Gabriel Peyré

Stéphane Mallat

DISCRETE BANDELETS WITH GEOMETRIC ORTHOGONAL FILTERS

This paper describes the construction of second generation bandelet orthogonal bases. The decomposition on a bandelet basis is computed using a wavelet filter bank followed by adaptive geometric orthogonal filters, that require O(N) operations. The resulting geometry is multiscale and calculated with a fast procedure that minimizes a Lagrangian cost at each scale. Image compression with the resulting bandelet transform code gives significantly better results than a wavelet transform code.

INTRODUCTION 1.Geometry is Discrete and Multiscale

Working with digital data means working in a discrete setting. A wavelet transform [START_REF] Mallat | A Wavelet Tour of Signal Processing[END_REF] can be applied on the discrete data to obtain a multiscale representation of the original data. In order to go one step further, today image processing algorithms try to exploit some geometrical regularity of the underlying function. But we must keep in mind that this geometry has to be defined in a discrete setting. In this paper we give a theoretic and algorithmic approach to compute such a geometric representation in the discrete wavelet domain. An application to image compression will be shown.

Geometrically Regular Images

Functions with geometric regularity are modeled as piecewise C α -regular functions outside a set of edges which are themselves regular. However, natural images often do not have sharp discontinuities, so the model also includes some smoothing by an unknown kernel. The resulting functions can be written as a convolution f = f * h where f is a function with sharp features (regular outside a set of edges) and h is the unknown smoothing kernel. We call this class of functions C α -geometrically regular functions (see figure 1,(a)).

Standard wavelet bases [START_REF] Mallat | A Wavelet Tour of Signal Processing[END_REF] are optimal to represent functions with pointwise singularities. However they fail to capture the geometric regularity along the singularities of a surfaces, because of their isotropic support. For C α -geometrically regular functions, the distortion-rate of a wavelet image transform code with R bits satisfies

|| f -f R || 2 C R -1 log(R).
To exploit the anisotropic regularity of a surface along edges, the basis must include elongated functions that are nearly parallel to the edges. Our goal is to build a new class of orthogonal bases for which the distortion rate has an optimal decay.

Previous Works

Several image representations have been proposed to capture geometric image regularity, and in particular curvelet frames [START_REF] Candès | Curvelets: A surprisingly effective nonadaptive representation of objects with edges[END_REF] and first generation bandelet bases [START_REF] Pennec | Sparse Geometrical Image Approximation with Bandelets[END_REF]. However, these constructions are not built directly in the discrete domain, and they do not provide a multiresolution representation of the geometry. In consequence, the implementation and the mathematical analysis is more involved and less efficient.

Contourlets [START_REF] Do | The contourlet transform: an efficient directional multiresolution image representation[END_REF] are also bases constructed with elongated basis functions using the combination of a multiscale and a directional filter bank. Our approach is different because it constructs a basis with a multiscale geometry that is adapted to the function that is represented. Asymptotically, the resulting bandelets are regular functions with a compact support, which is not the case of contourlets. Wedgeprints of [START_REF] Wakin | Wavelet-domain Approximation and Compression of Piecewise Smooth Images[END_REF] also provide a discrete compression scheme that is built on top of a wavelet decomposition. However, it does not define a new orthogonal basis but rather a scheme to perform a vector quantization of orthogonal wavelet coefficients, using a model of step edges.

CONSTRUCTION OF A BANDELET BASIS

The bandelet decomposition is computed with a geometric orthogonal transform that is applied on orthognal wavelet coefficients. It is thus computed with a wavelet filter bank followed by directional orthogonal filters. Each geometric direction leads to a different transform, and one can find the optimal set of filters using a best basis algorithm.

To describe the construction of the geometric orthogonal filters, we consider a wavelet transform at a fixed scale 2 j and we perform a zoom on the wavelet transform (by selecting a sub-square S), near a singularity (see figure 1). Observe that wavelet coefficients f , ψ jn are samples of an underlying regularized function f , ψ jn = f * ψ j (2 j n) where ψ j (x) = 1 2 j ψ(-2 -j x). As a result, although the original function may be singular at edge locations, the wavelet coefficients are samples of a regularized function, obtained by convolving the original function f with the "burring" kernel ψ j of width 2 j .

Original Image

Wavelet Transform In real applications the geometry must be estimated from the discrete image information. To make this problem more tractable, like in first generation bandelets, we • search for a regularity flow (arrows) along which the function is "as regular as possible", • search for a polynomial flow of degree p -1 parameterized either horizontally or vertically (on figure 1 one can see a linear flow). Until the end of this section, we suppose that we defined a polynomial flow τ on some sub-square S (we will later see how to find an optimal size for the squares and an optimal flow τ on each square).

If we impose that an integral curve of the geometric flow τ does not deviate more than 2 j (one pixel in wavelet space) from the real geometry, then one can prove an explicit bound of the derivatives of f in the direction τ of the flow and in the vertical direction:

∂ a+b f ∂ τ a ∂ y b C 2 j 2 -a/α j 2 -jb .
This control over the derivatives will drive the construction of a polynomial approximation for f * ψ j that is elongated and follows the flow in small "bands".

We want to approximate f j = f * ψ j on the regular grid of spacing 2 j , restricted to a small square S, knowing the approximate geometric flow τ. In order to do so, we construct an orthogonal filter bank that will decompose f j on functions that follows the geometrical flow. The support of the filters is obtained using a dyadic grouping of the sampling points inside S into bands {B k m } 2 k m=1 for each filtering step k (see figure 2). The exact filter responses are obtained using polynomials multiresolution restricted to the dyadic groups, and are in fact 2D extensions of Alpert multiwavelets. This orthogonal directional filter bank can be implemented using the fast linear-time algorithm of Alpert [START_REF] Alpert | Wavelets and Other Bases for Fast Numerical Linear Algebra[END_REF]. The underlined filters are calculated within the transform procedure using a Gram-Schmidt orthogonalization. The resulting filters have p vanishing moments, as the original wavelet basis, but they are elongated along the singularity, whereas the original wavelets have a square support.

f * ψ j k =1 k = 2 k = 5 ... S τ B 1 1 B 3 2 B 2 2 B 1 2 B 4 2 B 1 2

Fig. 2. 2D and continous-3D plot of f * ψ j restricted to S (top). Construction of a recursive binary partitions (bottom). Each B k m is displayed in a different grey level.

To construct a bandelet basis on the whole wavelet domain, we use a quadtree segmentation of each wavelet scale in dyadic squares, as shown on figure 3. Note that we define a different quadtree for each scale of the wavelet transform (on figure 3 only the quadtree of the finest scale is depicted), but we use the same quadtree for each of the three orientations of the wavelet transform at fixed scale. A complete representation in a bandelet basis B = {b n } is thus composed of:

• An image segmentation at each scale 2 j , defined by a quadtree. • For each dyadic square of the segmentation, -a polynomial flow, -bandelet coefficients { f , b n } n .

BEST BASIS TRANSFORM CODE

A bandelet transform code encodes the parameters that specify the geometry of the basis B = {b n } n that is adapted to the image, as well as the image coefficients in this bandelet basis. These bandelet coefficients are uniformly quantized with a step T and a zero-bin twice larger corresponding to the geometry are also quantized obtain a precision of (2 j )/4. The total number of bits R is decomposed into R = ∑ R j = ∑ (R jS + R jG + R jB ), where, for each scale 2 j : • R jS is the number of bits to code the dyadic segmentation.

• R jG is the number of bits to code the quantized polynomial geometric flow in each square. • R jB is the number of bits to code the quantized bandelet coefficients. The image restored from its quantized bandelet coefficients is written f R .

For a quantification step T , we would like to find the best basis B that minimizes the resulting distortion-rate. According to the approach in [START_REF] Pennec | Sparse Geometrical Image Approximation with Bandelets[END_REF], we minimize a Lagrangian which can be shown to approximate the Lagrangian of the true distortion-rate:

L ( f , R, B) = || f -f R || 2 + 3 4 T 2 ∑ j (R S j + R G j + R B j ) .
Thanks to the additivity of this Lagrangian and to the quadtree structure, the minimization of L can be performed using a fast CART-like bottom-up algorithm [START_REF] Pennec | Sparse Geometrical Image Approximation with Bandelets[END_REF].

Even though we make an exhaustive search for the optimal geometry, for an image of N pixels, the complexity of this best bandelet basis algorithm is O(N 3/2 ) for a linear geometry (i.e. p = 2). Some heuristics can also be used to reach a linear time complexity O(N). The following theorem computes the asymptotic decay rate of the distortionrate obtained with this best bandelet basis transform code.

|| f -f R || 2 C log α (R)R -α ,
with C a constant that depends only on the function f . We note the following important points: • This exponent α is a priori unknown. The algorithm adapts itself to the best possible α, and it is optimal. • The reconstructed function is as regular as the original function (bandelet functions are regular, see figure 5). • There is no blocking artifact due to the segmentation (in the spatial domain, bandelet functions do overlap with each other).

NUMERICAL COMPRESSION RESULTS

The bandelet transform is implemented with the 7/9 CDF biorthogonal wavelet basis. This best bandelet compression procedure was tested on various natural images. The PSNR improvement with respect to an equivalent wavelet transform coder is about 2dB for Barbara and 0.6dB for Lena (see figure 6). On figure 7 one can see, for the finest scale of the wavelet transform, the quadtree selected by the best basis algorithm, and a zoom on the orientation of the linear flow on each dyadic square. Figure 4 (upper row) shows a zoom on fine geometric structure of Barbara image, and one can see that Bandelets perform very well in these areas.

The flow-based approach improves the encoding of these geometrically regular patterns.

Wavelet transform

Segmentation and flow

CONCLUSION

We introduced second generation bandelet bases that are entirely discrete and orthogonal and are calculated from a discrete wavelet basis. The construction uses a multi-scale description of the underlying geometry and the corresponding bandelets are regular. Image compression in a best bandelet basis provide a clear improvement over an equivalent transform coder in a wavelet basis.

Fig. 1 .

 1 Fig. 1. Zoom on the wavelet coefficients near a singularity.

Fig. 4 .Fig. 3 .

 43 Fig. 4. Comparison of Wavelets and Second Generation Bandelets at 0.2 bit/pixel.

j = - 1 j = - 3 j = - 3 jFig. 5 .

 1335 Fig. 5. Graphical display of continuous bandelet functions for various scales j < 0, quad-tree levels ℓ, partition depth k and position m. Theorem: Given f a C α -geometrically regular function, the transform coding f R with R bits in the bandelet basis B minimizing L ( f , R, B),with R = R S + R G + R B , satisfies

Fig. 6 .

 6 Fig. 6. Distortion curves for Lena (PSNR gain ∼0.6dB) and Barbara (PSNR gain ∼2dB).

Fig. 7 .

