Claudia De Lima E Silva

Céline Pelosi
email: celine.pelosi@inrae.fr

Effects of glyphosate on earthworms: from fears to facts

Keywords: Ecotoxicology, Risk Assessment, Bioaccumulation, Endpoints, GHB 24/11/

Glyphosate is the most widely applied herbicide worldwide, contaminating water, soils and living organisms. Earthworms are emblematic soil organisms used as indicators of soil quality, but knowledge about the impacts of glyphosate and glyphosate-based herbicides (GBH) on these key soil organisms is scattered. Here, we examine this knowledge in detail to answer four questions: 1) Which endpoint is the most sensitive when assessing the effects of glyphosate or GBH in earthworms? 2) Which is most toxic to earthworms: glyphosate or GBH? 3) Are glyphosate and GBH harmful to earthworms when used at the recommended application dose (RAD)? 4) What are the interactions between glyphosate or GBH and other chemicals in earthworms? The results indicate that a weak legislation led to improper assessment of the ecotoxicity 24/11/

INTRODUCTION

The European authorisation for the manufacture and use of glyphosate was renewed in 2017, ten years after its initial approval, and again in 2022, until December Accepted Article 2023, following a heated debate in both civil and scientific circles. The controversial point was the recategorisation of this herbicide as being probably carcinogenic to humans (Group 2A) by the International Agency for Research on Cancer (IARC, 2016), contributing to the lack of consensus on the safety of its use for human health and biodiversity.

Despite the general agreement on its potential toxicity, sales in European countries have remained almost unchanged since 2013, with the purchase of approximately 46.527 tons of the active ingredient glyphosate, accounting for 33% of the total herbicides used in 2017 [START_REF] Antier | Glyphosate use in the European agricultural sector and a framework for its further monitoring. Sustainability 12, 5682. of glyphosate on the bumblebee proteome and microbiota[END_REF]. France contributed 20% of the European sales, followed by Poland (14%) and Germany (10%). In different parts of the globe, the development of herbicide-resistant crops, enabling the shift from conventional farming to conservation tillage, might have contributed in some way to the continuous reliance on glyphosate [START_REF] Rose | Impact of Herbicides on Soil Biology and Function. Chapter 3[END_REF][START_REF] Lucas | Is glyphosate toxic to bees? A metaanalytical review[END_REF] and other herbicides.

Reliable data on the toxicity of this herbicide to soil invertebrates are scarce and not consistent, leading to a lack of clarity on this subject. In order to be able to compare results, it is important to have some level of standardization, e.g., same guideline, same type of soil, same or similar applied concentrations. Unfortunately, this is not the case with glyphosate. Even when comparable data was available, the results can point towards different directions. For example, [START_REF] Lewis | An international database for pesticide risk assessments and management[END_REF] showed that glyphosate has low toxicity to honeybees and bumblebees, but other studies highlighted that it negatively affects the sleep of honeybees or their capacity to navigate (Balbuena et al., 2015;Vázquez et al., 2021). Similar contradictory results have been observed in other arthropods, with some depicting no direct effects of the use of glyphosate on canopydwelling arthropod (e.g., Coccinelidae) communities [START_REF] García-Ruiz | Dynamics of canopy-dwelling arthropods under different weed management options, including glyphosate, in conventional and genetically modified insect-resistant maize[END_REF]Imura et al., 2010) and others showing a reduction in the number of predators, chewing arthropods and sucking phytophagous arthropods [START_REF] Pereira | Glyphosate impact on arthropods associated to Roundup ready and conventional soybean (Glycine max L.)[END_REF]. Similarly, conflicting and scattered scientific data on earthworms hinder the understanding of the toxicity and risks linked to the use of glyphosate to these key soil organisms.

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Article

Earthworms are ecosystem engineers involved in soil structure maintenance, organic matter breakdown, nutrient cycling, and water regulation through their burrowing, feeding and casting activities [START_REF] Liu | Earthworms coordinate soil biota to improve multiple ecosystem functions[END_REF]. They are to soil what bees are to the aerial compartment: emblematic and even patrimonial indicators, functionally essential and to be protected against different anthropic activities such as the (over)use of pesticides (Blouin et al., 2013). Several studies have shown that a number of pesticides are toxic to earthworm populations and communities and earthworm-mediated functions in soils (Beaumelle et al., 2023;[START_REF] Pelosi | Searching for a more sensitive earthworm species to be used in pesticide homologation tests -A meta-analysis[END_REF], but the effects of glyphosate or glyphosate-based herbicides (GBH) on these key soil organisms are still not clear and have never been compiled.

To not only help provide clarity but also support risk assessors, politicians and scientists with robust information, this paper focuses on the effects of glyphosate or GBH on earthworms using a systematic review of the literature. Four questions were asked: 1) Which endpoint is the most sensitive endpoint when assessing the effects of glyphosate or GBH in earthworms? 2) Which is the most toxic to earthworms: glyphosate or GBH? 3) Are glyphosate and GBH harmful to earthworms when used at the recommended application dose (RAD)? 4) What are the interactions between glyphosate or GBH and other chemicals in earthworms?

LITERATURE SEARCH

A literature review was carried out on the basis of keywords in ISI Web of Knowledge and Web of Science, using the "All Databases" option, with the following This search encompassed papers published until December 2022 and was performed using two databases, INRAE and Wageningen University and Research, using the search engine provided by "Web of Science". For the first institution, the result showed 151 papers, and for the latter, 156. All papers were added to a common library in the software Endnote "glyphosate-Pelosi.enl". An evaluation of the content was performed in the following sequence: 1 st , removal of double/triple publications; 2 nd , analysis of the abstract aiming to check for availability of information that could help answering one or more questions posed by this review; 3 rd , analysis of the Materials and Methods and Results to check if the authors have provided sufficient and relevant information. All the peer-reviewed studies dealing with the assessment of glyphosate or GBH on earthworms were considered, thus not limiting ourselves to the criteria given in the EFSA guideline for the selection of scientific peer-reviewed papers to be used in a dossier for the placing of plant protection products on the market (EFSA, 2011). In the end, 63 papers were selected for use in this review.

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Which is the most sensitive endpoint when assessing the effects of glyphosate or GBH in earthworms?

Our systematic literature review yielded 63 papers (Table S1), among which 26 assessed the effects of glyphosate or GBH on adult survival (LC50, which is the concentration that kills 50% of the adult population), followed by sublethal indicators, such as reproduction, with 19 papers, and biomarkers (e.g., acetylcholinesterase Accepted Article enzyme), with 15 papers. Most of the papers analysed more than one level of indicators. Due to the different indicators assessed in the corpus, these were categorised into three levels (the sum is more than 100% as some papers addressed several levels): (i) the infra-individual level, with impacts measured at the cellular and histopathological levels (33% of the corpus), (ii) the individual level, with parameters such as e.g., biomass, growth, behaviour and bioaccumulation (59% of the corpus), and (iii) the ecological level, with parameters such as e.g., decomposition and density (16% of the corpus).

Ten out of the 26 papers that analysed toxicity to adult survival (LC50) performed exposure on filter paper or in an artificial soil during 7 or 14 days (Table S2). The remaining ones exposed the individuals in artificial or natural soil for 28 days or more. Data from the 26 papers showed that glyphosate, GHB or the metabolite aminomethylphosporic acid (AMPA) had no impact on adult survival (LC50), or at higher concentrations than environmental contamination.

Regarding the effects on reproduction, the results were more scarce and much more contrasting. Correia & Moreira (2010) showed that glyphosate had no effects on mortality (higher concentration 1000 mg kg -1 ), but no cocoons or juveniles were produced at the lowest concentration (10 mg kg -1 ) (E. fetida, technical glyphosate; natural soil), pointing towards a possible impact on reproduction. On the other hand, Von [START_REF] Merey | Glyphosate and aminomethylphosphonic acid chronic risk assessment for soil biota[END_REF] found no effect on reproduction at a concentration as high as 472.8 mg kg -1 (E. fetida; technical glyphosate; artificial soil). For AMPA, Von [START_REF] Merey | Glyphosate and aminomethylphosphonic acid chronic risk assessment for soil biota[END_REF] reported an EC50 reproduction of 654.7 mg kg -1 (E. fetida; technical AMPA; artificial soil), while [START_REF] Dominguez | Toxicity of AMPA to the earthworm Eisenia andrei Bouché, 1972 in tropical artificial soil[END_REF] showed negative effect on the number of cocoons at a concentration of 1 mg kg -1 (E. andrei; technical AMPA; tropical artificial soil).

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Different soil types, earthworm species and concentrations were used in these tests (Table S1), leading to a lack of consistency among studies. This situation per se already makes comparison of data difficult, but the low number of papers assessing toxicity to reproduction (19 papers) makes this task almost impossible, leading to more questions than answers. Adding to this scenario, studies generally assessed the effects of one application while in the field, glyphosate might be applied 3 to 4 times per year within a crop year. When comparing the sensitivity among the most used endpoints for risk assessment, reproduction is indisputably a more sensitive parameter. When under stress, the individual needs to choose how to better use its energy, so a process called trade-off occurs. An organism exposed to one or more contaminant(s) can activate different biochemical, physiological and/or behavioural responses that allow it to maintain physiological homeostasis. Such an exposure, however, can lead to a reduction in the rate of assimilation of food or to an overconsumption of energy (Kooijman, 2010). Without an equivalent increase in intakes, the increase in energy expenditure, e.g., for detoxification, can be detrimental to vital processes such as growth or reproduction. Thus, energy is a target of pesticides. They generally do not kill earthworms when the source of energy is sufficient, but they alter energy allocation processes and divert energy from other functions, with consequences on population and community dynamics (Johnston et al., 2014). These effects of pesticides on earthworm populations and communities can be assessed in field situations based on a guideline (ISO 11268-3, 2014) used as a higher-tier tests in environmental risk assessments when unacceptable risk is identified with lower-tier tests (OECD, 1984).

However, some improvements have been proposed in order to reliably detect negative effects on earthworms in natura, especially regarding the variability of the endpoints,

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Article the statistical significance of the results and the level of the statistically detectable effects of the tested chemicals [START_REF] Römbke | Necessary adaptations for a harmonized field-testing procedure and risk assessment of earthworms (terrestrial)[END_REF][START_REF] Amossé | A two years field experiment to assess the impact of two fungicides on earthworm communities and their recovery[END_REF].

During the license renewal process in 2017 (EC, 2017), seven unpublished and protected studies (i.e., we could not gain access to the produced data) focusing on the toxicity of glyphosate to earthworms were used as support for the ecotoxicity assessment. Three of them focused on acute adult survival, with two using artificial soil, and each of the three studies tested a different chemical (i.e., Sinon Glyphosate Technical [START_REF] Mallet | Sinon Glyphosate Technical: The acute toxicity to the earthworm Eisenia foetida[END_REF]; AMPA (Mostert and Römbke, 2000); and MON 52276 (Hoxter and Smith, 1992)). Four of them focused on the effects on reproduction (Friedrich, 2009;Heyward and Mallett, 2000;Noack, 2002;[START_REF] Servajean | Laboratory determination of the side-effects of aminomethyl phosphonic acid (AMPA) on the reproductive performance of earthworms (Eisenia fetida) using artificial soil substrate. Data Protection[END_REF].

