On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate |V(t)_{m,n}|0, p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and \epsilon is small enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where \sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was discussed earlier in the literature by Howland

Planck intermediate results. VIII. Filaments between interacting clusters

About half of the baryons of the Universe are expected to be in the form of filaments of hot and low density intergalactic medium. Most of these baryons remain undetected even by the most advanced X-ray observatories which are limited in sensitivity to the diffuse low density medium. The Planck satellite has provided hundreds of detections of the hot gas in clusters of galaxies via the thermal Sunyaev-Zel'dovich (tSZ) effect and is an ideal instrument for studying extended low density media through the tSZ effect. In this paper we use the Planck data to search for signatures of a fraction of these missing baryons between pairs of galaxy clusters. Cluster pairs are good candidates for searching for the hotter and denser phase of the intergalactic medium (which is more easily observed through the SZ effect). Using an X-ray catalogue of clusters and the Planck data, we select physical pairs of clusters as candidates. Using the Planck data we construct a local map of the tSZ effect centered on each pair of galaxy clusters. ROSAT data is used to construct X-ray maps of these pairs. After having modelled and subtracted the tSZ effect and X-ray emission for each cluster in the pair we study the residuals on both the SZ and X-ray maps. For the merging cluster pair A399-A401 we observe a significant tSZ effect signal in the intercluster region beyond the virial radii of the clusters. A joint X-ray SZ analysis allows us to constrain the temperature and density of this intercluster medium. We obtain a temperature of kT = 7.1 +- 0.9, keV (consistent with previous estimates) and a baryon density of (3.7 +- 0.2)x10^-4, cm^-3. The Planck satellite mission has provided the first SZ detection of the hot and diffuse intercluster gas.Comment: Accepted by A&

Planck early results XIV : ERCSC validation and extreme radio sources

Peer reviewe

Planck early results XXIII : The first all-sky survey of Galactic cold clumps

Peer reviewe

Planck early results XVII : Origin of the submillimetre excess dust emission in the Magellanic Clouds

Peer reviewe

Planck early results XVIII : The power spectrum of cosmic infrared background anisotropies

Peer reviewe

Planck intermediate results: III. the relation between galaxy cluster mass and Sunyaev-Zeldovich signal

We examine the relation between the galaxy cluster mass M and Sunyaev-Zeldovich (SZ) effect signal DA2 Y500 for a sample of 19 objects for which weak lensing (WL) mass measurements obtained from Subaru Telescope data are available in the literature. Hydrostatic X-ray masses are derived from XMM-Newton archive data, and the SZ effect signal is measured from Planck all-sky survey data. We find an MWL-D A2 Y500 relation that is consistent in slope and normalisation with previous determinations using weak lensing masses; however, there is a normalisation offset with respect to previous measures based on hydrostatic X-ray mass-proxy relations. We verify that our SZ effect measurements are in excellent agreement with previous determinations from Planck data. For the present sample, the hydrostatic X-ray masses at R500 are on average ~ 20 percent larger than the corresponding weak lensing masses, which is contrary to expectations. We show that the mass discrepancy is driven by a difference in mass concentration as measured by the two methods and, for the present sample, that the mass discrepancy and difference in mass concentration are especially large for disturbed systems. The mass discrepancy is also linked to the offset in centres used by the X-ray and weak lensing analyses, which again is most important in disturbed systems. We outline several approaches that are needed to help achieve convergence in cluster mass measurement with X-ray and weak lensing observations. © ESO, 2013

Planck early results. XVII. Origin of the submillimetre excess dust emission in the Magellanic Clouds

