Énergie des vortex dans un modèle abélien de Higgs en 2+1 dimensions avec un potentiel d’ordre six

Dans ce travail, j’étudierai principalement un modèle abélien de Higgs en 2+1 dimensions, dans lequel un champ scalaire interagit avec un champ de jauge. Des défauts topologiques, nommés vortex, sont créés lorsque le potentiel possède un minimum brisant spontanément la symétrie U(1). En 3+1 dimensions, ces vortex deviennent des défauts à une dimension. Ils ap- paraissent par exemple en matière condensée dans les supraconducteurs de type II comme des lignes de flux magnétique. J’analyserai comment l’énergie des solutions statiques dépend des paramètres du modèle et en particulier du nombre d’enroulement du vortex. Pour le choix habituel de potentiel (un poly- nôme quartique dit « BPS »), la relation entre les masses des deux champs mène à deux types de comportements : type I si la masse du champ de jauge est plus grande que celle du champ sca- laire et type II inversement. Selon le cas, la dépendance de l’énergie au nombre d’enroulement, n, indiquera si les vortex auront tendance à s’attirer ou à se repousser, respectivement. Lorsque le flux emprisonné est grand, les vortex présentent un profil où la paroi est mince, permettant certaines simplifications dans l’analyse. Le potentiel, un polynôme d’ordre six (« non-BPS »), est choisi tel que le centre du vortex se trouve dans le vrai vide (minimum absolu du potentiel) alors qu’à l’infini le champ scalaire se retrouve dans le faux vide (minimum relatif du potentiel). Le taux de désintégration a déjà été estimé par une approximation semi-classique pour montrer l’impact des défauts topologiques sur la stabilité du faux vide. Le projet consiste d’abord à établir l’existence de vortex classi- quement stables de façon numérique. Puis, ma contribution fut une analyse des paramètres du modèle révélant le comportement énergétique de ceux-ci en fonction du nombre d’enroulement. Ce comportement s’avèrera être différent du cas « BPS » : le ratio des masses ne réussit pas à décrire le comportement observé numériquement.I will consider a generalization of the Abelian Higgs model in 2+1 dimensions. The model describes a scalar field interacting with a U(1) gauge field and gives rise to vortex solutions carrying magnetic flux. In 3+1 dimensions, the vortex becomes a one-dimensional topological defect which appears in condensed matter physics as a vortex line in type-II superconductors. For a strong magnetic flux (large winding number), the vortex presents a thin-wall profile, which gives rise to certain simplifications in the analysis. I will present how the energy of the static configuration depends on the parameters of the model and in particular on the winding number of the vortex. For the usual choice of potential (quartic, called « BPS »), the relation between the masses of the two fields will lead to a type-I or a type-II vortex, as the energy dependence on the winding number show that vortices attract or repel each other respectively. The potential chosen here is a sixth-order polynomial (« non-BPS ») such that the core of the vortex is the true vacuum (absolute minimum) while the field at infinity goes to the false vacuum (local minimum of the potential). Their decay rate into an instable classical configura- tion with growing radius has already been estimated by a semi-classical approximation to show their impact on the stability of the false vacuum. The classical existence of vortex solutions will be shown numerically. My contribution to this work is a scan of the parameters of the model revealing the energetic behavior of the vortices. This behavior will be different from the « BPS » case : the masses ratio will not describe correctly the numerical calculation of the energy

High-resolution VLA low radio frequency observations of the Perseus cluster: radio lobes, mini-halo and bent-jet radio galaxies

We present the first high-resolution 230-470 MHz map of the Perseus cluster obtained with the Karl G. Jansky Very Large Array. The high dynamic range and resolution achieved has allowed the identification of previously-unknown structures in this nearby galaxy cluster. New hints of sub-structures appear in the inner radio lobes of the brightest cluster galaxy NGC 1275. The spurs of radio emission extending into the outer X-ray cavities, inflated by past nuclear outbursts, are seen for the first time at these frequencies, consistent with spectral aging. Beyond NGC 1275, we also analyze complex radio sources harbored in the cluster. Two new distinct, narrowly-collimated jets are visible in IC 310, consistent with a highly-projected narrow-angle tail radio galaxy infalling into the cluster. We show how this is in agreement with its blazar-like behavior, implying that blazars and bent-jet radio galaxies are not mutually exclusive. We report the presence of filamentary structures across the entire tail of NGC 1265, including two new pairs of long filaments in the faintest bent extension of the tail. Such filaments have been seen in other cluster radio sources such as relics and radio lobes, indicating that there may be a fundamental connection between all these radio structures. We resolve the very narrow and straight tail of CR 15 without indication of double jets, so that the interpretation of such head-tail sources is yet unclear. Finally, we note that only the brightest western parts of the mini-halo remain, near NGC 1272 and its bent double jets.Comment: 17 pages, 12 figures, Accepted for publication in MNRA