 7 Fig. 7. Wavelet coefficients and bandelets orientations at finest scale (quadtree and flow computed at 0.4 bit/pixel).5. CONCLUSION


Ph.D Charaf M'rabet
email: charaf.mrabet@gmail.com

Ons Kefi-Daly
email: onskefidaly@gmail.com

Nicolas Yahia

Frédéric Chomerat

Gwenaël Zentz

Olivier Bilien

Pringault

PhD Marta Staniszewska
email: marta.staniszewska@ug.edu.pl

Wan Jun Kit
email: wanjunkit@gmail.com

Jie Wei
email: weijie@dlou.edu.cn

PhD Hyeon Ho Shin

Dr Shin

PhD Suk Min Yun

Ons Kéfi-Daly Yahia

Nicolas Chomerat
email: nicolas.chomerat@ifremer.fr

Frédéric Zentz
email: frederic.zentz@gmail.com

Gwenaël Bilien
email: gwenael.bilien@ifremer.fr

Olivier Pringault
email: olivier.pringault@ird.fr

-(2-ethylhexyl) phthalate (DEHP) on the cosmopolitan marine diatom Chaetoceros decipiens-lorenzianus

Keywords: Chaetoceros decipiens-lorenzianus, bisphenol A, di-(2-ethylhexyl) phthalate, biomass, photosynthetic efficiency and activity Chaetoceros decipiens-lorenzianus, bisphenol A, di-(2-ethylhexyl) phthalate, biomass, photosynthetic efficiency and activity Capsule

Transient effect of bisphenol A (BPA) and di

Introduction

As marine plastic debris becomes a topic of emerging concern [START_REF] Galgani | Editorial: Impacts of marine litter[END_REF][START_REF] Hahladakis | Delineating the global plastic marine litter challenge: clarifying the misconceptions[END_REF], scientific interest on the environmental impact of this debris increased remarkably. The number of scientific publications dealing with this topic reached over 37,200 in the last decade [START_REF] Abalansa | The marine plastic litter issue: A social-economic analysis[END_REF][START_REF] Schmid | Microplastic's story[END_REF]. In aquatic environments, this plastic debris is accumulated and degraded by various means (e.g., biodegradation, hydrolysis), forming smaller particles called microplastics [START_REF] Booth | Microplastic in global and Norwegian marine environments: Distributions, degradation mechanisms and transport[END_REF][START_REF] Sharma | Microplastic pollution, a threat to marine ecosystem and human health: a short review[END_REF].

Furthermore, microplastic fragments release harmful compounds [START_REF] Hermabessiere | Occurrence and effects of plastic additives on marine environments and organisms: A review[END_REF], associated with plastic derived compounds or plastic additives, such as phthalic esters, bisphenol, lindane, atrazine and polybrominated diphenyl ethers [START_REF] Hong | Chemicals associated with marine plastic debris and microplastics: Analyses and contaminant levels, in: Microplastic contamination in aquatic environments: an emerging matter of environmental urgency[END_REF][START_REF] Lithner | Environmental and health hazard ranking and assessment of plastic polymers based on chemical composition[END_REF][START_REF] Sharma | Microplastic pollution, a threat to marine ecosystem and human health: a short review[END_REF]. Among these plastic additives, bisphenol A (BPA) and di-(2-ethylhexyl) phthalate (DEHP) are used extensively on a global basis as plasticizers [START_REF] Erythropel | Leaching of the plasticizer di(2-ethylhexyl)phthalate (DEHP) from plastic containers and the question of human exposure[END_REF][START_REF] Warner | Bisphenol A and phthalates: How environmental chemicals are reshaping toxicology[END_REF]. These two man-made compounds are known to act as endocrine disruptor chemicals [START_REF] Brossa | Occurrence of twenty-six endocrinedisrupting compounds in environmental water samples from catalonia , SPAIN[END_REF][START_REF] Oehlmann | A critical analysis of the biological impacts of plasticizers on wildlife[END_REF]. Moreover, in the environment, another potential danger is known as the 'cocktail effect' due to the occurrence of pollutants in the mixture [START_REF] Backhaus | The BEAM-project: Prediction and assessment of mixture toxicities in the aquatic environment[END_REF][START_REF] Lloyd-Smith | Ocean pollutants guide: Toxic threats to human health and marine life[END_REF][START_REF] Svingen | The risk of chemical cocktail effects and how to deal with the issue[END_REF]. Several studies reported the occurrence of these compounds in the marine environment at concentrations between 0.1-10 μg/L in estuaries [START_REF] Careghini | Bisphenol A , nonylphenols , benzophenones , and benzotriazoles in soils , groundwater , surface water , sediments , and food : a review[END_REF]Liu et al., 2010b;[START_REF] Zhang | Occurrence, distribution, and ecological risks of phthalate esters in the seawater and sediment of Changjiang River Estuary and its adjacent area[END_REF], < 0.1 μg/L in lagoons [START_REF] Pojana | Natural and synthetic endocrine disrupting compounds ( EDCs ) in water , sediment and biota of a coastal lagoon[END_REF], ≤ 0.1 -6 μg/L in coastal seawaters (M 'Rabet et al., 2019;[START_REF] Paluselli | Occurrence of phthalate acid esters (PAEs) in the northwestern Mediterranean Sea and the Rhone River[END_REF][START_REF] Sánchez-Avila | Organic micropollutants in coastal waters from NW Mediterranean Sea: Sources distribution and potential risk[END_REF] and < 0.1 μg/L in ocean [START_REF] Corrales | Global assessment of bisphenol A in the environment : Review and analysis of its occurrence and bioaccumulation[END_REF][START_REF] Zhang | Concentrations and distribution of phthalate esters in the seamount area of the Tropical Western Pacific Ocean[END_REF].

As they are associated with Endocrine Disruptor Chemicals (EDCs), studies have highlighted their hazardous impacts on marine organisms [START_REF] Pojana | Natural and synthetic endocrine disrupting compounds ( EDCs ) in water , sediment and biota of a coastal lagoon[END_REF][START_REF] Rehman | Endocrine disrupting chemicals (EDCs) and fish health-A brief review[END_REF][START_REF] Windsor | Endocrine disruption in aquatic systems: upscaling research to address ecological consequences[END_REF]. BPA and DEHP potentially affect the physiology, growth, metabolism, and reproduction of fishes [START_REF] Kim | Increased plasma levels of phthalate esters in women with advanced-stage endometriosis : a prospective casecontrol study[END_REF][START_REF] Saili | Neurodevelopmental low-dose bisphenol A exposure leads to early lifestage hyperactivity and learning deficits in adult zebrafish[END_REF], crustaceans [START_REF] Cole | Microplastics as contaminants in the marine environment: A review[END_REF][START_REF] Liu | Toxicity of seven phthalate esters to embryonic development of the abalone Haliotis diversicolor supertexta[END_REF], invertebrates [START_REF] Canesi | Bisphenol-A alters gene expression and functional parameters in molluscan hepatopancreas[END_REF][START_REF] Fromme | Occurrence of phthalates and bisphenol A and F in the environment[END_REF][START_REF] Porte | Endocrine disruptors in marine organisms: Approaches and perspectives[END_REF], seabirds [START_REF] Coffin | Fish and seabird gut conditions enhance desorption of estrogenic chemicals from commonly-ingested plastic items[END_REF] and marine mammals [START_REF] Hart | Urinary phthalate metabolites in common bottlenose dolphins (Tursiops truncatus ) from sarasota bay, FL, USA[END_REF][START_REF] Mathieu-Denoncourt | Plasticizer endocrine disruption: Highlighting developmental and reproductive effects in mammals and nonmammalian aquatic species[END_REF][START_REF] Net | Occurrence, fate, behavior and ecotoxicological state of phthalates in different environmental matrices[END_REF].

Studies on their toxic effect were more focused on aquatic organisms possessing an endocrine system while less attention has been given to those lacking this system, such as primary producers. Most studies focused on the ability of microalgae to bioaccumulate, biodegrade, and transfer these molecules to higher trophic levels with little attention being given to their ecotoxicological impact [START_REF] Crain | An ecological assessment of bisphenol-A : Evidence from comparative[END_REF]Liu et al., 2010a;[START_REF] Xu | Environmental fate and ecological risks of nonylphenols and bisphenol A in the Cape D ' Aguilar Marine Reserve , Hong Kong[END_REF]. Nevertheless, recent studies highlighted the significant negative impact of these EDCs on the growth and metabolic activity of some phytoplankton species. For example, contamination with DEHP at 10 mg/L, which is much higher than environmental concentrations, showed growth inhibition and physiological disruption associated with oxidative stress in Chlorophyceae Chlorella vulgaris [START_REF] Shen | Di-( 2-ethylhexyl ) phthalate induced the growth inhibition and oxidative damage in the microalga Chlorella vulgaris Di-( 2-ethylhexyl ) phthalate induced the growth inhibition and oxidative damage in the microalga Chlorella vulgaris[END_REF]. Similarly, a significant biomass decrease was reported with the dinoflagellate Cochlodinium polykrikoides, renamed Margalefidinium polykrikoides [START_REF] Gómez | Molecular characterization and morphology of Cochlodinium strangulatum, the type species of Cochlodinium, and Margalefidinium gen. nov. for C. polykrikoides and allied species (Gymnodiniales, Dinophyceae)[END_REF], upon 72 h of exposure to BPA at 68.5 mg/L [START_REF] Ebenezer | Evaluation of the sub-lethal toxicity of Cu , Pb , bisphenol A and polychlorinated biphenyl to the marine dinoflagellate Cochlodinium polykrikoides[END_REF]. Although the ecotoxicological response of phytoplankton to organic pollutants has been considerably investigated [START_REF] Echeveste | Toxicity of natural mixtures of organic pollutants in temperate and polar marine phytoplankton[END_REF][START_REF] Filimonova | Biochemical and toxicological effects of organic (herbicide Primextra® Gold TZ) and inorganic (copper) compounds on zooplankton and phytoplankton species[END_REF][START_REF] Menezes-Sousa | The plankton role in pollutants dynamics as a tool for ecotoxicological studies[END_REF], nowadays, and to our knowledge, few studies have assessed the impact of EDCs at realistic environmental concentrations.

Interestingly, relevant environmental concentrations of EDCs, resulted in a biomass decrease as well as physiological inhibition, for the potentially toxic dinoflagellate Alexandrium pacificum (C. M 'Rabet et al., 2018) and diatom Nitzschia palea [START_REF] Debenest | Comparative toxicity of a brominated flame retardant (tetrabromobisphenol A) on microalgae with single and multi-species bioassays[END_REF].

Among marine phytoplankton, diatoms are a highly productive and diverse group [START_REF] Norton | Algal biodiversity[END_REF][START_REF] Jensen | The genus Chaetoceros (Bacillariophyceae) in inner Danish coastal waters, Opera Botanica[END_REF]. Diatoms contribute to ocean biodiversity with 136 genera, with a considerable number of species without precise identification (20,000 -200,000) [START_REF] Guiry | How many species of algae are there ?[END_REF][START_REF] Mann | An inordinate fondness? the number, distributions, and origins of diatom species[END_REF]. They are cosmopolitan organisms, occurring in coastal ecosystems, open waters, temperate environments, and polar regions [START_REF] Deng | Growth and physiological responses of a marine diatom ( Phaeodactylum tricornutum ) against two imidazolium-based ionic liquids ([ C 4 mim ] BF 4 and[END_REF][START_REF] Gogorev | The genus Chaetoceros ( Bacillariophyta ) in Arctic and Antarctic[END_REF][START_REF] Malviya | Insights into global diatom distribution and diversity in the world's ocean[END_REF]. Diatoms are one of the principal sources of oxygen production in marine environments accounting for up to 40% of total production [START_REF] Hildebrand | Diatoms, biomineralization processes, and genomics[END_REF]. They are also involved in different biogeochemical cycles, ensuring approximately 20% of CO2 fixation [START_REF] Falkowski | Biogeochemical controls and feedbacks on ocean primary production[END_REF][START_REF] Field | Primary production of the biosphere : integrating terrestrial and oceanic components[END_REF][START_REF] Goldman | Potential role of large oceanic diatoms in new primary production[END_REF]. Due to their characteristics (cosmopolitan, short generation time and efficient proxy for environmental changes), diatoms are commonly used in ecotoxicological studies [START_REF] Fourtanier | Catalogue of the diatom genera[END_REF][START_REF] Puspitasari | Cu toxicity on growth and chlorophyll-a of Chaetoceros sp[END_REF][START_REF] Stevenson | Assessing environmental conditions in rivers and streams with diatoms[END_REF]. They have been classified as bioindicators of aquatic environmental perturbation [START_REF] Hourmant | Effect of Bentazona on growth and physiological responses of diatom: Chaetoceros Gracilis[END_REF][START_REF] Pandey | The use of diatoms in ecotoxicology and bioassessment: Insights, advances and challenges[END_REF].