However, at the time this report was compiled, the EFSA Scientific Opinion (EFSA, 2017) for in-soil organisms clearly stated that the use of acute toxicity was no longer going to be considered necessary for pre-emptive risk assessment, favouring the reproduction test with earthworms instead (OECD 222, 2009). Six years after this renewal report, EFSA published the "Peer Review Report on Glyphosate" in July this year (EFSA, 2023). In this document, 140 studies were analysed, out of which only 2 earthworm papers were available (not protected), but these were not considered further, either because they showed no changes in relation to the control [START_REF] Schmidt | Glyphosate Effects on Earthworms: Active Ingredients vs. Commercial Herbicides at Different Temperature and Soil Organic Matter Levels[END_REF] or due to other issues [START_REF] Pelosi | Glyphosate, AMPA and glufosinate in soils and earthworms in a French arable landscape[END_REF]. Our review indicates that more papers related to soil invertebrates, especially earthworms, could be considered in the renewal process. It is true that the low number of papers and the variable test conditions among studies (e.g., commercial or technical-grade formulations, soil types, earthworm species and origin) contribute to the lack of clarity; nonetheless, as shown in this review, a great number of papers became available since the 2017 renewal and

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Article

can help in generating a more balanced risk analysis among the compartments (soil, air, water).

To summarize, despite the low number of papers assessing one of the most sensitive earthworm endpoints used for risk assessment, we were able to conclude that glyphosate has potential toxic effects on reproduction. Other endpoints analysed and grouped in different categories also proved to be very sensitive to glyphosate, again indicating potential sublethal toxic effects.

What is the most toxic to earthworms: glyphosate or GBH?

The assessment of the impacts of GBH is performed without due consideration of the possible effects of the co-formulants (water and undisclosed "other ingredients"), which represent 5-15% of concentrated products by weight [START_REF] Mesnage | Insight into the confusion over surfactant co-formulants in glyphosate-based herbicides[END_REF]. When considering different kinds of organisms, some studies have reported that glyphosate alone has less or no relevant ecotoxicological effect compared to GBH (e.g., on mitochondrial bioenergetics, as shown in [START_REF] Peixoto | Comparative effects of the Roundup and glyphosate on mitochondrial oxidative phosphorylation[END_REF]; on human cells, as shown in Nagy et al., 2019; on cellular and physiological processes in the digestive tract of bumblebees, as shown in Cullen et al., 2023). The higher toxicity of GBH was attributed to co-formulants or to a synergic effect of glyphosate and formulation products. For earthworms, the comparison of the ecotoxicological effects of both glyphosate and GBH was found in only three studies. Nonetheless, the results contradict those reported for other organisms [START_REF] Pereira | Toxicity evaluation of three pesticides on non-target aquatic and soil organisms: commercial formulation versus active ingredient[END_REF][START_REF] Pochron | Glyphosate but not Roundup® harms earthworms (Eisenia fetida)[END_REF][START_REF] Zaller | Effects of glyphosate-based herbicides and their active ingredients on earthworms, water infiltration and glyphosate leaching are influenced by soil properties[END_REF]. [START_REF] Pochron | Glyphosate but not Roundup® harms earthworms (Eisenia fetida)[END_REF] found toxic effects on E. fetida survival (LC50 of 26.3 mg glyphosate (isopropylamine salt) kg -1 of dry soil) and biomass but no effects of two GBH formulations (Roundup Ready-to-Use III® and Roundup Super Concentrate®, same concentration of active ingredients) on both endpoints. The authors explained that nitrates and phosphates in the formulations must have Accepted Article compensated for the toxic effects of glyphosate by stimulating microbial growth and thus glyphosate degradation. [START_REF] Pereira | Toxicity evaluation of three pesticides on non-target aquatic and soil organisms: commercial formulation versus active ingredient[END_REF] found no effects on the avoidance behaviour of E. andrei against either Spasor® (360 g glyphosate l -1 ) or pure glyphosate at three times the recommended dose. [START_REF] Zaller | Effects of glyphosate-based herbicides and their active ingredients on earthworms, water infiltration and glyphosate leaching are influenced by soil properties[END_REF], under more realistic conditions (using the ecologically relevant earthworm species Lumbricus terrestris and natural soil in the presence of plants), found that GBH showed increased, reduced or similar effects as pure glyphosate on earthworm activity (casting and movement) and that soil properties such as soil organic matter content can influence the effects.

As hundreds of glyphosate-based formulations are used, with potentially many different « inert » undisclosed ingredients, deciphering the cause of the observed effects is tricky. This could explain why Piola et al. ( 2013) found that Roundup FG® (72% acid equivalent) was 4.5-fold more toxic than MON 8750® (85.4% acid equivalent) to E. andrei on filter paper. The differences were attributed to the direct toxicity of the "inert ingredients" or to an increase in the bioavailability and/or bioaccumulation of glyphosate. The bioaccumulation of glyphosate and AMPA in earthworms was found to be higher than expected based on the properties of the molecules [START_REF] Pelosi | Glyphosate, AMPA and glufosinate in soils and earthworms in a French arable landscape[END_REF], with potential risks of transfer in terrestrial food webs, as earthworms are prey for numerous animals. The co-formulants used are usually the manufacturer's trade secret, but these chemicals can negatively influence earthworms and soil fertility. Thus, they should be disclosed by manufacturers, and their effects should be properly assessed.

To summarize, we showed that the diversity of "inert ingredients" along with the lack of information on them has contributed to the low number of studies comparing pure glyphosate and GBH, making it difficult to determine which of these substances is the most toxic to earthworms.

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Are glyphosate and GBH harmful to earthworms when used at the recommended application dose (RAD)?

Glyphosate is a nonselective systemic herbicide that is taken up via leaves and shoots and is distributed throughout plant tissues. This chemical is known for its high sorption affinity for soil (especially clays and other minerals) and therefore is considered essentially nonmobile in soil. Glyphosate is not considered persistent, as it undergoes biotransformation to AMPA as the main metabolite [START_REF] Rose | Impact of Herbicides on Soil Biology and Function. Chapter 3[END_REF].

However, both are found in all environmental compartments at unexpectedly high levels when considering the properties of the molecules (Carles et al., 2019;[START_REF] Pelosi | Glyphosate, AMPA and glufosinate in soils and earthworms in a French arable landscape[END_REF]. Among the 63 papers of the corpus, and after removing those dealing with exposure on filter paper, 38 articles used the RAD. Among them, 27 studies were performed strictly under laboratory conditions, and more than half of them used composting worms (not present in natural soils) for testing (i.e., 15 articles).

As already mentioned for the first question, most of the papers using the RAD did not find any impact of glyphosate or GBH on earthworm survival (e.g., Bouazdia et al., 2020;Buch et al., 2013;[START_REF] Dalby | Glyphosate, 2,4-db and dimethoate: effects on earthworm survival and growth[END_REF][START_REF] Pochron | Glyphosate but not Roundup® harms earthworms (Eisenia fetida)[END_REF][START_REF] Pochron | Exposure to Roundup increases movement speed and decreases body mass in earthworms[END_REF]. Some exceptions were found, such as [START_REF] Stellin | Effects of different concentrations of glyphosate (Roundup 360®) on earthworms (Octodrilus complanatus, Lumbricus terrestris and Aporrectodea caliginosa) in vineyards in the North-East of Italy[END_REF], who reported marked effects of Roundup 360® at the RAD on the survival rate and cocoon production of two anecic species (L. terrestris and Octodrilus complanatus) and one endogeic species (Aporrectodea caliginosa). However, sublethal effects may occur while mortality is not affected. Bouazdia et al. (2020) found no effect on A. caliginosa mortality, but they showed significant effects on growth rate at lower doses of Glyphon® than the RAD. In the same way, Casabé et al. (2007) found that Roundup FG at the RAD impacted lysosomal destabilisation biomarkers (neutral red retention time or NRRT) and reduced cocoon viability, number of juveniles, and feeding activity of E. andrei

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under laboratory and field conditions, despite not having toxic effects on survival. [START_REF] Verrel | As the worm turns: Eisenia fetida avoids soil contaminated by a glyphosate-based herbicide[END_REF] also showed little evidence of E. fetida lethality under exposure to Ground Clear® at a nominal concentration (RAD); however, this GBH negatively influenced locomotor activity. Field studies are scarce (i.e., only 5 in the corpus) and generally conducted with short time intervals (i.e., a few days or weeks) with only one or two pesticide applications, making the chronic effects of glyphosate and GBH difficult to understand (e.g., [START_REF] Fusilero | Weed management systems and other factors affecting the earthworm population in a banana plantation[END_REF]Mohasin et al. 2005;[START_REF] Zaller | Biodiversity Decline as a Consequence of an Inappropriate Environmental Risk Assessment of Pesticides[END_REF]. Glyphosate and its main degradation product, AMPA have theoretical short persistence in soil (half-life DT50 field of 6.45 and 32 days, respectively; PPDB, 2021, [START_REF] Simonsen | Fate and availability of glyphosate and AMPA in agricultural soil[END_REF], but they are the two most commonly found pesticides in rivers and soils (Carles et al., 2019;Froger et al., 2023). Moreover, the half-life of glyphosate increases from 2.2 to 3.4 months when the number of applications is increased from one to four (de Andréa et al., 2023). This accumulation in soils can lead to detrimental effects on earthworms which accumulate glyphosate and AMPA more than expected [START_REF] Pelosi | Glyphosate, AMPA and glufosinate in soils and earthworms in a French arable landscape[END_REF].

Only one study investigated the effects of frequent application of GBH on earthworms in the field at the RAD. [START_REF] García-Pérez | Earthworm communities and soil properties in shaded coffee plantations with and without application of glyphosate[END_REF] used data collected from farms to test the long-term effects (22 years of application) of applications of two GBH (Glyfos®, Classical Faena® and Faena Fuerte®) at recommended doses (although not clearly specified) in coffee plantations, at least three times per year, and they compared them with plots free of herbicides for seven years. The results showed that one of two species of earthworms (i.e., Amynthas corticis) disappeared from the plots treated with GBH; they also found that the total density drastically decreased, and the biomass of Pontoscolex corethrurus was halved. [START_REF] García-Pérez | Interactive effect of glyphosate-based herbicides and organic soil layer thickness on growth and reproduction of the tropical earthworm Pontoscolex corethrurus (Müller, 1857)[END_REF] underlined the accumulated evidence showing that epigeic, endogeic and anecic earthworms are Accepted Article vulnerable to repeated applications of glyphosate. [START_REF] Springett | Effect of repeated low doses of biocides on the earthworm Aporrectodea caliginosa in laboratory culture[END_REF] also explained that biocides with apparently low levels of toxicity can have a substantial effect on the growth rates of earthworms under repeated applications. These authors found a reduction in A. caliginosa growth over 100 days under exposure to pure glyphosate in a laboratory experiment at doses at least five times lower than the RAD.

