of plant species diversity associated with the carob tree (Ceratonia siliqua, Fabaceae) at the Mediterranean scale[END_REF] shared 24 % of OTUs, whose only 7 % were dominant. Rhizobiales, a main keystone alphaproteobacterial taxa in forest and woodland ecosystems [START_REF] Banerjee | Keystone taxa as drivers of microbiome structure and functioning[END_REF], was the second most represented bacterial order among the dominant OTUs, as well as in the core microbiota between C. siliqua and P. lentiscus. The importance of Rhizobiales in carob funtionning remains controversial. Indeed, evidence of N-fixing bacteria in carob roots [START_REF] El Idrissi | Characterization of rhizobia isolated from Carob tree (Ceratonia siliqua)[END_REF] has been strongly questionned [START_REF] Konate | Characterization of endophytic bacteria associated with roots and epicotyls of carob tree (Ceratonia siliqua L.)[END_REF], and neither nodules or N-fixation were observed for field-grown carob trees (La [START_REF] Malfa | 15N natural abundance technique does not reveal the presence of nitrogen from biological fixation in field grown carob (Ceratonia siliqua L.) trees[END_REF]. Nevertheless, potential N-fixing Rhizobiales belonging to Microvirga [START_REF] Andrews | Specificity in legume-rhizobia symbioses[END_REF] appeared as predominant taxa in both carob habitats.

A significant North / South pattern was observed for the belowground microbiota, supported bydifferences in the soil properties. The soil properties are known as a major driver of belowground microbiota [START_REF] Bastida | Global ecological predictors of the soil priming effect[END_REF]Delgado-Baquerizo et al., 2018b;[START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF], but specific soil properties differently affects bacterial and fungal communities.

Soil pH has been described as shaping mostly the bacterial community structure, whereas soil nutrient status (C / N ratio, total N, total P) was more correlated with the fungal community structure [START_REF] Lauber | The influence of soil properties on the structure of bacterial and fungal communities across land-use types[END_REF][START_REF] Rousk | Soil bacterial and fungal communities across a pH gradient in an arable soil[END_REF]. Soil pH is undoubtedly the best predictor of bacterial diversity and biomass [START_REF] Griffiths | The bacterial biogeography of British soils[END_REF][START_REF] Karimi | Biogeography of soil bacteria and archaea across France[END_REF][START_REF] Lauber | Pyrosequencing-based assessment of soil pH as a predictor of soil bacterial community structure at the continental scale[END_REF], but it weakly contributed to the North / South pattern observed in the current study, due probably to a narrow pH range among soil samples, and rather explaining intra-habitat variabilities potentially related to differences in plant root exudates [START_REF] Herz | Linking root exudates to functional plant traits[END_REF][START_REF] Wang | Rhizosphere priming effect on soil organic carbon decomposition under plant species differing in soil acidification and root exudation[END_REF]. In the current study, C / N ratio was the best predictor of bacterial community structure, whereas the highest correlation with the fungal community was obtained for N-P-K and CaCO3 contents. The soil C / N ratio is rather highly correlated with fungal community structure [START_REF] Lauber | The influence of soil properties on the structure of bacterial and fungal communities across land-use types[END_REF][START_REF] Thomson | Soil conditions and land use intensification effects on soil microbial communities across a range of European field sites[END_REF], and has been previously described as one of the best predictors of fungal community structure in the Northern Moroccan forest [START_REF] Maghnia | Habitat-and soil-related drivers of the root-associated fungal community of Quercus suber in the Northern Moroccan forest[END_REF]. Nevertheless, the soil C / N ratio has been also reported as an important driver, though less significant than pH, of bacterial community structure [START_REF] Griffiths | The bacterial biogeography of British soils[END_REF], with an increasing significance for specific bacterial taxa [START_REF] Karimi | Biogeography of soil bacteria and archaea across France[END_REF][START_REF] Thomson | Soil conditions and land use intensification effects on soil microbial communities across a range of European field sites[END_REF]. P content is generally one of the most significant soil nutrient paramaters, though less significant than C / N ratio, correlated with fungal community structure [START_REF] Lauber | The influence of soil properties on the structure of bacterial and fungal communities across land-use types[END_REF][START_REF] Maghnia | Habitat-and soil-related drivers of the root-associated fungal community of Quercus suber in the Northern Moroccan forest[END_REF]. At contrary, few data are provided regarding the contribution of calcium carbonate (CaCO3 ) content in the structure of fungal communities, but soil calcium content has been shown as a strong predictor at the global scale [START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF].

A subset of habitat-related microbial indicators were characterized, emphasizing differences at the kingdom level, with a higher significance of fungal taxa to characterize the North habitat and bacterial taxa for the South habitat. In addition, functional divergences highlighted habitat-related microbial traits with mainly fungal plant/animal pathogens in the North, which may be related to more favorable climatic (higher humidity) and soil nutrient (Higher C-N-P) conditions in the North, as suggested in [START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF]. The South was on the contrary characterized by bacterial taxa with the ability to both resist to harsh conditions and promote plant growth, highlighting the importance to consider semi-arid environments as a reservoir of stress-tolerant plant-beneficial microorganims in futher studies of Mediterrean belowground microbiota. The use of microbiota as species / compositional indicators of environmental factors have shown its reliability in various environmental and spatial scales [START_REF] Bouffaud | Indicator species and co-occurrence in communities of arbuscular mycorrhizal fungi at the European scale[END_REF][START_REF] Fortunato | Determining indicator taxa across spatial and seasonal gradients in the Columbia River coastal margin[END_REF][START_REF] Maghnia | Habitat-and soil-related drivers of the root-associated fungal community of Quercus suber in the Northern Moroccan forest[END_REF][START_REF] Ritz | Selecting biological indicators for monitoring soils: A framework for balancing scientific and technical opinion to assist policy development[END_REF][START_REF] Stone | Selection of biological indicators appropriate for European soil monitoring[END_REF] but remains one of the least studied indicator groups [START_REF] Gao | Reviewing the strength of evidence of biodiversity indicators for forest ecosystems in Europe[END_REF][START_REF] Schloter | Microbial indicators for soil quality[END_REF].

