Shyam Selvadurai's Funny Boy

P Parivaraj's Shiva

Arun Sandeep Bakshi

The Crisis of Postcolonial Modernity: Queer Adolescence in

The decolonial concept of "coloniality of power" expounded by Aníbal Quijano and Walter Mignolo appears particularly apposite in relation to postcolonial social formations whereby discursive legacies of colonisation, such as modernity, rationality and progress, continue their operations of "management and control" (Mignolo 2018, 143). 1 As Mignolo suggests, "surrounding the idea of modernity is a discourse that promises happiness and salvation through conversion, progress, civilization, modernization, development, and market democracy" (142). Coloniality of power connects colonial to postcolonial societies such that formal decolonisation or independence from European imperial powers does not necessarily translate into dismantling structures of power in postcolonial societies. The following essay therefore focuses on those continuities of power held over subaltern subjects, such as women, queers and ethnic/caste subalterns for whom the coloniality of power -a fully functioning legacy of colonisation -is the most manifest in South Asia. Holding on to the usefulness of notions such as "revolution as evolution" in terms of independence from European powers and the temporal marker "post" of the postcolonial, i.e., the revolution that would encompass an evolution in time, I scrutinise the inability of this evolution to transform colonial into postcolonial modernity. Through a reading of queer adolescent fiction from South Asia, this essay analyses the contours of the promise of decolonisation from imperial powers, which materialises as a series of muted revolutions or revolutions-in-waiting.

2

In terms of staging the vexed encounter between queer adolescence, adulthood and postcolonial modernity, Shyam Selvadurai's first novel Funny Boy (1994) and P. Parivaraj's sole novel Shiva and Arun (1998) provide a generative ground for critical

investigation. Selvadurai's work engages with the narrative of unconventional childhood and adolescence, and Parivaraj's story addresses the question of queer adolescence and its continuation as well as disruption in adulthood. Set in Sri Lanka in the 1970s, Funny Boy recounts the gay childhood and adolescence of Arjie Chelvaratnam, the son of an affluent Tamil family. The narrative comprises six stories focusing on Arjie's relationship with one particular character represented as "subaltern in terms of race, sexuality or gender" (Rao 1997, 118). Documenting the Tamil/Sinhala interethnic rifts, the novel culminates in the 1983 riots when Arjie's family flee to Canada. Parivaraj's work narrates the queer experience of two adolescent boys, Shiva and Arun, in a small South-Indian town and captures the differing trajectories of the boys. Whilst Shiva's homosexuality leads to his eventual suicide, Arun faces the patriarchal ire to defend his queer identity. I suggest that the two narratives are significant in the manifold ways in which the materialisation of queer subjectivity in South Asia forms a fraught relationship to the category of the modern. In this regard, without implicating queerness in homonationalist tropes, my analysis signals how gay adolescence problematises the "queer" coming of age of postcolonial South Asian fiction.

Eurocentric modernity 3

Modernity, in decolonial thought, refers to the privilege of the Western world-system through its stake in modern forms of knowledge production, the idealisation of the French revolution as the originating point of human resistance and the secularisation of Christianity. These three key events mark the suturing of modernity to the West even though it remains an unfinished project. Further, as Enrique Dussel argues, it "appears when Europe affirms itself as the "center" of a World History that it inaugurates; the periphery that surrounds this center is consequently part of its selfdefinition" (1993,65). In this regard, Mignolo prefers the conceptualisation of the "rhetoric of modernity" which articulates itself through "modernity/coloniality" (2018,230). The embedded binaries of tradition/modernity, old/new and nonmodern/ modern acquire renewed sustenance through an assumed linear notion of time and history, which configures Europe/the West at the centre of time and modernity. The nonmodern in this configuration "is a flexible concept -not always mentioned -but presupposed and necessary for the invention, in the present, of underdeveloped uncivilized people: all that has to catch up to become modern" (Mignolo 2018, 117). Such universalising assumptions of Europe as the originary social, institutional and economic formation simultaneously imbricate the postcolonial worlds in teleological narratives of development and progress. Considered in relation to global queer paradigms, decoloniality's challenge to Euro-American modernity bears critical significance in terms of temporal distinctions that delineate the global North as a progressive/modern site of homosexual emancipation because of its visible queer movements. In such readings, the global South embodies, as Arnaldo Cruz-Malavé and Martin Manalansan observe, "a premodern, pre-political, non-Euro-American queerness" that must follow Western identity categories "in order to attain political consciousness, subjectivity, and global modernity" (2002,[START_REF]Ruth Vanita's specious claim that modern homophobia is a western import elides the myriad expressions of homophobia, which do not exclusively comprise verbal slurs and aggression[END_REF](6). In addition, the deployment of queerness as a marker of Western modernity and US exceptionalism is the focus of Jasbir Puar's theorisation of homonationalism. She explains how queer human rights discourse becomes complicit with a masculinist agenda of nationalism (2007,(49)(50).

A growing cohort of queer scholars has been re-examining and disputing the Western narrative of historical time as organised around the principle of linearity. Gayatri Gopinath, for example, develops the notion of a queer South Asian diaspora "as a conceptual apparatus that poses a critique of modernity and its various narratives of progress," thus unsettling the colonial construction of Third-World sexualities as "anterior, pre-modern and in need of Western political development" (2005,12). Similarly, Heather Love explains that since queer identities often appear as "a backward race" and "modernity's backward children," queer theorists must "take exception to the idea of a linear, triumphalist view of history" (2007,(3)[START_REF]This claim is premised on Mignolo's conceptualisation of modernity and decoloniality whereby "Christian teleology" operates as a marker of Western universalism[END_REF][START_REF]Ruth Vanita's specious claim that modern homophobia is a western import elides the myriad expressions of homophobia, which do not exclusively comprise verbal slurs and aggression[END_REF](6)(7). Finally, Kathryn Bond Stockton's analysis of childhood and "its intimate relations with queerness" interrupts "the vertical, forward-motion metaphor of growing up" in twentieth-century literature (2009,11). Borrowing from these sophisticated queer readings, I suggest that the novels provide a complex terrain of non-normative representation whereby same-sex desire in adolescence in the South Asian context prompts an interrogation of the category of modernity in postcolonial geography.

The queer nonmodern

Given the persistence of the discourse whereby non-Western discursive formations appear nonmodern, 2 the displacement of the Eurocentric stagist conception of historical time as uncritical linear movement becomes particularly apposite to comprehend the emerging queer discourse in South Asia that does not necessarily emanate from Euro-American queerness. I contend that Selvadurai and Parivaraj utilise queer South Asian adolescence as a focal point to disrupt eurocentred formulations of tradition and modernity. The protagonists of Funny Boy and Shiva and Arun appear as sexual subjects and thus challenge the conventional view of "oriental" boys as available objects of desire. Louis Lo suggests that Arjie in Funny Boy cannot be called "homosexual" since the term "comes from Western, Christian, medical discourse" (2018,203). Representations of non-normative desire in adolescence and adulthood in the South Asian context, as depicted in the novels, inevitably encompass a complex debate about the status of modernity in postcolonial spaces. Both novels explore questions of modernity whereby queer adolescence and adulthood in South Asia appear inextricably interlocked with the experience of postcolonial modernity. In my reading of Selvadurai and Parivaraj, therefore, I attempt to align queerness to postcolonial sites revealing a complex resignification of class, caste, ethnicity and religion.

Selvadurai and Parivaraj's narratives raise concerns over the status of postcolonial modernity through a process of interrogation of queer adolescence in South Asia. In fiction, queer identity construction hinges on teenage representations that produce the oft-celebrated genre of coming-out narratives since "most texts describe a boy in his early teens from a middle-class home" (Saxey 2008, 40, emphasis added). Although working within the parameters of the Western coming-out story, Funny Boy and Shiva and Arun rework the narrative of adolescent identity-in-crisis from the South Asian perspective. As the protagonists struggle with their respective closets, the novels signal a larger crisis of postcolonial definition of modernity, which refuses to be subsumed under Western classification of modern/non-modern binary, and simultaneously documents the difficulty of articulating queer subjectivity in the multiply-severed contexts of language, regional and ethnic identity, class and religion. If the novels represent the birth of modern queer subjectivity in South Asia, then this emergence carefully distances itself from any Eurocentric discourse.

8

In his examination of Selvadurai's account, Andrew Lesk laments the unavailability of a Western-style identity politics of homosexuality in Sri Lanka. For him, "despite its cultural Westernization, [Sri Lanka] does not favour the liberating sexual alternates" and "a certain sense of Western modernity and its attendant emancipatory trappings is […] most underdeveloped" (2006,(35)(36). Such a trenchant critique of Sri Lanka epitomises an orientalising tendency to make Euro-America the central point of reference in queer practices. Lesk's argument implicitly legitimises patronising assumptions built on a systematic dichotomy of the "progressive" West and the "underdeveloped" (both economically and culturally) Third World. By fixing the terms of modernity as a Western prerogative, it forecloses the possibility of a queer discourse arising from South Asia. 9 Although Lesk's critique serves to highlight the political inscription of global (Western) and local (South Asian) sites, it implicitly raises questions about postcolonial modernity and its relation to queerness in both novels. Queer adolescence becomes central to what I term the crisis of postcolonial modernity since concern about identity and identification that underline both same-sex narratives and the "in-between" period of adolescence interpellates the Eurocentric binary of tradition/modernity in several ways. As such, questions of caste, class, ethnicity, religion and language become intertwined with the representation of South Asian queer adolescence so that the identity crises of the protagonists mimic and inevitably interrogate the status of modernity in postcolonial spaces.

The queer nonmodern and heteropatriarchy 10 Following the convention of coming-out accounts, Funny Boy and Shiva and Arun frame the narratives within the distinctive component of exploration of the gender binary that differentiates the queer story from other non-queer fiction. Simultaneously, they depart from these Western models through an explicit cross-gender identification/ solidarity, often absent in the former. For instance, in Edmund White's much-acclaimed work A Boy's Own Story (1982), the narrator's early realisation of his unconventional behaviour as a "sissy" serves as a key signifier of the narrator's homosexuality (2002,7). As an identifiable physical trait therefore, effeminacy is policed and reprimanded and becomes central in the struggle to "love a man but not to be a homosexual" at the end of White's novel (238). In her critical investigation of coming-out fiction, Esther Saxey ascribes this suppression of effeminacy to "femme-phobia" or centrality of the "plot of concealment and revelation" whereby "it is common for a text to present a protagonist who isn't overtly feminine or camp" (2008,46). In this respect, White's narrator embodies a particular misogyny, especially regarding his mother, that several scholars attribute to gay male representations. However, both Shiva in Shiva and Arun and Arjie in Funny Boy deflect from the privilege of their masculine gender to produce a bond with other-gendered subjects of shared oppression. Shiva's sister Shanti is "more than a friend-she was his confidant" and Shiva is the sole person who is willing to help Shanti in the household chores when their mother is ill (Parivaraj 1998, 21). Shiva, Shanti and their mother constitute a triad, resisting the father's demand to send Shiva to a Sanskrit school in order to become a Hindu priest like him and his elder son, Govinda ( 22).