Despite the low number of papers dealing with the topic in this review, the results evidenced a toxic impact of cumulative doses of GBH or glyphosate on earthworms when applied at the RAD (or lower doses). Although data are scarce and somewhat contrasted (e.g., Nuutinen et al, 2020), it has been shown that earthworm activity and earthworm-mediated functions (i.e., casting and movement activity) can also be impacted. For instance, the surface activity of vertically burrowing earthworms (Lumbricus terrestris) decreased with the application of Roundup® at the RAD [START_REF] Gaupp-Berghausen | Glyphosate-based herbicides reduce the activity and reproduction of earthworms and lead to increased soil nutrient concentrations[END_REF][START_REF] Zaller | Effects of glyphosate-based herbicides and their active ingredients on earthworms, water infiltration and glyphosate leaching are influenced by soil properties[END_REF]. A potential explanation is that earthworms avoided glyphosate-contaminated leaf material on the soil surface (Nuutinen et al., 2020;[START_REF] Pochron | Exposure to Roundup increases movement speed and decreases body mass in earthworms[END_REF].

To summarize, our literature review showed no marked effect on earthworms of glyphosate or GBH used at the RAD when applied once over a short time interval. However, when assessing sensitive endpoints of species representative of natural soils, after several applications at the RAD per year, negative effects of glyphosate or GBH on earthworms can be observed at the subindividual, individual, population, and community levels, as well as on earthworm-mediated functions. These effects cannot be revealed with risk assessment procedures as currently used, which can explain why the negative effects of pesticides on biodiversity and, in particular, on earthworms are increasingly highlighted under real field conditions. In France, for the first time, the Paris Administrative Court recognised the occurrence of environmental damage Accepted Article resulting from the "widespread, diffuse, chronic and lasting contamination" of water and soil by plant protection products, as well as the decline in biodiversity and biomass. It requires the government to take "all appropriate measures" to repair this damage and prevent further damage by June 2024.

What is the potential impact of the interactions between glyphosate or GBH and other chemicals on earthworms?

Glyphosate can be considered a chelating agent because it binds tightly to metal ions through its functional groups (e.g., amine) to form metal complexes. Pure glyphosate was found to react with heavy metals (e.g., cadmium, copper), decreasing metal toxicity and bioavailability to E. fetida (Zhou et al., 2012;2013;2014). For heavy metals, Bouazdia (2020) found an antagonistic interaction of Glyphon® and the insecticide deltamethrin on the mortality of A. caliginosa in artificial soil. Moreover, the negative effects of the insecticide on the growth rate were alleviated by GBH. This was also reported by [START_REF] Santos | Evaluation of the joint effect of glyphosate and dimethoate using a smallscale terrestrial ecosystem[END_REF] for the growth rate of E. andrei exposed to a mixture of Roundup Ultras® (360 g AI/L) and the organophosphorus insecticide dimethoate (AGRORs®, 400 g AI/L). They concluded that the majority of the mixtures of glyphosate and dimethoate had weaker effects than predicted based on the individual responses on the growth of E. andrei. The same effect was reported with 2,4-dichlorophenoxyacetic acid (2,4-D) and glyphosate in E. fetida (Lazurick et al., 2017) and with glyphosate and Captan® in A. caliginosa [START_REF] Springett | Effect of repeated low doses of biocides on the earthworm Aporrectodea caliginosa in laboratory culture[END_REF], meaning that 2,4D and Captan® reduced the negative effect of glyphosate on earthworm growth. However, few studies have presented synergistic effects of glyphosate and other organic chemicals (e.g., Mohasin et al., 2005, with

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To summarize, approximately 15 studies addressed the combined effects of glyphosate and other molecules. Most of them showed that glyphosate can decrease the toxicity of other chemicals to earthworms. However, interactions between chemicals in soils are complex and should be addressed with more scrutiny.

CONCLUSIONS

The review showed that glyphosate and GHB can be toxic to earthworms.

Although different factors can influence toxicity and much remains unknown, data point towards impacts on reproduction and the provision of ecosystem services. We urgently recommend more research on glyphosate and GBH in the laboratory and in the field, using several applications at the RAD, at time intervals that are normally used by farmers, and in research of more than one year. Our results also indicate that the risk assessment process that leads to the renewal of a pesticide has gaps and is not strong enough to prevent future threats to biodiversity. There is an urgent need for government agencies to keep pace with updates on competent directives and other concerning legislation, standardised methodologies, and the development of the field of soil ecotoxicology, aiming to avoid possible underestimation of the potential risk of a pesticide in the near future.

Accepted

Article Mohasin, M. D., Bowmik, P., Banerjee, A., Somcboudhury, A. K. (2005). Effect of some herbicides on earthworm (Metaphire posthuma) under field condition. Crop and Weed, 2(1), 17-19. Mostert, T., Römbke, J. (2000). AMPA: Acute toxicity of AMPA technical material to the earthworm E. andrei in an artificial soil test. Data protection. In: European Commission. 2017. List of information, tests, and studies -Version 2: List of information, tests and studies which are considered as relied upon by the RMS for the evaluation with a view to renew the active substance approval. Version 2information, tests and studies relied upon by the RMS and identified in the Renewal Assessment Report (18 December 2013, rev. 29 January 2015, rev. 31 March 2015), Addendum 1 (31 August 2016) and Addendum 2 (30 March 2017). Nuutinen, V., Hagner, M., Jalli, H., Jauhiainen, L., Rämö, S., Sarikkaa, I., Uusi-Kämppä, J. (2020). Glyphosate spraying and earthworm Lumbricus terrestris L.

Journal of

  Article formula: 'earthworm* OR lumbric* OR aporrect* OR eisen* OR dendrob* OR alloloboph* OR octolas* OR dendrodril* OR diporodril* OR eophil* OR helodril* OR kritodril* OR octodril* OR prosellodril* OR scherothec* OR satchell* OR proctodril* orodril* OR postandril* OR perelia* OR andrei* OR fetid* OR foetid*; and (glyphosate or roundup or Round-up or glyphosate-based-herbicide*) in Topic'.

  Nagy, K., Tessema, R. A., Budnik L. T., Ádám, B. (2019). Comparative cyto-and genotoxicity assessment of glyphosate and glyphosate-based herbicides in human peripheral white blood cells. Environmental Research,. 179, 108851. Noack, M. (2002). AMPA -Earthworm (Eisenia fetida) effects on reproduction. Data Protection. In: European Commission. 2017. List of information, tests, and studies -Version 2: List of information, tests and studies which are considered as relied upon by the RMS for the evaluation with a view to renew the active substance approval. Version 2information, tests and studies relied upon by the RMS and identified in the Renewal Assessment Report (18 December 2013, rev. 29 January 2015, rev. 31 March 2015), Addendum 1 (31 August 2016) and Addendum 2 (30 March 2017).

  2,4D and glyphosate on Metaphire posthuma earthpod formation; Green, 2008 with bifenthrin and Round-up® on Lumbricus sp.).

This article is protected by copyright. All rights reserved.

Accepted Article

Balbuena, M. S., Tison, L., Hahn, M. L., Greggers, U., Menzel, R., Farina, W. M. (2015). Effects of sub-lethal doses of glyphosate on honeybee navigation. Journal of Experimental BiologyJul 10, 117291. Beaumelle, L., Tison, L., Eisenhauer, N., Hines, J., Malladi, S., Pelosi, C., Thouvenot, L., Phillips, H. R. P. (2023). Pesticide effects on soil fauna communities-A metaanalysis. Journal of Applied Ecology, 60(7), 1239-1253.

Blouin, M., Hodson, M. E., Delgado, E. A., Baker, G., Brussard, L., Butt, K. R., Dai, J., Dendooven, L., Pérès, G., Tondoh, J. E., Cluzeau, D., Brun, J. J. ( 2013). A review of earthworm impact on soil function and ecosystem services. 2013. European Journal of Soil Sciences, Vol (64), 2. Bouazdia, K. (2020). Combined Effect of Two Agrochemicals on Aporrectodea caliginosa in a Semi-arid Land. Journal of Biodiversity and Environmental Sciences14(42), 115-126. Buch, A. C., Brown, G. G., Niva, C. C., Sautter, K. D., Sousa, J. P. (2013). Toxicity of three pesticides commonly used in Brazil to Pontoscolex corethrurus (Müller, 1857) and Eisenia andrei (Bouché, 1972). Applied Soil Ecology 69, 32-38. Carles, L., Gardon, H., Joseph, L., Sanchís, J., Farré, M., Artigas, J. 2019. Metaanalysis of glyphosate contamination in surface waters and dissipation by biofilms. Environment International, 124, 284-293. Casabé, N., Piola, L., Fuchs, J., Oneto, M. L., Pamparato, L., Basack, S., Giménez, R., Massaro, R., Papa, J. C., Kesten, E. (2007). Ecotoxicological Assessment of the Effects of Glyphosate and Chlorpyrifos in an Argentine Soya Field. Journal of Soils and Sediments 7(4), 232-239. 24/11/2023 -Revised This article is protected by copyright. All rights reserved. Accepted Article Correia, F. V., Moreira, J. C. (2010). Effects of Glyphosate and 2,4-D on Earthworms (Eisenia foetida) in Laboratory Tests. Bulletin of Environmental Contamination and Toxicology, 85, 264-268. Cullen, M. G., Bliss, L., Stanley, D. A., Carolan, J. C. (2023). Investigating the effects

data are available at https://osf.io/yj72d/?view_only=ce6bbc5529b64b4eb0e2dbdeffbb75d7

Accepted Article

EFSA (European Food Safety Authority) (2023). Alvarez, F., Arena, M., Auteri, D., Binaglia, M., Castoldi, A. F., Chiusolo, A., Crivellente, F., Egsmose, M., Fait, G., Ferilli, F., Gouliarmou, V., Nogareda, L. H., Ippolito, A., Istace, F., Jarrah, S., Kardassi, D., Kienzler, A., Lanzoni, A., Villamar-Bouza, L. Peer review of the pesticide risk assessment of the active substance glyphosate. EFSA Journal, 21(7), 1-52.

European Commission (2017). List of information, tests, and studies -Version 2: List of information, tests and studies which are considered as relied upon by the RMS for the evaluation with a view to renew the active substance approval. Version 2information, tests and studies relied upon by the RMS and identified in the Renewal Assessment Report (18 December 2013, rev. 29 January 2015, rev. 31 March 2015), Addendum 1 (31 August 2016) and Addendum 2 (30 March 2017).