High-spectral-resolution Observations of the Optical Filamentary Nebula Surrounding NGC 1275

We present new high-spectral-resolution observations (R = λ/Δλ = 7000) of the filamentary nebula surrounding NGC 1275, the central galaxy of the Perseus cluster. These observations have been obtained with SITELLE, an imaging Fourier transform spectrometer installed on the Canada–France–Hawai Telescope with a field of view of 11′×11′ , encapsulating the entire filamentary structure of ionized gas despite its large size of 80 kpc × 50 kpc. Here, we present renewed fluxes, velocities, and velocity dispersion maps that show in great detail the kinematics of the optical nebula at [S ii] λ6716, [S ii] λ6731, [N ii] λ6584, Hα (6563 Å), and [N ii] λ6548. These maps reveal the existence of a bright flattened disk-shaped structure in the core extending to r ∼10 kpc and dominated by a chaotic velocity field. This structure is located in the wake of X-ray cavities and characterized by a high mean velocity dispersion of 134 km s−1. The disk-shaped structure is surrounded by an extended array of filaments spread out to r ∼ 50 kpc that are 10 times fainter in flux, remarkably quiescent, and have a uniform mean velocity dispersion of 44 km s−1. This stability is puzzling given that the cluster core exhibits several energetic phenomena. Based on these results, we argue that there are two mechanisms that form multiphase gas in clusters of galaxies: a first triggered in the wake of X-ray cavities leading to more turbulent multiphase gas and a second, distinct mechanism, that is gentle and leads to large-scale multiphase gas spreading throughout the core