The novels disrupt the traditional assumption of a naturalised link between heterosexuality and patriarchy through an implicit construction of queerness in opposition to the expectation of the father. Heteropatriarchy and heteronormalisation invariably function in tandem to deny the existence of a queer subject. This denial becomes more obvious when the queer subject is in a direct relation of subordination, such as the adolescent, so that the adult father appears as the key signifier of oppressive heteropatriarchy, embodying the threat to the non-normative identification of the queer teenager. The adolescents therefore construct their identity in an oppositional relation to their father. For instance, Shiva does not know "what his father really thought or felt about him" and therefore avoids him "because he would ask questions that always seemed difficult for a young person to answer" (Parivaraj 1998, 43, 20). He does not wish to follow the paternal occupation of being a priest but wants to go to college instead. College entails "the first step out of this house, away from his father's domination" (26). The novel figures this escape from heteropatriarchy as a crucial site of sexual freedom and queer subjectivity.

Similarly, Arun shares a problematic relationship with his father. Their relationship culminates in an open conflict when Arun refuses to marry according to his father's wishes and openly declares his homosexuality at the point of transition from adolescence to adulthood. Like Shiva, he does not follow the paternal profession although his younger brother Chitti "seemed to have no option but to join his father" as a building contractor (Parivaraj 1998, 121). Arun's decision to continue his studies to become a teacher after his graduation becomes "a point of contention with his father" (121). In contrast to Shiva, Arun overtly challenges paternal authority by refusing to marry and moving out of the family home. In addition, the novel connects subjects of shared oppression in a framework of solidarity through a trenchant critique of the father's wish to impose heterosexuality upon Arun. For instance, it ends with the powerful image of the inclusion of queer sexuality in the family structure and the marginalisation of the patriarch. Arun's sister Jyothi and his mother, who can be considered as conventional victims of patriarchy in terms of gender, forge a bond with Arun which contests the power of his father.

In Funny Boy, Arjie poses a direct threat to heteropatriarchy by his passion for crossdressing, and the relation with his father is based upon mutual avoidance. Nevertheless, when the adults discover Arjie's penchant for becoming the bride, the patriarch's intervention re-establishes the heteronormative order. His father's worry that Arjie may "turn out funny like that Rankotwera boy" and become "the laughingstock of Colombo" prompts his mother to force Arjie to play cricket with the boys even though she is unable to comprehend her husband's anxiety (Selvadurai 1994, 14). The effeminate Rankotwera boy appears as the maligned other and for his father, Arjie must be protected against such influences. Thus, he is rather pleased when his friend's son and his new employee Jegan befriends Arjie. For him, the absence of masculine identity, apparent in Arjie's unconventional activities such as playing with dolls and reading can be redressed in the company of a male influence like Jegan. Arjie's father thus embodies the threat of patriarchal homophobia in the novel such that queerness can only appear as a temporary chapter in the attainment of heteronormative adulthood.

Patriarchal homophobia manifests its control when Arjie's father withdraws Arjie from St. Gabriel's school and enrols him in the Queen Victoria Academy, the school that his brother Diggy attends. Explaining his decision, he asserts that "the [Victoria] Academy will force you to become a man" (1994,210). The paternal homophobic fear of Arjie's non-normative identity can only be overcome by calling to aid another "bastion of patriarchy," which is equally a "colonial vestige of the British public-school system" (Pennell and Stephens 2002, 181). This apparatus of patriarchal control is the colonialstyle all-boys school where, as Diggy warns Arjie, "you take it like a man" (Selvadurai 1994, 211). Diggy's comment explicitly points to the hegemonic model of masculinity that the school deploys for the construction of boyhood/manhood of its pupils.

Although Arjie submits to his father's wish, the homosocial space of the institution allows him to embark on his first homosexual relationship with his classmate Shehan.

The colonial/patriarchal enterprise of "becoming a man" is queered to reclaim the homosocial realm and re-signify it as a homosexual space.

Furthermore, the novel becomes a potent critique of gendered hierarchies. Like Shiva and Arun, it reinforces the alliance of queer subjects and women. By placing Arjie at the centre of such associations, the novel effectively challenges the dominant order from a queer perspective. Arjie's bond with Radha Aunty and his mother highlights the identification of the queer subject with the subjects of patriarchal subordination. The second story of the novel centres on Radha Aunty and her aborted attempt to love across the Tamil/Sinhalese ethnic divide. After pursuing her studies in the United States, she returns to Sri Lanka and commences a romantic liaison with a Sinhala boy, Anil. As a transgressive subject herself, Radha Aunty becomes an ally to Arjie's transgression of the gender binary: "She painted my eyelids with blue shadow, put rouge on my cheeks" (Selvadurai 1994, 49). Arjie's bond with her enables him to comprehend that romantic love and family operate in opposition to each other as Radha Aunty concedes to an arranged marriage. Conventional narratives of romantic love in western discourse often use the choice of partner as a metric for postcolonial modern subjectivity. However, Radha Aunty's embrace of an arranged marriage complicates such facile readings. Similarly, Arjie's identification with his mother develops beyond the "pleasure of watching Amma drape her sari" (15). In the third story of the novel, he witnesses once again the impossibility of a romantic union in the form of the adulterous liaison between his mother and her friend Daryl, a Sri Lankan burgher. Both the stories attest to the centrality of Arjie's observations as a privileged witness of the constraints of a patriarchal structure whereby romantic affection and love outside marriage for women systematically appear subservient to the demands of family.

The queer nonmodern and class, religion and ethnicity

In both novels, homosexuality becomes intelligible as one of the discursive sites of identification in its engagement with issues of class, caste, religion and ethnicity. The newness/modernity of Parivaraj and Selvadurai's texts lies in the contestation of dominant paradigms of class (master-servant), religion (Hindu-Muslim) and ethnic difference (Tamil-Sinhala) in South Asia since all three protagonists experience their initial homosexual encounters with boys across class, caste and ethnic divide. Shiva's awareness of same-sex desire for his aunt's houseboy, Chinni, Arun's sexual awakening with the servant Krishna, and Arjie's renewed attraction to Shehan point to the interpellation in terms of class, caste and religious difference for the queer subject.

Informed materialist critiques of queer politics underscore the immediacy of addressing inequalities of class in queer discourses.

Marxist scholars have advocated the inclusion of the analytic of class in queer debates such that queer formations can truly become agents of transformative criticism. In his critical assessment of the erasure of the dynamics of class in queer studies, Donald Morton argues that "for queer theory, class conflict turns out to be just another set of problems, marginal at best, which have no determinate relation to sexual politics" (1996,475). Similarly, Rosemary Hennessy deplores "the formation of a gay/queer imaginary in both corporate and academic circles (that) also rests on the suppression of a class analysis" (2000,139). However, the specificity of class, caste, religious and ethnic difference in India and Sri Lanka become central to the queer coming-out narratives in the novels. Same-sex desire and homosexual discovery are systematically structured around the severances of class, caste, religion and ethnicity, which characterise the postcolonial South Asian nations.

Shiva's foremost same-sex experience with Chinni critiques the organisation of a society/nation based on the dichotomy of master-servant and Brahmin-untouchable. As a Brahmin, whose father is a notable priest, Shiva is compelled to understand that Chinni, the untouchable and the servant, does not belong to the realm of humanity. Shiva realises that "Chinni wasn't a proper person or something" (Parivaraj 1998, 48). However, the novel contests the master-servant trope by staging the attraction of Shiva's desire for him. At home, when Chinni asks Shiva if he could bathe with him, Shiva is keenly aware of the inequalities of caste and class that separate them. He wonders, "Why in a so-called free India did people still accept it?" (50). Attempting to pulverise the class barriers, Shiva bathes with Chinni and they dry each other immediately after their mutual ejaculation. The episode references the subversive potential of queer love to over-ride class barriers through the proximity of their bodies.

Crucially, the emphasis on their same-sex experience defeats the potency of the master-servant hierarchy and re-arranges their roles in a more egalitarian framework. Shiva and Chinni's first experience of oral sex unsettles the impervious distinction between the two castes that occupy the highest and the lowest rung on the caste spectrum in India -the Brahmins and the Untouchables. 3 The disruption of the master/ servant and the Brahmin/Untouchable dichotomy functions as a key feature of homosexual relations in fiction that threaten the coherence of a national(ist) narrative. Shiva is aware that "it was just so contrary to everything a Brahmin learnt" but, "in an instant, the sensation of what was happening overran all the old taboos!" (Parivaraj 1998, 56). Shiva's assertion that the "old taboos" were "somehow imposed by the elders and parents" condemns the perpetuation of rigid caste politics through the device of an inter-generational control (50). His repeated caresses of Chinni's body "from the balls […] around the pubic 'nest' and up through the hair that ran in a fine line to Chinni's throat" defy the existing norms of social segregation (56). Thus, Shiva's discovery of non-normative sexuality is closely aligned to the refusal to accept imposed constructs of social hierarchy.

Similar to Shiva's contestation of class categories, Arun's sexual involvement with the servant Krishna transcends the limitations of the master-servant trope. The name Krishna not only signals the inter-implication of queerness and religion, but in the context of the novel, associates the divine with the underprivileged class. Arun's encounter with Krishna explicitly threatens the hierarchy of a structural relation based on authority and subordination. Their first experience commences on the conversation about "handpumping" but mutual masturbation leads to sharing a bed together and falling asleep in an embrace (Parivaraj 1998, 92). Arun and Krishna reverse the received normative roles of the servant performing fellatio on the master. Arun (the putative master) lets Krishna's (the alleged servant's) sperm flow into his mouth before it runs "out of his mouth and onto the floor" (97). Arun's subsequent gesture of fetching "two glasses of water" secures the absolute subversion of the master-servant binary (99). It uncovers the fictive character of social hierarchy and affirms the queer subject's capacity to effectively contest as well as subvert it even though in a private gesture.