Accepted

Article which are considered as relied upon by the RMS for the evaluation with a view to renew the active substance approval. Version 2information, tests and studies relied upon by the RMS and identified in the Renewal Assessment Report (18 December 2013, rev. 29 January 2015, rev. 31 March 2015), Addendum 1 (31 August 2016) andAddendum 2 (30 March 2017


Frédéric Marin

Nicolas Grosso

COMPUTATION OF THE TRANSMITTED AND POLARIZED SCATTERED FLUXES BY THE EXOPLANET HD 189733b IN X-RAYS

Keywords: Planetary systems -radiative transfer -stars, individual (HD 189733) -techniques, polarimetric -X-rays, stars

Thousands of exoplanets have been detected, but only one exoplanetary transit was potentially observed in X-rays from HD 189733A. What makes the detection of exoplanets so difficult in this band? To answer this question, we run Monte-Carlo radiative transfer simulations to estimate the amount of X-ray flux reprocessed by HD 189733b Despite its extended evaporating-atmosphere, we find that the X-ray absorption radius of HD 189733b at 0.7 keV, the mean energy of the photons detected in the 0.25-2 keV energy band by XMM-Newton, is ∼1.01 times the planetary radius for an atmosphere of atomic Hydrogen and Helium (including ions), and produces a maximum depth of ∼2.1% at ∼±46 min from the center of the planetary transit on the geometrically thick and optically thin corona. We compute numerically in the 0.25-2 keV energy band that this maximum depth is only of ∼1.6% at ∼±47 min from the transit center, and little sensitive to the metal abundance assuming that adding metals in the atmosphere would not dramatically change the density-temperature profile. Regarding a direct detection of HD 189733b in X-rays, we find that the amount of flux reprocessed by the exoplanetary atmosphere varies with the orbital phase, spanning between 3-5 orders of magnitude fainter than the flux of the primary star. Additionally, the degree of linear polarization emerging from HD 189733b is <0.003%, with maximums detected near planetary greatest elongations. This implies that both the modulation of the X-ray flux with the orbital phase and the scattered-induced continuum polarization cannot be observed with current X-ray facilities.

INTRODUCTION

Hitherto, the main exoplanet detection technique relies on spectroscopic and photometric transits 1 . If a planet passes in front of a star, the star will be partially eclipsed and its flux will be dimmed by the successive coverage and uncoverage of the stellar surface by the transiting planet, resulting in detectable dips in the stellar light curve. In the optical and infrared bands, where most of the transit detection occurred, those transit depths are of the order of 1-3%, e.g., 1.6% for HD 209458b (Charbonneau et al. 2000;Brown et al. 2001), and 2.45% for HD 189733b (Lecavelier Des Etangs et al. 2008;[START_REF] Bott | [END_REF]. If the photospheric disk has a uniform emission (i.e., there is no limb-darkening), these depths are equal to the square of the ratio of the exoplanet radius (R p ) to the stellar radius (R ). From multiwavelength light curves, it becomes possible to characterize the atmosphere and exosphere of giant exoplanets (e.g., Redfield et al. 2008), but additional measurements are needed to estimate the mass of the planet, the orbital parameters, and the inclination angle. These results can be achieved thanks to radial velocity measurements, orbital brightness modulations, gravitational microlensing, direct imaging, astrometry, and polarimetry. The later is probably one of the most delicate methods since the anticipated white light polarization degree (about 10 -5 , Carciofi & Magalhães 2005;Kostogryz et al. 2014;Kopparla et al. 2016) resulting from scattering of stellar photons onto the atmospheric layers of Hot frederic.marin@astro.unistra.fr 1 In December 2016, 2695 planets out of a total of 3547 have been discovered by transit techniques, see http://exoplanet.eu/ Jupiters is expected to be just about detectable given the current limits of current optical, broad-band, stellar polarimeters (Schmid et al. 2005;Hough et al. 2006;Wiktorowicz 2009). Berdyugina et al. (2008Berdyugina et al. ( , 2011) ) reported to have successfully achieved a B-band polarimetric detection of HD 189733b and found a peak polarization of 2×10 -4 (i.e. 0.02 %) and a cosine-shaped distribution of polarization over the orbital period. From those results, Berdyugina et al. (2008) inferred additional constraints on the size of the scattering atmosphere of HD 189733b, and on the orientation of the system with respect to the Earth-primary line of sight. Yet there is no reliable measurement of the true scattered light polarization from HD 189733b in the B-band, as Wiktorowicz et al. (2015) and [START_REF] Bott | [END_REF] reported an absence of large amplitude polarization variations. Even if their observations are consistent with a plausible polarization amplitude from the planet, the low significance of the polarimetric observations cannot be used as a claim for detection. This highlights the difficulty of polarimetric measurements of exoplanets in the optical band. However, spectroscopic detection of exoplanets has been quite successful at all wavebands, except at X-rays energies.

It is unfortunate since X-ray photometry, spectroscopy, and polarimetry could help to constrain the composition and morphology of the exoplanet's atmosphere. Poppenhaeger et al. (2013) reported for HD 189733 the detection in the 0.25-2 keV energy band of a transit depth estimate ranging from 4.0±2.7% to 7.3±2.5% (see in their Table 6 the limb-brightened model), which might be larger than the transit depth in optical of 2.391±0.001%, computed for a uniformly emitting disk using the planetary radius of Torres, Winn & Holman (2008). These values of transit depths in X-rays were obtained by fitting the X-ray broad-band light curve using the analytic chromospheric transit of Schlawin et al. (2010) that assumes a geometrically thin emission. However, the corona of the Sun (a normal star) is by definition located above the chromosphere and the solar coronal plasma is extended above the photosphere (see for a review on the solar corona, e.g., [START_REF] Aschwanden | Physics of the Solar Corona. An Introduction[END_REF], therefore, a zero thickness is not appropriate to describe the geometry of the corona of HD 189733A, a moderately active star. Moreover, the normalized phase-folded X-ray light curve of HD 189733A is affected for a phase binning of 0.005 (corresponding to 958 s) by large statistical noise (∼5%; Poisson noise from added-up raw count rate out transit in Table 5 of Poppenhaeger et al. 2013) and astrophysical (white noise) scatter (∼4%; see bottom right panel of Fig. 12 in the Appendix of Poppenhaeger et al. 2013) that hinders any fitting. Therefore, more sensitive X-ray observations of the transit of HD 189733b are mandatory to obtain an accurate measurement of the shape of the planetary transit of the corona of HD 189733A and to better constrain its maximum depth.

In any case, the first indirect detection of an extrasolar planet in the 0.1 -10 keV energy range opens new questions: What is the expected X-ray absorption radius and scattered flux from giant exoplanets? Is a direct detection of giant exoplanets feasible in this energy band? Is, similarly to the optical band, a polarimetric detection within the reach of future instruments? To solve those issues, it is necessary to estimate the host-star flux reprocessed by the exoplanet gaseous surface first, and then to compute the resulting scattering-induced polarization. It is a particularly relevant issue since we have known for decades that stellar X-ray polarimetry is a very powerful diagnostic tool (e.g., [START_REF] Manzo | [END_REF].

In this regards, HD 189733b is one of the best laboratories for giant exoplanet studies. HD 189733 is a binary system, situated at a distance of about 19.45 pc from the Sun (van Leeuwen 2007). The primary component HD 189733A is a main-sequence star of stellar type K1.5 V, mass 0.846 M (de Kok et al. 2013), radius 0.805 R (van Belle & von Braun 2009;Boyajian et al. 2015) and rotational period 11.953 days (Henry & Winn 2008). HD 189733A emits about 10 28 erg.s -1 in the 0.25 -2 keV band, corresponding to 10 -5 times its bolometric luminosity, which is about 10 times larger than the ratio of X-ray to bolometric luminosity observed from the Sun at its maximum (Poppenhaeger et al. 2013). The secondary component of spectral type M4 V is located at an angular separation of 11. 4 (∼ 216 au) from HD 189733A with an orbital period is 3200 years (Bakos et al. 2006) and it is approximatively two orders of magnitude fainter in X-rays than HD 189733A (Poppenhaeger et al. 2013). The exoplanet HD 189733b with mass 1.162 M J (de Kok et al. 2013) and radius 1.26 R J , was discovered by transit observations in optical [START_REF] Bott | [END_REF]. Orbiting around HD 189733A in 2.219 days (Triaud et al. 2009), this Hot Jupiter is situated at only 0.031 au from its host star. Due to its proximity from Earth and its favorable observing geometrical conditions -its orbital plane is parallel within about 4 • of our line of sight (Triaud et al. 2009) and its orbit is nearly circular (Berdyugina et al. 2008) -HD 189733b stands as the perfect object for observations and numerical modeling. Hence, in this paper, we aim to investigate the HD 189733A planetary system in terms of photometry and continuum polarization. Focusing our study on soft X-rays, where the stellar coronal emission peaks, we build in Sect. 2 a template X-ray spectrum for the corona of HD 189733A and a model for the atmosphere of HD 189733b according to the latest observational constraints. We present the Monte-Carlo code that we used to perform our calculations of radiative transfer and report the very first estimations of the reprocessed flux emerging from the outer atmospheric layers of HD 189733b, along with its resulting X-ray polarization, in Sect. 3. In Sect. 4, we discuss our results in the context of present and future X-ray facilities, and conclude our paper in Sect. 5.

MODELING THE HD 189733A CORONA AND THE

HD 189733b ATMOSPHERE

Probing the gases and plasmas that form exoplanet atmospheres is a challenging task, as extra-solar bodies are usually very faint. Yet, constraints on the atmospheric composition and temperature of the external layers of hot Jupiter and hot Neptune-like planets can be derived from primary and secondary eclipses for transiting exoplanets (Seager & Sasselov 2000). Numerical models are thus very useful to evaluate the detection capabilities of our current and forthcoming generation of telescopes, together with fitting observed spectra with atmospheric models. It is in this scope that we now present a planetary system model for HD 189733 derived from observations. A sketch of our model is presented in Fig. 1. We list in Tab. 1 the physical properties of HD 189733A and HD 189733b that we use in this work. Note that our results are likely to vary if a new set of input parameters is derived from future observations. 2.1. Template X-ray spectrum of the HD 189733A quiescent corona The moderately active corona of HD 189733A emits X-ray photons from an optically thin plasma in collisional ionization-equilibrium; the X-ray spectrum is a b We use this reference to be consistent with the physical properties used by Salz et al. (2015) to compute their atmospheric model; see the header of the file hd189733.dat available at ftp://cdsarc.u-strasbg.fr/pub/cats/J/A%2BA/586/A75/ . c Works reporting X-ray observations used a distance of 19.3 pc (Pillitteri et al. 2010(Pillitteri et al. , 2011(Pillitteri et al. , 2014;;Poppenhaeger et al. 2013). van Leeuwen (2007) reported a distance of 19.45 ± 0.26 pc from the new reduction of the Hipparcos parallax. d R J is the nominal jovian equatorial radius following IAU's recommandation (R N eJ = 7.1492 × 10 7 m; Mamajek 2015). e The jovian mass is computed following IAU's recommandation [START_REF] Mamajek | [END_REF]: M J = (GM) N J /G with (GM) N J = 1.266 865 3 × 10 23 cm 3 s -2 the nominal jovian mass and G = 6.67384 × 10 -11 cm 3 kg -1 s -2 the Newtonian constant.

bremsstrahlung continuum emission plus line emission from metals. The X-ray spectra of the quiescent corona obtained with XMM-Newton and Chandra are well described by two-isothermal plasma (Pillitteri et al. 2010(Pillitteri et al. , 2011(Pillitteri et al. , 2014;;Poppenhaeger et al. 2013). Each isothermal plasma is characterized by an electronic temperature and a corresponding emission measure, defined as EM = n 2 e dV for a fully ionized plasma where the electronic density, n e , is equal to the ion density. The photoelectric absorption above 0.2 keV along the line of sight is negligible since the distance of this star is low.

