Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Propagation of ultrahigh energy nuclei in clusters of galaxies: resulting composition and secondary emissions

We study the survival of ultrahigh energy nuclei injected in clusters of galaxies, as well as their secondary neutrino and photon emissions, using a complete numerical propagation method and a realistic modeling of the magnetic, baryonic and photonic backgrounds. It is found that the survival of heavy nuclei highly depends on the injection position and on the profile of the magnetic field. Taking into account the limited lifetime of the central source could also lead in some cases to the detection of a cosmic ray afterglow, temporally decorrelated from neutrino and gamma ray emissions. We calculate that the diffusive neutrino flux around 1 PeV coming from clusters of galaxies may have a chance to be detected by current instruments. The observation of single sources in neutrinos and in gamma rays produced by ultrahigh energy cosmic rays will be more difficult. Signals coming from lower energy cosmic rays (E < 1 PeV), if they exist, might however be detected by Fermi, for reasonable sets of parameters.Comment: 19 pages, 15 figures, version to appear in ApJ (minor changes

The 0.4-Mo Eclipsing Binary CU Cancri: Absolute Dimensions, Comparison with Evolutionary Models and Possible Evidence for a Circumstellar Dust Disk

Photometric observations in the R and I bands of the detached M-type double-lined eclipsing binary CU Cnc have been acquired and analysed. The photometric elements obtained from the analysis of the light curves have been combined with an existing spectroscopic solution to yield high-precision (errors<2%) absolute dimensions: M_A=0.4333+/-0.0017 Mo, M_B=0.3980+/-0.0014 Mo, R_A=0.4317+/-0.0052 Ro, and R_B=0.3908+/-0.0094 Ro. The mean effective temperature of the system has been estimated to be Teff=3140+/-150 K by comparing multi-band photometry with synthetic colors computed from model atmospheres. Additionally, we have been able to obtain an estimate for the age (~320 Myr) and chemical composition ([Fe/H]~0.0) of the binary system through its membership of the Castor moving group. With all these observational constraints, we have carried out a critical test of recent stellar models for low-mass stars. The comparison reveals that most evolutionary models underestimate the radius of the stars by as much as 10%, thus confirming the trend observed by Torres & Ribas (2002) for YY Gem and V818 Tau. In the mass-absolute magnitude diagram, CU Cnc is observed to be dimmer than other stars of the same mass. After ruling out a number of different scenarios, the apparent faintness of CU Cnc can be explained if its components are some 10% cooler than similar-mass stars or if there is some source of circumstellar dust absorption. The latter could be a tantalizing indirect evidence for a coplanar (Vega-like) dusty disk around this relatively young M-type binary.Comment: 14 pages, 5 figures, 6 tables. Accepted for publication in A&A. Tables 1 and 2 available in electronic form at the CDS after publicatio

Metallicity, temperature, and gravity scales of M subdwarfs

The aim of the project is to define a metallicity/gravity/temperature scale vs spectral types for metal-poor M dwarfs. We obtained intermediate-resolution ultraviolet (R~3300), optical (R~5400), and near-infrared (R~3900) spectra of 43 M subdwarfs (sdM), extreme subdwarfs (esdM), and ultra-subdwarfs (usdM) with the X-shooter spectrograph on the European Southern Observatory Very Large Telescope. We compared our atlas of spectra to the latest BT-Settl synthetic spectral energy distribution over a wide range of metallicities, gravities, and effective temperatures to infer the physical properties for the whole M dwarf sequence (M0--M9.5) at sub-solar metallicities and constrain the latest state-of-the-art atmospheric models. The BT-Settl models reproduce well the observed spectra across the 450-2500 nm wavelength range except for a few regions. We find that the best fits are obtained for gravities of log(g) = 5.0-5.5 dex for the three metal classes. We infer metallicities of [Fe/H] = -0.5, -1.5, and -2.0+/-0.5 dex and effective temperatures of 3700-2600 K, 3800-2900 K, and 3700-2900 K for subdwarfs, extreme subdwarfs, and ultra-subdwarfs, respectively. Metal-poor M dwarfs tend to be warmer by about 200+/-100 K and exhibit higher gravity than their solar-metallicity counterparts. We derive abundances of several elements (Fe, Na, K, Ca, Ti) for our sample but cannot describe their atmospheres with a single metallicity parameter. Our metallicity scale expands the current scales available for midly metal-poor planet-host low-mass stars. Our compendium of moderate-resolution spectra covering the 0.45--2.5 micron range represents an important legacy value for large-scale surveys and space missions to come.Comment: 31 pages, 4 pages, 4 tables + 1 appendix with 12 figures and 5 tables. Accepted for publication in A&A. Version prior to language editio

Rotation and accretion of very low mass objects in the SigmaOri cluster

We report on two photometric monitoring campaigns of Very Low Mass (VLM) objects in the young open cluster around SigmaOrionis. Our targets were pre-selected with multi-filter photometry in a field of 0.36 sqdeg. For 23 of these objects, spanning a mass range from 0.03 to 0.7 MS, we detect periodic variability. Of these, 16 exhibit low-level variability, with amplitudes of less than 0.2 mag in the I-band, which is mostly well-approximated by a sine wave. These periodicities are probably caused by photospheric spots co-rotating with the objects. In contrast, the remaining variable targets show high-level variability with amplitudes ranging from 0.25 to 1.1 mag, consisting of a periodic light variation onto which short-term fluctuations are superimposed. This variability pattern is very similar to the photometric behaviour of solar-mass, classical T Tauri stars. Low-resolution spectra of a few of these objects reveal strong Halpha and Ca-triplet emission, indicative of ongoing accretion processes. This suggests that 5-7% of our targets still possess a circumstellar disk. In combination with previous results for younger objects, this translates into a disk lifetime of 3-4 Myr, significantly shorter than for solar mass stars. The highly variable objects rotate on average slower than the low-amplitude variables, which is expected in terms of a disk-locking scenario. There is a trend towards faster rotation with decreasing mass, which might be caused by shortening of the disk lifetimes or attenuation of magnetic fields.Comment: 19 pages, 14 figures, A&A, in pres

Large Amplitude Photometric Variability of the Candidate Protoplanet TMR-1C

In their HST/NICMOS observations, Terebey et al. 1998 detected a candidate protoplanet, TMR-1C, that lies at a separation of about 10" (~1000 AU) from the Class I protobinary TMR-1 (IRAS 04361+2547). A narrow filament-like structure was observed extending south-east from the central proto-binary system towards TMR-1C, suggesting a morphology in which the candidate protoplanet may have been ejected from the TMR-1 system. Follow-up low-resolution spectroscopy could not confirm if this object is a protoplanet or a low-luminosity background star. We present two epochs of near-infrared photometric observations obtained at the CFHT of TMR-1C. The time span of ~7 years between the two sets of observations provides with an opportunity to, (a) check for any photometric variability similar to that observed among young stellar objects, which would indicate the youth of this source, and, (b) determine the proper motion. TMR-1C displays large photometric variability between 1 and 2 mag in both the H- and Ks-bands. From our 2002 observations, we find a (H-Ks) color of 0.3 mag, which is much bluer than the value of 1.3 mag reported by T98 from HST observations. Also, we observe brightening in both the H- and Ks-bands when the colors are bluer, i.e. the object gets redder as it becomes fainter. We have explored the possible origins for the observed variability, and find extinction due to the presence of circumstellar material to be the most likely scenario. The observed large-amplitude photometric variations, and the possible presence of a circumstellar disk, are strong arguments against this object being an old background star.Comment: Accepted in A&