Plant host species weakly contributed to microbiota structure compared to the soil properties, which is in accordance with previous observation in woodlands and grasslands [START_REF] Bonito | Plant host and soil origin influence fungal and bacterial assemblages in the roots of woody plants[END_REF][START_REF] Kuramae | Soil and plant factors driving the community of soil-borne microorganisms across chronosequences of secondary succession of chalk grasslands with a neutral pH: Plant and microbial communities in soil neutral pH[END_REF], but plant host effect appeared more important on the Glomeromycota community. Differences in the composition of Glomeromycota community related to plant host species as been widely shown in semi-arid ecosystems [START_REF] Alguacil | Plant type differently promote the arbuscular mycorrhizal fungi biodiversity in the rhizosphere after revegetation of a degraded, semiarid land[END_REF][START_REF] Martinez-Garcia | Shrubs influence arbuscular mycorrhizal fungi communities in a semi-arid environment[END_REF][START_REF] Sanchez-Castro | Analyzing the community composition of arbuscular mycorrhizal fungi colonizing the roots of representative shrubland species in a Mediterranean ecosystem[END_REF]. Nevertheless, the lack of North / South pattern could be explained by the low number of Glomeromycota sequences retrieved, due, among other things, to the molecular approach used, i.e. a general fungal ITS marker sequencing rather than a Glomeromycota-specific 18S marker sequencing, known as potential biase affecting the Glomeromycota abundance, diversity and composition [START_REF] Berruti | ITS fungal barcoding primers versus 18S AMF-specific primers reveal similar AMF-based diversity patterns in roots and soils of three mountain vineyards: ITS fungal barcoding versus 18S AMFspecific primers[END_REF][START_REF] Lekberg | More bang for the buck? Can arbuscular mycorrhizal fungal communities be characterized adequately alongside other fungi using general fungal primers?[END_REF]. Glomeromycota was abundant mostly in the rhizosphere of L. dentata, reaching 3 % of the total fungal community, which supports the promoting effect of L. dentata on the soil mycorrhizal potential [START_REF] Hafidi | Managing Mediterranean nurse plants-mediated effects on soil microbial functions to improve rock phosphate solubilization processes and early growth of Cupressus atlantica[END_REF]Ouahmane et al., 2006a).

The abundance of Glomeromycota in lavandula-associated soils corresponded to the top levels observed in soils using general fungal ITS marker sequencing [START_REF] Clemmensen | Carbon sequestration is related to mycorrhizal fungal community shifts during long-term succession in boreal forests[END_REF][START_REF] Guo | Soil fungal assemblage complexity is dependent on soil fertility and dominated by deterministic processes[END_REF][START_REF] Leff | Consistent responses of soil microbial communities to elevated nutrient inputs in grasslands across the globe[END_REF][START_REF] Orgiazzi | Unravelling soil fungal communities from different mediterranean land-use backgrounds[END_REF][START_REF] Tedersoo | Global diversity and geography of soil fungi[END_REF]. Benefits of mycorrhizal symbiosis were demonstrated on carob growth and drought stress tolerance [START_REF] Essahibi | Influence of arbuscular mycorrhizal fungi on the functional mechanisms associated with drought tolerance in carob (Ceratonia siliqua L.)[END_REF][START_REF] Manaut | Potentialities of ecological engineering strategy based on native arbuscular mycorrhizal community for improving afforestation programs with carob trees in degraded environments[END_REF][START_REF] Ouahmane | Inoculation of Ceratonia siliqua L. with native arbuscular mycorrhizal fungi mixture improves seedling establishment under greenhouse conditions[END_REF], but different effects depending on Glomeromycota taxa was observed [START_REF] Essahibi | Influence of arbuscular mycorrhizal fungi on the functional mechanisms associated with drought tolerance in carob (Ceratonia siliqua L.)[END_REF], highlighting the need to better characterize mycorrhizal partners of carob trees. The current results extended the range of Glomeromycota taxa previously described as associated with carob trees using older methodologies [START_REF] Manaut | Potentialities of ecological engineering strategy based on native arbuscular mycorrhizal community for improving afforestation programs with carob trees in degraded environments[END_REF], with notably the detection of Diversispora spp., expanding the potentialities of carob habitats as reservoir of mycorrhizal ressources to improve carob afforestation strategies [START_REF] Manaut | Potentialities of ecological engineering strategy based on native arbuscular mycorrhizal community for improving afforestation programs with carob trees in degraded environments[END_REF]. Nevertheless, a deeper investigation of carob habitats and cross-compartment surveys (soils vs roots; [START_REF] Berruti | ITS fungal barcoding primers versus 18S AMF-specific primers reveal similar AMF-based diversity patterns in roots and soils of three mountain vineyards: ITS fungal barcoding versus 18S AMFspecific primers[END_REF][START_REF] Varela-Cervero | The composition of arbuscular mycorrhizal fungal communities differs among the roots, spores and extraradical mycelia associated with five Mediterranean plant species: AMF community composition of mycorrhizal propagules[END_REF] are necessary to fully decipher the mycorrhiza community associated with carob trees.

CONCLUSION

The current work provided new insights on rarely assessed belowground biodiversity of Moroccan carob habitats. Microbiota community structure appeared as a relevant variable to characterize carob habitat heterogeneity in addition to floristic diversity and soil properties.

