Loop homology of spheres and complex projective spaces

In his Inventiones paper, Ziller (Invent. Math: 1-22, 1977) computed the integral homology as a graded abelian group of the free loop space of compact, globally symmetric spaces of rank 1. Chas and Sullivan (String Topology, 1999)showed that the homology of the free loop space of a compact closed orientable manifold can be equipped with a loop product and a BV-operator making it a Batalin-Vilkovisky algebra. Cohen, Jones and Yan (The loop homology algebra of spheres and projective spaces, 2004) developed a spectral sequence which converges to the loop homology as a spectral sequence of algebras. They computed the algebra structure of the loop homology of spheres and complex projective spaces by using Ziller's results and the method of Brown-Shih (Ann. of Math. 69:223-246, 1959, Publ. Math. Inst. Hautes \'Etudes Sci. 3: 93-176, 1962). In this note we compute the loop homology algebra by using only spectral sequences and the technique of universal examples. We therefore not only obtain Zillers' and Brown-Shihs' results in an elementary way, we also replace the roundabout computations of Cohen, Jones and Yan (The loop homology algebra of spheres and projective spaces, 2004) making them independent of Ziller's and Brown-Shihs' work. Moreover we offer an elementary technique which we expect can easily be generalized and applied to a wider family of spaces, not only the globally symmetric ones.Comment: 10 pages, 8 figure

Loop space homology associated with the mod 2 Dickson invariants

Peer reviewedPublisher PD

WASP-14 b: Transit Timing analysis of 19 light curves

Although WASP-14 b is one of the most massive and densest exoplanets on a tight and eccentric orbit, it has never been a target of photometric follow-up monitoring or dedicated observing campaigns. We report on new photometric transit observations of WASP-14 b obtained within the framework of "Transit Timing Variations @ Young Exoplanet Transit Initiative" (TTV@YETI). We collected 19 light-curves of 13 individual transit events using six telescopes located in five observatories distributed in Europe and Asia. From light curve modelling, we determined the planetary, stellar, and geometrical properties of the system and found them in agreement with the values from the discovery paper. A test of the robustness of the transit times revealed that in case of a non-reproducible transit shape the uncertainties may be underestimated even with a wavelet-based error estimation methods. For the timing analysis we included two publicly available transit times from 2007 and 2009. The long observation period of seven years (2007-2013) allowed us to refine the transit ephemeris. We derived an orbital period 1.2 s longer and 10 times more precise than the one given in the discovery paper. We found no significant periodic signal in the timing-residuals and, hence, no evidence for TTV in the system.Comment: 12 pages, 10 figures, 7 table

New transit observations for HAT-P-30 b, HAT-P-37 b, TrES-5 b, WASP-28 b, WASP-36 b, and WASP-39 b

We present new transit light curves for planets in six extrasolar planetary systems. They were acquired with 0.4-2.2 m telescopes located in west Asia, Europe, and South America. When combined with literature data, they allowed us to redetermine system parameters in a homogeneous way. Our results for individual systems are in agreement with values reported in previous studies. We refined transit ephemerides and reduced uncertainties of orbital periods by a factor between 2 and 7. No sign of any variations in transit times was detected for the planets studied.Comment: Submitted to Acta Astronomic

A Possible Detection of Occultation by a Proto-planetary Clump in GM Cephei

GM Cep in the young (~4 Myr) open cluster Trumpler 37 has been known to be an abrupt variable and to have a circumstellar disk with very active accretion. Our monitoring observations in 2009-2011 revealed the star to show sporadic flare events, each with brightening of < 0.5 mag lasting for days. These brightening events, associated with a color change toward the blue, should originate from an increased accretion activity. Moreover, the star also underwent a brightness drop of ~1 mag lasting for about a month, during which the star became bluer when fainter. Such brightness drops seem to have a recurrence time scale of a year, as evidenced in our data and the photometric behavior of GM Cep over a century. Between consecutive drops, the star brightened gradually by about 1 mag and became blue at peak luminosity. We propose that the drop is caused by obscuration of the central star by an orbiting dust concentration. The UX Orionis type of activity in GM Cep therefore exemplifies the disk inhomogeneity process in transition between grain coagulation and planetesimal formation in a young circumstellar disk.Comment: In submission to the Astrophysical Journal, 4 figure