Within the diatom group, the Chaetoceros genus is considered as one of the most abundant diatoms in marine phytoplankton [START_REF] De Luca | Global distribution and diversity of Chaetoceros ( Bacillariophyta , Mediophyceae ): integration of classical and novel strategies[END_REF], with an abundance that can exceed 8•10 5 during phytoplankton bloom Cells/L [START_REF] Leblanc | A global diatom database -abundance , biovolume and biomass in the world ocean[END_REF][START_REF] Shevchenko | The genus Chaetoceros (Bacillariophyta) from Peter the Great Bay, Sea of Japan[END_REF]. Chaetoceros decipiens is a cosmopolitan species, commonly found in coastal waters as well as in the open sea [START_REF] Balzano | Morphological and genetic diversity of Beaufort Sea diatoms with high contributions from the Chaetoceros neogracilis species Complex[END_REF][START_REF] Batistić | Winter phytoplankton blooms in the offshore south Adriatic waters (1995-2012) regulated by[END_REF][START_REF] Li | Diversity in the globally distributed diatom genus Chaetoceros (bacillariophyceae): Three new species from warm-Temperate waters[END_REF]. In the Mediterranean sea, C. decipiens is one of the dominant phytoplankton species [START_REF] Tas | Diversity and distribution of the planktonic diatom genus Chaetoceros (Bacillariophyceae) in the Golden Horn Estuary (Sea of Marmara)[END_REF][START_REF] Yahia-Kéfi | Spatio-temporal distribution of the dominant Diatom and Dinoflagellate species in the Bay of Tunis (SW Mediterranean Sea)[END_REF]. For example, in the northeastern Adriatic Sea, C. decipiens occurred among the dominant phytoplankton species with 9•10 4 Cells/L [START_REF] Viličić | Composition and annual cycle of phytoplankton assemblages in the northeastern Adriatic Sea[END_REF]. Notably, that several studies reported remarkable similarities between C. decipiens and C. lorenzianus, suggesting the existence of an intermediate form between these two species, the C. decipiens-lorenzianus complex [START_REF] Bosak | Dynamics of the marine planktonic diatom family Chaetocerotaceae in a Mediterranean coastal zone[END_REF][START_REF] Kownacka | Non-indigenous species Chaetoceros cf. lorenzianus Grunow 1863 -A new, predominant component of autumn phytoplankton in the southern Baltic Sea[END_REF][START_REF] Sunesen | Marine diatoms from buenos aires coastal waters (Argentina). V. species of the genus Chaetoceros[END_REF].

In this study, we aimed to understand the impact of two commonly used plastic additives, BPA and DEHP on the cosmopolitan diatom C. decipiens-lorenzianus. Since plastic derived chemicals can have a negative impact on phytoplankton activities, we hypothesized that a representative EDC would provoke growth inhibition and damage of the photosynthetic apparatus expressed through the reduction of photosynthetic efficiency and activity.

Material and methods

2.1-Diatom culture

A strain of the C. decipiens-lorenzianus complex, an autotrophic diatom species, was isolated from Bizerte Channel (South-Western Mediterranean Sea 37.269˚N, 9.877˚E) in December 2016. This diatom strain was grown in F/2 medium (34.5‰ salinity) enriched with silicates [START_REF] Guillard | The ecology of marine planktonic diatoms[END_REF]. The species was maintained under controlled laboratory condition at 22˚C and illuminated at an irradiance level of approximately 110 µmol photons /m 2 •s 1 under a 12:12 light: dark cycle.

Taxonomic identification of the strain

Taxonomic identification was performed using PCR amplification of a partial large subunit of ribosomal DNA (LSU rDNA, 28S). A polymerase chain reaction (PCR) was carried out using 1 µl of concentrated culture resuspended in distilled water. According to Taq Polymerase (Promega) instructions, amplification of the region D1/D2 was obtained using primers D1R and D3B (Nézan et al., 2012). Sequencing products were run on an ABI PRISM 3130 Genetic Analyzer (Applied Biosystems). The obtained sequence was aligned with 145 other sequences of different putative Chaetoceros spp. and two outgroup sequences used by Chen et al (2018) using BioEdit v. 7.0.9.0 software (Hall 1999). Alignment was produced using the MUSCLE v. 3.7 algorithm [START_REF] Edgar | MUSCLE : multiple sequence alignment with high accuracy and high throughput[END_REF]. The resulting matrix comprised 148 OTU and 650 characters. The evolutionary model and parameters were selected after running Smart Model Selection in PhyML [START_REF] Lefort | SMS : Smart model selection in PhyML[END_REF]. For the present dataset, SMS selected the general time reversible (GTR) model with a gamma correction (G) for among-site rate variation and invariants sites. Maximum likelihood analyses were performed using PhyML version 3.0. [START_REF] Guindon | New Algorithms and methods to estimate maximum-likelihood phylogenies : assessing the performance of PhyML 3 . 0[END_REF] and Bayesian analyses were run using Mr Bayes version 3.1.2 [START_REF] Ronquist | MrBayes 3 : Bayesian phylogenetic inference under mixed models[END_REF]. Bootstrap analysis (1000 replicates) was used for the maximum likelihood (ML) to assess the relative robustness of branches (bootstrap values, bv). Initial Bayesian analyses were run with a GTR model (nst = 6) with rates set to invgamma and nucleotide frequencies set to equal. Each analysis was performed using four Markov chains (MCMC) with two millions cycles for each chain. Trees were saved to a file every 100 cycles and the first 2000 trees were discarded. Therefore, a majority-rule consensus tree was created from the remaining 18000 trees to examine the posterior probabilities (pp) of each clade. The consensus trees were edited using TreeView version 1.6.6. The best ML phylograms were shown with their robustness values for each node (ML, bv / BI, pp).

Experimental design

Toxicity experiments were performed with non-axenic batch cultures of C. decipienslorenzianus exposed to BPA and DEHP in 250 mL Erlenmeyer flasks following the protocols of M 'Rabet et al (2018). Inoculum of 300 cells/mL were used to start the culture experiments.

Different nominal concentrations of BPA and DEHP were added separately to the cultures and in mixture (BPA and DEHP), as follow: BPA at 2 μg/L and 20 μg/L, DEHP at 1 μg/L and 10 μg/L, and mixtures with BPA 2 μg/L + DEHP 1 μg/L and BPA 20 μg/L+ DEHP 10 μg/L. Incubations were run in triplicate, with respect to the control conditions (no BPA and DEHP addition), for 144h.

Chemical analyses

Analytical analyses are described in more detail in the supplementary material. BPA and DEHP analysis were performed at the beginning of the experiment (T0) to validate the nominal concentration added, using LC/MS and SPME coupled with GC/MS (M 'Rabet et al., 2019).

Growth measurement

A 1 mL aliquot of each treatment was fixed with acidic lugol to enumerate cell abundances at 0 (incubation-start), 24, 48, 72, 96 and 144 h (incubation-end), to assess the impact on the short, mid-, and long-term exposure to pollutants. Like all phytoplankton species, C. decipienslorenzianus has an exponential growth (lag phase, exponential phase, stationary phase and decline phase). In this study, the cellular concentration was checked by inverted microscope counting (Leica 521,234) during the incubation period. For each treatment, the growth rate (GR) was calculated after logarithmic transformation of the cell density. The following equation was applied: GR = (Ln Ni -Ln Ni-1) / (Ti -Ti-1), where Ni and Ni-1 represent the cell density (cells/mL) at the beginning (Ti-1) and end (Ti) of the exponential phase of the incubation period, respectively [START_REF] Guillard | Kinetics of silicon-limited growth in the marine diatom Thalassiosira pseudonana hasle and heimdal (= Cyclotella nana hustedt)[END_REF].

Photosystem II (PSII) efficiency 2.6.1. Quantum yield of the PSII: FV/FM measurements

To assess the effect of BPA and DEHP on photosynthetic performance, in vivo chlorophyll fluorescence was measured using a portable Pulse Amplitude Modulation fluorometer PSI-AP-100 (AquaPen-Photon Systems Instruments). The OJIP-transient protocol was applied to calculate FV/FM [START_REF] Strasser | The fluorescence transient as a tool to characterize and screen photosynthetic samples[END_REF]. Before measurement, a subsample of 3 mL of each treatment was dark-adapted for 30 min to inactivate the photosynthetic activity according to the manufacturer's operating manual. The quantum yield of PSII was calculated according to the following equation FV/FM = (FM -F0/ FM), where F0 is the minimum fluorescence in the darkadapted state, FM is the maximum fluorescence in the dark-adapted state, and FV is the maximum variable fluorescence yield.

Light curves and photosynthetic parameters (α, PMAX, and EK)

To determine the relative electron transport rate versus irradiance (rETR versus E) curves, the LC3 protocol of the Pulse Amplitude Modulation fluorometer PSI-AP-100 (AquaPen-Photon Systems Instruments) was used. A 3 mL subsample of the phytoplankton culture (from each treatment) were submitted to seven actinic light levels from 10 to 1000μmoL/m 2 •s 1 (10, 20, 50, 100, 300, 500, and 1000 μmoL/m 2 •s 1 ). The hyperbolic tangent model fitted to rETR versus E curves were obtained as indicated by rETR= α * EK * tanh (E * EK -1 ) [START_REF] Jassby | Mathematical formulation of the relationship between photosynthesis and light for phytoplankton[END_REF][START_REF] Silsbe | Modeling the irradiance dependency of the quantum efficiency of photosynthesis[END_REF]. This model was used to estimate the light curve parameters: α (the coefficient of maximal utilization of energy) and EK (the photon flux density from which the quantum efficiency of photosynthetic activity does not increase proportionally to the light intensity). Then, light saturated PMAX was deduced as PMAX = α * EK.

Oxygen metabolism

To evaluate the impact of BPA and DEHP on primary production (GPP) and respiration (R), dissolved oxygen evolution was determined using an oxygen microelectrode (Unisense, Denmark) and the light-dark method [START_REF] Pringault | Consequences of respiration in the light on the determination of production in pelagic systems[END_REF]. A 1 mL vial filled with subsamples from each treatment were used to measure net production (NP) during the light phase and respiration (R) during the dark phase. All vials were exposed to controlled light-dark and temperature conditions. GPP was then calculated as GPP =NP + |R|.