Observations multi-longueur d’onde d’amas et de groupes de galaxies proches

Les amas et les groupes de galaxies sont des environnements dynamiques constamment perturbés. D’une part, le trou noir supermassif de la galaxie centrale peut produire de puis- sants jets relativistes compensant les pertes radiatives du milieu intra-amas ou intra-groupe. C’est le mécanisme de rétroaction des noyaux actifs de galaxies. D’autre part, l’interaction de l’amas ou du groupe de galaxies avec d’autres galaxies peut aussi créer d’importantes perturbations sous forme de chocs ou de fronts froids par exemple. En général, ces per- turbations, internes ou externes, peuvent laisser des empreintes dans les observations des groupes et des amas, et ce, dans tout le spectre électromagnétique. Dans cette thèse, l’étude observationnelle multi-longueur d’onde d’un groupe et d’un amas de galaxies proches est pré- sentée. L’ensemble de ces travaux auront permis de mieux comprendre certains des processus physiques complexes qui caractérisent ces environnements. D’abord, l’analyse d’observations profondes (380 ks) de l’observatoire de rayons X Chan- dra de la galaxie NGC 4472 (z = 0.0038), galaxie dominante d’un groupe de galaxies plon- geant dans l’amas de la Vierge, est présentée. Ces nouvelles données ont permis l’étude détaillée de la dynamique des lobes radio. Des coquilles de gaz froid entourant les lobes radio ont été détectées et semblent être constituées de gaz provenant du centre du groupe. Nous estimons l’énergie requise pour soulever ce gaz à partir du centre de NGC 4472 à ∼ 1056 erg. Nous avons également mené l’analyse de la distribution de l’abondance de différents éléments (O, Ne, Mg, Si et Fe) à partir du spectre rayons X. Ensuite, nous avons produit une carte à basse fréquence radio de l’amas de Persée (z = 0.018) obtenue à partir de nouvelles observations du Karl G. Jansky Very Large Array à 230- 470 MHz en configuration B. Les étapes de réduction des données et de calibration de même que le processus d’imagerie ont été spécifiquement adaptés à l’analyse de ces observations, tenant compte à la fois de la forte présence des interférences des fréquences radio à ces fréquences et de la présence du noyau actif de galaxie très brillant au centre de l’amas. Ces observations ont révélé une multitude de nouvelles structures associées à l’émission radio centrale diffuse dans l’amas, le mini-halo. Ces structures incluent plusieurs filaments radiaux s’étendant dans diverses directions, une structure concave corrélant avec la baie et plusieurs autres correspondances avec les structures rayons X telles que les fronts froids. Ces résultats montrent que les mini-halos ne sont donc pas de simples sources radio diffuses et uniformes, mais possèdent plutôt une riche variété de structures complexes. Un portrait complet de la dynamique des filaments de la nébuleuse de gaz ionisé entou- rant la galaxie NGC 1275, galaxie dominante de l’amas de Persée, a également été révélée grâce aux observations de SITELLE («Spectromètre Imageur à Transformée de Fourier pour l’Étude en Long et en Large des raies d’Émission»), un nouveau spectro-imageur à transfor- mée de Fourier au télescope Canada-France-Hawaii. Grâce à son champ de vue de 11′ × 11′, il s’agit du seul instrument de ce type capable de couvrir la nébuleuse de 80kpc × 55kpc (3.8′ × 2.6′ à la distance de NGC 1275) de large dans son entièreté. Notre analyse de ces observations montre un gradient radial du ratio des raies [N II]λ6583/Hα, suggérant un changement dans la source et le mécanisme d’ionisation à travers la nébuleuse. Nous avons produit pour la première fois une carte de vitesse complète et détaillée des filaments. Cette carte révèle une structure dynamique complexe inconnue jusqu’à ce jour. Celle-ci ne montre pas de tendance radiale générale ni de signe de rotation globale, indiquant que les filaments ne sont pas en train de tomber uniformément vers la galaxie ni d’être uniformément entraînés vers l’extérieur. Une comparaison entre ces mesures et les résultats de Hitomi obtenus pour l’amas de Persée est également présentée. Enfin, nous avons créé une image haute résolution à 230-470 MHz de l’amas de Persée grâce aux nouvelles observations en configuration A du Karl G. Jansky Very Large Array. La gamme dynamique élevée et la haute résolution de cette image ont permis l’identification de nouvelles structures. Dû à la haute résolution, la majorité de l’émission étendue du mini- halo occupant le centre de l’amas disparait dans ces observations et seules les parties les plus brillantes vers l’ouest demeurent visibles. L’émission radio centrale remplit les cavités internes visibles en rayons X et s’étend vers les cavités externes. Les cavités externes étant visibles à plus basses fréquences radio, nous détectons donc une partie courbe dans le spectre à environ 350 MHz. Au-delà de l’émission centrale entourant NGC 1275, nous décrivons et analysons également la morphologie de plusieurs sources radio complexes situées dans l’amas de Persée : IC 310, NGC 1265, CR 15 et NGC 1272. Ces galaxies radio sont en train de tomber dans l’amas de Persée. Nous détectons des distorsions dans la queue d’émission radio de la source IC 310 de même que deux jets distincts. Nous rapportons la présence d’une structure filamenteuse globale associée à la galaxie NGC 1265. Finalement, les galaxies radio CR 15 et NGC 1272 sont également résolues dans l’image haute-résolution obtenue.Clusters and groups of galaxies are dynamic environments, continually perturbed. On the one hand, the supermassive black hole of the central galaxy can release powerful rela- tivistic jets compensating the radiative losses of the intracluster or intragroup medium. This mechanism is called active galactic nucleus feedback. On the other hand, the interaction between the cluster or