Taxonomy and function of bacteria and fungi differed in their significance to define the type of habitat, strenghtening the need to survey both bacterial and fungal communities in biodiversity surveys, and highliting different microbial reservoirs with functionalities of interest (PGPR, stress-tolerant bacteria, Mycorrhiza) for biotechnology developments.

Locality Taxonomic (genus) assigment Functional assigment (1) Probability (2) (A ; B )

Indicator value (3) (Indval.g) p-value (4) North Morocco

  were selected, localized respectively in North Morocco (the Rif, 35°17'55.1"N, 5°13'40.0"W), and South Morocco (the Ourika valley, High Atlas, 31°17'45"N, 7°42′36"W). Soil samples were collected in April 2017 in close contact with the roots of carob trees (C. siliqua) or six other plant species (Vachellia gummifera (Willd.) Kyal. & Boatwr. 1806 ; Cistus albidus L. ; Globularia alypum L. ; Lavandula dentata L. ; Pistacia lentiscus L. ; Retama monosperma Boiss. 1840) localized 2 m around carob trunks. For each plant species, 3 to 5 kg of soil samples at 20 cm depth from five individuals, mixed and sieved through a 2 mm mesh sieve. The soil under C. siliqua and P. lentiscus were sampled in both sites, L. dentata, C. albidus in the North site, and G. alypum, R. monosperma and V. gummifera in the South site. All soil samples were stored at 4°C before processing. Soil properties were determined by the Laboratory of soil analysis (INRA, Arras, France) (Table

( 2 )Figure 1 .

 21 Figure 1. Phylum level distribution of (A) bacterial and (B) fungal communities among plant species from the South and North habitats.

Figure 2 .

 2 Figure 2. Microbiota structure analysis from plant species of the North (red) and South (blue) habitats. Two methods were used to visualize the bacterial (A, B) and fungal OTU (C, D) community structures, hierarchical clustering (A, C) and non-metric multidimensional scaling (B, D). Vg, Vachellia gummifera; Ca, Cistus albidus; Cs, Ceratonia siliqua; Ga, Globularia alypum; Ld, Lavandula dentata; Pl, Pistacia lentiscus; Rm, Retama monosperma. Differences in community structure between the North and South habitats were assesed by PERMANOVA. R 2 and P-values from PERMANOVA are indicated on non-metric multidimensional scaling (B, D). Heterogenity of data dispersion (HOMOVA) between North and South habitats were non significant.

Figure 3 .

 3 Figure 3. Principal component analysis of soils collected under different plant species from North and South habitats based on soil properties. (A) Structuration of soil samples according their physico-chemical characteristics. (B) Correlation circle indicating the contribution of each soil property in the structuration of soil samples.

Figure 4 .

 4 Figure 4. Comparison of (A) bacterial and (B) fungal community membership (Venn diagram analysis) among C. siliqua and P. lentiscus from both the North and South habitats. For each venn category, the number of OTUs is indicated. Color pie charts represents the taxonomic distribution (order) of the most dominant OTUs (top 10 % of most abundant;present in all samples) shared between the two plants. The category "Others" combines taxa representing less than 5%. Cs, Ceratonia siliqua; Pl, Pistacia lentiscus.

Figure 5 .

 5 Figure 5. Glomeromycota genus distribution among plant species from the North and South habitats. The total number of sequences is indicated above each barplot.

Figure 6 .

 6 Figure 6. Bipartite interaction network formed by Glomeromycota (genus taxonomic level; lower boxes) and major plants species (upper boxes) in the North (A) and South (B) habitats.

  For fungi, functional assignment was based on FUNGuild database (http://www.funguild.org/). For bacteria, traits related to plant pathogeny, plant-promoting effect, soil cycling or stress tolerance based on literrature were indicated (Web of Science, TOPIC:genus name AND TOPIC:soil). nd, not defined. PGPR, Plant growth promoting rhizobacteria

		Calonectria, Kellermania	Plant pathogen organic compound degrading	1.00 ; 0.75	0.87	*
		Malassezia, Phaeoacremonium Uncharacterized Beijerinckiaceae	Animal pathogen nd	1.00 ; 0.75 0.86 ; 1.00	0.87 0.93	* *
		Ophionectria, Quadricrura No significant fungal indicator	Undefined Saprotroph	1.00 ; 0.75	0.87	* ns
	(1)	Bacteria Guttulispora	nd	1.00 ; 0.75	0.87	*
		Parafilimonas Bacteria	nd	1.00 ; 1.00	0.95	*
		Fungi Kocuria	PGPR, metal resistant, halotolerant	1.00 ; 1.00	1.00	**
		Pestalotiopsis Naasia	Plant pathogen / Endophyte nd	1.00 ; 1.00 1.00 ; 1.00	1.00 1.00	** **
		Pleurostoma, Spirosphaera Cellulomonas	Undefined Saprotroph PGPR, nitrogen fixer, lignin degrading,	1.00 ; 1.00 0.98 ; 1.00	1.00 0.99	** **
		Purpureocillium	Fungal parasite halotolerant	0.97 ; 1.00	1.00	*
		Cylindrosympodium Rhodocytophaga	Plant pathogen / Endophyte nd	0.97 ; 1.00 0.94 ; 1.00	1.00 0.97	* *
		Geosmithia Rubellimicrobium, Geminicoccus	nd Potential global stress tolerant	0.97 ; 1.00 0.92 ; 1.00	1.00 0.96	** **
		Dothiorella Segetibacter	Plant pathogen / Endophyte nd	0.95 ; 1.00 0.90 ; 1.00	0.97 0.95	* *
		Macrophomina Rhodococcus	Plant pathogen / Endophyte PGPR, metal resistant, hydrocarbon	0.93 ; 1.00 0.88 ; 1.00	0.97 0.94	* **
	South Morocco	Exophiala Lecanicillium Lautropia Myxococcus	Animal pathogen Animal pathogen degrading Potential hydrocarbon degrading Plant pathogen antagonist, insoluble 0.87 ; 1.00 0.93 ; 1.00 0.87 ; 1.00 0.87 ; 1.00	0.97 0.94 0.93 0.93	* * * *

ACKNOWLEDGEMENT

This study is part of the DYNAMIC project (https://dynamic.cirad.fr/en) supported by the French national agency of research (ANR-14-CE02-0016). H.K benefited from PhD scholarships funded by the Partenariat Hubert Curien TOUBKAL in the framework of the BARACA project (TBK/17/50) and by CIRAD incentive actions. The authors thank the Genotoul sequencing facility (Get-PlaGe, Toulouse, France) for MiSeq sequencing.