Statistical analyses

Difference between treatments were analyzed by a two-way analysis of variance (ANOVA), considering the incubation time and concentrations of the plastic derived chemicals as independent variables. Data normality and homoscedasticity were checked before the ANOVA test. The growth rate was analyzed by a one-way ANOVA and the Tukey's post hoc test.

Differences were considered as significant at p ≤ 0.05. All statistical analyses were performed using STATGRAPHICS Centurion software (STATGRAPHICS 12.0).

Results

Strain identification

The molecular identification dataset was comprised of 148 LSU and 650 characters. The sequences obtained were aligned with sequences of Chaetoceros spp. from GenBank using MUSCLE (EMBL-EBI) software. The ML phylogenetic tree inferred from the LSU rDNA (28S) dataset revealed that the sequence obtained for the Bizerte strain (MW111279) formed a well-supported group, together with accession number KX065227 and EF423436 of C. decipiens and C. lorenzianus, respectively (ML bootstrap 90). This confirmed that the identified species belonged to the C. decipiens-lorenzianus complex (Figure 1).

Plastic derived chemicals measurement

To confirm the nominal concentrations added to the Chaetoceros cultures, dissolved BPA and DEHP were measured at the beginning of incubation. For all treatments, the measured concentrations of dissolved BPA and DEHP were close to the nominal one (Table S1), regardless of the conditions (single compounds or mixture).

Effect of BPA and DEHP on the growth of C. decipiens-lorenzianus

Cell density in the control showed a regular increase from the beginning (an average of 315 Cells/L) until the end of the incubation period (7 days, 1.56•10 5 Cells/L), associated with a growth rate of 0.82 ±0.05 day -1 . Upon short-term exposure (i.e., during the first 72h), BPA and DEHP contamination induced a slight but significant increase (p < 0.05) in the diatom cell number relative to the control (Figure 2). Simultaneously, growth rates were significantly enhanced (p < 0.05), particularly with the presence of DEHP (Table 1). The most pronounced density increase was observed with BPA and DEHP mixture, both at low and high concentrations, with a growth rate of 1.17 ± 0.07 day -1 and 1.19 ± 0.02 day -1 , respectively, relative to 0.82 ± 0.05 day -1 in the control. Short-term cell stimulation was observed, followed by a return to control levels at the end of the incubation period for all treatments (Figure 2).

Impact of BPA and DEHP on the photosynthetic efficiency

Impact of BPA and DEHP on the quantum yield of PSII

The quantum yield of PSII (FV/FM) in C. decipiens-lorenzianus from the control treatment showed a continual increase from 0.3 to 0.71 during incubation (Figure 3). FV/FM in the contaminated treatments exhibited the same trend as the control conditions. An increase was observed for all treatments from 0.3 to about 0.69 (Figure 3), with no significant differences relative to the control conditions (p > 0.05).

Impact of BPA and DEHP on the photosynthetic performances:

Light-response-curves (LR-curves) and photosynthetic efficiency parameters

The initial measurement of the Light Response-Curve (LR-curve) of C. decipienslorenzianus showed an increase and saturation between 300 to 500 µmol photon/ m 2 •s 1 , followed by clear photo-inhibition above 500 µmol photon/ m 2 •s 1 . Using the photosynthetic model of [START_REF] Jassby | Mathematical formulation of the relationship between photosynthesis and light for phytoplankton[END_REF], characteristic LR-Curve parameters were calculated. The efficiency (α) with which C. decipiens-lorenzianus cells harvested the light was about 0.5 (µmol O2/ mg 1 Chl a•h 1 )/ (µmol photons/ m 2 •s 1 ) in control conditions. The maximum photosynthetic production (PMAX) was about 236.41 (mg C/ mg Chl a l •h l ), at an irradiance (EK) of 117.47 (µmol photon/ m 2 •s 1 ). As observed previously with FV/FM, the same pattern was obtained with photosynthetic performance.

No changes were observed on the LR-curves for all treatments, with no significant differences between contaminated treatments and controls (Figure S1). Concomitantly, no significant differences were observed on the parameters of the photosynthetic efficiency (α, EK, PMAX) (Table S3). Alpha values increased with incubation time to an average of 0.71 (µmol O2/ mg 1 Chl a•h 1 )/(µmol photons/ m 2 •s 1 ), independent of the contamination conditions (Table S3). This increase of α was followed by an increase of Ek and a decrease of PMAX for all treatments (Table S3).

Impact of BPA and DEHP on O2 metabolism

O2 metabolism was evaluated through the measurement of gross primary production (GPP) and respiration (R). In the control treatment, the photosynthetic activity varied between GPP0h = 0.3 ± 0.1 μmol O2/ L •min (R0h= 0.1 ± 0.001 μmol O2/ L •min) and GPP144h = 1.46 ± 0.01 μmol O2/ L •min (R144h= 0.38 ± 0.02 μmol O2/ L •min). As observed previously with the biomass of C. decipiens-lorenzianus, GPP in the contaminated treatments showed a slight, but significant (p < 0.05) stimulation (Figure 4A-C) within the first 72 h of incubation relative to the control conditions, particularly with BPA at a high concentration (0.6 ±0.1 μmol O2/ L •min) relative to the control (0.4 ± 0.04 μmol O2/ L •min, Figure 4A). Similarly, GPP stimulation was concomitant to slight but significant (p < 0.05) respiration stimulation within the first hours of incubation (Figure 4D-F). Short-term O2 metabolism stimulation was followed by a return to control levels in all treatments. Overall, no significant differences were observed in the ANOVA test (p > 0.05) when the whole incubation time was considered. From GPP values and cell densities, the specific phytoplankton activity was calculated (specific GPP = GPP / Cell density). Considering the total experimental period (7 days), the specific GPP of all treatments did not vary significantly relative to the control (Figure 5).

Discussion

Molecular analyses performed on the strain isolated from the Bizerte lagoon (MW111279) formed a common sub-group between C. decipiens and C. lorenzianus (Figure 1). This signature led us to confirm that the identified strain belongs to the C. decipiens-lorenzianus complex.

Previous studies reported close similarities between these two diatom species in different areas of the world including the north-eastern Adriatic Sea, the southern Baltic Sea, and the coast of Buenos Aires Province, Argentina [START_REF] Bosak | Dynamics of the marine planktonic diatom family Chaetocerotaceae in a Mediterranean coastal zone[END_REF][START_REF] Kownacka | Non-indigenous species Chaetoceros cf. lorenzianus Grunow 1863 -A new, predominant component of autumn phytoplankton in the southern Baltic Sea[END_REF][START_REF] Sunesen | Marine diatoms from buenos aires coastal waters (Argentina). V. species of the genus Chaetoceros[END_REF], suggesting the existence of an intermediate form of both C. decipiens and C. lorenzianus.

Despite the high accumulation of plastic debris in the marine environments, BPA and DEHP occur at low concentrations, in the range of 6 µg/L (M' RABET et al., 2019;[START_REF] Paluselli | Occurrence of phthalate acid esters (PAEs) in the northwestern Mediterranean Sea and the Rhone River[END_REF][START_REF] Sánchez-Avila | Organic micropollutants in coastal waters from NW Mediterranean Sea: Sources distribution and potential risk[END_REF], close to those used in the present study (Table S1). To assess their toxicity on a representative of marine primary producers, we selected the cosmopolitan diatom C. decipiens-lorenzianus, considering its large marine occurrence. This species is commonly observed in coastal ecosystems, as well as in open waters [START_REF] Bosak | Dynamics of the marine planktonic diatom family Chaetocerotaceae in a Mediterranean coastal zone[END_REF][START_REF] Gogorev | The genus Chaetoceros ( Bacillariophyta ) in Arctic and Antarctic[END_REF]. Species belonging to the genus Chaetoceros contribute considerably to ocean primary production [START_REF] Booth | Dynamics of Chaetoceros socialis blooms in the North Water[END_REF]. In this study, we isolated strains of C. decipiens-lorenzianus, that were grown under non-axenic conditions, as microscopic observation revealed the presence of bacteria associated with the diatom. Moreover, the experimental conditions were chosen to mimic in situ conditions as much as possible, where the diatoms are naturally associated to bacteria [START_REF] Amin | Interactions between Diatoms and Bacteria[END_REF][START_REF] Vincent | Diatoms Are Selective Segregators in Global Ocean Planktonic Communities[END_REF].

Transient stimulation of C. decipiens-lorenzianus: first hypothesis

At realistic environmental concentration of EDCs, the cosmopolitan diatom C. decipienslorenzianus showed a relative tolerance to BPA and DEHP after 7 days of incubation. In all treatments, a transient slight but significant stimulation of biomass and photosynthetic activity was observed, especially upon DEHP exposure. Two hypotheses can be proposed to explain this significant transient stimulation.

First, the stimulation of biomass and oxygen gross production might be explained by the direct impact of the environmental concentration of EDCs on the photosynthetic apparatus, as recently observed in microalgae cultures. A recent work highlighted that BPA released from small fragments of expanded polystyrene (EPS) at a concentration of 1.5 ng/L provoked a significant stimulation of the photosynthetic efficiency of Chlorophyceae species [START_REF] Chae | Photosynthesis enhancement in four marine microalgal species exposed to expanded polystyrene leachate[END_REF]. They showed that BPA exposure significantly stimulated the quantum yield of PSII (FV/FM), which consequently induced a growth stimulation of several phytoplankton strains (Dunaliella salina, Scenedesmus rubescens, Chlorella saccharophila, and Stichococcus bacillaris) [START_REF] Chae | Photosynthesis enhancement in four marine microalgal species exposed to expanded polystyrene leachate[END_REF].

Furthermore, this would suggest that BPA and DEHP contamination at environmental concentrations can stimulate the photosynthetic apparatus of phytoplanktonic cells, subsequently inducing the stimulation of biomass and photosynthetic activity. Nevertheless, in our study photosynthetic efficiency of PSII, measured through the Fv/Fm ratio, as well as specific activity (Figure 3 and 5), were not significantly impacted by the presence of BPA or DEHP. Consequently, a direct transient effect of EDCs on PSII of C. decipiens-lorenzianus cannot explain the short-term stimulation observed for growth and oxygen production.

Transient stimulation of C. decipiens-lorenzianus: second hypothesis

The second hypothesis to explain this transient significant stimulation relies on the presence of bacteria in the diatom culture. Recently, Romera-castillo et al (2018) demonstrated that bacterial activity was stimulated in response to phthalate exposure when released from polyethylene (PE) and polypropylene (PP). They observed that PE and PP particles in seawater promoted the release of dissolved organic carbon (DOC), which induced the stimulation of bacterial activity.

In the present study, although DOC was not measured, we speculated that BPA and DEHP promoted the metabolic activity of bacteria associated with C. decipiens-lorenzianus, which in turn induced biomass and photosynthetic stimulation. The microbiome associated with the non-axenic diatom might have benefited from diatom-bacterium interactions. In fact, this association can promote synergistic interactions between both compartments, through the availability of nutrients, such as vitamins (B1 and B12), iron, DOC, and nitrogen [START_REF] Amin | Interactions between Diatoms and Bacteria[END_REF][START_REF] Seymour | Zooming in on the phycosphere: The ecological interface for phytoplankton-bacteria relationships[END_REF].