In Funny Boy, ethnic difference between Arjie and Shehan functions as a parallel subtext to Arjie's developing sense of his own queerness. In his assessment of Sri Lankan politics, Tariq Jazeel points to the "racialised polarisation of identity politics" in which Sinhalese and Tamil ethnicities "become the primary markers of identity" (2005,232).

In relation to the novel, Minoli Salgado observes a "reinforcement of constructed, essentialised ethnicities," bearing a direct contrast to Arjie's fluid gender identity (2007,122; see also [START_REF] Gairola | Limp Wrists, Inflammatory Punches: Violence, Masculinity, and Queer Sexuality in Shyam Selvadurai's Funny Boy[END_REF]. Arjie and Shehan's same-sex romantic union ironically reflects the dismemberment of the Sri Lankan state based on ethnic division and the last two stories place the question of queer adolescence at the centre of interethnic disharmony.

On the first day of Arjie's arrival at Victoria Academy, a fellow pupil, Salgado, questions Arjie's presence in a Sinhalese class even though he is Tamil. When Arjie explains that he has always attended Sinhalese classes and "didn't even speak Tamil" (216), Salgado dismisses the explanation and commands Arjie to go to the Tamil class. Although Shehan is Sinhalese, he comes to Arjie's rescue by using the rhetoric of the Sinhalese who want Tamils to assimilate: "But Salgado, aren't you always saying that Tamils should learn Sinhalese?" (Salvadurai 1994, 216). The increasingly violent interethnic disharmony is responsible for the separation of classes in the school. This divide is manifest in the incident that Arjie witnesses where Salgado and his friends corner a Tamil boy in a cubicle of the toilets in the school. Shehan explains to Arjie that the school is divided into two factions, the supporters of Black Tie, the principal who desires both Tamil and Sinhalese pupils to co-exist, and the followers of Lokubandara, the vice principal who wishes for a more "traditional, vernacular education" with emphasis on Buddhist-Sinhala heritage (220). The school becomes a microcosm of the competing ethnic versions of the nation.

Like Arun, Arjie subverts the relation between established hierarchies. Belonging to a Tamil minority, he needs the support of Shehan to survive in the Sinhala-dominated environment of the school. As their romance develops into a sexual relationship (with their first homosexual encounter in the garage of the Chelvaratnam house), it becomes implicitly dependent on a mutual offer of service and help. For instance, Shehan's long hair often results in unjust punishment by the principal Black Tie. Arjie realises that "powerful people like Black Tie or my father […] got to decide what was right or wrong" (Salvadurai 1994, 274). Arjie redresses the wrongs done to Shehan by disrupting the balance of power. Black Tie needs Arjie to recite poems at the school prize-giving event.

As a Tamil, he appeals to the ethnic solidarity with Arjie. However, Black Tie's cruelty towards both Shehan and Arjie (punished and beaten when Arjie does not learn the poems properly) makes Arjie wonder about ethnic loyalty:

I thought of Mr. Lokubandara and the way Salgado and his friends had assaulted that Tamil boy. I thought of the way Black Tie had beaten both Shehan and me. Was one better than the other? I didn't think so. Although I did not like what Mr. Lokubandra stood for, at the same time I felt that Black Tie was no better. (247)

Arjie's resistance to Black Tie's authoritarian management of the school consists of shaming Black Tie in public by consciously mixing up the verses of the poem on the day of the school gathering. For Arjie, the act becomes an attempt to seek justice for the unfair treatment of Shehan at the hands of Black Tie. When questioned by Shehan on the motive behind his act, Arjie replies, "I did it for you" (284). Arjie's disloyalty to ethnicity and family members who are disappointed at his failed recital reinforces the bond between Shehan and him.

24 Arjie's failed performance at the school prize-giving event crucially works as a mockery of an earlier colonial system of education, which extends into the "new" postcolonial nation. Arjie's "ultimate counter-performance," as Mita Banerjee observes, involves an assertive refusal to become an agent of colonial mimicry (2005,155). The "post" in postcolonial inevitably suggests the transition from a colonial to a modern independent state. Black Tie, the homophobic principal, represents the earlier colonial model of education. Arjie's refusal to articulate the poems on which Black Tie's career depends becomes a critique of a former public-school system that can no longer wield the pressures of ethnic divisions in the modern postcolonial nation. By intentionally muddling the sentences of the English-language poems, which pay a tribute to the colonial situation, Arjie not only complicates the relation between the past and the present, the old and the new, but undermines the continuation of colonial public schools in modern Sri Lanka as well. Furthermore, the crisis of postcolonial modernity "jumbles all differences into a single performance of non-sense: the difference between the colonial and the postcolonial, as well as that between queerness and 'straight' sexual orientation" (Banerjee 2005, 155-56). Selvadurai demonstrates the agency of queer adolescence to upset the category of the postcolonial by incorporating colonial as well as postcolonial referents in Arjie's performance. The presence of the old colonial system in modern Sri Lanka, through cricket and the education system, hints at an incomplete decolonisation of South Asia. The modernity of the postcolonial nation defined by independence from a former colonial power becomes increasingly problematic as Arjie's performance repeatedly references the former colonial situation.

25 Another significant debate on the status of postcolonial modernity functions around the category of religion in Shiva and Arun. The hierarchical relationship of a modern West and a nonmodern South Asia is constructed around the distinction between secularised Christianity in the West and the continual inclusion of religion in South Asia. 4 Shiva and his Muslim friend Abdullah's lives in the novel are certainly dependent upon the demands of their respective religions. However, the novel queers both the religions in the bond that Shiva and Abdullah establish and thus makes a passionate plea for the queer sacred. For example, when Krishna enters Arun's room, he discovers the posters of male sportsmen juxtaposed with the "print of Lord Krishna and the Milkmaids" (Parivaraj 1998, 92). The heterosexual eroticism that is usually associated with Lord Krishna and the milkmaids is queered when considered in relation to the Arun/Krishna sexual liaison. The significance of a "traditional" past to questions of queer identity in the "present" is further reinforced in Abdullah's struggle to explain the compatibility of Islam with homosexuality: "He had tried to tell his father about famous Muslim leaders and rulers who had both male and female love affairs" (123). By reclaiming a religious past, Abdullah attempts to legitimate his desire for men, just as a "Brahmin gay" would tell his father "that the Kama Sutra and the wall engravings at Puri temple were real" (124). The incorporation of putatively past sexual practices to frame Abdullah's sexuality reveals the potency of nonmodern, nonsecular forms to affect, in this case affirmatively, modern debates about queer identity. Outlining the pre-colonial archives as same-sex practices legitimises the claim to South Asian queerness in contemporary times without a recourse to the colonial interregnum. The genealogical connection between Abdullah's sexuality and South Asian pasts appears more significant than present-day Western models of queerness.

The queer nonmodern and language 26 Language also becomes a significant marker in the definition of postcolonial modernity in Funny Boy. Black Tie and Mr Lokubandara's struggle over Tamil/Sinhala education reflects the war of national language in Sri Lanka in the 1970s. The presence of English as the over-arching language of reference in the novel and in Sri Lanka further complicates the linguistic landscape. The language of the coloniser, English, affords privilege and power which is apparent in Amma's dealing with the police after Uncle Daryl's disappearance. Amma is able to hide the adulterous nature of her liaison with Uncle Daryl through recourse to English, which immediately signifies her superior status in Sri Lankan society (Selvadurai 1994, 127). However, English is made to signify a product of Western import that cannot embody the entirety of the Sri Lankan experience. The appended glossary of Sri Lankan terms at the end of the novel attests to the inadequacy of English in the Sri Lankan context.

27 Additionally, the repeated use of the adjective "funny" to define Arjie's homosexuality by the adults refers to the incompleteness of English to incorporate local versions of same-sex desire. Throughout the novel, Arjie's queerness appears as an attribute suggested by the term "funny" in the title. The persistent refusal to name and classify same-sex experience consolidates the resistance to Western practices of categorisation. Moreover, homophobia literalises as a Western influence and attaches to the Western lexicon in terms of English language. Tanuja, Arjie's cousin from Canada, brings terms of homophobic insult to the game of bride-bride. When Arjie refuses to let her play the bride, she calls him "a pansy," "a faggot," and "a sissy" (Selvadurai 1994, 11). Tanuja's act of naming (and consequently shaming) Arjie's queerness symbolises the Western practice of category formation. The general incomprehension of the insults by the group points to the local development of queer subjectivity in Sri Lanka whereby Arjie and his cousins categorically reject Western discourses of identity classification. Tanuja's isolation in the group literalises a critique of homophobia that becomes available in the novel through a Western construction of identity sites. This does not imply that homophobia is a Western import. Instead, it points to the ready availability of homophobic slurs in English, which in other South Asian contexts are to a certain extent articulated through patriarchy as I suggest below. 5 For all three protagonists, the realisation of homosexuality is embodied as a crisis of postcolonial modernity in terms of language. Arjie, Shiva and Arun attempt to formulate a critical vocabulary for their queerness. Although written in English, Selvadurai and Parivaraj's queer fiction signals the inability of the English language to articulate the multiply-positioned South Asian queer subjectivity. When asked by his brother Chitti whether he is a "homo," Arun responds: "That's a foreign brand name Chitti. I don't like it, but o.k. it's one way to describe me" (Parivaraj 1998, 152).

Although spoken in English, the conversation between the brothers becomes symptomatic of the expropriation of English as an alien, non-Indian language. "Foreign brand name" is coterminous with the commodification of "gay" identities in Western capitalist systems that results in what Puar terms "queer consumer citizenship" (2007,62), and which the South Asian queer subject runs the risk of replicating. Arun, Shiva and Abdullah define themselves in contrast to the Western construct of a homosexual identity as men "who loved men" (Parivaraj 1998, 116, italics in original). The urgency of describing his queerness becomes even more importunate when Arun's father confronts him on the question of marriage. Connecting homosexuality to effeminacy and paedophilia, the patriarch calls him a chamma chacka and disowns him, thereby effectively framing homophobia as integral to patriarchy (149). As a literal translation, chamma chacka implies that Arun is an effeminate man who has a penchant for crossdressing. Again, Arun's retort -"I just don't want to get married because my sexual preference is for men not women" (150) -affirms the critical significance of selfdefinition which does not include the naming of sexuality as homosexual, gay or queer.