Pascal Descamps
email: descamps@imcce.fr

F Vachier

J Berthier

J Normand

P Wiggins

H De Groot

J Coudert

V Chojnacki

O Labrevoir

S Joly

J.-P Marcon

S Olimpiade

B Dargoui-Pister

C Delhaume

T Duval

Y El Farissi

M Giraud

V Grieco

S Kaderi

A Laidi

T Lauze

H Mary

M Medour

F Negre

K Passabet

A Perret

M Peyron

N Ramos

M Soridi

Physical Characterization of Double Asteroid (3905) Doppler

Keywords: Asteroids, rotation, surfaces -Satellites of asteroids -Eclipses -Photometry

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

Introduction

Twin asteroid systems are particularly sought after because they allow not only to know their main physical characteristics, such as their mass and density, fundamental physical quantity that is otherwise difficult or impossible to obtain, but also to work on the scenarios of their formation.

Current shape knowledge of observed doubly synchronous binaries is mainly derived from photometric observation of mutual events between poorly-resolved components of the system, coupled with a theoretical approach based on hydrostatic equilibrium shapes [START_REF] Leone | Equilibrium models of binary asteroids[END_REF]. Such equilibrium shape models are elongated ellipsoids, which is a condition for a binary system to remain in a stable doubly synchronous orbit such that the mutual gravity torques exist to enforce the tidal locking. (Davis, A.B. and D.J. Scheeres, 2019). Mutual events enable measurement of the sizes and albedos of both objects, of their distinct surface compositions, and even of albedo patterns on their surfaces [START_REF] Michalowski | Eclipsing events in the binary system of the asteroid 90 Antiope[END_REF].

(3905) Doppler is a small main-belt asteroid. Its doubly synchronous binary nature was discovered fortuitously by graduate students in October 2013 [START_REF] Hayes-Gehrke | Lightcurve analysis of main-belt binary system 3905 Doppler[END_REF]. The composite light curve recorded in 2013 showed amplitude greater than 1 magnitude with sudden and deep luminosity drops, correctly interpreted as conspicuous features of mutual events between two well-detached components tidally locked in doubly synchronized rotation. For observable mutual events to happen either the observer or the Sun (or both) must be temporarily aligned with a system's orbit plane. An "occultation-type" event occurs when one component of the system passes in front of, and fully or partially occults, the other component from the observer's point of view. An "eclipse-type" event takes place when the system components are aligned with the Sun and the shadow of one falls on the other.

Whenever the Sun and Earth have nearly equal lines of sight to the system, mutual events observable from the Earth are combinations of occultation-type and eclipse-type events.

The small system of Doppler has been hitherto never monitored through a number of aspect and phase angles, so that the position of its spin axis remains unknown. As with other binaries, the eclipses present a unique opportunity to accurately measure the bulk density as well as the full geometry of the system in terms of shapes and mutual separation. The 2017 opposition was close to the 2013 opposition (Fig. 1) in terms of heliocentric ecliptic longitude so that it was reasonable to assume that mutual phenomena could occur again within the system. Moreover, this opposition is very favorable because it occurs near the perihelion putting Doppler at a distance of 1.0721au (opposition on October, 18 2017). This was the last opportunity before long (the next opposition similar to the 2013 opposition will occur in 2054, see Fig. 1) of a favorable opposition able to show such mutual phenomena. In this paper, we report the results of a coordinated campaign to observe such events and better constrain the physical parameters of the system. The following opposition of 2019 was also observed although the general geometric configuration of the system could not be conducive to the observation of phenomena (Fig. 1). However, it allows checking the validity of the general parameters of the system deduced from the observations of 2013 and 2017.

Observations

As the asteroid (3905) Doppler had an R-band magnitude of 14 at this time, all data were collected with small telescopes (D ≤ 1m) equipped with affordable CCD cameras. During three months, we performed photometric observations in the R-band. Aspect data are given in Table 1, including the date of the observation, the heliocentric longitude (λ) and latitude (β) of the asteroid, its phase angle (α) and its geocentric distance in au (r).

Table 1: To be inserted

The preliminary determination of the rotation period gave a long period of more than 50 hours. In order to obtain a composite light curve as complete as possible, a network of observers well distributed in terrestrial longitude has been set up (see Table 2). In this way, it was possible to catch several phenomena, partially or totally. Such detections are valuable because they impose strong constraints on the global model of the system and its spatial orientation.

It was also the opportunity to set up a collaboration with two French high schools as part of a teaching project related to the photometric study of asteroids. To this end, the Haute Provence Observatory has made available a 50cm telescope equipped with a CCD 2048 x 2048 -the IRIS telescope (iris.lam.