We hypothesized that the short-term observed stimulation of C. decipiens-lorenzianus upon EDC exposure at environmental conditions could be the consequence of a cascading effect of BPA and DEHP on its phycosphere, which subsequently induced cell growth and photosynthetic activity stimulation. Furthermore, phytoplankton possess a unique microbiome [START_REF] Behringer | Bacterial communities of diatoms display strong conservation across strains and time[END_REF] that could act as a protective barrier [START_REF] Fouilland | Influence of bacteria on the response of microalgae to contaminant mixtures[END_REF][START_REF] Ramanan | Algae -bacteria interactions : Evolution , ecology and emerging applications[END_REF] against toxic contaminant effects, ensuring an optimal phytoplankton production. The association between the cosmopolitan C. decipiens-lorenzianus and its phycosphere could form an effective consortium able to cope with the toxic effects of BPA and DEHP at realistic environmental concentrations. In addition, the large size of C. decipiens-lorenzianus might represent a defense mechanism, relative to other smaller phytoplankton cells. The low cell volume ratio of diatoms reduces the diffusion of organic pollutants through the cell relative to smaller phytoplankton cells, favoring their tolerance to chemical contamination [START_REF] Ben Othman | Toxicity of benz(a)anthracene and fluoranthene to marine phytoplankton in culture: Does cell size really matter?[END_REF][START_REF] Staniszewska | The role of phytoplankton composition, biomass and cell volume in accumulation and transfer of endocrine disrupting compounds in the Southern Baltic Sea (The Gulf of Gdansk)[END_REF].

Situation of the ecotoxicological answer of C. decipiens-lorenzianus compared to other species

Previous works studying the ecotoxicological impacts on microalgae have often used higher concentrations of EDCs than those employed in the present study (Table S1). Significant toxic effects of EDCs on phytoplankton were reported for concentrations far above the observed in situ concentrations. For example, growth and activity inhibition were observed with diatom species at high BPA concentration of > 0.04 mg/L with Ditylum brightwelli and Navicula incerta [START_REF] Lee | Different transcriptional responses of heat shock protein 20 in the marine diatom Ditylum brightwellii exposed to metals and endocrine-disrupting chemicals[END_REF]Liu et al., 2010a). Similarly, a high EC50 was measured for the Chlorophyceae Chorella vulgaris (6.02 mg/L) with DEHP [START_REF] Shen | Di-( 2-ethylhexyl ) phthalate induced the growth inhibition and oxidative damage in the microalga Chlorella vulgaris Di-( 2-ethylhexyl ) phthalate induced the growth inhibition and oxidative damage in the microalga Chlorella vulgaris[END_REF] and for the diatom Chaetoceros muelleri (EC50 at 96 h: 194 mg/L) with diethyl phthalate [START_REF] Chi | Interaction between three marine microalgae and two phthalate acid esters[END_REF]. Recent ecotoxicological works studying the impact of EDCs at environmental realistic concentrations have observed contrasting effects depending on the phytoplankton species studied. Exposure to EDCs drastically inhibited the biomass and physiological activity of the toxic dinoflagellate Alexandrium pacificum at concentrations of 2 and 20 µg/L BPA and 1 and 10 µg/L DEHP, similar to those used in the present study M 'Rabet et al (2018). Similarly, [START_REF] Cunha | Ecotoxicological and biochemical e ff ects of environmental concentrations of the plastic-bond pollutant dibutyl phthalate on Scenedesmus sp[END_REF] observed significant inhibition of cell abundance after exposure of a Chlorophyceae Scenedesmus sp. to dibutyl phthalate (DBP).

They reported an EC50 after 48 h of DBP exposure of 41.88 µg/L. In contrast, [START_REF] Chae | Photosynthesis enhancement in four marine microalgal species exposed to expanded polystyrene leachate[END_REF] showed that BPA at 0.0019 µg/L enhanced the photosynthetic activity, as well as the growth of Chlorophyceae species. Thus, these observations indicate that the ecotoxicological impact of EDCs on phytoplankton at relevant environmental concentrations is very likely species dependent.

Conclusions

Overall, results of the present study highlighted that in simulating environmental conditions, the cosmopolitan diatom C. decipiens-lorenzianus was not significantly impacted by BPA and DEHP contamination, the two most observed EDCs in contaminated marine ecosystems.

This apparent tolerance might rely on the heterotrophic compartment associated with the diatom Chaetoceros. This laboratory ecotoxicological study confirms what was observed at the community scale, where environmentally relevant EDC contamination promoted the dominance of the genus Chaetoceros relative to other phytoplankton species (M 'Rabet et al., 2019). Future ecotoxicological studies are required to better understand the possible role of the phycosphere associated with Chaetoceros to face EDC contamination.

Tables and figures

Figure 1 :Figure 2 :Figure 3 :FFigure 4 :Figure 5 :

 12345 Figure 1: Maximum likelihood (ML) phylogenetic tree based on LSU rDNA sequences (148 sequences/650 characters). The tree was rooted using Lithodesmium / Ditylum as out-group

Table S3 :Figure S1 :

 S3S1 photon. m -2 .s -1 . The letters (a-c) indicate homogeneity of different treatments (P < 0.05)

Table 1 :

 1 Growth rate (/day) of Chaetoceros decipiens-lorenzianus during the exposure to BPA and/or DEHP mean of three replicate ± standard deviation (SD), the letters (a-d) indicate homogeneity of different treatments (P < 0.05).

	Treatment	Growth rate
	Control	0.82 ±0.05 a
	BPA 2µg/L	0.85 ±0.02 a
	BPA 20µg/L	0.80 ±0.05 a
	DEHP 1µg/L	1.11 ±0.03 c
	DEHP 10µg/L	0.98 ±0.02 b
	BPA 2µg/L & DEHP 1µg/L	1.17 ±0.07 cd
	BPA 20µg/L & DEHP 10µg/L	1.19 ±0.02 d

relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This study was supported by the LMI COSYS-MED project and the Tunisian National Agronomic Institute (INAT) -IRESA, LR18ES41 laboratory (Laboratoire des Sciences de l'Environnement, Biologie et Physiologie des Organismes Aquatiques, Faculté des Sciences de Tunis, Université Tunis EL Manar). Charaf M'RABET benefited from a PhD grant by the French Institute of Research for Development (IRD). The authors would like to thank Mrs. Elizabeth Nézan (Ifremer) for sharing her Chaetoceros microscopic pictures and Ms. Diana M'Rabet for designing the logo used in the graphical abstract.

Conflict of interest

The authors declare that they have no known competing financial interests or personal

Supplementary material

BPA and DEHP chemical analysis

DEHP was analyzed using Solid-Phase Micro-Extraction (SPME) coupled with Gas Chromatography/Mass Spectrometry (GC/MS). For the extraction of water samples, 100 μm fiber SPME-PFMS (Supelco) was used. The quality parameters of the SPME were: i) an immersion of the fiber in liquid phase (15 mL of the sample), ii) an incubation temperature of 65 °C, iii) an incubation time of 5 min, iv) agitation 250 rpm and v) 30 min for extraction and 3 min for desorption. DEHP analysis was performed with GC/MS working in electro-ionization impact mode (GC-7890 A; MSD-5975C, Agilent Technologies). An HP5MS-UI column (5% phenyl methyl siloxane, 30 m × 0.25 mm ID × 0.25 μm phase thickness, Agilent Technologies) was used.

BPA analysis was performed using Liquid Chromatography/tandem Mass Spectrometry (LC/MSMS) in a negative ionization mode (UPLC Acquity; MSMS-Quattro Premier XE, Waters).

The cartridge used was an Acquity UPLC BEH C18 (50 mm × 2.1 mm ID × 1.7 μm granulometry, Waters). Direct injection volume was set at 40 μL. The quality parameters of chromatography were as follows: i) solvent tank A: milliQ-water with 0.5 mM ammonium acetate, ii) solvent tank B: methanol, iii) a mobile phase flow rate of 0.5 mL min-1. BPA and DEHP were analyzed following the analytical protocols of (Dévier et al., 2013) for DEHP and of (Gagnaire et al., 2009) for BPA (information about the validation parameters in Table S2).


F Abbate
email: abbate@mpifr-bonn.mpg.de

A Ridolfi

E D Barr

S Buchner

M Burgay

D J Champion

W Chen

P C C Freire

T Gautam

J M Grießmeier

L Künkel

M Kramer

P V Padmanabh

A Possenti

S Ransom

M Serylak

B W Stappers

V Venkatraman Krishnan

J Behrend

R P Breton

L Levin

Y Men

Four pulsar discoveries in NGC 6624 by TRAPUM using MeerKAT

Keywords: Star, neutron -Pulsars, general -globular clusters, individual, NGC 6624

We report 4 new pulsars discovered in the core-collapsed globular cluster (GC) NGC 6624 by the TRAPUM Large Survey Project with the MeerKAT telescope. All of the new pulsars found are isolated. PSR J1823-3021I and PSR J1823-3021K are millisecond pulsars with period of respectively 4.319 ms and 2.768 ms. PSR J1823-3021J is mildly recycled with a period of 20.899 ms, and PSR J1823-3022 is a long period pulsar with a period of 2.497 s. The pulsars J1823-3021I, J1823-3021J, and J1823-3021K have position and dispersion measure (DM) compatible with being members of the GC and are therefore associated with NGC 6624. Pulsar J1823-3022 is the only pulsar bright enough to be re-detected in archival observations of the cluster. This allowed the determination of a timing solution that spans over two decades. It is not possible at the moment to claim the association of pulsar J1823-3022 with the GC given the long period and large offset in position (∼ 3 arcminutes) and DM (with a fractional difference of 11 percent compared the average of the pulsars in NGC 6624). The discoveries made use of the beamforming capability of the TRAPUM backend to generate multiple beams in the same field of view which allows sensitive searches to be performed over a few half-light radii from the cluster center and can simultaneously localise the discoveries. The discoveries reflect the properties expected for pulsars in core-collapsed GCs.

O R I G I N A L U N E D I T E D M A N U S C R I P T 1 INTRODUCTION
NGC 6624 is a globular cluster (GC) located in the bulge close to the Galactic center (Galactic coordinates 𝑙 = 2 • .78, 𝑏 = -7 • .91) at a distance from the Sun of 8.0 ± 0.1 kpc (Baumgardt & Vasiliev 2021) and a Galactocentric radius of 1.2 kpc1 . The stellar distribution in the central regions of the GC is not flat but shows a "cusp" that is typical of systems that have undergone core collapse (Sosin & King 1995;Noyola & Gebhardt 2006). This GC is known to contain eight pulsars (Biggs et al. 1994;Lynch et al. 2012;Ridolfi et al. 2021) of which six are millisec-ond pulsars (MSPs) and two long-period pulsars. Only two pulsars J1823-3021F and J1823-3021G are known to be part of binary systems. J1823-3021G is a binary pulsar in an eccentric orbit typical of an exchange encounter that has the potential of being one of the most massive known pulsars (Ridolfi et al. 2021). Two pulsars have long spin periods, J1823-3021B has a period of 378.59 ms and J1823-3021C has a period of 405.93 ms. Both have short characteristic ages, respectively 190 and 30 Myr, which is at odds with the regular pulsar formation scenario. The pulsars should have formed recently but the lack of star formation in this globular cluster in the last few Gyrs implies that no massive stars were around to form them. This could suggest that these pulsars were old, unrecycled NSs that were, thanks to exchange encounters, incorporated in X-ray binaries, where they started being spun up by accretion of matter from their new companions. Because of the high stellar densities in these clusters, these X-ray binaries were disrupted before the pulsar's magnetic field decreased to the typical values observed in "fully recycled" MSPs [START_REF] Verbunt | [END_REF]. Alternative formation scenarios have been put forward to explain the presence of such pulsars like accretion-induced collapse, direct collisions with a main sequence star (Lyne et al. 1996), or electron capture supernova of an OMgNe white dwarf (Boyles et al. 2011).