We use the spectral fitting parameters of the quiescent corona obtained on April 17, 2007 with XMM-Newton by Pillitteri et al. (2011) for a distance of d = 19.3 pc: a cool plasma component with kT 1 = 0.24 ± 0.01 keV (corresponding to T e,1 = 2.8 ± 0.1 MK) and EM 1 = 4.7 +0.4 -0.3 × 10 50 cm -3 , and warm plasma component with kT 2 =0.71 +0.04 -0.03 keV (corresponding to T e,2 = 8.2 +0.5 -0.3 MK) and EM 2 = (2.8 ± 0.3) × 10 50 cm -3 .

We model this quiescent coronal emission with XSPEC (version 12.9.0) using two vapec models (Smith et al. 2001) with element abundances of Anders &Grevesse (1989) andFe=0.57, O=0.51, andNe=0.3 (Pillitteri et al. 2011). We simulate an XMM-Newton observation of this coronal model with the European Photon Imaging Camera (EPIC) pn instrument (Strüder et al. 2001) and the medium filter 2 (Strüder et al. 2001) which determines in the 0.25-2.0 keV energy range an X-ray flux 2 We use the most recent canned response matrix for pn (epn e2 ff20 sdY9 v14.0.rmf) and the ancillary response file for a 40 -radius extraction region centered on this on-axis source, obtained from the XMM-Newton Serendipitous Source Catalogue 3XMM-DR4 (Watson et al. 2009).

Figure 2. XMM-Newton/pn template spectrum of HD 189733A used in this work. The energy range is 0.25-2 keV. Top panel: instrumental spectrum simulated from X-ray observations, grouped with a minimum of 25 counts. The dashed-dotted and dotted vertical lines are the energies of the median (50th-percentile), lower and upper quantiles (25th and 75th-percentiles) of the observed count rates, respectively. The red, blue, and black lines are the cool, warm, and total plasma components, respectively. Bottom panel: unfolded spectrum. The red, blue, and black dots are the cool, warm, and total plasma components used for our modeling of the X-ray corona, respectively. of 2.9 × 10 -13 erg.cm -2 .s -1 (corresponding to an X-ray luminosity of 1.3 × 10 28 erg.s -1 for d=19.3 pc) with a count rate of 0.188 pn count s -1 .

The count rate distribution versus energy, i.e., the simulated instrumental spectrum, is shown in the top panel of Fig. 2. Among the total counts detected in the 0.25-2.0 keV energy range, 25% have energy lower than 0.51 keV (see lower dotted vertical line), 50% have energy lower than 0.69 keV (see lower dashed-dotted vertical line), 75% have energy lower than 0.86 keV (see upper dotted vertical line). The bottom panel of Fig. 2 is the so-called unfolded spectrum with an energy sampling 3 of ∼5 eV.

We will use this template spectrum to compute numerically the depth of the transit observed in the 0.25-2 keV 3 Our energy grid is defined by the nominal ranges of energy for the detector channels that are listed in the EBOUNDS extension of the response matrix file.

energy range with XMM-Newton (Sect. 2.4).

We will perform in Sect. 2.5 Monte-Carlo radiative transfer simulations at the mean energy of the photons detected in the 0.25-2 keV energy band, E mean = 0.70 keV, where the X-ray emission is mainly bremsstrahlung continuum emission. The coronal photon flux at this energy is 11.8 × 10 -5 photons cm -2 s -1 , with F ph,1 = 9.2 × 10 -5 and F ph,2 = 2.6 × 10 -5 photons cm -2 s -1 , the photon flux from the cool and warm plasma, respectively (bottom panel of Fig. 2). We will assess the impact on the transmitted flux of X-ray observation in a broad energy-band in Sect. 2.4.3.

Model of the HD 189733 quiescent corona

The X-ray emitting plasma of the Sun corona is visible both in active regions where it is confined in magnetic loops and in the most homogeneous parts of the quiet Sun corona where there is any detectable features of magnetic loops; both coronal regions extending well above the photosphere. For HD 189733A only the large-scale magnetic topology is accessible from Zeeman-Doppler imaging, Moutou et al. (2007) showed that "it is significantly more complex than that of the Sun ; it involves in particular a significant toroidal component and contributions from magnetic multipoles of order up to 5". However, it is beyond the scope of this article to use this magnetic topology as a scaffold to build a model of the X-ray emitting plasma of the HD 189733A corona (see, e.g., Jardine et al. 2006). We focus on the quiescent and diffuse corona, which is more representative of the average plasma distribution on the stellar surface. Therefore, following our template spectrum, we model the quiescent corona as two isothermal-plasma in hydrostatic equilibrium (see Sect. 3.3 of Aschwanden 2004).

In the isothermal approximation, the pressure scale height is defined as:

λ p (T e ) = 2kT e µm H g , ( 1
)
where k is the Boltzmann's constant, µ ≈ 1.27 is the mean particle weight, m H is the mass of the hydrogen atom, and g = GM /R 2 is the stellar gravitational field. For HD 189733, we obtain: λ p (T e ) = 3.4 × 10 9 × (T e /MK) cm. Therefore, λ p (T e,1 ) = 0.18R and λ p (T e,2 ) = 0.53R . Since the pressure is obtained by p = 2n e kT e , the electronic density scale height is identical to the pressure scale height in the isothermal approximation. Neglecting the variation of the gravitational field with the height above the photosphere, h, the electronic density, n e , follows an exponential profile:

n e (h) = n e (0) exp -h λ p (T e ) . ( 2
)
We introduce, f obs , the fraction of the corona outer area that is not eclipsed by the stellar disk for an observer on Earth (Eq. 5 of Schmitt 1990):

f obs (x) = 0.5 × 1 + x(2 + x) 1 + x , (3)
with x = h/R . Obviously, only half of the coronal area is visible when h = 0 (f obs (0) = 0.5), and the coronal area is fully visible when h = ∞ (f obs (∞) = 1.0). Coronal emission profile integrated along the line of sight versus the distance from the stellar center. The vertical dashed line is the solar limb. All the profiles have been normalized at the solar limb (vertical dashed line). The red and blue lines are the most compact and extended coronal emission profiles occuring at 0.57 and 2.00 keV, respectively. The green line is the coronal emission profile at 0.7 keV that we use in our simulation.

The observed emission measure must be computed on the coronal volume that is not eclipsed by the stellar disk:

EM obs = ∞ 0 dEM (h) dh f obs h R dh , (4)
with the differential emission measure

dEM (h) dh = n e (h) 2 4π(R + h) 2 .
(5)

From Eq. 1-5 and the values of the observed electronic temperatures and emission measures, we derive numerically the electronic density at the base of the corona: n e,1 (0) = 1.9 × 10 9 cm -3 and n e,2 (0) = 6.7 × 10 8 cm -3 ; Fig. 3 shows the corresponding profiles of the coronal electronic density.

We obtain the profile of the photon number emitted by the corona for an energy, E, and a height, h, above the corona:

dN (E i , h) dh = ∆E i × 10 -14 4πd 2 × vapec(E i , kT 1 ) × ( dEM 1 (h) dh + vapec(E i , kT 2 ) vapec(E i , kT 1 ) × dEM 2 (h) dh ) , (6)
where ∆E i is the width of the spectral bin of the ancillary response file at energy E i , and vapec(E i , kT j ) is the X-ray photon flux (in unit of photons cm -2 s -1 keV -1 ) for a plasma temperature of kT j and a normalization of 1 (i.e., vapec parameter norm ≡ 10 -14 EM/4πd 2 = 1).

The ratio of warm-to-cool plasma emissivity in Eq. 6 is plotted versus the energy in Fig. 4, using the energy sampling of the unfolded spectrum. Peaks and dips are due to emission lines from the warm and cool plasma, respectively. In the 0.25-2 keV energy band, the minimum and maximum values are 0.06 and 262 achieved at 0.57 and 2.00 keV, respectively. For a spectral energy resolution of ∆E i = 5 eV, vapec(E, kT 2 )/vapec(E, kT 1 ) is equal to 0.45 at E = E mean = 0.7 keV. Figure 5 shows the resulting normalized profile of the photons emitted by the corona at E mean obtained using Eq. 6. Figure 6 shows the corresponding emission intensity integrated along the line of sight versus R, the distance from the stellar center. The emission intensity is maximum at the stellar limb and decreases from it with the distance, more or less slowly depending of the small or large contribution, respectively, of the warm plasma compared to the cool plasma to the coronal emission. Therefore, the size of the coronal emission varies with energy: the smallest and largest sizes are observed at 0.57 and 2.00 keV, respectively.

We define the quiescent corona has layers of constant, isotropic, and optically thin emission, above an optically thick sphere of radius R (Fig. 5). Since ordinary bremsstrahlung emission from plasma shows no intrinsic polarization due to the random motions of electrons (Dolan 1967), we consider only unpolarized X-ray photons from the stellar corona.

Model of the HD 189733b atmosphere

The physical properties of the upper atmosphere of HD 189733b can be constrained with transmission spec-troscopy of HD 189733A (for a review of exoplanetary atmospheres see Madhusudhan et al. 2014). Assuming that the transmission spectrum of HD 189733A from optical to near-infrared is dominated by Rayleigh scattering, Lecavelier Des Etangs et al. ( 2008) derive an atmospheric temperature of 1340 ± 150 K at 0.1564 R . They prefer scattering by condensates of Enstatite (MgSiO 3 , with radius between ∼ 10 -2 and ∼ 10 -1 µm) rather than by molecular hydrogen. Assuming solar abundances, they derive at 0.1564 R for particle sizes of about 10 -2 -10 -1 µm, a pressure of 2 × 10 -3 -2 × 10 -6 bar and a particle density of 1.1 × 10 16 -1.1 × 10 13 cm -3 . The revised transmission spectrum across the entire visible and infrared range is well dominated by Rayleigh scattering, which is interpreted as the signature of a haze of condensed grains extending over more than two orders of magnitude in pressure, with a possible gradient of grain sizes in the atmosphere due to sedimentation processes (Pont et al. 2013).