In this essay, I have argued for a reconsideration of queer adolescence in conjunction with a reading of specific sites of ethnicity, caste, class, religion and language in South Asia. I have also suggested that the illustration of queer subjectivity and queer selfdefinition in South Asia raises questions about the definition of modernity in the novels. The difficulty of defining queerness in the South Asian context reinforces the impossibility of postcolonial modernity, which complicates and revises the colonial version of the tradition/modern binary. Queer adolescence, as I have shown, disputes the applicability of Western/global constructs to examine queerness in South Asia appropriately. Despite the availability of Western identity categories through the presence of English in South Asia, the novels problematise the articulation of the South Asian queer subject by a disavowal of the English language. Simultaneously, the Arjie-Shehan, Shiva-Chinni and Arun-Krishna bonds underscore the importance of local alliances between marginalised subjects.

The novels signal an inclusion of queerness in South Asian fiction in English. As Jazeel argues, in relation to Funny Boy, the novels are "an important political intervention" (2005,231). They belong to an emerging body of potentially subversive fiction that locates queer South Asian subjectivity as a site of contest and contradictions. The interaction between global queer narratives and local South Asian versions of same-sex desire appears as a fraught relationship. A significant shift in South Asian attitudes to the master discourse of the West is evident in the way these novels negotiate Western constructs such as modernity and sexuality. In the process, they expose the flaws of globalising discourses based on the principle of universalism, which is neither achievable nor desirable.

4

 4

  The Crisis of Postcolonial Modernity: Queer Adolescence in Shyam Selvadurai's...

Commonwealth Essays

and Studies, 42.1 | 2019

  The Crisis of Postcolonial Modernity: Queer Adolescence in Shyam Selvadurai's...

	Commonwealth Essays and Studies, 42.1 | 2019

  The Crisis of Postcolonial Modernity: Queer Adolescence in Shyam Selvadurai's...

Commonwealth Essays

and Studies, 42.1 | 2019

The Crisis of Postcolonial Modernity: Queer Adolescence in Shyam Selvadurai's...Commonwealth Essays andStudies, 42.1 | 2019

ABSTRACTS

In this essay, I offer a queer reading of two works of the postcolonial canon from South Asia to ask what alternative meanings emerge when ethnic, religious, cultural and national matrices are brought to bear upon queer epistemology. Exploring the interconnections between queer adolescence, revolutions and postcoloniality, I disturb neat narratives of postcolonial modernity to suggest the reorientation of South Asian fiction as a crucial outcome of the crossings.


J.-M Carquillat

N Ginestet

J.-L Prieur

Contribution to the search of binaries among Am stars II. HD 81976 and HD 98880, double-lined spectroscopic binaries

Keywords: individual, HD 81976, HD 98880 -binaries, spectroscopic -Stars, fundamental parameters

 in addition to orbital parameters and Hipparcos data: T eff = 7000 K, log 10 g = 4.0, M1 = 1.9 M , M2 = 1.6 M , log 10 (age) = 9.12. The components do not rotate synchronously contrary to HD 81976. Both binaries appear to be detached systems without possibility of eclipses.

Introduction

HD 81976 (HIP 46588) and HD 98880 (HIP 55565) belong to our sample of Am-type stars that we have been observing with the CORAVEL instrument of "Observatoire de Haute-Provence" (OHP, Haute-Provence Observatory) in order to contribute to the study of the frequency of binaries in this stellar family (Cf. Ginestet & Carquillat 1998, Paper I;North et al. 1998).

The first of these two stars, HD 81976, was reported as Am in a paper by Bidelman (1988), in his "Miscellaneous spectroscopic notes", whereas the second, HD 98880, was included in the "Third catalogue of Am stars with known spectral types" (Hauck 1986), which was the main source used for constructing our sample. Note that the Am type was attributed to HD 98880 by Abt (1984) during his spectroscopic investigation of a sample of possible peculiar Send offprint requests to: J.-M. Carquillat, e-mail: jean-michel.carquillat@obs-mip.fr

Based on observations made at the Haute-Provence Observatory, France.

stars which had peculiar indices in Strömgren photometry (Olsen 1980). Concerning their binarity, only HD 81976 had already been reported in the past as having a double lined spectrum (Adam 1915) from observations carried out at Mount Wilson, but to our knowledge, no spectroscopic orbit had ever been obtained.

Our observations lead to the determination of the orbital parameters for these two double-lined spectroscopic binaries.

Radial velocity observations and determination of the orbital parameters

The radial velocities (RV ) have been obtained with the CORAVEL spectro-velocimeter (Baranne et al. 1979) mounted at the Cassegrain focus of the 1-m Swiss telescope of OHP. The measurements were processed and included into the data base of Geneva Observatory by S. Udry. The RV are in the IAU standard system. HD 81976 was observed during the years 1995 to 1998. Forty one observations have been performed (Table 1), which cover 186 orbital cycles. The mean internal standard error of the RV measurements is 0.9 km s -1 for the primary component and 1.0 km s -1 for the secondary. The correlation dips (i.e. the profiles of the crosscorrelation function of the absorption lines as measured by CORAVEL) of both components are very similar. HD 98880 was observed from 1992 to 1998. Forty two observations were performed (Table 1), which cover 162 orbital cycles. Contrary to the previous case, the correlation dips of both components are rather different, the profile of the secondary component being much shallower. The mean internal standard error for the RV are respectively 0.5 km s -1 and 1.1 km s -1 for the main and secondary components.

We have computed the orbital elements with our BS2 program (Nadal et al. 1979) which was improved by one of us (J.-L. P.). Taking into account the mean standard errors of the measurements, the RV of each component were weighted as follows: for HD 81976, 1.0 for the primary component and 0.8 for the secondary, and for HD 98880, 1.0 for the primary and 1/4 for the secondary.

The orbital elements that we obtained are given in Table 3 and the RV curves in Figs. 1 and2. Note the small eccentricity of 0.06 for HD 81976, which has nevertheless the shortest period. On the contrary, for the second system, the eccentricity had to be set to zero for a good fit.

Discussion

HD 81976

As mentioned in the previous section, the correlation dips of both components are quite similar, which indicates that the two stars must have a similar type (Am in that case). This is supported by the value of the mass ratio r = 0.97, very close to unity. Assuming that these stars have a mass of the order of 2 M , the value obtained for M 1 sin 3 i = 0.5875 M would lead to i = 42 • , which implies a quasi-certain impossibility of eclipse occurrence. With the same assumption, we would have a = a 1 + a 2 = 14.66 Gm = 21 R , and the system would appear as detached.

Comparison with the Hipparcos measurements

For HD 81976 = HIP 46588, the Hipparcos catalogue [START_REF] Esa | The Hipparcos and Tycho Catalogues[END_REF] gives: V = 8.17, π = 5, 65 ± 1.18 mas, B -V = 0.285, V -I = 0.32.

From the value for the trigonometric parallax, the distance of this system is about 180 pc, and the absolute V magnitude can be estimated at 1.93±0.46, assuming negligible interstellar absorption. If we assume both component have the same luminosity, we obtain M V = 2.68 ± 0.46 for each component. This value is compatible with Am-type stars as shown by [START_REF] North | Proc. ESA Symp. Hipparcos-Venice'97[END_REF], who obtained absolute V magnitues in the range +0.3 and +2.8 for a sample of 96 Am stars observed with the Hipparcos satellite.

Note also that the color indices as measured by Hipparcos are consistent with a late A-type star, about A7-A8 [START_REF] Schmidt-Kaler | Landolt-Brnstein[END_REF]. Such a spectral type should correspond to the strength of hydrogen lines and the effective temperature of the star (Bidelman does not give any detail for his classification but only the result: "Am"). This is also consistent with the dA7 classification given in the Mount Wilson catalogue [START_REF] Wilson | General Catalogue of Stellar Radial Velocities[END_REF]), since such a classification was done at a time when the Am stars were not yet known as a family of its own.

Rotation-revolution synchronism

Since the orbital period is rather short, a synchronism can be expected between the axial rotation and the orbital revolution of the components. The test proposed by Kitamura & Kondo (1978) consists of calculating the radii that the two stars would have if synchronism was effective. If the values found for these radii are compatible with those expected for stars of similar spectral type, one can deduce that the hypothesis of synchronism is plausible. Actually, the equatorial velocity for synchronism is V s = 50.6(R/R )/P . In our case, V s can be estimated from v. sin i as deduced from the profile of the correlation dips (method described in Benz & Mayor 1981), which is 14.5±0.5 km s -1 . Assuming i = 42 • and the coplanarity between the equatorial and the orbital planes, one finds V s = 21.8 km s -1 and hence R = 2.4 R . This value is quite compatible with those deduced from the study of similar systems showing eclipses (Kitamura & Kondo 1978). We can then conclude that the hypothesis of synchronism is relevant for HD 81976.

Hypothesis of a third body

In Sect. 2, we noticed that the eccentricity of the orbit of HD 81976 was not zero and that the other system studied here has a period nearly 2.5 times larger with a circular orbit. The existence of a non-circular orbit for a system with a period as short as 5.6 days is surprising. Actually, the study of a sample of Am stars belonging to the Hyades and Praesepe clusters by Debernardi et al. (2000) shows that orbits are quasi circular for P < 10 days, and the authors note that this is in agreement with the theoretical work of [START_REF] Zahn | [END_REF].

On the other hand, when plotting the residuals (O-C) of Table 1 versus time (Fig. 3), one notes they seem to decrease with time, which shows a possible drift of the velocity V 0 of the system's gravity center.

These two points lead us to suggest the presence of a third body in this system. We have already formulated such an hypothesis for the Am-type system HD 66068/9 (Carquillat et al. 1994), which also showed a V 0 drift and exhibited an abnormally high eccentricity for a period close to 8 days.

HD 98880

For this binary, the mass ratio of 0.86 is an indication that the two components have a similar type, but contrary to the previous case, the depths of the correlation dips are significantly different, which implies that their luminosities are also different. Actually, the magnitude difference of the two components can be inferred from the value of the ratio of the integrated aeras of the dips (Lucke & Mayor 1980). For HD 98880, we obtain ∆m B = 1.25 ± 0.1 mag.