The isolated MSP J1823-3021A also has a very high spin period derivative, and also a small characteristic age of 25 Myr. It was suggested that the period derivative is heavily influenced by the gravitational potential of the GC and that it could be a sign of the presence of an intermediate mass black hole in the centre of NGC 6624 (Perera et al. 2017a,b). However, the pulsar also shows remarkably strong gamma-ray flux implying that a significant fraction of the spin down must be intrinsic and the magnetic field has to be considerably higher than that of the average MSP (Freire et al. 2011). A higher number of pulsars close to the cluster centre would allow to test whether an intermediate mass black hole is really present.

The properties of the pulsars in NGC 6624 are quite different from the typical GC but are similar to those GCs that have undergone corecollapse. [START_REF] Verbunt | [END_REF] have shown that this difference can be quantified by the encounter rate for a single binary in the GC which represents the likelihood of any particular binary system to undergo dynamical encounters; this is ∼ 4 times higher for core collapsed clusters than non collapsed clusters. GCs with high values of this parameter usually show a larger fraction of isolated pulsars, pulsars with longer spin periods, pulsars distributed over large radii outside of the core, and binaries produced in exchange encounters.

The high value of the encounter rate of this GC (the ninth highest of all the Galactic GCs and ∼ 1.1 times the value of 47 Tucanae, Bahramian et al. 2013) suggests that a larger population of pulsars is still undiscovered in this GC, while the high encounter rate per binary (second highest within all GCs with 3 or more known pulsars and ∼ 6 times the value of 47 Tucanae, Verbunt & Freire 2014) suggests the new discoveries might have gone through dynamical interactions like exchange encounters that could form exotic objects such as eccentric double neutron star systems. For these reasons, NGC 6624 was considered as a high priority target in the pulsar searches in GCs with the MeerKAT radio telescope in South Africa (Jonas & MeerKAT Team 2016;Camilo et al. 2018). Two of the Large Survey Projects (LSP) that are observing with the telescope, MeerTime2 [START_REF] Bailes | MeerKAT Science: On the Pathway to the SKA[END_REF][START_REF] Bailes | [END_REF] and TRansients And PUlsars with Meerkat (TRAPUM)3 [START_REF] Stappers | MeerKAT Science: On the Pathway to the SKA[END_REF] have the search and timing of pulsars in GCs as one of the science goals. Together the two projects have discovered more than 40 new pulsars in GCs4 .

Given the scientific overlap, the two projects have decided to share resources and observing time. The collaboration has already resulted in two publications regarding NGC 6624: a detailed study of the giant pulses from J1823-3021A (Abbate et al. 2020) and the discovery of two new MSPs (Ridolfi et al. 2021) in this cluster. The massive eccentric binary J1823-3021G discovered in the latter work is an example of the interesting new pulsars still to be discovered. These results were obtained using observations taken with the Pulsar Timing User Supplied Equipment (PTUSE) machines made available by MeerTIME with data from only the central 44 antennas of the 64 available. This number was chosen so that the maximum baseline would be below 1 km and the tied array beam would be large enough to cover the central regions of the cluster. The observations were carried out at L-band (856-1712 MHz) and the tied array beam had a radius of ∼ 0.5 arcmin.

In this paper we present the observations and discoveries made using the Filterbanking Beamformer User Supplied Equipment (FB-FUSE) and Accelerated Pulsar Search User Supplied Equipment (APSUSE) backend provided by TRAPUM. Together these machines are able to synthesize and record of order 500 coherent beams for use in pulsar and fast transient searching. Using all of the available antennas it is possible to cover, with a large number of small tiedarray beams, an area as large as 1 -4 arcmin in radius depending on the configuration (Chen et al. 2021). This is enough to extend up to more than twice the reported half-light radius of the GC of ∼ 1 arcmin (Baumgardt & Hilker 2018). The sensitivity is ∼ 1.5 times higher when compared with the previous PTUSE observations in the center of the GC and it gets increasingly higher the further away we look. The area that can be searched is also larger allowing for further discoveries in this GC.

TRAPUM OBSERVATIONS

The observations performed with the FBFUSE and APSUSE machines of TRAPUM that have been searched for new pulsars were performed using 60 antennas in L-band (856-1712 MHz) on the 21st of May 2020 and the 11th of August 2020. In both observations we synthesized 288 coherent beams. The beam shape depends on the exact configuration of the antennas and position in the sky, we can estimate its size with an elliptical fit. In both observations the semimajor axis of the elliptical fit at 50 percent of the power is 17 arcsec at the central frequency of 1284 MHz and semi-minor axis is 10 arcsec. In the first observation, the average overlap fraction between neighbouring beams at the central frequency was ∼ 0.8 resulting in a total area covered of ∼ 2.6 arcmin in radius from the center. For the second observation the overlap was set at ∼ 0.7 and the area covered was increased to ∼ 3.1 arcmin in radius. The tiling pattern of the two observations was determined using the software Mosaic5 (Chen et al. 2021) and is shown in Figure 1. In both cases, the observation length was 4 hours. The first observation was already described in Ridolfi et al. (2021) and was used to localise the known pulsars.

The total intensity data from each coherent beam was recorded in filterbank mode with a time resolution of 76 𝜇s and a bandwidth of 856 MHz, centred around 1284 MHz and divided into 4096 channels. After the observation was concluded, the data were incoherently de-dispersed at the dispersion measure (DM) of 86.88 pc cm -3 , corresponding to the DM of J1823-3021A located near the center of the cluster as measured by MeerKAT observations in the same band (Abbate et al. 2020). The Inter-Quartile Range Mitigation algorithm6 (Morello et al. 2021) was applied to filter out the brightest Radio Frequency Interference (RFI) and the channels were averaged by a factor of 16 resulting in 256 channels across the full bandwidth to reduce disk usage.

Most of the known pulsars in NGC 6624 have DMs between 86.2 and 87.0 pc cm -3 with the exception of J1823-3021E that has a DM of 91.4 pc cm -3 . We decided to search for pulsars between a DM of 80 and 95 pc cm -3 with a DM step size of 0.05 pc cm -3 to allow for a greater spread in DM in the potential candidates. Given the reduced number of channels, the pulse of a potential pulsar will be affected by smearing if the DM does not match the value applied during de-dispersion of 86.88 pc cm -3 . The smearing caused by the DM in the worst affected channel goes from 0.3 ms for a DM of 80 pc cm -3 to 0.4 ms for a DM of 95 pc cm -3 . This effect will reduce the sensitivity of our search for rapidly spinning pulsars if the DM is far from the value chosen before reducing the number of channels.

O R I G I N A L U N E D I T E D M A N U S C R I P T 3 2 1 0 1 2 3 RA -18h 23m 40.
The searching procedure was carried out using PULSAR_MINER7 based around the PRESTO pulsar searching package (Ransom et al. 2002) and described in detail in Ridolfi et al. (2021). The beams were searched for both isolated and binary pulsars by performing a search in Fourier space. In the case of binary pulsars, the acceleration along the line of sight, 𝑎 𝑙 , shifts the observed spin frequency of a potential pulsar over the length of the observation, 𝑡 obs , by a number of 𝑧 = 𝑡 2 obs 𝑎 𝑙 /𝑐𝑃 Fourier bins, where 𝑐 is the speed of light and 𝑃 is the period of the potential pulsar. The search is performed up to a maximum of 𝑧 max of 200. This type of search is effective as long as the acceleration remains constant over the observation which is a reasonable assumption if 𝑡 obs ≲ 0.1𝑃 b , where 𝑃 b is the orbital period (Ransom et al. 2003). In order to search for binary pulsars with short orbital periods, we split the observation in to segments of 60 minutes and 20 minutes and repeated the search in each segment. This strategy allowed us to be sensitive to pulsars in orbits longer than ∼ 200 minutes.

Of all the candidates that were found in the search only the ones with a Fourier significance of more than 4𝜎 in adjacent DM trials were kept. After removing harmonically related candidates and periodic RFI, the remaining candidates were visually inspected. In order to confirm that the candidates found are real pulsars, we checked if the same candidate appears in neighbouring beams of the same observation or in beams pointing in the same direction in both observations. Additionally, for the most interesting candidates, we folded the corresponding beam of the other observation at the period and DM of the candidate for further confirmation. After a candidate has been confirmed, we derived an approximate ephemeris based on the detection, folded the observation using the DSPSR8 pulsar package (van Straten & Bailes 2011) and run the pdmp routine of PSRCHIVE9 (Hotan et al. 2004;van Straten et al. 2012) to improve the quality of the detection. To obtain the best value of DM we first averaged the frequency channels of the best detection from 256 to 8 and extracted times-of-arrival (ToAs) at each channel with the pat routine of PSRCHIVE using a single template. We used TEMPO210 (Hobbs et al. 2006) to fit these ToAs leaving the DM as the only free parameter.

Finally, the flux density of the pulsars was measured using the radiometer equation [START_REF] Lorimer | Handbook of Pulsar Astronomy[END_REF]:

𝑆 = (S/N) best 𝑇 sys 𝐺 √ 𝑛 𝑝 𝑡 obs Δ 𝑓 √ 𝑊 𝑃 -𝑊 , (1)
where (S/N) best is the signal to noise ratio (S/N) of the best detection of the pulsar, 𝑇 sys is the system temperature of the telescope taken to be 26 K for the observations11 , 𝐺 = (𝑁 ant /64)×2.8 K Jy -1 is the gain of the telescope and depends on 𝑁 ant the number of antennas used in the observation, 𝑛 𝑝 = 2 is the number of polarisations summed, 𝑡 obs knowledgebase/latest/articles/view/277315585

is the length of the observation, Δ 𝑓 is the effective bandwidth taken to be 700 MHz after the RFI cleaning and 𝑃 is the period of the pulsar. 𝑊 is the equivalent width of the pulse defined as the width of a top-hat function with the same height and same total area as the pulsar profile.

DISCOVERIES

Four new pulsars were discovered of which three can safely be considered members of the GC. The profiles of the new discoveries are shown in Fig. 2 while the period, position, values of DM and flux density are shown in Table 1 and in Fig. 3.

J1823-3021I

PSR J1823-3021I is an isolated MSP with a rotational period of 4.319 ms and DM of 87.31 pc cm -3 . The profile has a single component with equivalent width of 0.61 ms. It was detected by the pipeline in the first observation in the central beam and in two neighbouring beams south of the center. After folding the second observation at the discovery period and DM, the pulsar showed up in the central beam.

The position near the center of the cluster and the value of the DM which is compatible with the other pulsars suggest that this new discovery is associated with the cluster.

J1823-3021J

PSR J1823-3021J is another isolated pulsar. It has a rotational period of 20.899 ms, DM of 86.82 pc cm -3 and was found in the central beam of the second observation. The profile has a single component with equivalent width of 1.96 ms. It was confirmed after folding the central beam of the first observation at the discovery period and DM.