The gas of the HD 189733b atmosphere is photoionized by the UV emission of HD 189733A (e.g., Sanz-Forcada et al. 2011) and cools by radiation from collisionally excited atomic hydrogen, which leads similarly to H ii regions to a temperature of about 10, 000 K. This high temperature produces a (slow) evaporative-wind (Yelle 2004;Murray-Clay et al. 2009). Huitson et al. (2012) detected an upper atmospheric heating of HD 189733b from HST sodium observations, i.e., evidence of a thermosphere. Salz et al. (2015) obtained a 1D, spherically symmetric hydrodynamic simulations of the escaping atmosphere of HD 189733b, predicting gas velocity of ∼9 km s -1 at the Roche's radius, R Roche = 4.35 R p (Fig. 7), by coupling a detailed photoionization and plasma simulation code with a general MHD code, and assuming only atomic Hydrogen an Helium in the atmosphere. Since the resulting temperaturepressure profile (see below Fig. 12) is consistent with the rise of temperature with the altitude observed by Huitson et al. (2012), we adopt the Salz et al. (2015)'s profiles to describe for r ≥ R p the thermosphere of HD 189733b. Line et al. (2014) showed from secondary eclipse spectroscopy that for R p ≥ r ≥ r in , corresponding to an atmospheric pressure increasing from p(R p ) ∼10 to p(r in ) ∼ 1000 dyn cm -2 , the lower atmosphere of HD 189733b is isothermal, with an equilibrium temperature of T eq ∼ 1200 K. Therefore, we use the hydrostatic equilibrium to extent the pressure and density profiles into this lower atmospheric layer. The pressure scale height of this neutral atmospheric layer is:

λ atm p (T eq ) = kT eq µ(R p )m H g p ( 7
)
where g p = GM p /R 2 p is the planetary gravitational field, and T eq = 1190 K and µ(R p ) = 1.28015 (Salz et al. 2016), which leads to λ atm p (T eq ) = 0.0043 R p (i.e., 350 km). The pressure and density follow the same exponential profile:

p(r) = p(R p ) × f (r) (8) n H (r) = n H (R p ) × f (r) (9)
where 2016) used in our X-ray simulation. From top to bottom panels, the total Hydrogen number density, temperature, pressure, velocity, and Hydrogen (green) and Helium (red) ionic fractions of the planetary atmosphere are represented versus the distance from the planetary center, ranging from the planetary radius to the Roche's radius.

f (r) = exp - r -R p λ atm p (T eq ) (10)
when neglecting the variation of the planetary gravitional field with the depth below the planetary radius, and p(R p ) = 12.7 dyn cm -2 and n H (R p ) = 7.7 × 10 13 cm -3 (Salz et al. 2016). Therefore, r in = 0.981R p and n H (r in ) = 6.0 × 10 15 cm -3 .

Analytic computation of the transmitted flux

X-ray absorption radius

The planetary absorption radius during transit is defined as the distance in the plane of the sky from the planetary center where the optical depth through the atmosphere along the line-of-sight, τ , is equal to unity. The total photon extinction cross-section in X-rays is the sum of photoelectric absorption and scattering crosssections. The latter is the sum of coherent (Rayleigh) and incoherent (Compton) scattering by bound electrons in atoms/molecules (Hubbell et al. 1975). For comparison, we compute these cross-section components for an atmosphere of neutral Hydrogen and Helium with solar abundances [START_REF] Asplund | [END_REF] 4 with the XCOM (Berger & Hubbell 1987) 5 . At 1 keV the total photon cross-section is 46.5 barn/H atom, composed at 98.1% by the photoelectric absorption (45.6 barn/H atom), this proportion decreases with higher energy. The scattering cross-section at 1 keV is dominated by the coherent (Rayleigh) process with 0.8 barn/H atom compared to 0.1 barn/H atom for the incoherent (Compton) scattering. Therefore, we will neglect the scattering crosssections in our analytic computation at 0.7 keV.

The simplified solution of the absorption radius proposed by Fortney (2005) is only valid for a geometrically thin atmosphere and can not be used a priori here due to the extended evaporative-wind. From the geometrical parameters introduced in Fig. 8, the optical depth at energy E through the planetary atmosphere along the line-of-sight is computed versus the distance from the planetary center, r, as follows:

τ X (r, E, Z) 2 = L 0 σ X ( r 2 + l 2 , E, Z) n H ( r 2 + l 2 ) dl (11) with L = R 2
Roche -r 2 , n H the total Hydrogen number density, and σ X (r, E, Z) the photoelectric crosssection per Hydrogen atom, where Z is the metallicity.

The photoelectric cross-section at the distance r from the planetary center and energy E is computed as:

σ X (r, E, Z) = f H (r) σ X,H (E) + A He f He (r) σ X,He (E) + f He + (r) σ X,He + (E) + Z k / ∈[H,He] A k σ X,k (E) (12)
with f H , f He , and f He + the ionic fractions (see bottom panel of Fig. 7); A i the abundance in number of the neutral element i relative to the hydrogen (Asplund 4 The largest solar abundances relative to hydrogen in [START_REF] Asplund | [END_REF] are: A H = 1, A He = 8.51 × 10 -2 , A O = 4.9 × 10 -4 , A C = 2.69 × 10 -4 , A Ne = 8.51 × 10 -5 , A N = 6.76 × 10 -5 , A Mg = 3.98 × 10 -5 , A Si = 3.24 × 10 -5 , and A Fe = 3.16 × 10 -5 .

5 The XCOM: Photon Cross Section Database (version 1.5; Berger et al. 2010) is available at http://physics.nist.gov-/PhysRefData/Xcom/Text/intro.html for the energy range of 1 keV-100 GeV.

Figure 9. Photon cross-section of photoelectric absorption in Xrays versus metallicity. The green and blue solid-lines are the X-ray cross-sections of atomic and molecular Hydrogen, respectively. The solid and dashed red-lines are the X-ray cross-sections of neutral and one-times ionized Helium, respectively. The black solid lines are the X-ray cross-section for neutral atomic Hydrogen and Helium with no metals, solar metallicity and ten times solar metallicity (no metallic ions). The main ionization-edges of the inner electronic-shells are labeled with element names and shell name except for K.

Figure 10. Optical depth through the planetary atmosphere along the line-of-sight at Emean = 0.7 keV versus the distance to the planet center. The planetary atmosphere is composed of atomic H, He and He + with no metals, solar metallicity and ten times solar metallicity (no metallic ions). The vertical dotted lines indicate the corresponding X-ray absorption radius.

et al. 2009) and σ X,i the photoelectric cross-section of the neutral or ionized element i relative to the hydrogen (Verner & Yakovlev 1995). Since the dust grains in the planetary atmosphere are optically thin to X-rays due to their small sizes ( 1 µm), there is no self-blanketing effect, i.e., no decrease of the X-ray cross-section due to some element in the solid phase (Bethell et al. 2011).

Following Salz et al. (2016), we will only consider in our simulation atomic Hydrogen and Helium photoelectric cross-sections (Fig. 9). Since σ X,H2 = 2.85 σ X,H (Wilms et al. 2000) and A H2 = 0.5, the contribution of the molecular Hydrogen in the low atmosphere to an increase of the photoelectric cross-section is small. However, metal abundances has a strong impact on the photoelectric absorption. Since ions (e.g., He + ) have lower photoelectric cross-section than neutral elements (fully ionized elements have obviously a null photoelectric cross-section), the ionized escaping atmosphere is more transparent to X-rays than the lower atmosphere.

Figure 10 shows the variation of the optical depth (Eq. 12) at 0.7 keV versus the distance to the planetary center. We find that the planetary absorption radius at 0.7 keV, R X (0.7 keV) is 1.008 R p (corresponding to 0.156 R ), i.e., located at z =634 km above the planetary radius. Figure 11 shows that 99% of the absorption Figure 11. Cumulative contribution of the atmosphere at elevation z above the planetary radius to the optical depth at the X-ray absorption radius at 0.7 keV (vertical dashed line). The maximum elevation value on the x-axis corresponds to the atmospheric layer contributing for 99% to the optical depth.

Figure 12. Atmospheric structure of HD 189733b (adapted from Salz et al. 2016). The top and bottom panels are the pressuretemperature and the density-temperature profile, respectively. The crosses are the HST Sodium observations of Huitson et al. (2012). The vertical labels give the distance from the planetary center in planetary radius. The thick grey region with percent-labeled asterisks indicates the contribution of the atmospheric layers to the absorption at the X-ray absorption radius at 0.7 keV (Fig. 11).

at R X (0.7 keV) is produced by the upper (z=634-4243) atmospheric layers that intersect the line of sight (e.g., the dashed circle in Fig. 8). In this absorbing atmospheric shell with a width of 3,609 km the total Hydrogen number density and temperature ranges are 1.1 × 10 13 -1.2 × 10 11 cm -3 and 1870-7004 K, respectively (Fig. 12). The physical properties of the atmospheric layers that contribute to the bulk of the X-ray absorption are constrained by the optical measurements of Huitson et al. (2012).

Assuming that adding metals in the atmosphere would not change dramatically the density-temperature profile (see, however, the discussion in Salz et al. 2016), we esti-mate that R X (0.7 keV) increases from 1.008 to 1.059 R p (or equivalently from 0.156 to 0.164 R ) when the neutral metals increase from zero to ten times the solar metallicity (Fig. 10).

Transmitted flux at 0.7 keV during the planetary transit on the stellar corona

For comparison purpose, we compute the phases of the first, second, third and fourth contacts of the primary eclipse in the optical6 : φ 1 = -φ 4 = -0.0169 and φ 2 = -φ 3 = -0.0091 (vertical dotted lines in Fig. 13). The corresponding photospheric transit of a uniformly emitting disk (e.g., Mandel & Agol 2002) has a maximum transit depth of (R p /R ) 2 = 2.39% (dotted line in Fig. 13).

The chromospheric transit was computed analytically by Schlawin et al. (2010), assuming an optically thin and geometrically thin shell of emission (zero thickness). It is characterized by a W-profile with a maximum depth of approximately δ chrom max,approx = 0.5(R p /R ) 3/2 , i.e., 0.5(R p /R ) -1/2 times deeper than the maximum transit depth of a uniformly emitting disk. These two minimums occur slightly before and after the second and third contacts, respectively, with a depth here of exactly δ chrom max = 3.10% (dashed line in Fig. 13). This characteristic shape is due to the strong limb brightening that occurs since the zero-thickness chromosphere has its largest column density at the disk's edge.

We compute numerically the normalized light curve of the planetary transit on the stellar corona from the coronal emission profile integrated along the line of sight, I (Fig. 6), and the optical depth through the planetary atmosphere, τ (Fig. 10), using the formula:

I transit (t) = +∞ -∞ +∞ -∞ I( √ X 2 + Y 2 ) e -τ r(X,Y,t) Rp dXdY +∞ -∞ +∞ -∞ I( √ X 2 + Y 2 ) dXdY (13
) where X and Y are the cartesian coordinates in the plane of the sky expressed in stellar radius (Fig. 1), and r(X, Y, t) = (X -X p (t)) 2 + (Y -Y p (t)) 2 is the distance from the position of the planetary center at time t, X p (t) = a cos(i) sin(2πt/P ) and Y p (t) = -a cos(i) cos(2πt/P ). We obtain a similar W-profile since the coronal emission is also optically thin (solid line in Fig. 13). But, the coronal transit is less deep and more extended than the chromospheric transit since the corona is extended above the photosphere (green line in Fig. 6). We find δ max = 2.06% at φ = ±0.0143, corresponding to a temporal shift of ±45.8 min from the transit center. At the transit center the depth is reduced to only 0.77%.