Physical parameters and evolution state of the system

The Hipparcos parallax, π = 4.25 ± 0.91 mas (i.e. d = 235 pc), combined with the apparent magnitude V = 8.06 leads to a global absolute magnitude of M V = 1.20 ± 0.46 for the system, if we neglect the interstellar absorption. If we assume that the effective temperatures of the two components are similar (T 1 ≈ T 2 ), ∆m V ≈ ∆m B , and if we use the value of ∆m B = 1.25 mag found previously, we obtain the absolute V magnitudes of both components: M V 1 = 1.5 ± 0.5 and M V 2 = 2.75 ± 0.5. For HD 98880, Olsen (1983) gives the following Strömgren photometry indices V = 8.063, by = 0.228, m 1 = 0.243, c 1 = 0.642; the β index was not given by Olsen. The calibration by Crawford (1979) leads to β = 2.72 and δm 1 = -0.066 (blanketing parameter). These data allows us to estimate the effective temperature and the metallicity. The effective temperature, as well as the surface gravity, can be obtained with the theoretical grids computed by Moon & Dworetsky (1985). In this case we find: T ≈ 7000 K and log 10 g ≈ 4.0. This value for T seems both compatible with the classification made by Abt (1984): A4-F3-F5 respectively for the K line, the Balmer lines and the metallic lines, and with the color index B -V = 0.39 reported in the Hipparcos catalogue [START_REF] Esa | The Hipparcos and Tycho Catalogues[END_REF]. As for the metallicity, it can be estimated from the relation δm 1 versus [Fe/H] established by Crawford (1975). In this case, [Fe/H] ≈ 0.8 dex, which is a good signature of Am character.

On the other hand, if we refer to the theoretical HR diagram computed by Schaller et al. (1992) for solar metallicity stars (Fig. 4), the masses of the two components would be about 1.9 M and 1.6 M , whose ratio is close to that of the RV curve amplitudes. To locate each component in this diagram, we applied a correction of -0.1 mag to the absolute magnitude, (i.e., bolometric correction for T = 7000 K) to derive M bol and the luminosity L.

We can then propose the following (rough) model: the system HD 98880 is about 1.3 10 9 years old and constituted by two Am stars with effective temperature close to 7000 K; the primary (1.9 M ) would be already a rather evolved main sequence star whereas the secondary (1.6 M ) would be only about 1 mag above the zero-age main sequence. The corresponding theoretical radii would be 3.3 R for the primary and 1.9 R for the companion.

System dimensions, rotation-revolution synchronism

The value of 1.9 M found for the mass of the primary would imply i = 43 • , a = 26.16 Gm = 37.6 R . Hence, like HD 81976, HD 98880 is a detached system without the possibility of eclipses. The values of v. sin i deduced from the correlation dip profiles are 10.6 ± 0.2 km s -1 for the primary and 9.2 ± 0.7 kms -1 for the secondary. We applied the Kiramura & Kondo test with these values and i = 43 • . Assuming the coplanarity between the orbital and equatorial planes, the rotation-revolution synchronism would require radii of respectively 4.35 R and 3.8 R for the primary and secondary. These values are significantly (2) components for the HD 98880 system in the HR diagram with theoretical evolution curves for solar metallicity stars computed by Schaller et al. (1992) larger than those (3.3 R and 1.9 R ) corresponding to the model described above. We conclude that, unlike HD 81976, the HD 98880 system has not yet reached the synchronism state, which is not surprising in view of its much longer orbital period.

Fig. 3 .

 3 Fig. 3. Variation of the residuals (O-C) versus time for HD 81976. Filled circles: primary component, open circles: secondary component. The straight line with a negative slope corresponds to the least square fit

Fig. 4 .

 4 Fig. 4. Estimated location of the primary (1) and secondary(2) components for the HD 98880 system in the HR diagram with theoretical evolution curves for solar metallicity stars computed bySchaller et al. (1992)

Table 1 .

 1 Radial velocities of HD 81976. RV1, (O-C)1: radial velocities and residuals for the primary; RV2, (O-C)2: same data for the secondary. The phases are from the periastron passage

	1	'DWH	+-'	3KDVH	59	2 ±&	59	2 ±&
					NP V	NP V	NP V	NP V

Table 2 .

 2 Radial velocities of HD 98880. RV1, (O-C)1: radial velocities and residuals for the primary; RV2, (O-C)2: same data for the secondary. The phases are from the ascending node passage

	1	'DWH	+-'	3KDVH	59	2 ±&	59	2 ±&
					NP V	NP V	NP V	NP V

Table 3 .

 3 Orbital elements and their standard errors for the systems HD 81976 and HD 98880

	(OHPHQW	+'	6WG HUU	+'	6WG HUU
	3 GD\V 7 +-'
	ZGHJUHHV H . NP V . NP V 9 NP V D VLQ L *P D VLQ L *P 0 VLQ L 0/ 0 VLQ L 0/			IL[HG
	8 2 & NP V
	8 2 &NP V

7 SHULDVWURQ SDVVDJH IRU +' DVFHQGLQJ QRGH SDVVDJH IRU +'

Acknowledgements. We are indebted to Michel Mayor, Director of Geneva Observatory, for giving us observing time with CORAVEL and to Stéphane Udry for processing the radial velocity measurements. For bibliographic references, this work made use of the SIMBAD database, operated at the "Centre de Données astronomiques de Strasbourg" (France).


J.-L Prieur

G Daigne
email: daigne@observ.u-bordeaux.fr

R Avila
email: r.avila@astrosmo.unam.mx

SCIDAR measurements at Pic du Midi

Keywords: atmospheric effects -site testing -turbulence -methods, data analysis -techniques, image processing

We present SCIDAR measurements made at the Pic du Midi Observatory with PISCO. A series of vertical profiles of the refractive-index structure constant C 2 N (h) was obtained with the observations of the binary stars γ Del and γ Ari, with 30 second time sampling. In the free atmosphere, the turbulence was dominated by the contribution of a few well-separated atmospheric layers at altitudes in the range 8-20 km, with significant changes within a few minutes. We describe a new method based on the CLEAN algorithm applied on the 2-D covariance function of the irradiance fluctuations in the pupil plane and compare it with the widely-used Maximum Entropy Method applied on a slice of this 2-D function. Our method is much less sensitive to the noise. Vertical profiles of the wind velocity and direction were obtained with an automatic procedure working on the mean cross-correlation function of consecutive frames. Furthermore, we validate a model for the SCIDAR detectivity threshold in terms of distance to the turbulent layers.

Introduction

A direct estimate of the vertical distribution of turbulence and its time variations can be obtained through the observation of stellar-light irradiance fluctuations in the entrance pupil of a telescope. Indeed, the coherence radius of the scintillation pattern due to a single diffractive layer depends on its distance to the entrance pupil of the telescope, and varies as the square root of this distance. The experiment conducted at Nice Observatory in 1974 by Rocca, Roddier and Vernin (Rocca et al. 1974), on spatio-temporal correlation of scintillations, has shown that the most reliable results can be obtained with the observation of a double star and the so-called spatio-angular correlation of the compound scintillation pattern. Since then, the technique is known as SCIDAR, for SCIntillation Detection And Ranging. It has been used on different telescopes in many astronomical observatories for site testing, as a complement to seeing measurements (for a review, see Send offprint requests to: J.-L. Prieur, e-mail: jean-louis.prieur@obs-mip.fr

Based on observations made with the Télescope Bernard Lyot at Pic du Midi Observatory, France. Avila 1998). Its spatial resolution along the line of sight cannot compete with in situ measurements for detailed studies of the turbulence distribution, but it may bring some new insights on turbulence lifetime at different altitudes, from a few kilometers upwards.

Our purpose is not site testing, but a preliminary investigation of SCIDAR technique as a support to groundbased differential astrometry. Optical turbulence produced high in the atmosphere will be the main limiting factor in narrow-angle measurements to be performed with dual-field interferometers (DFI) [START_REF] Scardia | [END_REF]Colavita 1994). Its deteriorating effects have to be clearly evaluated before one can try and reduce them. Furthermore, since the SCIDAR technique can be performed with a telescope aperture about the size of the entrance pupil of an optical interferometer observing in the near-IR range (D 1.5 m), it could be a unique technique, along with DFI, for probing and tracking turbulence distribution and wind velocity.

Numerous in situ measurements of temperature fluctuations carried out with balloon sounding have shown that regions responsible for optical turbulence are usually localized in a few thin layers, about 10-50 m thick (Coulman et al. 1995). Unfortunately, little (Avila et al. 1998) is known about their temporal variations, on time scales of one minute or so, which are typical integration times for measurements with DFI's in the near IR, see e.g. descriptions of the Palomar Tesbed Interferometer or PTI (Colavita et al. 1999;Lane et al. 2000).

In this paper, we report SCIDAR observations with the Telescope Bernard Lyot (TBL) at Pic du Midi. The 2 m pupil is large enough for the observation of well separated binary stars, about 10 apart, so that a spatial resolution of about 1 km can be achieved at a distance of 10 km. We may recall previous turbulence measurements at Pic du Midi: in the 1980's, it was investigated with the SONATE experiment [START_REF] Dubosclard | [END_REF]Hecquet & Klauss 1989), which involved acoustic soundings of the lower atmosphere together with image quality measurements in the visible. Seeing variations were found to be strongly correlated with the turbulence content in the first few hundred meters above the site.

We shall keep in mind that the turbulence content reported here is just a (small) part of the whole optical turbulence above the observatory site. Turbulence in the first few kilometers was not detected, since the observations were not performed in the Generalized SCIDAR mode (Avila et al. 1997;Fuchs et al. 1998).

We first recall the basic principle of SCIDAR measurements in Sect. 2 and describe the observations in Sect. 3. We then describe the analysis of the data and the two methods based on Maximum Entropy Method (MEM hereafter) and CLEAN that we have used to derive C 2 N profiles. Results on the atmospheric turbulence, wind velocity profiles and their time variations are presented in Sect. 5 with a detailed analysis of the achieved sensitivity.

The SCIDAR technique

Basic principle with a single turbulent layer

Classical SCIDAR is based on the observation of irradiance fluctuations of a double star at ground level (Rocca et al. 1974;Caccia et al. 1987;Avila 1998). With a single turbulent layer at distance d j (cf. Fig. 1), two stars with angular separation θ 1 cast to the ground similar diffraction patterns shifted by r j = d j θ. The covariance C 2 (ρ) of the irradiance fluctuations exhibit two secondary peaks at ±r j :

C 2 (ρ) = A C 1 (ρ) + B [C 1 (ρ + d j θ) + C 1 (ρ -d j θ)]
(1)

with A = (1 + α 2 )/(1 + α) 2 and B = α/(1 + α) 2 (2)
where α is the brightness ratio of the binary components (related to the magnitude difference ∆m by α = 10 -0.4∆m ) and C 1 (ρ) is the normalized covariance function of the irradiance fluctuations for single star observations. C 1 (ρ) is the Fourier transform of the power spec-1 In this paper, two-dimensionnal vectors will be noted in bold. trum W I of the irradiance fluctuations at ground level, given by [START_REF] Roddier | The effects of atmospheric turbulence in optical astronomy in Progress in Optics[END_REF]:

Turbulent layer

W I (f ) = 4 W Φ (f ) sin 2 (πλd j f 2 ) ( 3 )
where λ is the observed wavelength and W Φ is the power spectrum for the phase fluctuations at the level of the layer, generally assumed to follow Kolmogorov statistics.