The DM is compatible with the other known pulsars and it is located in the core of NGC 6624, this suggests that this pulsar is a member of the cluster. Its rotational period is higher than what we would expect for MSPs if the recycling process was allowed to continue uninterrupted. A possible explanation is that the binary was disrupted by a dynamical interaction during the accretion phase. These types of pulsars are known to be present not only in NGC 6624 (B and C), but also in several other GCs with high encounter rate per binary like e.g. M 15, NGC 6440, NGC 6441 (Freire et al. 2008) and NGC 6517 [START_REF] Lynch | [END_REF]Pan et al. 2021).

J1823-3021K

PSR J1823-3021K is the third new isolated pulsar we found in the cluster. It has a rotational period of 2.768 ms and a DM of 87.50 pc cm -3 . It has a single broad component with equivalent width of 0.89 ms. It was found in a beam of the first observation distant ∼ 1.4 arcminutes from the center and in two neighbouring beams with lower S/N. It was also found by the pipeline in the four beams of the second observation corresponding to the same location. It is the most rapidly spinning known pulsar in this GC.

This pulsar is located at about ∼ 1.4 arcminutes from the center at about ∼ 1.4 times the half-light radius. Given that the DM is close to the rest of the known pulsars and that it is an isolated MSP, it is reasonable to assume that it is a member of NGC 6624. Table 1. Properties of the newly discovered pulsars in the observations of NGC 6624. We report the barycentric period, DM, position and flux density derived from the radiometer equation. For pulsars I and K we report the position found using the SeeKAT software. For pulsar J the software could not be used and we report the position of the beam at the center of the cluster were the pulsar was found. For pulsar J1823-3022 we report the position derived by timing. Numbers in parentheses represent 1-𝜎 uncertainties in the last digit.

O R I G

Summary of

J1823-3022

PSR J1823-3022 is an isolated bright pulsar with a period of 2.4978 seconds and a DM of 96.7 pc cm -3 . It has a single component with equivalent width of 49 ms. It was found near the edge of the tiling of the second observation appearing brightest in the beam on the edge of the tiling and, with lower S/N, in 4 surrounding beams. This position was not covered in the tiling of the first observation but the pulsar still appears by folding at the discovery period and DM in one beam of the first observation as shown in Fig. 1. The pulsar was so bright that it was possible to see single pulses coming from the pulsar. We detected 27 single pulses with S/N higher than 7 corresponding to 0.5 percent of all the rotations of the pulsar over the course of 4 hours of observations.

The pulsar was found with the highest S/N in a beam at the edge of the tiling. It is possible, therefore, that the true position is further away from the cluster center than we measured. In order to localise the source we made an additional observation on the 7th of November 2021 using only 38 antennas in L-band and forming only 17 beams with an average overlap at the central frequency of ∼ 0.7 around the position of the beam with the highest S/N as shown in Fig. 4. The pulsar was detected in all of the beams of this observation but also in this case the beam with the highest S/N was the furthest from the centre along the edge of the tiling.

Using the detected period and provisional position, we folded archival observations of the cluster made over the years with MeerKAT, the Parkes radio telescope and the Green Bank Telescope (GBT). Previous MeerKAT observations carried out with the PTUSE backend had a tied array beam of just ∼ 0.5 arcminutes while the pulsar appears to be located at ∼ 3 arcminutes. Despite this, the pulsar was detected in an observation made at UHF-band (550-1050 MHz) where the beam size is significantly larger. We were able to detect the pulsar in an observation at Parkes from 1999 using the Analog Filterbank in the frequency range 1240-1497 MHz and in a recent one from 2019 using the Pulsar Digital Filterbank 4 in the same frequency range. We were also able to detect the pulsar in observations taken around 2009 at the GBT with the GUPPI backend in the frequency range 1600-2400 MHz and in a set of observations taken around 2020 using the VEGAS backend both in the frequency range 1100-1900 MHz and in the frequency range 1600-2400 MHz. This was possible because the beams of Parkes and GBT in the sky are large enough to cover the position of J1823-3022. The pulsar was not detected sooner in these observations likely because of the bright broadband RFI that appear at these long periods. These RFI can also be seen in the TRAPUM observations and cause the variations in the baseline of the profile shown in Fig. 2.

Thanks to these detections, we were able to determine a phaseconnected timing solution for J1823-3022 that spans over two decades from 1999 to 2022. The timing solution is shown in Table 2 and the residuals of the ToAs are shown in Fig. 5. The position found coincides with the beam with highest S/N in the observation of the 7th of November 2021 as shown by the black ellipse in Fig. 4.

The position of the pulsar derived by timing places it at 2.99 arcminutes from the center or ∼ 3 times the half-light radius of the cluster. This is almost twice the half-mass radius of ∼ 1.58 arcminutes (Baumgardt & Hilker 2018), but still inside the estimated tidal radius of the cluster, corresponding to ∼ 8. Table 2. Timing solution for J1823-3022 as derived from the timing of the observed ToA with TEMPO2. The time units are TDB, the adopted terrestrial time standard is TT(TAI) and the Solar System ephemeris used is JPL DE421 (Folkner et al. 2009). Numbers in parentheses represent 1-𝜎 uncertainties in the last digit. pulsars so far from the center of a GC is rare but a few exceptions are known in other core collapsed clusters like B1718-19A (Lyne et al. 1993), located ∼ 2.6 half-mass radii from the center, J1911-5958A (D'Amico et al. 2001), distant ∼ 1.4 half-mass radii from the center, and J1801-0857D, located ∼ 1.4 [START_REF] Lynch | [END_REF] half-mass radii from the center.

The DM is ∼ 10 pc cm -3 higher than the average DM value than for the pulsars located in the center of the GC and significantly higher than the rest of the known pulsars. It is outside the range of DM initially searched but it was still detected thanks to its slow period. The incorrect DM causes a delay in the arrival times of the pulse at different frequencies that is in the order of 5 ms for every unit of DM in L-band. This is smaller than the pulse width of the new discovery and therefore does not impact the detectability. Such a high difference in DM has only been seen in two GCs, Terzan 5 and NGC 6517 but in both cases the central value of DM is more than twice that of NGC 6624.

The DM distribution of the known pulsars in the GC is shown in Figure 3. Most of the pulsars have DM within 86 and 88 pc cm -3 while J1823-3021E has a DM significantly higher than the rest at 91.4 pc cm -3 . J1823-3021E is certainly associated with the cluster given that it is an isolated MSP and is located within the half-light radius. We can conclude that the intervening medium along the line of sight can change the DM of the order of 4 pc cm -3 over a distance of ∼ 1 arcminute. This intervening medium can either be located inside the cluster or in the Galaxy along the line of sight. Applying this argument to J1823-3022 we can conclude the DM excess of ∼ 10 pc cm -3 over 3 arcminutes could be explained by foreground material and that the pulsar could be part of the cluster. Alternatively we can look at a Galactic model of electron density distribution to estimate the distance of this pulsar based on the value of DM. Using the models NE2001 from Cordes & Lazio (2002) and YMW16 from Yao et al. (2017) we find that the cluster should be located at 2.4 kpc according to NE2001 (3.1 kpc according to YMW16) and the pulsar J1823-3022 at 2.6 kpc (3.8 kpc). This would imply that J1823-3022 is 0.2 kpc (0.7 kpc) further than the center of the cluster. However, the distance to the cluster estimated this way is a factor of 3 (2) smaller than the distance of the cluster of 8.0 kpc measured from spectroscopy and kinematics (Baumgardt & Vasiliev 2021). This implies that the electron density models largely underestimate the distances along gardt et al. 2019). For details see: https://people.smp.uq.edu.au/ HolgerBaumgardt/globular/parameter.html this line of sight and are therefore not reliable regarding the position of J1823-3022.

The period of 2.497 s is very long for a GC pulsar and more typical for Galactic disk pulsars. The slowest pulsar known to be associated with a GC is B1718-19A with a period of 1.002 seconds (Lyne et al. 1993). It must be stated, however, that the GC NGC 6624 already has two other long period pulsars suggesting that apparently young pulsars are able to survive in the cluster.

The period derivative measured through timing of J1823-3022 is 8.123 ± 0.001 × 10 -16 s s -1 . This corresponds to a surface magnetic field of 1.44 × 10 12 G and a characteristic age of ∼ 50 Myr. The corresponding position in the 𝑃-𝑃 diagram is shown in Fig. 6. If the pulsar is associated with the GC it would be the strongest magnetic field measured in a GC pulsar but still close to that of B1718-19A that has a magnetic field of 1.26 × 10 12 G (Lyne et al. 1993). The small characteristic age suggests that J1823-3022 is either very young or the recycling process stopped recently. If the pulsar is part of the cluster and the recycling process was stopped by a dynamical encounter that also displaced the pulsar, it would also explain the large positional offset as it would not have had time to sink back in the core. Similarly, if the pulsar was born recently after an accretioninduced collapse or an electron capture supernova, it could have been displaced by a kick.

If the pulsar has gone through a recycling episode in the recent past, it should be located below the spin-up line in the 𝑃-𝑃 diagram, [START_REF] Verbunt | [END_REF]. This line corresponds to the shortest period that can be reached during the recycling process by accretion at the Eddington limit on the pulsar (see Pringle & Rees 1972):

𝑃 min ≃ 1.3 s × B 10 12 G 6/7
≃ 1.6 s × (10 15 𝑃) 3/4 (2)

where we used (B/10 12 ) 2 ≃ 10 15 𝑃 𝑃. Considering the uncertainties in the models behind equation 2, an alternative spin-up line where P is 7 times higher for the same 𝑃 has been suggested [START_REF] Verbunt | [END_REF]. All of the pulsars with high magnetic field strengths in GCs lie below such a line in the 𝑃-𝑃 diagram. This line is shown in Fig. 6 alongside some of the pulsars associated with GCs with the highest magnetic fields. J1823-3022 is well below this line making it possible that is has gone through a recent recycling episode. However, the period derivative of this pulsar is similar to that of young Galactic pulsar with similar periods. Based on this parameter we cannot say whether it is associated with the cluster or not. If the pulsar is not associated we can estimate the probability of it being aligned along the same line of sight. The number of known pulsars in an area of 10 degrees in radius surrounding the cluster according to the PSRCAT catalogue13 (version 1.66, Manchester et al. 2005) is 147. The probability of finding one within 3 arcminutes is ∼ 0.003 corresponding to about 3𝜎. Of all of them only 9 have a DM within 10 pc cm -3 of the central value of NGC 6624. However, it must be noted that the pulsars in the PSRCAT catalogue are significantly brighter than the newly discovered pulsar so this should be considered as a lower limit to the probability.

LOCALISATION

The small size of the beams in the TRAPUM observations can determine the position of the newly discovered pulsars with a precision J1823-3022 (black). The plot shows lines of constant magnetic field, the spin-up line as adjusted by [START_REF] Verbunt | [END_REF] to fit B1821-24A and J1823-3021A, and four models of the death line marked from I to IV following Cruces et al. (2021). The pulsars associated with GCs with the highest magnetic fields are plotted in red for comparison, for these the effect of the cluster acceleration on the measured 𝑃 is significantly smaller than the intrinsic 𝑃. These pulsars were likely old, unrecycled NSs within the clusters that have recently (within the last 2% of the age of the cluster, as inferred from their characteristic ages) gone through a recycling episode, hence their location below the spin-up line. This was then interrupted by further stellar interactions, otherwise they would have become "normal" MSPs in the lower left of the diagram; this is consistent with the fact that we only see these systems in GCs with very high interactions rates per binary. The position of J1823-3022 in this diagram is consistent with this hypothesis, but also with it being an unassociated, normal pulsar in the background (grey dots); these represent all the pulsars present in the PSRCAT catalogue (Manchester et al. 2005, version 1.66). Note the presence of at least three, possibly four systems associated with NGC 6624 in this plot.

of 10-20 arcseconds. If the new discovery has been detected in more than one beam, it is possible to improve on the localisation using the SeeKAT mulitbeam localiser 14 (Bezuidenhout et al. in prep.). This code compares the S/N of the detections of the various beams with the Point Spread Function (PSF) of the beam calculated using the Mosaic software. The PSF will be dependent on the specific antennas used in the array during the observations, the position in the sky and the frequency. We obtain the best improvement on the localisation when we compare detections from different observations with different PSFs.