Impact of the broad energy-band on the observed transmitted flux

Due to the limited sensitivity of the current X-ray facilities, any tentative detection of planetary transits must The black solid line is the coronal transit at 0.7 keV computed for R X (0.7 keV) = 1.008Rp (corresponding to a planetary atmosphere of H, He, and He + ). For comparison, the vertical dotted lines indicated the first, second, third, and fourth contacts of the photospheric transit in the optical. The dotted and dashed lines are the photospheric transit (uniformly emitting disk, e.g., Mandel & Agol 2002) and the chromospheric transit (Schlawin et al. 2010), respectively. The cross data are the coronal transit signature obtained by our simulation at 0.7 keV (see Fig. 17).

use light curves in a broad energy band to increase the signal-to-noise ratio. The extension and depth of the coronal transit is modified by the variations with energy of the coronal emission profile, the photon extinction cross-section (determining the absorption radius), and the observed stellar flux. It is therefore important to assess in a broad energy band the effective transit. This effective transit is the weighted average of the monoenergetic transit on the broad energy-band, using the observed X-ray count rate versus energy (i.e., the observed X-ray spectrum; top panel of Fig. 2) as weight.

For a given metallicity, we compute at each grid energy the coronal profile and the absorption radius, and the corresponding light curve of the coronal transit. The top panel of Fig. 14 shows the absorption radius decreasing with the energy, with local jump associated to the ionization edges of metals. When there is no metals, the X-ray absorption radius becomes lower than the planetary radius -the lower boundary of Salz et al. (2016)'s simulation-at energies larger than ∼1.1 keV. Therefore, the optical depth used to compute the absorption factor in Eq. 13 has also to be estimated inside lower atmosphere, which requires an extension of the density model as we did in Sect. 2.3. This leads for comparison at r in to τ (Z = 0, E = 2.0 keV) ∼ 12.

The mid and bottom panels of Fig. 14 show the maximum depth of the coronal transit and its temporal shift from the transit center, respectively, vs. energy. Both values are mainly correlated with the warm-to-cool plasma emissivity ratio (Fig. 4) that controls the extension of the corona.

Then, we compute the weighted average light curve of the coronal transit in the 0.25-2 keV energy band for XMM-Newton/pn using the template instrumental spectrum of HD 189733A as weight (Fig. 15). We obtain maximum transit depths of 1.62%, 1.67%, and 1.82%, for no metals, and one and ten times solar metallicity (no metallic ions), respectively, at φ = ±0.0148 corresponding to a temporal shift of ±47.4 min from the transit center; at the transit center the depth is reduced to 0.61%, 0.64%, and 0.72%, respectively.

Figure 14. Characteristics of the coronal transit versus X-ray energy. Top panel: X-ray absorption radius given in planetary radius. Middle panel: maximum depth of the coronal transit in percent. Bottom panel: temporal shift of the maximum depth from the transit center. Black, green, and red lines are for a planetary atmosphere composed of atomic H, He, He + with no metals, solar metallicity and ten times solar metallicity (no metallic ions), respectively.

Figure 15. Planetary transit in the 0.25-2.0 keV energy band. For comparison purpose, the vertical dashed lines are the eclipse contact in the optical and the grey line is the planetary transit at 0.7 keV for no metals.

Therefore, the maximum transit depth in the 0.25-2 keV energy band is little sensitive to the metal abundance. Moreover, the transit light curve at 0.7 keV (grey line in Fig. 15) is a correct approximation of the transit light curve in the 0.25-2 keV energy band.

Monte Carlo radiative transfer

To simulate the transit of HD 189733b in front of its host star, we used the radiative transfer code stokes. Originally written for polarimetric investigations of active galactic nuclei, stokes has been extended over the last years to cover a much larger panel of astrophysical sources (a detailed list of examples can be found in [START_REF] Marin | SF2A[END_REF]. The code and its characteristics are extensively described in Goosmann & Gaskell (2007), Marin et al. (2012) and Marin et al. (2015) for the optical/UV part, and in [START_REF] Marin | [END_REF] for the X-ray band, so we will simply summarize the principal aspects of stokes relevant for our computations.

The code can handle a large panel of emitting, scattering and/or absorbing geometries in a fully threedimensional environment. Multiple scattering enables the code to radiatively couple all the different regions of a given model, and a web of virtual detectors arranged in a spherical geometry is used to record the photon wavelength, intensity, and polarization state, according to the Stokes formalism ( S = (I, Q, U, V ) T ). About 10 11 photons have been sampled for our analysis. The total intensity (flux), polarization degree P (= Q 2 + U 2 + V 2 /I), and polarization angle ψ (= 0.5 tan -1 (U/Q)) are computed by averaging all the detected photons, at each lineof-sight in polar and azimuthal directions. Mie, Rayleigh, Thomson, Compton and inverse Compton scattering are included from the near-infrared to hard X-ray bands.

For planetary atmospheres in the X-ray domain, Rayleigh and Compton scattering of photons onto bound electrons will be the major mechanism to alter the net polarization, and a visual representation of the integrated and differential scattering cross sections produced by stokes is presented in Fig. 16. Note that for molecular hydrogen the incoherent scattering cross-section is two-times larger than for atomic hydrogen (Sunyaev et al. 1999).

Photo-ionization and recombination effects, which also influence the resulting polarization by absorption and unpolarized re-emission processes, are based on quantum mechanics computations from Lee (1994) and Lee et al. (1994). We use fluorescent yields and energy of the subsequently re-emitted Auger photons from the Opacity Project (Cunto & Mendoza 1992), and X-ray photoelectric cross-sections and inner-shell edge energies of Verner & Yakovlev (1995). Finally, we opt for elemental abundances from [START_REF] Asplund | [END_REF] and ten times solar metallicity to allow direct comparison with Poppenhaeger et al. (2013).

Since the X-ray scattering by dust grains (Mathis & Lee 1991) is not yet implemented in stokes, we consider only gaseous components. We do not consider additional soft X-ray emission from the exoplanet itself induced by the stellar wind charge exchange mechanism since it was estimated in the case of the close-in exoplanet HD 209458b to be about five orders of magnitude fainter than the emission from the host star [START_REF] Kislyakova | [END_REF].

We divide our two-zone model with constant-density shells sampling any 0.1-dex variation of the density from a density of 7.697×10 13 cm -3 corresponding to a pressure of 12.739 bar, a temperature of 1190.2 K, and a 0.7 keV optical depth of ∼4.608.

PHOTO-POLARIMETRIC RESULTS

We present the outcomes of our simulations in Fig 17 .  Results are plotted with respect to the orbital phase of HD 189733b, also converted into transit hours. Each data-point is associated with its 1σ Monte Carlo error bars resulting from the simulation. The Monte Carlo statistical error is estimated using the standard deviation σ that is roughly proportional to Var(X)/ √ N for large N , with N the number of photons sampled in the direction of the observer and Var(X) the variance of the estimate.

Photometry

The top panel of Fig 17 shows the light curve of HD 189733A at 0.7 keV, normalized to unity. The exoplanet orbits in front of HD 189733A from orbital phase -0.25 to orbital phase +0.25, with an eclipse of the stellar corona (i.e., a planetary transit) occuring between orbital phases -0.0169 and +0.0169. During this planetary tran-sit, the 0.7 keV flux decreases by 2.00±0.15 % between the first and second contacts, as the exoplanet starts to cover the X-ray corona, then rises to 1.07±0.15 % at orbital phase 0. It then decreases back to 2.02±0.15 % between the third and fourth contacts before resuming to the non-eclipsed flux, showing no more variation during the remainder of the orbit of HD 189733b. A close up representation of the transit is shown in Fig. 13 for clarity purposes. We find a perfect agreement between numerical and simulation results within the Monte-Carlo statistical error of our modeling.

Using the stokes code, we isolated photons that are re-emitted/scattered from HD 189733b, and plotted the resulting light curve (normalized with respect to the unitary flux of HD 189733A) in Fig 17 (second panel from the top). To increase the statistics of the photon-starved results, the phase resolution of the re-emitted/scattered radiation has been decreased compared to Fig. 13. Due to the strong photoelectric absorption processes that prevail at soft X-ray energies, the X-ray flux from the exoplanet is found to be three to five orders of magnitude lower than the photon flux from the main star. From the HD 189733A flux of 2.9 × 10 -13 erg cm -2 s -1 at 0.7 keV, the flux of HD 189733b is about 10 -16 -10 -18 erg cm -2 s -1 , depending on the orbital phase of the planet. The flux reprocessed onto the atmospheric layers of HD 189733b strongly depends on the angle between the source, the exoplanet atmosphere and the observer; this effect is due to the differential scattering phase function of incoherent scattering, as presented in Fig. 16 (bottom). In the case of Rayleigh scattering, forward and backward reprocessing prevails while, for incoherent scattering onto bound electrons, forward and perpendicular scattering are less probable. However, backscattering is very strong and when the gaseous planet passes beyond the plane-of-the-sky, its reprocessed flux rises up to a normalized flux of ∼ 4.7 × 10 -4 . Then, HD 189733b disappears behind its star and flux drops to zero.

Polarization

The middle panel of Fig 17 is a visualization of the linear continuum polarization degree P , ranging from 0 (unpolarized) to 100 % (fully polarized). It is the polarization resulting from scattered light only, i.e. not diluted by the unpolarized stellar flux. The shape of the polarization curve is very similar to the results obtained by Stam et al. (2004), who evaluated the spectra of visible to near-infrared starlight reflected by Jupiter-like extrasolar planets. As Stam et al. (2004), we find polarization maximums close to orbital phases ±0.25, i.e., near planetary greatest elongations, with P = 64.9±2.9 % which is slightly larger than in infrared. Since the planet's orbital plane is inclined by 4 • , the polarization degree does not drop to zero at zero orbital phase as a small fraction of photons scatters onto the top of the atmospheric layers towards the Earth. Hence, we are sure that our model produces correct results and extends the near-infrared/optical investigation of Stam et al. (2004) to X-ray energies.

The P diluted = Q 2 + U 2 /(I + I p,scatt ). The overall shape of the polarization curve, associated with a polarization degree below 0.003 %, is quite different from the intrinsic P . In fact, maximum polarization is found when the exoplanet transits behind the plane-of-the-sky, with a local diminution to zero when HD 189733b is occulted by its primary star. The departure from a purely sinusoidal waveform is again due to the scattering phase function of incoherent scattering that promotes backscattering. Associated with maximum fluxes from HD 189733b that are not located at maximal planetary elongations, the net diluted polarization degree peaks at orbital phases +0.35 and +0.65. The highest degrees of P are of the order of 0.0025 ± 0.0002 % at 0.7 keV, similarly to the polarization found in the optical band (Carciofi & Magalhães 2005).