In that case C 1 (ρ) is isotropic and proportional to J j , the optical turbulence factor [START_REF] Tokovinin | [END_REF]) of the thin layer, which is related to the refractive index structure parameter, C 2 N (h), by:

J j = hj +δhj /2 hj-δhj /2 C 2 N (h)dh, ( 4
)
δh j being the thickness of the layer. With a line of sight at zenith angle z, the observed turbulence factor is Jj = J j sec(z). The expression of C 1 (ρ) is then:

C 1 (ρ) = Jj K(ρ, d j ) ( 5 )
with:

K(ρ, d j ) = 0.243k 2 ∞ 0 f -8/3 sin 2 (πλd j f 2 )J 0 (2πf ρ)df. (6)
It is plotted in Fig. 2 for different distances to the turbulent layer and was observed in the experiment reported here, with its negative feet. The correlation radius of the irradiance fluctuations is about the radius of the first Fresnel zone λd/2π [START_REF] Tatarskii | Wave propagation in a Turbulent Medium[END_REF], so that spatial resolution along the line of sight (i.e., the ability to separate two turbulent layers of equal J factor) is given by:

∆d j 0.78 λd j θ • (7)
We derived the value of 0.78 from the F W HM (Full Width at Half Maximum) of the curves C 1 (ρ) in Fig. 2.

Principle with a vertical distribution of turbulence

Several turbulent layers along the line of sight are statistically independent, so that the different contributions will sum in quadratic form. More precisely, the power spectra of the relative irradiance fluctuations δI/I will add [START_REF] Tatarskii | Wave propagation in a Turbulent Medium[END_REF][START_REF] Roddier | The effects of atmospheric turbulence in optical astronomy in Progress in Optics[END_REF]. In SCIDAR measurements, only a few turbulent layers will contribute to the covariance function at a given ρ value, away from the central peak, so that the weak-scintillation approximation can be safely used: the covariance function C sci (ρ) outside the central peak is estimated from irradiance fluctuations instead of from the logarithm of the irradiance. With a continuous distribution of turbulence along the line of sight, the covariance profile in the θ direction will be:

C sci (ρ) = B sec(z) ∞ 0 K (ρ, h sec(z)) C 2 N (h) dh (8)
which is a Fredholm-type integral with kernel K(ρ, h sec(z)). A maximum entropy method (MEM) can be used to recover the distribution of the index structure parameter (Avila 1998).

An alternative is to consider a multi-layer model with a discrete distribution of turbulence along the line of sight:

C sci (ρ) = B j Jj K(|ρ -r j |, d j ) ( 9 )
which can be solved in 2-D space with a CLEAN algorithm. In Sect. 5, we shall compare the results obtained with one and the other method.

Limited pupil size and sensitivity

In practice, the covariance function is estimated with a limited pupil size, and the incoming radiation has to be multiplied by a pupil function P (r) (P = 0 or 1).

Experimentally, the normalized covariance function of irradiance C 2 (ρ) will be approximated with:

C 2 (ρ) ≈ C δI (ρ)/C I0 (ρ) (10)
where C I0 (ρ) is the covariance of the average pupil irradiance function I 0 (ρ) estimated on a large ensemble of frames and

C δI (ρ) = [I(ρ) -I 0 (ρ)]
2 is the covariance of the irradiance fluctuations, per frame, relative to I 0 (ρ). Let us now estimate the expected limiting sensitivity of our measurements. The statistical rms noise of C sci (ρ), per frame is given by [START_REF] Tokovinin | [END_REF]:

∆C sci (ρ) = (C 2 (0) + 1/N ph )/ M (ρ) (11)
where N ph is the mean number of photons per coherence area and C 2 (0) is the intensity dispersion (= Aσ 2 I , where σ 2 I is the scintillation index). The read-out noise and/or recording noise are not considered here. The number of independent cells M (ρ) is given by the ratio of the overlapping pupil area S to the coherence area of the scintillation patterns. Following the detailed analysis performed by (Vernin & Azouit 1983), we take it as the Fresnel zone area (λd 0 /2) where d 0 is the distance of the dominant turbulent layer which governs the size of the noisy structures in the covariance function. With circular aperture of diameter D, the overlapping pupil area is

S(x) = f (x) D 2 /2 with x = ρ/D and f (x) = arccos(x)-x(1-x 2 ) 1/2 . Hence: M (ρ) = D 2 f (x) λ d 0 • (12)
From Eq. ( 9) applied at ρ = r j , the location of the maximum of the jth component, we deduce the expression of the uncertainty of the optical turbulence factor, for the layer at distance d j :

∆ Jj = ∆C sci (r j ) B K(0, d j ) • (13)
With K(0, d j ) = 19.12 λ -7/6 d 5/6 j , we obtain a general expression for the rms noise per frame in SCIDAR measurements:

∆ Jj = 5.23 10 -2 λ 5/3 d -5/6 j d 1/2 0 (C 2 (0) + 1/N ph ) B D f (x) (14)
with x = θd j /D. For N independent frames, ∆ Jj is multiplied by N -1/2 . It is plotted in Fig. 3 in terms of the distance d j to the turbulent layer for N = 1500, B = 0.25 (i.e., components of equal magnitude) and λ = 0.53 µm.

The coefficients (C 2 (0) + 1/N ph ) = 0.15 and d 0 = 17 km are close to the measured values with our observations (Sect. 5.3). Hence with aperture diameters larger than 1.5 m, the altitude range above ∼9 km can be probed with an uncertainty smaller than 10 -15 [m 1/3 ] for the turbulence factor.

Observations

Instrumental setup

The observations were carried out with the PISCO2 speckle camera (Prieur et al. 1998), developed by Observatoire Midi-Pyrénées and operated at the Cassegrain Focus of the 2-meter Télescope Bernard Lyot (TBL) of the Pic du Midi Observatory (altitude: 2880 m). It is a remotely controlled versatile instrument that can be configured in various observing modes during the observations (i.e., direct imaging, spectroscopy and pupil imaging) which provides a powerful tool for investigating the field of close binary stars, as already shown in previous publications (Aristidi et al. 1999;[START_REF] Scardia | [END_REF]Prieur et al. 2000).

The PISCO speckle camera was used in its pupil imaging mode with the ICCD (intensified CCD with a multichannel plate) of Nice University (Aristidi et al. 1997). An example of the pupil image is given in Fig. 4. The oval shape is due to an internal diaphragm that was left there by error. The scale on the output digitized 284× 388 pixel images was 0.763 cm/pixel in the pupil plane which corresponds to a scale of distance d = r/θ of 208.5 m/pixel for γ Ari and 141.8 m/pixel for γ Del along the line of sight.

For the orientation of the detector, we used the calibration done for a program of speckle observations during the same night [START_REF] Scardia | [END_REF].

Observed stars

The binaries best suited for our purpose in September were γ Del and γ Ari (cf. Table 1), with a small brightness difference and bright enough to be detected by the ICCD in the pupil image with a short exposure time. We also

Observing conditions

Binary star observations were performed during two short periods during the night of 5-6th Sep. 1998, with a seeing value of ∼1.5 and some atmospheric absorption, especially during γ Del observations. Data from the weather station (Table 2) show an unusual temperature rise at ground level during that night because of the arrival of a perturbation from the West (see Sect. 5.2).

Data processing and analysis

Pre-processing

The SVHS tapes recorded during the observations were digitized by a specially-designed C++ program which controls a Video Cassette Recorder (VCR hereafter) Panasonic AG-7355 with a RS232 link and a digitizing board (Ellips/Full Rio) connected to the PCI bus of a Penthium MMX 166 MHz. Sets of 200 frames were processed at a rate of 50 frames/s and buffered to the RAM memory of the PC to allow for the computation of the mean normalized covariance function as defined in Eq. ( 10). This step was rather lengthy (a few hours) due to the number of elementary frames (∼15 000 for γ Del).

Experimental C 2 (ρ) functions

For γ Ari and γ Del, the C 2 (ρ) functions exhibit an elongated knotty pattern aligned along the direction of the line joining the two components of the double star (cf. Fig. 5).

The central peak and the central line are perturbed by a read-out noise which shows a correlation between pixels along the lines. Fortunately, this did not affect the SCIDAR measurements since they were done outside this peak (cf. Sect. 2.2). Another instrumental contribution was an oblique fringed pattern in C 2 (ρ) which was removed by Fourier filtering. This video noise appears when the level of the intensity is very low, as it is the case here because of the very short exposure time (τ < 3 msec). This noise was larger in the case of γ Del, for which the intensity level was lower and τ = 2 msec. It is probably due to interferences of the line frequency of the camera and/or the VCR when recording the data.

To verify the robustness of our results we performed the following tests:

(i) we changed the parameters of the digitization of the frames. It appeared that the results were stable and that the standard set of parameters was optimal in terms of noise (Contrast = 70, Brightness = 140 for the Ellips/RIO card); (ii) we only used a subset of the data by putting a smaller square mask on the pupil: the results were more noisy but very similar; (iii) we also performed the same processing on the data of the single star β Ari, which did not exhibit any significant pattern.

Derivation of the C 2 N profile with MEM

Theoretically, all the information needed to retreive C 2 N (h) is contained in a radial section of C 2 (ρ), along the double star separation (cf. Sect. 2.2). In order to eliminate the central peak which contains the uncorrelated noise and where the contribution of each layer is undistinguishable from that of the others, since they are added, we compute the difference of the sections of the measured autocorrelation function parallel and perpendicular to the star separation, C 2 (ρ) and C ⊥ 2 (ρ) respectively. This quantity can be written as Eq. ( 8) plus an additive noise function N (ρ): The resulting equation is of Fredholm type and can be inverted by finding a solution that maximizes the joint entropy of the unknown quantities C 2 N (h) and N (ρ). The entropy is calculated analytically. Its maximization, using the Lagrange multipliers method, leads to a system of non-linear equations, which is solved by a Newtonian iterative algorithm. In each iteration, an auto-correlation function is calculated from the retrieved C 2 N (h) and N (ρ). The iterations are stopped when the difference between this calculated auto-correlation and the measured one has a variance which is less than the estimated variance of the noise. This method was originally developed by (Vernin 1984). The program used here was written by J. Vernin and R. Avila (Avila 1998).