Period determination

The Phase Dispersion Minimization (PDM) technique [START_REF] Stellingwerf | Period determination using phase dispersion minimization[END_REF] was used to search for the synodic rotation period within the photometric data. Based on a trial period, PDM bins data according to the rotational phase, where we assumed that two maxima and minima occurred per rotation, the average variance of these subsets is compared to the overall variance of the full set of observations. The best estimate of the period is that for which the ratio of the average variance within a bin to the variance of the sample, which defines the statistic θ, reaches a minimum. This method does not assume any sinusoidal variation of the lightcurve and is well suited for unevenly spaced observations. PDM finds all periodic components or subharmonics (alias periods). Thanks to our three months long span of observations, the periodogram for light-time corrected data of (3905) Doppler shows a salient minimum (θ = 0.17) corresponding to the synodic fundamental period Psyn = 2.1177±0.0008d (50.826 ± 0.002 h) (Fig. 2).

Fig.2: To be inserted

The inferred final composite light curve is shown in Figure 3. The abscissa is the rotational phase corrected for light time. The m1 and m2 eclipsing minima occur at 0.25 and 0.75 rotational phase. The photometric accuracy is of ~0.02mag. Light curves exhibit two components: the fundamental rotational light curve and the eclipsing light curve. The 2017 and 2019 light curves all show a regular amplitude variation of ~0.45 mags identical to that recorded in 2013 when the (3905) Doppler binarity was discovered. This indicates that in this dual system, the shape of each of the components is very different from a sphere, even slightly flattened. Several notches are clearly visible at the level of the minima of the light curves of 2017. These brief but significant drops come from phenomena of occultation of one of the components of the system by the other. Their shape and amplitude evolve over the duration of the three months of observation. This results from the slow change of appearance as well as the variation of the phase angle which attains 26° during the last observation of December 12, 2019.

Fig. 3: To be inserted

A geometric model of the system

Thanks to these notches in the nominal light curve, it will be possible to accurately determine the physical structure of the system as well as its spatial orientation. While in 2013 the magnitude drop caused by mutual occultation phenomena could reach 1.22 mag significant of a very low sub-observer latitude, during the campaign of 2017, we were able to record several phenomena of slightly variable amplitude ranging between ~0.15 mag (October 27, 2017) and ~0.3 mag (November 22, 2017). This means that in 2017 the system is no longer seen edge-on but its orbital plane has a slight inclination to the line of sight.

We applied a model of heterogeneous Roche equilibrium ellipsoids to the problem [START_REF] Descamps | Equilibrium figures of inhomogeneous synchronous binary asteroids[END_REF] assuming the same composition for each component. In this model, the internal structure is not uniform and is described by a power law distribution. It was already successfully applied to small double asteroids such as Lundia, Berna, Debussy and Tama [START_REF] Descamps | Equilibrium figures of inhomogeneous synchronous binary asteroids[END_REF]. It allows at the same time to determine the bulk density and the grain density on the surface and thus the macroscopic porosity. The only parameter of this density law is the exponent n. In the case n = 0, we have a uniform mass distribution as it is the case for (90) Antiope [START_REF] Descamps | A giant crater on 90 Antiope ?[END_REF], the first double asteroid discovered (Merline et al., 2000). From such a density law, we can infer a simple relation between the bulk density ρb and the grain density ρg of the constituent material:

3 2 3 b g n ρ ρ = + (1)
Four free parameters should be fitted: the normalized angular velocity Ω , which is a function of bulk density b ρ , the orbital frequency 2 P ω π = where P is the orbital period, the mass ratio q between the secondary and the primary , the exponent n of the internal density distribution power law and the limbdarkening parameter k if we adopt the simple Minnaert light scattering law [START_REF] Minnaert | The reciprocity principle in lunar photometry[END_REF]. The normalized angular velocity Ω is defined by

4 3 b G ω πρ Ω = (2)
Three of the four parameters -Ω , q and k -can be determined by simple graphical measurements of the light curve when the system is seen edge-on. The methodology is as follows. The duration of each event, T ∆ , when the system is observed equatorially, depends only two parameters: Ω and q. The relationship between the relative duration ΔT/P and the normalized angular velocity Ω can be readily derived from the equation for spherical bodies according to appendix A :

( )

3 3 3 1 3 1 1 q T P q π + ∆   Ω =     + (3)
In other words, whatever the ellipsoid shapes and the mass ratio q, the value of Ω can be inferred simply by measuring the relative duration of events. To this end, we first considered the 2013 observation assuming that at this time the orbital plane lies in the line-of-sight plane. In short, the latitude of the sub-Earth point is near zero, which means that the rotation pole of the system is in the plane of the sky. The duration of each event is straightforwardly inferred from the light curve itself. We measured T ∆ = 2,67h ( 0.052 T P ∆ = in orbital phase). It is then necessary to estimate the mass ratio q. This is carried out graphically from the smallest minima according to the relation (see appendix B):

( )

2 3 2.5log 1 s mag q ∆ = + (4)
Fig. 4: To be inserted

If we adopt the reasonable assumption that the two components are identical in composition and therefore have identical albedos, it is remarkable to point out that the drop of the shallow minima depends only on the mass ratio and not on the light scattering by the surfaces. In addition, this allows us to determine very precisely the mass ratio. As for the deepest minima, it depends on both the mass ratio and the limb darkening. The magnitude drop of the first minima is of 0.701 0.02 ± mag (Fig. 4), we infer 0.83 0.03 q = ± (or a size ratio of 0.94 0.01 ± ).

The knowledge of the mass ratio then makes it possible to determine the limb darkening parameter. It Due to a high relative separation, it is remarkable to note that the phenomena cannot exist as long as is sep l lower than 8°. This is found from the parameters of the solution because the limit angle

+ +     ≈ ≈ = = °        (5)
The relative separation D is defined as ( )

p s a a d +
, where d is the orbital separation of the system, p a the semi-major axis of the primary and s a the semi-major axis of the secondary.

Fig. 6 shows the total amplitude of the light curve of Doppler and the magnitude differential between the two minima. As long as the latitude of the sub-Earth point is less than 0.3°, the light curve remains unchanged in amplitude, as does the differential in magnitude.