The integrated spectral energy distributions (SED) of the Large Magellanic Cloud (LMC) and SmallMagellanic Cloud (SMC) appear significantly flatter than expected from dust models based on their far-infrared and radio emission. The still unexplained origin of this millimetre excess is investigated here using the Planck data. The integrated SED of the two galaxies before subtraction of the foreground (Milky Way) and background (CMB fluctuations) emission are in good agreement with previous determinations, confirming the presence of the millimetre excess. In the context of this preliminary analysis we do not propose a full multi-component fitting of the data, but instead subtract contributions unrelated to the galaxies and to dust emission. The background CMB contribution is subtracted using an internal linear combination (ILC) method performed locally around the galaxies. The foreground emission from the Milky Way is subtracted as a Galactic Hi template, and the dust emissivity is derived in a region surrounding the two galaxies and dominated by Milky Way emission. After subtraction, the remaining emission of both galaxies correlates closely with the atomic and molecular gas emission of the LMC and SMC. The millimetre excess in the LMC can be explained by CMB fluctuations, but a significant excess is still present in the SMC SED. The Planck and IRAS–IRIS data at 100 μm are combined to produce thermal dust temperature and optical depth maps of the two galaxies. The LMC temperature map shows the presence of a warm inner arm already found with the Spitzer data, but which also shows the existence of a previously unidentified cold outer arm. Several cold regions are found along this arm, some of which are associated with known molecular clouds. The dust optical depth maps are used to constrain the thermal dust emissivity power-law index (β). The average spectral index is found to be consistent with β =1.5 and β =1.2 below 500 μm for the LMC and SMC respectively, significantly flatter than the values observed in the Milky Way. Also, there is evidence in the SMC of a further flattening of the SED in the sub-mm, unlike for the LMC where the SED remains consistent with β =1.5. The spatial distribution of the millimetre dust excess in the SMC follows the gas and thermal dust distribution. Different models are explored in order to fit the dust emission in the SMC. It is concluded that the millimetre excess is unlikely to be caused by very cold dust emission and that it could be due to a combination of spinning dust emission and thermal dust emission by more amorphous dust grains than those present in our Galaxy

Planck early results. XXII. The submillimetre properties of a sample of Galactic cold clumps

We perform a detailed investigation of sources from the Cold Cores Catalogue of Planck Objects (C3PO). Our goal is to probe the reliability of the detections, validate the separation between warm and cold dust emission components, provide the first glimpse at the nature, internal morphology and physical characterictics of the Planck-detected sources. We focus on a sub-sample of ten sources from the C3PO list, selected to sample different environments, from high latitude cirrus to nearby (150 pc) and remote (2 kpc) molecular complexes. We present Planck surface brightness maps and derive the dust temperature, emissivity spectral index, and column densities of the fields. With the help of higher resolution Herschel and AKARI continuum observations and molecular line data, we investigate the morphology of the sources and the properties of the substructures at scales below the Planck beam size. The cold clumps detected by Planck are found to be located on large-scale filamentary (or cometary) structures that extend up to 20 pc in the remote sources. The thickness of these filaments ranges between 0.3 and 3 pc, for column densities NH2 ∼ 0.1 to 1.6 × 1022 cm−2, and with linear mass density covering a broad range, between 15 and 400 M pc−1. The dust temperatures are low (between 10 and 15K) and the Planck cold clumps correspond to local minima of the line-of-sight averaged dust temperature in these fields. These low temperatures are confirmed when AKARI and Herschel data are added to the spectral energy distributions. Herschel data reveal a wealth of substructure within the Planck cold clumps. In all cases (except two sources harbouring young stellar objects), the substructures are found to be colder, with temperatures as low as 7 K. Molecular line observations provide gas column densities which are consistent with those inferred from the dust. The linewidths are all supra-thermal, providing large virial linear mass densities in the range 10 to 300 M pc−1, comparable within factors of a few, to the gas linear mass densities. The analysis of this small set of cold clumps already probes a broad variety of structures in the C3PO sample, probably associated with different evolutionary stages, from cold and starless clumps, to young protostellar objects still embedded in their cold surrounding cloud. Because of the all-sky coverage and its sensitivity, Planck is able to detect and locate the coldest spots in massive elongated structures that may be the long-searched for progenitors of stellar clusters