To facilitate the localisation of the pulsars close to the centre of the cluster we performed another observation on the 18th of June 2021 in L-band using 60 antennas with an average overlap of ∼ 0.85 covering only the central 1 arcminute with an observation time of 3.5 hours. In this observation we were able to detect both J1823-3021I and J1823-3021J but only the first was detected in more than one beam. Using this observation it was possible to improve the localisation of J1823-3021I. The numerous detections of J1823-3021K in the two observations also allow a precise determination of its position. The best positions of the new pulsars are shown in Table 1 and in Fig. 3.

14 https://github.com/BezuidenhoutMC/SeeKAT

DISCUSSION

The TRAPUM pulsar searches in the GC NGC 6624 have resulted in the discovery of four new pulsars. For one of them, J1823-3022, the association with the cluster is not certain. The total number of pulsars with confirmed association in the cluster is now 11. All of the new pulsars discovered are isolated even though we searched also for binary pulsars. The pulsar population can therefore be divided in to 9 isolated pulsars and only 2 binaries. This result is quite unusual for a typical GC but it is common for core-collapsed cluster with a very high encounter rate per binary [START_REF] Verbunt | [END_REF]) like NGC 6624. Another characteristic of GCs with high encounter rate per binary is the presence of mildly recycled pulsars that were disrupted before the spin-up process was completed. The newly discovered pulsar J1823-3021J with a period of 20.899 ms belongs in this category.

Verbunt & Freire (2014) also noted that in GCs with high encounter rate per binary a few pulsars tend to be located far from the central regions. Because of dynamical friction, the neutron stars would concentrate in the cores, but close encounters have the effect of displacing them. If the close encounters are frequent enough, there is a chance of observing a few pulsars while they are displaced before they drift back to the core. Thanks to the capability of TRAPUM to localize a pulsar in the cluster, Ridolfi et al. (2021) showed that this is true also in NGC 6624. Pulsar J1823-3021E has been found to be offset from the center at a distance of roughly one half-light radius. This is further confirmed by the new discovery of J1823-3021K being located ∼ 1.4 times the half-light radius. These two pulsars have likely been involved in dynamical encounters that displaced them in the recent past and did not have time to fall back in the center. The newly discovered pulsars certainly associated with the GC are either too weak or too offset to be detected by the large number of observations made of the cluster using up to 44 antennas of MeerKAT with the PTUSE machines and we were not able to derive a timing solution for any of them. With further observations with more antennas it will be possible to find a timing solution for these discoveries. The measurement of the acceleration felt by the two new discoveries close to the center, J1823-3021I and J1823-3021J, will be very helpful in testing the presence of the intermediate mass black hole claimed by Perera et al. (2017a).

Pulsar J1823-3022 is an intriguing new discovery. We do not have enough information to conclude whether the pulsar is associated with the GC. The period, period derivative, isolated nature and position far from the center of the cluster are more common features of the Galactic field pulsar population than the GC population. However, it is still inside the projected tidal radius of NGC 6624 and the cluster already contains two apparently young isolated pulsars with relatively high magnetic field strengths. The high period derivative and offset could be explained by a recent dynamical event that stopped the recycling and kicked the pulsar far from the cluster center. Alternatively the pulsar could be born recently via the process of accretion-induced collapse (Lyne et al. 1996) or electron capture supernova (Boyles et al. 2011) and have received a kick. In order to determine the pulsar's association with the GC, further observations are needed. A measurement of the proper motion would verify if the pulsar's velocity through space is in agreement with the kinematics of the GC. The discovery of more pulsars associated with the cluster at a similar distance or DM of J1823-3022 could also help solve the mystery.

The discovery of J1823-3021K and J1823-3022, both with a very high positional offset from the center, would not have been possible without the multiple beamforming capabilities and tiling patterns made available by TRAPUM. This shows that a significant number of interesting and potentially bright pulsars might still be waiting to be found in the outskirts of well known clusters. Among the GC surveys currently in progress at the various telescopes around the world, TRAPUM has the best chances of finding and localizing these pulsars.

O R I G

O2

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Figure 1 .O4

 1 Figure 1. Tiling pattern of the beams of the TRAPUM observations of NGC 6624 performed on the 21st of May 2020 (top) and on the 11th of August 2020 (bottom). The light pink ellipses show the single beams up to 80 percent of the boresight power. The blue dots are the pulsars with precisely known positions. The black dashed circle shows the half-light radius of the cluster, ∼ 1 arcminute (Baumgardt & Hilker 2018). The red dotted circles are the maximum extent of the size of the tiling in the two observations plotted for comparison. The value of the S/N of the detection of the new pulsars are reported in each beam where the pulsars are seen with the highest value reported in bold. All of the beams shown have been searched for new pulsars.

Figure 2 .

 2 Figure 2. Profiles of the four pulsars discovered in the TRAPUM observations of NGC 6624. The name, period and DM for each pulsar are reported in each plot. The bar under the DM shows the quadrature sum of the time resolution of 76 𝜇s of the observations and the DM smearing in the worst affected channel in comparison to the period of the pulsars. The profile of J1823-3022 shows variations of the baseline that are caused by broadband RFI.

OFigure 3 .

 3 Figure 3. Map of the cluster NGC 6624 with all the known pulsars. The previously known pulsars are marked with a blue letter while the new discoveries are shown in black. The black dashed circle shows the half-light radius of the cluster while the red dotted curves show the extension of the tiling of the three observations as in Figure 1 and in Figure 4. The color of the pulsars represents the value of DM according to the color bar at the right of the plot. Of the new discoveries, pulsar J1823-3021I and K have been localised using SeeKAT and J1823-3022 with timing.

Figure 4 .

 4 Figure 4. Tiling pattern of the beams of the TRAPUM observations of NGC 6624 performed on the 7th of November 2021 in order to localise J1823-3022. The light pink ellipses show the single beams up to 84 percent of the boresight power. The red cross marks the position of the detection with highest S/N of J1823-3022 in the previous observations. The number in each beam represents the value of the S/N of the detection. The beam with the highest S/N is highlighted in blue. The red dotted circles are the maximum extent of the size of the tiling in this and the two previous observations plotted for comparison. The black ellipse shows the position of J1823-3022 as determined by the timing. The size of ellipse represents the 1𝜎 uncertainty on the position.

Figure 5 .

 5 Figure 5. Timing residuals of J1823-3022 as a a function of time. The points in blue represent the ToAs obtained from TRAPUM observations at MeerKAT, the red point is from a PTUSE observation at MeerKAT, the orange points are from GBT observations and the green points from observations at Parkes.

Figure 6 .

 6 Figure 6. 𝑃-𝑃 diagram showing the measured period derivative ofJ1823-3022 (black). The plot shows lines of constant magnetic field, the spin-up line as adjusted by[START_REF] Verbunt | [END_REF] to fit B1821-24A and J1823-3021A, and four models of the death line marked from I to IV followingCruces et al. (2021). The pulsars associated with GCs with the highest magnetic fields are plotted in red for comparison, for these the effect of the cluster acceleration on the measured 𝑃 is significantly smaller than the intrinsic 𝑃. These pulsars were likely old, unrecycled NSs within the clusters that have recently (within the last 2% of the age of the cluster, as inferred from their characteristic ages) gone through a recycling episode, hence their location below the spin-up line. This was then interrupted by further stellar interactions, otherwise they would have become "normal" MSPs in the lower left of the diagram; this is consistent with the fact that we only see these systems in GCs with very high interactions rates per binary. The position of J1823-3022 in this diagram is consistent with this hypothesis, but also with it being an unassociated, normal pulsar in the background (grey dots); these represent all the pulsars present in the PSRCAT catalogue(Manchester et al. 2005, version 1.66). Note the presence of at least three, possibly four systems associated with NGC 6624 in this plot.

O

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A list of the structural parameters of GCs is available at the website: https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ parameter.html

http://www.meertime.org

http://www.trapum.org

An up-to-date list of the new pulsars discovered can be seen at: http: //www.trapum.org/discoveries/

https://github.com/wchenastro/Mosaic

https://github.com/v-morello/iqrm Downloaded from https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stac1041/6568555 by guest on 02 May 2022

https://github.com/alex88ridolfi/PULSAR_MINER

http://dspsr.sourceforge.net

http://psrchive.sourceforge.net

https://bitbucket.org/psrsoft/tempo2/

https://skaafrica.atlassian.net/rest/servicedesk/

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calculated using eq. 8 of(Webb et al. 2013) using data from (Baum-Downloaded from https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stac1041/6568555 by guest on 02 May 2022

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ACKNOWLEDGEMENTS

The MeerKAT telescope is operated by the South African Radio Astronomy Observatory, which is a facility of the National Research Foundation, an agency of the Department of Science and Innovation. SARAO acknowledges the ongoing advice and calibration of GPS systems by the National Metrology Institute of South Africa (NMISA) and the time space reference systems department of the Paris Observatory. PTUSE was developed with support from the Australian SKA Office and Swinburne University of Technology. Meer-Time data is housed on the OzSTAR supercomputer at Swinburne University of Technology. The OzSTAR program receives funding in part from the Astronomy National Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by the Australian Government. The authors also acknowledge MPIfR funding to contribute to MeerTime infrastructure. TRAPUM observations used the FBFUSE and APSUSE computing clusters for data acquisition, storage and analysis. These clusters were funded and installed by the Max-Planck-Institut für Radioastronomie and the Max-Planck-Gesellschaft. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. FA, AR, EDB, DJC, WC, PCCF, TG, MK, PVP and VVK acknowledge continuing valuable support from the Max-Planck Society. FA gratefully acknowledges support from ERC Synergy Grant 'BlackHoleCam' Grant Agreement Number 610058. SMR is a CIFAR Fellow and is supported by the NSF Physics Frontiers Center awards 1430284 and 2020265. This work is supported by the Max-Planck Society as part of the "LEGACY" collaboration on low-frequency gravitational wave astronomy. AR MBu and AP gratefully acknowledge financial support by the research grant "iPeska" (P.I. Andrea Possenti) funded under the INAF national call Prin-SKA/CTA approved with the Presidential Decree 70/2016. AR, MBu and AP also acknowledge support from the Ministero degli Affari Esteri e della Cooperazione Internazionale -Direzione Generale per la Promozione del Sistema Paese -Progetto di Grande Rilevanza ZA18GR02. BWS acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 694745). RPB acknowledges support ERC Starter Grant 'Spiders', Grant Agreement Number 715051.

DATA AVAILABILITY

The data underlying this article will be shared upon reasonable request to the MeerTime and TRAPUM collaborations.