C 2 (ρ) -C ⊥ 2 (ρ) = C sci (ρ) + N (ρ). ( 15
)

Derivation of the C 2 N profile with CLEAN

We Eq. ( 1)). The maxima are searched within two regions of the C 2 (ρ) image: the "binary zone", i.e., a sector centered on the direction joining the two components of the binary and whose opening angle is ajusted to the width of the covariance function C sci (ρ) (cf. Fig. 2), and the "test zone", i.e. a region further out (see Fig. 6c) which is used to determine the noise level of the image. When this noise level is reached, the process is stopped. It then outputs a CLEAN map (Fig. 6b), a final residual map (Fig. 6c) and a list of components ( Jk ).

We then follow the general scheme used in radioastronomy which convolves the CLEAN components by the "CLEAN beam", generally Gaussian, to generate the CLEAN map (Schwarz 1978). The final C 2 N profile is obtained by the convolution of the list ( Jk ) with a set of normalized Gaussian functions centered at d k whose sigma is equal to the resolution ∆d k of the SCIDAR measurements at this distance d k :

C 2 N (d) ≈ k Jk × 1 ∆d k √ 2π exp - (d -d k ) 2 2∆d k (17)
with ∆d k = 0.34 √ λd k /θ (cf. Eq. ( 7) which gives ∆ j the F W HM , i.e., 2.3σ of a Gaussian). One could object that this operation degrades the resolution, but (i) this convolution is part of the CLEAN algorithm and regularizes it and (ii) it takes into account the physics governing the SCIDAR detection, more precisely, the Fresnel propagation (cf. Sect. 2). A higher resolution as in the case of our current implementation of MEM (cf. Sect. 5) would actually be a "super-resolution" relative to the data and possibly subject to artefacts.

Results and discussion

C 2 N (h) profiles

A set of 9 C 2 N profiles was computed for each binary star observation with MEM (Fig. 7) and CLEAN (Fig. 8). Each profile corresponds to a sequence of 30 s, and the sequences are contiguous. We have checked that both programs were consistent in the case of good signal to noise ratio (SNR) and in particular lead to similar values of the integral C 2 N (h)dh: we found an agreement within ∼4%.

In the case of faint C 2 N components, these programs lead to slightly different results (Figs. 7 and8).

The MEM program provides a higher resolution in altitude and (consequently) more noisy results. This method is known to lead to slightly "over-resolved" structures. Another reason for a higher noise level is that our current implementation of MEM works on a slice of the C 2 (ρ) function, whereas our CLEAN program operates on the full 2-D C 2 (ρ). A future improvement of the MEM program will consist of extending it to a full 2-D analysis.

In Figs. 7 and 8 we see a rapid change in the the turbulence content in the case of γ Ari observations. During the first 3 min the uppermost turbulent layer at h = 19 km fades, whereas the layer at 12 km becomes more turbulent and dominates the whole profile. It then decreases leading to a quiet featureless turbulent profile. If we take into account the big difference of the wind velocity of these two layers (∆v ∼ 40 m/s as we shall see in Sect. 5.2), we understand that a significant change would have had occurred for observations with an adaptive optics system, for instance, in terms of temporal anisoplanetism (Klückers et al. 1998). This example shows the interest of a continuous monitoring of the turbulence profile to improve the performance of adaptive optics for very large telescopes or interferometers.

The profiles obtained with γ Del do not show such dramatic changes and are dominated by a turbulent layer at h = 14 km. The lower part of the curves (below ∼8 km) should be taken with cautious since the conventional SCIDAR technique is limited to rather high altitudes.

Profiles of wind velocity and direction

The wind velocity and direction were derived from the analysis of C w 2 (ρ): andc), the upper part shows all the clean components within the "binary" and the "test" zone, the bottom part shows the components selected within the "binary" zone only mean images (cf. Eq. ( 10)). Examples of experimental C w 2 (ρ) functions are shown in Fig. 9. Each turbulent layer produces triplets, as in the case of C 2 (ρ), but these triplets are translated from the center because of the wind (Taylor's hypothesis of "frozen" turbulence transported by the wind). This shift allows the measurement of the wind velocity and direction, whereas the distance of the furthest components gives the altitude of the layer. This method was proposed by Avila (1998) and Klückers et al. (1998) and was recently shown to give very reliable velocity measurements on the whole upper atmosphere, in full agreement with simultaneous balloon measurements (Avila et al. 2001).

C w 2 (ρ) = C(ρ, ∆t) -C I0 (ρ) C I0 (ρ) (18
We have developed a program based on the CLEAN algorithm to measure the wind velocity and direction on these cross-correlation functions. This program looks for "triplets" aligned with the direction of separation of the binary. For each triplet, the center of the central patch is accurately determined by fitting a Gaussian to this patch and the two other components are "cleaned" by removing covariance functions C 1 (ρ) (Fig. 2), following the same iterative process as described in Sect. 4.4. An example of such a reduction process is given in Fig. 10, whereas the whole profiles obtained from our measurements are given in Fig. 11. For γ Ari the mean direction of the wind was nearly perpendicular to the separation of the two stars, which facilited the measurements, whereas these two directions were nearly parallel for γ Del. This (and a worse SNR of the data) explains the smaller number of measurements in that case.

The velocity profiles are similar for γ Ari and γ Del and in good agreement with the profiles obtained at Cerro Tololo by Avila et al. (2001). In our case we note the presence of high velocity winds at an altitude of ∼13 km with speeds of ∼50 m/s, which is larger than the maximum of ∼40 m/s observed by Avila et al. (2001).

As shown by the ground level measurements (Table 2), a hot front was coming from the West during that night. In the second part of the night (γ Ari observations) the air masses at altitude were moving along two distinct directions, ∼260 • and ∼290 • , the latter corresponding to the direction measured during the first part of the night (with γ Del). This rapid change in the atmospheric conditions explains the (transient) co-existence of two wind directions at the same altitude of ∼20 km. The arrival of this hot front could also explain the detection of turbulence at very high altitudes ∼24 km, which is rather unusual for SCIDAR measurements.

Limiting sensitivity of our observations

As shown in Fig. 12, in the extraction process of turbulence distribution with CLEAN, the components cannot be detected below some sensitivity threshold which is dependent on distance.

Since the size of the components increases with the distance as d 1/2 , the curve of detection with constant SNR (solid line in Fig. 12) can be obtained by multiplying the rms noise ∆ Jj (as given in Eq. ( 14)) by (d j /d 0 ) 1/2 (dashed line in Fig. 12). As in Sect. 2.3, we assume here a constant area for the noise fluctuations which is proportional to the distance d 0 of the dominant turbulent layer responsible for scintillations.

The model correctly fits variations of sensitivity threshold for γ Ari. Actually, a high sensitivity of a few 10 -16 m 1/3 has been reached for the upper most turbulent layers. Probing the layers below ∼8 km would have required "generalized" SCIDAR but in that case the scintillation index would have increased because of the contribution of the lower layers. Hence the noise level would have been larger. Turbulence detection is not as good for γ Del and is worse than expected by our model. This can be explained by the low level of the input signal; noise contributions from the detection and recording systems should be added in Eq. ( 14) for such a weak signal. Another uncertainty concerns the amount of atmospheric absorption which was significant during γ Del observations. In Fig. 12, we have assumed an atmospheric transmission of 0.5 for γ Del and 0.8 for γ Ari, which is only a raw estimate. We also note that this model of sensitivity does not take into account a possible elongation of the noise pattern and the attenuation of the SCIDAR signal due to the finite integration time of each observation (next section), which could explain why the detectivity threshold of γ Del observations is not consistent with a constant SNR.

Temporal filtering

The finite integration time τ of the measurement causes an attenuation of the signal compared to the case of an "instantaneous" measurement which was assumed in Sect. 2. Let V j be the wind velocity of the turbulent layer at a distance d j . Assuming a frozen turbulence, the K function 5) and ( 6)) becomes [START_REF] Tokovinin | [END_REF]:

K(ρ, d j , V j τ ) = 1.53 λ -2 f -11/3 sin 2 (πλd j f 2 ) × sinc 2 (f • V j τ ) exp(2iπf • ρ) df . ( 19
)
This relation is valid as long as V j τ is much smaller than the diameter of the pupil. Figure 13 shows that the value of the central peak K(0, d j , V j τ ) decreases significantly from its theoretical value of one as soon as V j τ > 0.05 m with a larger effect for the lower turbulent layers. Using (Eq. ( 19)), the attenuation was computed for the secondary peaks of γ Ari with τ = 3 msec in Table 3. The effect is significant for the layers at altitudes in the range 10-15 km which have high velocity winds. Likewise, for γ Del, with a turbulent layer at 12 km and τ = 2 msec, the attenuation factor of the central peak is ∼0.5.

Note that the K attenuation factor of Table 3 is that of the peak, not of the integral of the useful signal in the covariance plane, so that the "Corrected J amplitude" 2). Note the significant change of the wind direction at the ground level due to the arrival of a perturbation should be taken as an upper bound to the detected turbulence factor. Using (Eq. ( 19)), we also computed the deformation of the 2-D profile of the covariance function along two directions: parallel to the wind and perpendicular to it (Fig. 14). It appears that the profile is elongated along the direction of the wind and nearly unaffected perpendicularly. This is visible in the experimental C 2 (ρ) functions: the secondary peaks for altitudes at ∼12 km are elongated along the wind direction (e.g., Fig. 6a). A possible improvement of our 2-D CLEAN algorithm could take into account the actual shape of the profile, elongated along the wind direction, but this is beyond the scope of this paper.

Contribution to the seeing from different altitudes

A seeing of 1.55 ± 0.05 was determined just before and after γ Ari observations, that is a Fried parameter r 0 = 0.068 m. Since

r 0 =   0.423 2π λ 2 j J j   -3/5 , ( 20
)
the corresponding total optical turbulence factor JT = 1.48 10 -12 m 1/3 . The upper limit of the total content for turbulent layers above 11 km, measured with our observations of γ Ari (sum of the last row of Table 3) is ∼6.6 10 -14 m 1/3 , which is less than 5% of JT . Such a result is consistent with previous findings (Rocca et al. 1974). The contribution of the first kilometers, including the dome seeing and the orographic effects of the site are dominant for the seeing.