Fig. 5: To be inserted

With n = 9, we derived a non-physical value of the grain density of 28 g/cm 3 . It means that, despite the fact we successfully used a model in hydrostatic equilibrium inferred from the third law of Kepler, the system is clearly not in hydrostatic equilibrium. Nevertheless the inferred triaxial ellipsoids provide a good geometrical solution. Each component cannot be likened to a rotating fluid mass. We will deal with this issue in section 5.

Fig. 6: To be inserted

Pole solution

The change of shape of the light curve collected during the 2017 campaign, especially during the detected events, will enable us to determine as accurately as possible the position of the pole of the system. This time we can no longer consider that the orbital plane is in the line-of-sight plane. We will therefore seek to solve the following system which gives the position of the rotation pole from simple and relevant assumptions on the latitude of the sub-Earth point sep l [START_REF] Descamps | Nature of the small main belt asteroid 3169 Ostro[END_REF]

δ δ δ δ α α δ α α δ δ δ δ α α = - - - = - - = - - (6)
Fig. 7: To be inserted By taking two periods of observation for which the latitude of the sub-Earth point is known, we then obtain a system of two equations with two unknowns which it is easy to solve. We assume that 0.0 0.3 sep l = ± ° in 2013. This is a reasonable assumption given the amplitude of the magnitude drop (Fig. 4). For the observed event of October 27, 2017 and November 22, 2017 (Table 1), Fig. 6

Discussion

Measurements of asteroid bulk density, along with data on the grain densities of analogue meteorites, provide valuable insight into asteroid porosity and internal structure. Given the bulk density that we derived ( 3.86 0.01 ± g/cm 3 ), the candidate meteoritic analogs should have a grain density no less than ~4 g/cm 3 which quite obviously rules out enstatite (typical density of 3.2-3.8 g/cm 3 ) and carbonaceous chondrites (density of ~1.6-3.1 g/cm 3 ) analogues [START_REF] Macke | Enstatite chondrite density, magnetic susceptibility, and porosity[END_REF][START_REF] Macke | Density, porosity, and magnetic susceptibility of carbonaceous chondrites[END_REF][START_REF] Carry | Density of asteroids[END_REF][START_REF] Britt | Asteroid density, porosity and structure[END_REF]. This density is typical of M-type asteroids [START_REF] Pätzold | Asteroid 21 Lutetia : Low mass, High density[END_REF][START_REF] Demeo | The taxonomic distribution of asteroids from multi-filter all-sky photometric surveys[END_REF][START_REF] Shepard | Radar observations and shape model of asteroid 16 Pysche[END_REF][START_REF] Viikinkoski | Psyche: A mesosiderite-like asteroid[END_REF]. So far, it has been possible to accurately measure the density of only two M-type asteroids with one or more orbiting moonlets. These are ( 22) Kalliope with a bulk density of 3.4 ± 0.2 g/cm 3 [START_REF] Descamps | New determination of the size and bulk density of the binary asteroid 22 Kalliope from observations of mutual eclipses[END_REF] and ( 216) Klepoatra with a bulk density of 3.6 ± 0.4 g/cm 3 and a macroscopic porosity of ~ 30-50% [START_REF] Descamps | Triplicty and physical characteristics of asteroid (216) Kleopatra[END_REF]. Furthermore, ( 21)

Lutetia was flew by ESA Rosetta spacecraft on July 2010 and its bulk density was precisely determined to 3.4 ± 0.3 g/cm 3 [START_REF] Pätzold | Asteroid 21 Lutetia : Low mass, High density[END_REF]. Finally, these lines of evidence tend to support the hypothesis that (3905) Doppler would be a M-type asteroid. The most likely meteoritic analogs for M-class asteroids and their associated grain densities are irons (~7.5 g/cm 3 ), CH/CB/bencubbinite (metal rich) carbonaceous chondrites or silicate-bearing iron meteorites (~5.0 g/cm 3 ), or even stony-iron meteorites such as mesosiderites (4.25 g cm -3 ) suggested in the case of asteroid ( 16) Psyche [START_REF] Viikinkoski | Psyche: A mesosiderite-like asteroid[END_REF]. Vernazza et al. ( 2011) reported that asteroid (21) Lutetia has spectral and physical properties similar to the class of meteorites knwon as even enstatite chondrites (~3.5 g/cm 3 ), however this analog may be ruled out due to a too low bulk density. Finally, our bulk density of 3.86 g/cm 3 could suggest a macroscopic porosity ranging between 20-40%. Such high porosities are suggestive of extensively fractured or loosely packed asteroids [START_REF] Britt | Asteroid density, porosity and structure[END_REF][START_REF] Scheeres | Asteroid interiors and morphology[END_REF].

However, the use of an inhomogeneous Roche model in the present work provided us with a physically unacceptable result in terms of macroscopic porosity or grain density (see Table 3). This means that the shapes of the components of the system are not equilibrium figures of rotating liquid masses. We can nevertheless make the hypothesis that these bodies have stopped deforming due to the combined effect of moderate porosity and high density of the material. Beyond a certain point, internal friction between boulders may have prevented any fluid-type deformation. All synchronous double systems studied so far have a much lower internal density while having equivalent macroscopic porosity. This is probably the reason why the modeling using rotating fluid masses in hydrostatic equilibrium gives good results.