Radio-frequency discharges in Oxygen. Part 1: Modeling

In this series of three papers we present results from a combined experimental and theoretical effort to quantitatively describe capacitively coupled radio-frequency discharges in oxygen. The particle-in-cell Monte-Carlo model on which the theoretical description is based will be described in the present paper. It treats space charge fields and transport processes on an equal footing with the most important plasma-chemical reactions. For given external voltage and pressure, the model determines the electric potential within the discharge and the distribution functions for electrons, negatively charged atomic oxygen, and positively charged molecular oxygen. Previously used scattering and reaction cross section data are critically assessed and in some cases modified. To validate our model, we compare the densities in the bulk of the discharge with experimental data and find good agreement, indicating that essential aspects of an oxygen discharge are captured.Comment: 11 pages, 10 figure

Towards the Rosetta Stone of planet formation

Transiting exoplanets (TEPs) observed just about 10 Myrs after formation of their host systems may serve as the Rosetta Stone for planet formation theories. They would give strong constraints on several aspects of planet formation, e.g. time-scales (planet formation would then be possible within 10 Myrs), the radius of the planet could indicate whether planets form by gravitational collapse (being larger when young) or accretion growth (being smaller when young). We present a survey, the main goal of which is to find and then characterise TEPs in very young open clusters.Comment: Poster contribution to Detection and Dynamics of Transiting Exoplanets (Haute Provence Observatory Colloquium, 23-27 August 2010

Multi-site campaign for transit timing variations of WASP-12 b: possible detection of a long-period signal of planetary origin

The transiting planet WASP-12 b was identified as a potential target for transit timing studies because a departure from a linear ephemeris was reported in the literature. Such deviations could be caused by an additional planet in the system. We attempt to confirm the existence of claimed variations in transit timing and interpret its origin. We organised a multi-site campaign to observe transits by WASP-12 b in three observing seasons, using 0.5-2.6-metre telescopes. We obtained 61 transit light curves, many of them with sub-millimagnitude precision. The simultaneous analysis of the best-quality datasets allowed us to obtain refined system parameters, which agree with values reported in previous studies. The residuals versus a linear ephemeris reveal a possible periodic signal that may be approximated by a sinusoid with an amplitude of 0.00068+/-0.00013 d and period of 500+/-20 orbital periods of WASP-12 b. The joint analysis of timing data and published radial velocity measurements results in a two-planet model which better explains observations than single-planet scenarios. We hypothesize that WASP-12 b might be not the only planet in the system and there might be the additional 0.1 M_Jup body on a 3.6-d eccentric orbit. A dynamical analysis indicates that the proposed two-planet system is stable over long timescales.Comment: Accepted for publication in A&

Transit Timing Analysis in the HAT-P-32 system

We present the results of 45 transit observations obtained for the transiting exoplanet HAT-P-32b. The transits have been observed using several telescopes mainly throughout the YETI network. In 25 cases, complete transit light curves with a timing precision better than $1.4\:$min have been obtained. These light curves have been used to refine the system properties, namely inclination $i$, planet-to-star radius ratio $R_\textrm{p}/R_\textrm{s}$, and the ratio between the semimajor axis and the stellar radius $a/R_\textrm{s}$. First analyses by Hartman et al. (2011) suggest the existence of a second planet in the system, thus we tried to find an additional body using the transit timing variation (TTV) technique. Taking also literature data points into account, we can explain all mid-transit times by refining the linear ephemeris by 21ms. Thus we can exclude TTV amplitudes of more than $\sim1.5$min.Comment: MNRAS accepted; 13 pages, 10 figure