Conclusion

The PISCO speckle camera of Observatoire Midi-Pyrénées has produced SCIDAR measurements for the first time and allowed the derivation of C 2 N and wind profiles. Our implementation of the CLEAN algorithm on the 2-D C 2 (ρ) function showed a higher robustness to the noise which is suitable for the analysis of the time variations. The other traditional MEM approach would also gain from a full use of the 2-D data instead of a slice only. The elongation of the scintillation covariance function due to strong winds in altitude also suggests that a full 2-D processing taking this effect into account would be desirable.

Following the CLEAN approach, an automatic procedure was developed for measuring wind parameters in altitude (velocity and direction) which allowed a full characterization of the turbulence in the upper atmosphere.

The parameters derived from these observations have already been used for simulations of astrometric uncertainties with a dual-field optical interferometer [START_REF] Daigne | Astronomical site evaluation in the visible and radio range[END_REF]. SCIDAR measurements are not sensitive to turbulence scales larger than a few 0.1 m, whereas astrometric uncertainty is mainly dependent on the shape of turbulence spectra at much larger scales (a few 10 m). A more complete remote investigation of atmospheric turbulence in altitude could be performed with simultaneous observations of differential angle-of-arrival between field stars.

For γ Del, we have observed a rapid change of the turbulence profile with a time-scale of a few minutes only which shows the interest of a continuous turbulence monitoring to improve the performances of future adaptive optics systems in the case of very large telescopes or interferometers.

Fig. 1 .

 1 Fig. 1. Schematic of the irradiance fluctuations and their correlation with double star observation, or the SCIDAR basic principle

Fig. 2 .

 2 Fig. 2. Covariance function C1(ρ) of irradiance due to a single turbulent layer, with optical turbulence factor J = 3.10 -14 [m 1/3 ], at different distances: h = 5, 10, 15, 20, 25 km. The wavelength is λ = 0.53 µm

Fig. 3 .

 3 Fig. 3. Noise level (rms) in SCIDAR measurements of the optical turbulence factor J (in 10 -15 m 1/3 ), with different circular apertures, whose diameter D is in the range 1-2 m. The angular separation of the observed binary star is 8 (solid line), or 12 (dashed line)

Fig. 4 .

 4 Fig. 4. Image of the pupil

  have written a new program in C based on the CLEAN algorithm which takes advantage of the 2-D information in order to improve the robustness of the inversion. For each step k, it looks for the location ρ k and value z k of the maximum in the 2-D residual map, then computes d k , its corresponding distance along the line of sight, and subtracts a fraction of the 2-D function C sci (ρ, d k ) = B Jk K(ρ, d k ) from the residual map, with: Jk = z k 19.12 λ -7/6 d where B = 0.25 for γ Ari, and B = 0.23 for γ Del (cf.

Fig. 5 .

 5 Fig. 5. Examples of C2( ) for γ Ari (left) and γ Del (right). North is in the upper part of the image, East to the left. The central bright line is an artefact due to the video scanning

Fig. 6 .

 6 Fig. 6. Example of C 2 N inversion of C2( ) function a) of γ Ari with the CLEAN derived method. b) clean image; c) residuals; d) restored C 2 N profile. For b)and c), the upper part shows all the clean components within the "binary" and the "test" zone, the bottom part shows the components selected within the "binary" zone only

Fig. 7 .

 7 Fig. 7. Set of C 2 N profiles computed with γ Ari (top) and γ Del (bottom) (every 30 s) with MEM

Fig. 8 .

 8 Fig. 8. Set of C 2 N profiles computed with γ Ari (top) and γ Del (bottom) (every 30 s) with CLEAN

Fig. 9 .Fig. 10 .

 910 Fig. 9. C w 2 ( ) of γ Ari with ∆t = 20 msec: wind determination at two moments separated by 2 min

Fig. 11 .

 11 Fig. 11. Vertical wind velocity (top) and direction (bottom) profiles measured with γ Del at 23h00 U.T. (left) and γ Ari at 3h00 U.T. (right). Filled circles: automatic determination, open circles: interactive. The lowest point was provided by ground measurements (cf. Table2). Note the significant change of the wind direction at the ground level due to the arrival of a perturbation

Fig. 12 .

 12 Fig. 12. J amplitude of the components (small circles) detected with the CLEAN algorithm along the different observing sequences. The sensitivity threshold of our SCIDAR observations is shown as a solid curve. The dashed curve is the noise floor as given by (Eq. (14)) for the TBL (D = 2 m plus central obscuration). a) γ Ari (top) with σ 2 I = 0.14, N ph = 110 photons and d0 = 17 km; b) γ Del (bottom) with σ 2 I = 0.18, N ph = 30 photons and d0 = 12 km

Fig. 13 .

 13 Fig. 13. Attenuation factor of the central peak of the scintillation covariance function due to the finite integration time of the measurements, for distance values of the turbulent layer in the range 5-25 km

Table 1 .

 1 List of observed objects. V : total magnitude, Elev.: elevation above the horizon, τ : integration time of elementary frames

	Name	HD number	V	Date	Time	Elev.	τ	Comments
					(U.T.)	•	(msec)
	γ Del HD 197963-64 3.9 05/09/98 22h46	60.4	2	θ = 11 1, posi. angle: 268 • , ∆m = 0.7
	α Del	HD 196867	3.8 05/09/98 21h52	62.9	2	Reference for γ Del
	γ Ari	HD 11502-03	3.9 06/09/98	3h00	67.8	3	θ = 7 55, posi. angle: 0.7 • , ∆m = 0.05
	β Ari	HD 11636	2.6 06/09/98	3h02	67.8	3	Reference for γ Ari

Table 2 .

 2 Measurements made at the weather station of Pic du Midi at the ground level. The temperature (Col. 2) is in degrees Celsius. The direction orientation (Col. 3) is such that North = 360 • and West = 270 •

	Time	T	Wind direction	Wind speed
	(U.T.)	• C	•	(m/s)
				(mean) (maxi)
	21h00	4.9	330	12	14
	22h30	5.2	310	6	12
	23h00	6.5	330	9	14
	00h00	7.4	310	7	13
	03h00	8.6	270	9	14
	06h00	9.2	280	9	8
	08h00 11.0	270	11	14

Table 3 .

 3 Parameters of the optical turbulence for the 6 layers detected beyond a distance of 8 km in Scidar observation of γ Ari during the first two minutes of observation. J is in 10 -15 [m 1/3 ]

	Turbulence parameters for the different layers
	distance [km]	19.6 18.8 17.1 13.7 13.1 9.4
	altitude [km]	21.0 20.3 18.7 15.6 15.0 11.6
	wind velocity [m/s]	14.5 14.5 6.9 28.6 38.1 46.9
	wind direction [degree] 253 301 247 274 286 276
	J amplitude	2.2 3.0 11.2 3.0 5.0 10.7
	Vj τ [m]	.043 .043 .021 .086 .114 .141
	K attenuation	0.86 0.85 0.95 0.59 0.45 0.33
	Corrected J amplitude 2.6 3.5 11.8 5.1 11.1 32.4

PISCO stands for "Pupil Interferometry Speckle camera and COronagraph".

Although β Ari is a spectroscopic binary, the two components are close enough to be considered as a single star in scintillation measurements.

Acknowledgements. We are indebted to M. Scardia and E. Aristidi for giving us time during their observing run. We are grateful to Météo-France and Mr Bornuat, director of the Weather Center of Tarbes-Lourdes-Pyrénées Airfield, for kindly providing us with data from the weather unit of Pic du Midi for Table 2. We also thank the technical staff of the "Télescope Bernard Lyot" for providing assistance during the observations. R. Avila was supported by the grant J32412E from CONACyT.


Uffe Thomas Jankvist

Marja Van Den Heuvel-Panhuizen

Michiel Veldhuis

Introduction to the Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11)

Uffe Thomas Jankvist 1 ; Marja van den Heuvel-Panhuizen 2 ; Michiel Veldhuis 3 1 Danish School of Education, Aarhus University, Denmark, utj@edu.au.dk 2 Freudenthal Group & Freudenthal Institute, Utrecht University, Netherlands, m.vandenheuvelpanhuizen@uu.nl; Nord University, Norway, m.vandenheuvel-panhuizen@nord.no 2 Freudenthal Group, Utrecht University, Netherlands, m.veldhuis@uu.nl; iPabo University of Applied Sciences, Amsterdam, Netherlands, m.veldhuis@ipabo.nl

About CERME11

The

Editorial information

These proceedings are available as a complete volume online on the ERME website and each individual text is also available on the HAL open archive, where it can be found through keywords, title or author name. This has been the practice since CERME9, to increase the visibility of the huge work done in CERME conferences.

This volume begins with texts corresponding to the four plenary activities of CERME11: the plenary lecture by Paul Drijvers (The Netherlands) on "Embodied instrumentation: combining different views on using digital technology in mathematics education"; the plenary lecture by Kathleen M. Clark (USA) on "History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future"; the plenary lecture by Sebastian Rezat (Germany) on "Extensions of number systems: continuities and discontinuities revisited"; and finally the "ERME anniversary panel on the occasion of the 20th birthday of the European Society for Research in Mathematics Education" by Konrad Krainer (Austria), Hanna Palmér (Sweden), Barbara Jaworski (UK), Susanne Prediger (Germany), Paolo Boero (Italy), Simon Modeste (France), Tommy Dreyfus (Israel), and Jana Žalská (Czech Republic).

After the plenaries, the reader will find 26 chapters corresponding to the work done in the TWGs of CERME11 (all the split TWGs chose to do combined introductions). These chapters follow a similar structure: they start with an introduction; then the long contributions (8-page papers) and the short contributions (2 pages) are presented -in alphabetical order by first author's name. However, TWG17 has chosen a different order, corresponding to subthemes in the group.

There are two kinds of introductions to the TWGs, according to the team's choice: short introductions (4 pages) presenting the contributions; or long introductions (8 pages), which propose, in addition, an analysis of the current research on the theme of the TWG, and perspectives for the future. TWGs 06, 07, 09, 14, 15, 17, 19, 22, 23, 25 and 26 have chosen this form of long introduction.

The publication of these proceedings is the result of a collaborative work, involving CERME11 IPC, the TWG leaders and co-leaders, and the LOC co-chair. We warmly thank all these people for their involvement, and hope that this volume will contribute to the development of mathematics education research in Europe and beyond.