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Register a new userThe GL 569 Multiple System
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M. Simon SUNY Stony Brook
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We report the results of high spectral and angular resolution infrared observations of the multiple system GL 569 A and B that were intended to measure the dynamical masses of the brown dwarf binary believed to comprise GL 569 B. Our analysis did not yield this result but, instead, revealed two surprises. First, at age ~100 Myr, the system is younger than had been reported earlier. Second, our spectroscopic and photometric results provide support for earlier indications that GL 569 B is actually a hierarchical brown dwarf triple rather than a binary. Our results suggest that the three components of GL 569 B have roughly equal mass, ~0.04 Msun.
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We report observations obtained with the Keck adaptive optics facility of the nearby (d=9.8 pc) binary Gl~569. The system was known to be composed of a cool primary (dM2) and a very cool secondary (dM8.5) with a separation of 5 (49 Astronomical Units). We have found that Gl~569~B is itself double with a separation of only 0.101$pm$0.002 (1 Astronomical Unit). This detection demonstrates the superb spatial resolution that can be achieved with adaptive optics at Keck. The difference in brightness between Gl~569~B and the companion is $sim$0.5 magnitudes in the J, H and K bands. Thus, both objects have similarly red colors and very likely constitute a very low-mass binary system. For reasonable assumptions about the age (0.12~Gyr--1.0~Gyr) and total mass of the system (0.09~M$_odot$--0.15~M$_odot$), we estimate that the orbital period is $sim$3 years. Follow-up observations will allow us to obtain an astrometric orbit solution and will yield direct dynamical masses that can constrain evolutionary models of very low-mass stars and brown dwarfs.
We study the spectroscopic binary system Gl 375. We employ medium resolution echelle spectra obtained at the 2.15 m telescope at the Argentinian observatory CASLEO and photometric observations obtained from the ASAS database. We separate the composite spectra into those corresponding to both components. The separated spectra allow us to confirm that the spectral types of both components are similar (dMe3.5) and to obtain precise measurements of the orbital period (P = 1.87844 days), minimum masses (M_1 sin^3 i = 0.35 M_sun and M_2 sin^3 i =0.33 M_sun) and other orbital parameters. The photometric observations exhibit a sinusoidal variation with the same period as the orbital period. We interpret this as signs of active regions carried along with rotation in a tidally synchronized system, and study the evolution of the amplitude of the modulation in longer timescales. Together with the mean magnitude, the modulation exhibits a roughly cyclic variation with a period of around 800 days. This periodicity is also found in the flux of the Ca II K lines of both components, which seem to be in phase. The periodic changes in the three observables are interpreted as a sign of a stellar activity cycle. Both components appear to be in phase, which implies that they are magnetically connected. The measured cycle of approximately 2.2 years (800 days) is consistent with previous determinations of activity cycles in similar stars.
On a Fock space constructed from $mn$ free bosons and lattice ${Bbb {Z}}^{mn}$, we give a level $n$ action of the quantum toroidal algebra $mathscr {E}_m$ associated to $mathfrak{gl}_m$, together with a level $m$ action of the quantum toroidal algebra ${mathscr E}_n$ associated to ${mathfrak {gl}}_n$. We prove that the $mathscr {E}_m$ transfer matrices commute with the $mathscr {E}_n$ transfer matrices after an appropriate identification of parameters.
Let $phi$ be a Hecke-Maass cusp form for $SL(3, mathbb{Z})$ with Langlands parameters $({bf t}_{i})_{i=1}^{3}$ satisfying $$|{bf t}_{3} - {bf t}_{2}| leq T^{1-xi -epsilon}, quad , {bf t}_{i} approx T, quad , , i=1,2,3$$ with $1/2 < xi <1$ and any $epsilon>0$. Let $f$ be a holomorphic or Maass Hecke eigenform for $SL(2,mathbb{Z})$. In this article, we prove a sub-convexity bound $$L(phi times f, frac{1}{2}) ll max { T^{frac{3}{2}-frac{xi}{4}+epsilon} , T^{frac{3}{2}-frac{1-2 xi}{4}+epsilon} } $$ for the central values $L(phi times f, frac{1}{2})$ of the Rankin-Selberg $L$-function of $phi$ and $f$, where the implied constants may depend on $f$ and $epsilon$. Conditionally, we also obtain a subconvexity bound for $L(phi times f, frac{1}{2})$ when the spectral parameters of $phi$ are in generic position, that is $${bf t}_{i} - {bf t}_{j} approx T, quad , text{for} , i eq j, quad , {bf t}_{i} approx T , , , i=1,2,3.$$
In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system attached to an n-dimensional RACP automorphic representation of GL_n of the adeles of Q is automorphic, for any positive integer n, under some natural hypotheses (namely regularity and irreducibility).
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