Keeping the same bulk density but imposing a porosity of 40% (and thus a realistic grain density g ρ = 7 g/cm 3 ), one realizes that one can find equilibrium figures which are identical to the ellipsoidal shapes found in this paper but for a lower value of the orbital period of 10.34h ( 0.159 Ω =

), which implies that the system could have been much tighter in the past with a relative separation of 0.581 D =

, typical of small double asteroids observed so far [START_REF] Descamps | Equilibrium figures of inhomogeneous synchronous binary asteroids[END_REF]. Beyond this point, the system might have been able to continue to tidally evolve up to its present equilibrium state without any subsequent distortion of the shapes of both components. In other words, depending on the level of macroscopic porosity and bulk density, a loosely packed doubly synchronous asteroidal system, tidally locked, could exhibit fluid-like behavior in hydrostatic equilibrium as long as internal friction effects remain low enough to be able to counteract any deformation of the bodies. Discovery of other synchronous double systems with relative separation D significantly lower than 0.5 could provide some answers concerning the links between equilibrium figures and bulk density ( )

3 1 p R q d   Ω = +     (A.3) Let p p R d ε = and s s R d ε =
, the angles defined on Fig. A1. During an event of duration T ∆ , the occulting body (secondary) have described along its orbit an angle 2 2 p s ε ε + . Since the time taken to complete a complete orbit is P, the orbital period, we have ( )

2 2 1 2 p s p s T P ε ε ε ε π π + ∆ = = + (A.4)
Replacing p ε and s ε by their expressions ( )

1 3 1 1 1 1 2 p p s p R R R T q P d R d π π   ∆ = + = +       (A.5)
We infer ( )

1 3 1 1 1 2 1 p p s p R R R T d d R P q π π   ∆ = + =     +   (A.6)
Hence, from equation (A.3) we derive the general relationship ( )

3 3 3 1 3 1 1 q T P q π + ∆   Ω =     + (A.7)
In the case of a double system have with a mass ratio very close to 1, (A.7) simplifies such that the angular velocity is then very poorly sensitive to the mass ratio

3 3 4 T P π ∆   Ω =     (A.8)
Finally, the measurement of the duration of an eclipsing event inside the system, gives the value of the specific angular frequency and therefore the value of the bulk density from equation (A.1).

Where ( ) A α and ( ) k α are the two Minnaert parameters which are functions of α and of the wavelength. It is well known that Eq. (B.1) is only a crude approximation to the scattering properties of real surfaces. However phase angle lower than ~30°, Minnaert's law can be used as a convenient approximation (except in the immediate neighborhood of the limb where the Minnaert function predicts values approaching either infinity, when k is less than one, or zero, when k is greater than one). ( )

k α
cannot be easily interpreted according to physical properties of the surface; it presents the degree of limb darkening, e.g. 0.5 k =

, indicates that there is no limb darkening, while limb darkened surfaces have 0.5 k > . On the condition 1 k = , Minnaert model shrinks to the Lambert model which describes the reflected light behavior from high-albedo surfaces.

Let us adopt a rectangular system of coordinates, two axis of which lie in the "photometric equator".

The photometric equator is the great circle passing through the subsolar and sub-earth points. Photometric longitude, λ , is measured along the photometric equator, and photometric latitude, ϕ , is measured along the central meridian which is the perpendicular great circle (Fig. B1). At phase angle α , the photometric longitude runs from 90° at the limb to ( ) The total light loss from the primary is then

( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 2 2 , 2 2 2 1 , 2 , , ,
, , cos cos cos cos cos

p p Min k k k p Min I R k q R r i e d d R d d ϕ λ λ π ϕ λ α λ ϕ λ λ π ϕ λ α λ α α λ ϕ ϕ λ λ λ α ϕ ϕ λ -   -+ -     + -   -+ -     = = - ∫ ∫ ∫ ∫ (B.7)
Hence it follows that the deepest magnitude drop

d mag ∆ is expressed by ( ) ( ) 2 3 2 3 1 2.5log 2.5log , , , 1 , , , p s d s p p p p I I q mag I I I R k q q I R k q I α α     + +     ∆ = =     + - + -     (B.8)
The offset in magnitude drop is straightforward The effect of the latitude of the sub-Earth point shows that very quickly, as soon as the orbital plane of the system is sufficiently inclined over the line of sight, the events disappear.

( ) ( ) 2 3 1 , , 2.5log 1 , , , d s p p dmag k q mag mag q I R k q I α α     = ∆ -∆ =   + -   (B.
α (°) δ (°) sep l (°) α (°) δ (°) sep l (°) 0 α (°) 0 δ (°) 0 α (°) 0 δ (

Fig. 1 :

 1 Fig.1: To be inserted

  fr)dedicated to teachers in the framework of the program Introduction to astronomy research for schoolchildren driven by the Laboratoire d'astrophysique de Marseille (LAM).

  Fig 5 shows the deformation of the light curve as a function of the latitude of the sub-Earth point sep l .

  . The latitude of the sub-Earth point ( sep l ) and the North Pole position angle ( p n ) are related to the equatorial coordinates of the rotation pole ( )

  allows us to estimate the value of sep l knowing the maximum amplitude of the magnitude drop. With an amplitude of 0.6mag in October 2017 and 0.75mag in November 2017 (Fig.7November 2017. With these initial values, we find one unique pole solution able to account for all observations. Table4gives the final solutions to the system [6] for two pairs of dates. The correct solution is the one that is common to both systems. We found the better solution for the pole solution in equatorial

Fig. 8 :

 8 Fig.8: To be inserted

  at the terminator. From Fig.B1, obviously we have the following relation between (i,e) and ( ) , λ ϕ for a given phase angle : for the radius of the body. Each element of area ds on the planet is weighed by its apparent projected area ( cos eds ds µ =) and surface brightness. The total light of sunlit body the Earth at any particular phase will then be obtained by integrating the light element over the entire visible surface ( 0 when the secondary is occulted by the primary (Fig.B1) depend on both phase angle and scattering by surfaces. The problem is slightly more complicated in the case where the secondary occults the primary. Part of the light scattered by the primary is then intercepted by the secondary and is somehow replaced by that from the secondary. The surface area of the primary that is masked by the secondary appears hatched in Fig.B1. The intersection of the projection of the secondary on the surface of the primary defines a circular contour whose points are linked by the following

  on Fig. B.2 for different phase angles and values of the limb darkening parameter k. The offset in magnitude is an increasing function of the limb darkening parameter, however it remains below ~0.2mag for most of the applications.

