Exponential asymptotics for line solitons in two-dimensional periodic potentials

As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multi-scale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multi-line-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.Comment: 27 pages, 8 figures. To appear in Stud. Appl. Mat

From nonlocal gap solitary waves to bound states in periodic media

Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become nonlocal owing to the presence of growing tails of exponentially-small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such nonlocal solitary waves, higher-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two nonlocal solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.Comment: To appear in Proc. Roy. Soc. Lond.

Solitary waves and their linear stability in nonlinear lattices

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, hinge upon a certain recurrence relation which contains information beyond all orders of the usual two-scale perturbation expansion. It follows that only two such positions are permissible, and of those two solitary waves, one is linearly stable and the other unstable. For a cosine lattice, in particular, the two possible solitary waves are centered at a maximum or minimum of the lattice, with the former being stable, and the analytical predictions for the associated linear stability eigenvalues are in excellent agreement with numerical results. Furthermore, a countable set of multi-solitary-wave bound states are constructed analytically. In spite of rather different physical settings, the exponential asymptotics approach followed here is strikingly similar to that taken in earlier studies of solitary wavepackets involving a periodic carrier and a slowly-varying envelope, which underscores the general value of this procedure for treating multi-scale solitary-wave problems.Comment: To appear in Stud. Appl. Mat

Compton Thick AGN in the XMM-COSMOS survey

Heavily obscured, Compton Thick (CT, NH>10^24 cm^-2) AGN may represent an important phase in AGN/galaxy co-evolution and are expected to provide a significant contribution to the cosmic X-ray background (CXB). Through direct X-ray spectra analysis, we selected 39 heavily obscured AGN (NH>3x10^23 cm^-2) in the 2 deg^2 XMM-COSMOS survey. After selecting CT AGN based on the fit of a simple absorbed two power law model to the XMM data, the presence of CT AGN was confirmed in 80% of the sources using deeper Chandra data and more complex models. The final sample of CT AGN comprises 10 sources spanning a large range of redshift and luminosity. We collected the multi-wavelength information available for all these sources, in order to study the distribution of SMBH and host properties, such as BH mass (M_BH), Eddington ratio (\lambda_Edd), stellar mass (M*), specific star formation rate (sSFR) in comparison with a sample of unobscured AGN. We find that highly obscured sources tend to have significantly smaller M_BH and higher \lambda_edd with respect to unobscured ones, while a weaker evolution in M* is observed. The sSFR of highly obscured sources is consistent with the one observed in the main sequence of star forming galaxies, at all redshift. We also present optical spectra, spectral energy distribution (SED) and morphology for the sample of 10 CT AGN: all the available optical spectra are dominated by the stellar component of the host galaxy, and a highly obscured torus component is needed in the SED of the CT sources. Exploiting the high resolution Hubble-ACS images available, we conclude that these highly obscured sources have a significantly larger merger fraction with respect to other X-ray selected samples of AGN. Finally we discuss implications in the context of AGN/galaxy co-evolutionary models, and compare our results with the predictions of CXB synthesis models.Comment: Revised version after referee comments. Accepted for publication in Astronomy & Astrophysics on 25 November 2014. 23 pages, 2 tables, 16 figure