Finally, the bottom panel of Fig 17 presents the absolute polarization position angle ψ to be observed with an X-ray polarimeter. When HD 189733b does not transit on HD 189733A, its polarization angle is equal to 90 • (the E-vector of the radiation is aligned with the projected rotational axis of the orbit). However, when the planet is about to transit in front of its primary star, ψ oscillates around 90 • . The canceling contribution of unpolarized fluxes from the star and the 90 • oriented polarization position angle resulting from scattering prevent the ψ value from stabilizing, resulting in a chaotic signal. This behavior is strengthened due to the edge-on orientation of the exoplanet's orbit. As the illuminated side of HD 189733b, producing the scattering-induced polarization signal, is facing the star, an observer situated on Earth no longer detects the bright side of the atmosphere and the signal is almost canceled. Only photons that have scattered on the top of the atmosphere carry a non-random polarization signal. Since most of the radiation comes from HD 189733A, the resulting polarization signal is highly diluted and thus ψ randomly oscillates.

Another variation of ψ is detected when the planet passes behind HD 189733A: at the ingress (egress) point, the polarization position angle increases (decreases) by ∼ 30 • , due to the partial obscuration of the reprocessing target. The inclination of the system and the partial obscuration of the planetary disk suppresses the averaging of polarization and results in ψ variations before a pure cancellation of polarization due to the planet disappearance. The amplitude of the fluctuation of ψ is directly correlated with the orbital inclination of the exoplanet and could be, in principle, used to estimate the impact parameter of the transit.

IS DIRECT DETECTION OF THE EXOPLANET IN X-RAYS POSSIBLE?

We presented the first quantification of the amount of X-ray flux reprocessed by the Hot Jupiter exoplanet HD 189733b, along with the first estimation of the net polarization a future X-ray polarimeter could detect.

Scattered X-ray flux

We find that the 0.7 keV flux of HD 189733b is three to five orders of magnitude lower than its primary main sequence K1.5 V star, depending on the orbital phase of the exoplanet. Considering a stellar flux of 2.9×10 -13 erg cm -2 s -1 at 0.7 keV and at a distance of 19.45 pc, it implies that the reprocessed flux from HD 189733b is lower than 1.0×10 -16 erg cm -2 s -1 at best before ingress and after egress.

Since the planetary emission cannot be spatially resolved from the stellar emission in X-rays (angular separation lower than 1. 6 mas), one can only look for flux modulation with orbital phase. As a guideline, we can use a planetary relative the observation of N planetary orbits (of period P in seconds) in two parts. During the orbital phase ∆φ, where f p is lower than f limit p , the X-ray count rate of HD 189733 is CR low =< CR > (1+ < f p >) with < CR > the count rate of the host star and < f p > the average planetary relative flux on ∆φ. During the orbital phase 1 -∆φ, where f p is larger than f limit p , the X-ray count rate of HD 189733 is CR high =< CR > (1 + α < f p >), with α the average increase of the relative planetary flux. The increase of count rate ∆CR ≡ CR high -CR low is statistically significant if ∆CR ≥ nσ with n = 4 and assuming Poisson noise σ 2 = (CR low /∆φ + CR high /(1 -∆φ))/(N P ). Straightforward algebra leads to:

N n 2 /(f 2 (α -1) 2 ∆φ(1 -∆φ)P < CR >).

(

) 14
Using < CR >= 0.188 pn count s -1 (Sect. 2.1), we find a minimum value of 13, 315 orbits for f limit p = 7.5 × 10 -5 , α = 8.7, and ∆φ = 0.89. Since the needed accuracy requires a total exposure time of 81 years, the modulation of the X-ray flux with the orbital phase cannot be observed.

4.2. X-ray polarization Fig. 17 shows that the continuum polarization degree resulting from the interaction of stellar photons with the inner layers of the HD 189733b's atmosphere is very low, ranging from 0 to 0.003 %. Due to strong dilution by the unpolarized primary source, this level of polarization corresponds to an amplitude of ∼ 10 -4 . Coupled to a low X-ray luminosity, such degree of polarization is, by any standard, by far too low to be detected with the current generation of X-ray polarimeters. Such statement includes the Gas Pixel Detector technology (Soffitta et al. 2013), Time Projection Chamber polarimeter concepts [START_REF] Black | Proceedings of the SPIE[END_REF], and polarimeters based on Bragg diffraction and Thomson scattering [START_REF] Kaaret | Proceedings of the SPI[END_REF]. Note that most of those polarimeter concepts are also limited to energies higher than 0.7 keV.

CONCLUSIONS

In this paper, we adopted the Salz et al. (2016)'s model of the atmosphere of HD 189733b to run a Monte-Carlo radiative transfer code to estimate the amount of X-ray photons emitted from the corona of HD 189733A reprocessed on this Hot-Jupiter like exoplanet. We obtained the predictive X-ray transit light curve of HD 189733A and quantified the flux and polarization emerging from scattering onto the atmospheric layers.

We have found that the maximum depth of the planetary transit on the geometrically thick and optically thin corona of HD 189733A in the 0.25-2 keV energy band is ∼1.7%. With the assumption that adding metals in the atmosphere would not change dramatically the density-temperature profile, we the maximum transit depth is little sensitive to the metal abundance. Since the maximum depth of the X-ray transit of HD 189733b estimated from the current modeling of its atmosphere is small, forthcoming deeper observations with the current X-ray observatories may not have the required X-ray sensitivity to accurately constrain the transit shape. The next generation of large X-ray mission from the ESA, Athena, thanks to its larger mirror area (e.g., the proposed Athena+ mission had at 1 keV a mirror area about 14 times larger than the FM2-pn mirror of XMM-Newton; Nandra et al. 2013;Jansen et al. 2001) should allow deeper investigations of the X-ray planetary transits of HD 189733A (Branduardi-Raymont et al. 2013).

We have quantified the amount of flux reprocessed onto the Hot Jupiter surface. The exoplanet's flux is three to five orders of magnitude fainter than its primary star, with maximums at egress and ingress points due to the asymmetrical scattering phase function of Compton and Rayleigh scattering. At most, the reprocessed flux is lower than 1.0×10 -16 erg cm -2 s -1 . A detection of the flux modulation with orbital phase is in pratical not achievable since requiring tremendous exposure time.

The reprocessed flux is associated with a very weak, diluted, amount of linear polarization. The polarization degree being less than to 0.003 %, it is impossible to measure it with the current technology of X-ray polarimeters.

However, the direct detection of the X-rays scattered by HD 189733b might be considered in the future with the possible advent of interferometric facilities in Xrays, e.g., the Black Hole Mapper visionary-mission with (sub)microarcsecond resolution (see NASA Astrophysics in the Next Three Decades, Kouveliotou et al. 2014).

Figure 1 .

 1 Figure 1. Artist representation of the exoplanet HD 189733b. HD 189733b orbits in nearly circular motion around its host-star HD 189733A; its orbital plane is parallel within about 4 • of the Earth-primary line of sight. Note the limb brightening effect emerging from the optically thin, stellar corona.

Figure 3 .

 3 Figure 3. Coronal electronic density versus the height above the corona. The red and blue lines are for the cool and warm coronal plasma, respectively.

Figure 4 .

 4 Figure 4. Ratio of warm-to-cool plasma emissivity (with identical normalization) versus energy. The cross is the value corresponding to Emean = 0.7 keV (vertical dashed line).

Figure 5 .

 5 Figure5. Normalized photon emission at Emean = 0.7 keV versus the height above the corona. The red and blue are for the cool and warm coronal plasma, respectively. The solid line is for the cool+warm coronal plasma and is normalized at the peak.

Figure 6 .

 6 Figure6. Coronal emission profile integrated along the line of sight versus the distance from the stellar center. The vertical dashed line is the solar limb. All the profiles have been normalized at the solar limb (vertical dashed line). The red and blue lines are the most compact and extended coronal emission profiles occuring at 0.57 and 2.00 keV, respectively. The green line is the coronal emission profile at 0.7 keV that we use in our simulation.

Figure 7 .

 7 Figure7. Atmospheric model of HD 189733b ofSalz et al. (2016) used in our X-ray simulation. From top to bottom panels, the total Hydrogen number density, temperature, pressure, velocity, and Hydrogen (green) and Helium (red) ionic fractions of the planetary atmosphere are represented versus the distance from the planetary center, ranging from the planetary radius to the Roche's radius.

Figure 8 .

 8 Figure 8. Definition of the geometrical parameters of the planetary atmosphere.

Figure 13 .

 13 Figure13. Light curves of the planetary transits of HD 189733b. The black solid line is the coronal transit at 0.7 keV computed for R X (0.7 keV) = 1.008Rp (corresponding to a planetary atmosphere of H, He, and He + ). For comparison, the vertical dotted lines indicated the first, second, third, and fourth contacts of the photospheric transit in the optical. The dotted and dashed lines are the photospheric transit (uniformly emitting disk, e.g.,Mandel & Agol 2002) and the chromospheric transit(Schlawin et al. 2010), respectively. The cross data are the coronal transit signature obtained by our simulation at 0.7 keV (see Fig.17).

Figure 16 .

 16 Figure16. Elemental photon scattering cross-section versus energy. Top: integrated cross-section for Compton scattering onto a variety of elements chosen accordingly to[START_REF] Asplund | [END_REF] for their high abundance. Solid black line: coherent (Compton) scattering on free electrons (Klein-Nishina cross-section). Incoherent (Compton) scattering on bound electrons: long-dashed violet line of H, short-dashed blue line of He, dot-short-dashed green line of C, double-dot-dashed orange line of O, dot-long-dashed red line of Fe. The black dotted line shows coherent (Rayleigh) scattering onto an hydrogen atom for comparison. Bottom: Emean = 0.7 keV differential cross section versus scattering angle for the same free and bound electrons.

Figure 17 .

 17 Figure 17. Photometry at Emean=0.7 keV of HD 189733A, and reprocessed flux from the surface of HD 189733b (first two panels). The fluxes are normalized to the initial flux of the star. Polarimetric results are shown in terms of P (polarization percentage) and ψ (polarization position angle, defined with respect to the vertical axis of the system). The error bars correspond to 1σ statistical errors in the Monte Carlo simulation. The vertical dashed lines are the first, second, third and fourth contacts of the primary (planetary transit) and secondary eclipses in the optical. The gray box indicates a region where polarization measurement of HD 189733b is impossible due to the disappearance of the exoplanet behind its star.

The formulae for the phases of the first and second contacts are respectively:φ 1 = -arcsin( (R + Rp) 2 -a 2 cos i 2 /a sin i)/2π and φ 2 = -arcsin( (R -Rp) 2 -a 2 cos i 2 /a sin i)/2π.

This research has been supported by the Academy of Sciences of the Czech Republic, the COST Action MP1104 "Polarization as a tool to study the Solar System and beyond", and the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 312789 "StrongGravity". FM is grateful to Sylvain Bugier (sylvain.bugier@gmail.com) for his artwork of the HD 189733 system.