den Hartog, Roland, Absil, Olivier, Kaltenegger, L., Gondoin, P., Wilhelm, R., and Fridlund, M.

In M., Fridlund & T., Henning (Eds.), Towards Other Earths: DARWIN/TPF and the Search for Extrasolar Terrestrial Planets (pp. 399-402). Noordwijk, Netherlands: ESA (2003).

Subjects

Nulling Interferometer, Extrasolar Planets, Physical, chemical, mathematical & earth Sciences :: Space science, astronomy & astrophysics, and Physique, chimie, mathématiques & sciences de la terre :: Aérospatiale, astronomie & astrophysique

Abstract

The prime objective of GENIE (Ground-based European Nulling Interferometry Experiment) is to obtain experience with the design, construction and operation of an IR nulling interferometer, as a preparation for the DARWIN/TPF mission. In this context, the detection of a planet orbiting another star would provide an excellent demonstration of nulling interferometry. Doing this through the atmosphere, however, is a formidable task. In this paper we assess the prospects of detecting, with nulling interferometry on ESO's VLT, a Hot Jupiter, a giant planet in a close orbit around its parent star. First we discuss the definition of the optimal target. Then we present a simulated observation of the Tau Bootis system, which suggests that GENIE, in a L'-band single Bracewell configuration, could detect the hot Jupiter in a few hours time with a signal-to-noise ratio of up to ~80. Although there are strong requirements on the control-loop performance, background subtraction and accuracy of the photometry calibration, we conclude that at present there do not seem to be fundamental problems that would prevent GENIE from detecting hot Jupiters. Hence the answer to the question in the title is yes.

Physical, chemical, mathematical & earth Sciences :: Mathematics and Physique, chimie, mathématiques & sciences de la terre :: Mathématiques

Abstract

We choose the abelian group ($\bbZ_2^n, +$) where $\bbZ_2 = \bbZ / 2 \bbZ$ and define a $\bbZ_2^n$-graded vector space \[E = \bigoplus_{x \in \bbZ_2^n} E_x \]together with a multiplication $ \cdot :E \times E \longrightarrow E$respecting the grading \[E_x \cdot E_y \subset E_{x+y} \quad \forall x,y \in \bbZ_2^n.\]This is called a $\bbZ_2^n$-graded algebra. We are interested in particular $\bbZ_2^n$-graded algebras where the product in noncommutative and nonassociative. This talk consists of two parts. The first one is the study of a series of $\bbZ_2^n$-graded algebras of finite dimension ($2^n$) where $n \geq 3$. This series of real noncommutative and nonassociative algebras, denoted $\bbO_{p,q}$ ($p+q=n$), generalizes the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. The first \emph{question} is to classify these algebras up to isomorphisms. The classification table of $\bbO_{p,q}$ is quite similar to that of the real Clifford algebras $\cC l_{p,q}$. The second \emph{question} is to find a periodicity between these algebras. The periodicity for the algebras $\bbO_{p,q}$ is analogous to the periodicity for the Clifford algebras $\cC l_{p,q}$. In the second part we study $\bbZ_2$-graded algebras ($n=0$, ``superalgebras'') that can be of infinite dimension.We consider two kind of superalgebras $\cL_{g,N}$ and $\cJ_{g,N}$ that are noncommutative and nonassociative\footnote{The construction coming from spaces on a compact Riemann surface of genus $g$ with $N$ punctures}. Nevertheless, these superalgebras link together the classical Lie algebras and the classical commutative and associative algebras. The two last \emph{questions} are can we ``extend'' the algebras $\cL_{g,N}$ and $\cJ_{g,N}$? The first answer is yes (for $\cL_{g,N}$), while the second one is no (for $\cJ_{g,N}$). However, we can ``extend'' module $\cJ_{g,N}^*$.