Fig

  Fig.B.2: To be inserted

Figure 1 :

 1 Figure 1: List of oppositions of Doppler in the interval 2013-2055 reported in ecliptic longitudes. In blue the Earth orbit and in red the Doppler orbit. Doppler was discovered as a double system during the 2013 perihelic opposition. P is the perihelia and N the ascending node.

Figure 4 :

 4 Figure 4: Synthetic light curve superimposed to the light curve of Doppler observed in 2013. Durationsof the events are shown as well as the amplitudes of the rotational light curve (0.45 mag) and the magnitude drops (0.701 mag and 0.775 mag). The durations should be equal. The amplitude of the first drop depends only on the mass ratio of the components. The amplitude of the second drop depends on both the mass ratio and the limb darkening parameter. The duration of an event depends on the bulk density and, to a lesser extent, on the mass ratio. Therefore, from the graphical analysis of the light curve, we can unambiguously determine the type of light scattering by the surfaces, the mass ratio between components and the bulk density as well.

Figure 5 :

 5 Figure 5: Synthetic light curves resulting from the solution obtained for the binary system of Doppler.

Figure 6 :

 6 Figure 6: Evolution of the amplitude of the light curve of Doppler and the magnitude differential as a function of the latitude of the sub-Earth point. In October and November 2017, small amplitude events were detected, which makes it possible to estimate the value of the latitude of the sub-Earth point for these epochs required for deriving the pole orientation.

Figure 8 :

 8 Figure8: Full events detected on the same minima on October, 27 and December, 12. Owing to the fact that the phase angle was important, the phase effects and mutual shadowing play a crucial role in defining the morphology of the light curve.

Figure A. 1 :Fig. B. 1 :

 11 Figure A.1: Schematic diagram of a double system whose components are spherical.

Fig. B. 2 :

 2 Fig. B.2:Offset in magnitude between minima as a function of phase angle, α , mass ratio, q, and limb darkening parameter, k.

Table 2 :

 2 To be inserted

Table 1 :

 1 [2003][2004][2005][2006][2007] observational circumstances. The heliocentric longitude (λ) and latitude (β) of the asteroid, its phase angle (α) and its geocentric distance in UA (r).

	* see Table 2

Table 2 :

 2 List of the observers with theirs facilities.

	Observers	Observatory	Aperture
			(m)

Table 3 :

 3 -Solutions of the inhomogeneous Roche problem. The bulk porosity includes the small-scale microporosity and the large-scale macroporosity (empty space). The primary and the secondary are

	described by their semi-axes (	, , p a b c p	p	)	and (	) a b c . The relative separation D is defined , , s s s
	as (	) / a a d p s +	, where d is the orbital separation of the system. Values of macroscopic physical
	parameters (grain densities and bulk porosities) are intrinsically connected with the adopted model of
	internal density distribution.
	Synodic period (h)		Ω	q	n	b (g/cm 3 ) ρ	g (g/cm 3 ) ρ	p	p b a	p	p c a	p	s b a	s	s c a	s	D
	50.826	0.033 0,88	9	4.02		28.1		86% 0.746 0.676 0.699 0.637 0.207

Table 4 :

 4 -Resolution of the system[5] for two pairs of dates. sep l is the latitude of the sub-Earth point. J2000 equatorial coordinates of (3905) Doppler are given for each epoch. The pole solutions are given

	in J2000 equatorial coordinates.
	31 October 2013	27 October 2017	Pole 1	Pole 2

Code

Berthier, J., Descamps, P.,

Appendix A: Duration of an event within a binary system

Where G is the gravitational constant and b ρ the bulk density. The synchronous system is made of two components of radius p R (primary) and s R (secondary) with s p R R ≤ . p M and s M are the masses of the primary and the secondary respectively. Let q the secondary to primary mass ratio: ( )

The separation between each component of the system is equal to d. From the third law of Kepler, we have ( )

Then the specific angular momentum reads Appendix B: General magnitude drops in a binary system seen edge-on We propose to calculate the drops in magnitude occurring within a binary system as a function of phase angle and photometric behavior of surfaces, assuming that it is seen edge-on. Furthermore, it is reasonable to assume that the two components are largely identical in composition and therefore should have very similar albedos as it was already observed for a couple of binary systems [START_REF] Laver | Component-resolved nearinfrared spectra of the (22) Kalliope system[END_REF], Marchis et al., 2011). For example, mutual events within the binary system Patroclus-Menoetius were used to derive thermo-physical properties of the surface of both objects [START_REF] Mueller | Eclipsing binary Trojan asteroid Patroclus: Thermal inertia from Spitzer observations[END_REF]. The observations are consistent with identical surface regolith properties. Therefore, in the rest of the work, we have assumed identical surface properties of both components. To this purpose we model the scattering by the Minnaert's function [START_REF] Minnaert | The reciprocity principle in lunar photometry[END_REF]. The Minnaert model is an empirical photometric function with two parameters, the Minnaert albedo and the limb-darkening coefficient, representing the light scattering behavior across the surface. The bidirectional reflectance refers to the fraction of light scattered into direction e when the surface is illuminated by collimated incident light in direction i. It is the intensity of scattered radiance in a specific direction to the incident solar irradiance on a unit area of the surface. The reflectance ( )

r i e α is usually a function of phase angle α , incidence angle i of sunlight (through its cosine 0 cos i µ =

), i.e., the zenith distance of the Sun, and emission angle e (through cos e µ =

), i.e., the zenith distance to the observer :