Cold gas in massive early-type galaxies: The case of NGC 1167

We present a study of the morphology and kinematics of the neutral hydrogen in the gas-rich (M_HI=1.5x10^{10}Msun), massive early-type galaxy NGC 1167, which was observed with the Westerbork Synthesis Radio Telescope (WSRT). The HI is located in a 160kpc disk (~3xD_25) and has low surface density (<2Msun pc^{-2}). The disk shows regular rotation for r<65kpc but several signs of recent and ongoing interaction and merging with fairly massive companions are observed. No population of cold gas clouds is observed - in contrast to what is found in some spiral galaxies. This suggests that currently the main mechanism bringing in cold gas to the disk is the accretion of fairly massive satellite galaxies, rather than the accretion of a large number of small gas clumps. NGC 1167 is located in a (gas-) rich environment: we detect eight companions with a total HI mass of ~6x10^9Msun within a projected distance of 350kpc. Deep optical images show a disrupted satellite at the northern edge of the HI disk. The observed rotation curve shows a prominent bump of about 50km/s (in the plane of the disk) at r=1.3xR_25. This feature in the rotation curve occurs at the radius where the HI surface density drops significantly and may be due to large-scale streaming motions in the disk. We suspect that both the streaming motions and the HI density distribution are the result of the interaction/accretion with the disrupted satellite. Like in other galaxies with wiggles and bumps in the rotation curve, HI scaling describes the observed rotation curve best. We suggest that interactions create streaming motions and features in the HI density distribution and that this is the reason for the success of HI scaling in fitting such rotation curves.Comment: 17 pages, 11 figures; A&A in pres

Hamiltonian form and solitary waves of the spatial Dysthe equations

The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.Comment: 6 pages, 9 figures. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

The XMM-Newton Serendipitous Survey. VI. The X-ray Luminosity Function

We present the X-ray luminosity function of AGN in three energy bands (Soft: 0.5-2 keV, Hard: 2-10 keV and Ultrahard: 4.5-7.5 keV). We have used the XMS survey along with other highly complete flux-limited deeper and shallower surveys for a total of 1009, 435 and 119 sources in the Soft, Hard and Ultrahard bands, respectively. We have modeled the intrinsic absorption of the Hard and Ultrahard sources (NH function) and computed the intrinsic X-ray luminosity function in all bands using a Maximum Likelihood fit technique to an analytical model. We find that the X-ray luminosity function (XLF) is best described by a Luminosity-Dependent Density Evolution (LDDE) model. Our results show a good overall agreement with previous results in the Hard band, although with slightly weaker evolution. Our model in the Soft band present slight discrepancies with other works in this band, the shape of our present day XLF being significantly flatter. We find faster evolution in the AGN detected in the Ultrahard band than those in the Hard band. The fraction of absorbed AGN in the Hard and Ultrahard bands is dependent on the X-ray luminosity. We find evidence of evolution of this fraction with redshift in the Hard band but not in the Ultrahard band, possibly due to the low statistics. Our best-fit XLF shows that the high-luminosity AGN are fully formed earlier than the less luminous AGN. The latter sources account for the vast majority of the accretion rate and mass density of the Universe, according to an anti-hierarchical black hole growth scenario.Comment: 16 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

Recurrent radio emission and gas supply: the case of the radio galaxy B2 0258+35

Outlined is the discovery of a very faint, diffuse, low surface-brightness (0.5 \mJybeam, 1.4 \mJyarcminsq on average) structure around the radio source B2 0258+35 hosted by an HI-rich early-type galaxy (NGC 1167). Since B2 0258+35 is a young Compact Steep Spectrum (CSS) source, the newly discovered structure could represent a remnant from an earlier stage of AGN activity. We go on by explaining in detail all the possibilities for triggering the radio activity in B2 0258+35 regarding gas accretion in a recurrent AGN activity framework. NGC 1167 hosts a very regular, extended and massive \HI\ disc that has been studied in great detail. Previous studies of the \HI\ closer to the core seem to go against the assumption of a circum-nuclear disc of \HI\ as the source of the accreting gas. We consider the cooling of gas from the hot, X-ray halo as a possible alternative option for the fueling of the AGN, as suggested in the case of other sources of similar radio power as B2 0258+35. Estimates are given for the age of the faint diffuse emission as well as for the current accretion rate, which are in good agreement with literature values. If our assumptions about the accretion mechanism are correct, similar large-scale, relic-like structures should be more commonly found around early-type galaxies and this will be hopefully confirmed by the next generation of sensitive, low-frequency radio surveys.Comment: 3 figures, accepted for publication in Astronomy and Astrophysics (17.07.2012