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. 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

Planck early results. IX. XMM-Newton follow-up for validation of Planck cluster candidates

We present the XMM-Newton follow-up for confirmation of Planck cluster candidates. Twenty-five candidates have been observed to date using snapshot (∼10 ks) exposures, ten as part of a pilot programme to sample a low range of signal-to-noise ratios (4 < S/N < 6), and a further 15 in a programme to observe a sample of S/N > 5 candidates. The sensitivity and spatial resolution of XMM-Newton allows unambiguous discrimination between clusters and false candidates. The 4 false candidates have S/N ≤ 4.1. A total of 21 candidates are confirmed as extended X-ray sources. Seventeen are single clusters, the majority of which are found to have highly irregular and disturbed morphologies (about ∼70%). The remaining four sources are multiple systems, including the unexpected discovery of a supercluster at z = 0.45. For 20 sources we are able to derive a redshift estimate from the X-ray Fe K line (albeit of variable quality). The new clusters span the redshift range 0.09 <∼ z <∼ 0.54, with a median redshift of z ∼ 0.37. A first determination is made of their X-ray properties including the characteristic size, which is used to improve the estimate of the SZ Compton parameter, Y500. The follow-up validation programme has helped to optimise the Planck candidate selection process. It has also provided a preview of the X-ray properties of these newly-discovered clusters, allowing comparison with their SZ properties, and to the X-ray and SZ properties of known clusters observed in the Planck survey. Our results suggest that Planck may have started to reveal a non-negligible population of massive dynamically perturbed objects that is under-represented in X-ray surveys. However, despite their particular properties, these new clusters appear to follow the Y500–YX relation established for X-ray selected objects, where YX is the product of the gas mass and temperature

Planck early results. XXV. Thermal dust in nearby molecular clouds

Planck allows unbiased mapping of Galactic sub-millimetre and millimetre emission from the most diffuse regions to the densest parts of molecular clouds. We present an early analysis of the Taurus molecular complex, on line-of-sight-averaged data and without component separation. The emission spectrum measured by Planck and IRAS can be fitted pixel by pixel using a single modified blackbody. Some systematic residuals are detected at 353 GHz and 143 GHz, with amplitudes around −7% and +13%, respectively, indicating that the measured spectra are likely more complex than a simple modified blackbody. Significant positive residuals are also detected in the molecular regions and in the 217 GHz and 100 GHz bands, mainly caused by the contribution of the J = 2 → 1 and J = 1 → 0 12CO and 13CO emission lines. We derive maps of the dust temperature T, the dust spectral emissivity index β, and the dust optical depth at 250 μm τ250. The temperature map illustrates the cooling of the dust particles in thermal equilibrium with the incident radiation field, from 16−17 K in the diffuse regions to 13−14 K in the dense parts. The distribution of spectral indices is centred at 1.78, with a standard deviation of 0.08 and a systematic error of 0.07. We detect a significant T − β anti-correlation. The dust optical depth map reveals the spatial distribution of the column density of the molecular complex from the densest molecular regions to the faint diffuse regions.We use near-infrared extinction and Hi data at 21-cm to perform a quantitative analysis of the spatial variations of the measured dust optical depth at 250 μm per hydrogen atom τ250/NH. We report an increase of τ250/NH by a factor of about 2 between the atomic phase and the molecular phase, which has a strong impact on the equilibrium temperature of the dust particles

Planck early results XIV : ERCSC validation and extreme radio sources

Peer reviewe

Planck early results. XIII. Statistical properties of extragalactic radio sources in the Planck Early Release Compact Source Catalogue

The data reported in Planck’s Early Release Compact Source Catalogue (ERCSC) are exploited to measure the number counts (dN/dS) of extragalactic radio sources at 30, 44, 70, 100, 143 and 217 GHz. Due to the full-sky nature of the catalogue, this measurement extends to the rarest and brightest sources in the sky. At lower frequencies (30, 44, and 70 GHz) our counts are in very good agreement with estimates based on WMAP data, being somewhat deeper at 30 and 70 GHz, and somewhat shallower at 44 GHz. Planck’s source counts at 143 and 217 GHz join smoothly with the fainter ones provided by the SPT and ACT surveys over small fractions of the sky. An analysis of source spectra, exploiting Planck’s uniquely broad spectral coverage, finds clear evidence of a steepening of the mean spectral index above about 70 GHz. This implies that, at these frequencies, the contamination of the CMB power spectrum by radio sources below the detection limit is significantly lower than previously estimated

Planck Early Results XVIII: The power spectrum of cosmic infrared background anisotropies

Using Planck maps of six regions of low Galactic dust emission with a total area of about 140 deg2, we determine the angular power spectra of cosmic infrared background (CIB) anisotropies from multipole ℓ = 200 to ℓ = 2000 at 217, 353, 545 and 857 GHz. We use 21-cm observations of Hi as a tracer of thermal dust emission to reduce the already low level of Galactic dust emission and use the 143 GHz Planck maps in these fields to clean out cosmic microwave background anisotropies. Both of these cleaning processes are necessary to avoid significant contamination of the CIB signal. We measure correlated CIB structure across frequencies. As expected, the correlation decreases with increasing frequency separation, because the contribution of high-redshift galaxies to CIB anisotropies increases with wavelengths. We find no significant difference between the frequency spectrum of the CIB anisotropies and the CIB mean, with ∆I/I=15% from 217 to 857 GHz. In terms of clustering properties, the Planck data alone rule out the linear scale- and redshift-independent bias model. Non-linear corrections are significant. Consequently, we develop an alternative model that couples a dusty galaxy, parametric evolution model with a simple halo-model approach. It provides an excellent fit to the measured anisotropy angular power spectra and suggests that a different halo occupation distribution is required at each frequency, which is consistent with our expectation that each frequency is dominated by contributions from different redshifts. In our best-fit model, half of the anisotropy power at ℓ=2000 comes from redshifts z 2 at 353 and 217 GHz, respectively