the group with other galaxies can also generate important perturba- tions such as shocks or cold fronts. In general, these internal or external perturbations leave their footprints into the observations of clusters and groups covering the entire electromag- netic spectrum. In this thesis, the multi-wavelength observational study of one group and one cluster of galaxies, both nearby, is presented. Overall, this work has contributed to the comprehension of some of the complex processes characterizing these environments. First, the analysis of deep observations (380 ks) from the X-ray observatory Chandra of the galaxy NGC 4472 (z = 0.0038), the dominant galaxy of a group falling into the Virgo cluster, is presented. These new observations have allowed the detailed study of the radio lobe dynamics. Rims of cold gas surrounding the radio lobes have been detected and seem to be constituted of gas originating from the group center. We estimate the energy required to lift this gas from the center of NGC 4472 to be ∼ 1056 erg. We have also led the analysis of the abundance distribution of different elements (O, Ne, Mg, Si et Fe) from the X-ray spectrum. Second, we have produced a radio-frequency map of the Perseus cluster (z = 0.018), obtained from new Karl G. Jansky Very Large Array observations at 230-470 MHz in B configuration. The data reduction and calibration steps as well as the imaging process were specifically adjusted for the analysis of these observations, taking into account the strong presence of radio frequency interferences at these frequencies and the presence of the ex- tremely bright central active galactic nucleus in the cluster center. The observations have revealed a multitude of new structures associated with the cluster central diffuse radio emis- sion, the mini-halo. These structures include several radial filaments stretching in different directions, a concave structure correlating with the bay and several other correspondences with the X-ray structures such as cold fronts. These results show that mini-halos are there- fore not simply diffuse, uniform radio sources, but rather have a rich variety of complex structures. A comprehensive picture of the dynamics of the filamentary emission-line nebula sur- rounding NGC 1275, the dominant galaxy of the Perseus cluster, has been revealed with the observations of SITELLE («Spectromètre Imageur à Transformée de Fourier pour l’Étude en Long et en Large des raies d’Émission»), a new optical imaging Fourier transform spec- trometer at Canada-France-Hawaii Telescope. With its wide field of view of 11′ × 11′, it is the only instrument of this type covering the 80kpc × 55kpc (3.8′ × 2.6′ at the distance of NGC 1275) large nebula in its entirety. Our analysis of these observations shows a smooth radial gradient of the [N II]λ6583/Hα line ratio, suggesting a change in the ionization source and mechanism across the nebula. We have produced for the first time a complete detailed velocity map of the filaments. This map reveal a previously unknown rich velocity structure. The velocity map shows no visible general radial trend or rotation, indicating that filaments are not falling uniformly onto the galaxy, nor being uniformly pulled out from it. A com- parison between these measurements and the Hitomi results on the Perseus cluster is also presented. Finally, we have created a high-resolution image at 230-470 MHz of the Perseus cluster with new Karl G. Jansky Very Large Array A configuration observations. The high dynamic range and resolution achieved in this image have allowed the identification of new structures. Most of the extended mini-halo emission filling the core of the Perseus cluster disappears in these observations due to the high resolution and only some of the brightest western parts remain visible. The central radio emission fills the inner X-ray cavities and extends toward the outer cavities. As the outer cavities are visible at lower frequencies, we are therefore catching the spectral turnover at around 350 MHz. Beyond the central emission surrounding NGC 1275, we also describe and analyze the morphology of four complex radio sources harbored in the Perseus cluster: IC 310, NGC 1265, CR 15 and NGC 1272. These radio galaxies are infalling into the Perseus cluster. We detect distortions in the tail of IC 310 as well as two distinct jets. We report the presence of a global radio filamentary structure associated with the galaxy NGC 1265. Lastly, the radio galaxies CR 15 and NGC 1272 are also resolved in this high-resolution image

Signature of Supersonic Turbulence in Galaxy Clusters Revealed by AGN-driven Hα\alpha Filaments

The hot intracluster medium (ICM) is thought to be quiescent with low observed velocity dispersions. Surface brightness fluctuations of the ICM also suggest that its turbulence is subsonic with a Kolmogorov scaling relation, indicating that the viscosity is suppressed and the kinetic energy cascades to small scales unscathed. However, recent observations of the cold gas filaments in galaxy clusters find that the scaling relations are steeper than that of the hot plasma, signaling kinetic energy losses and the presence of supersonic flows. In this work we use high-resolution simulations to explore the turbulent velocity structure of the cold filaments at the cores of galaxy clusters. Our results indicate that supersonic turbulent structures can be "frozen" in the cold gas that cools and fragments out of a fast, $10^7$ K outflow driven by the central active galactic nucleus (AGN), when the radiative cooling time is shorter than the dynamical sound-crossing time. After the cold gas formation, however, the slope of the velocity structure function (VSF) flattens significantly over short, 10 Myr timescales. The lack of flattened VSF in observations of H$\alpha$ filaments indicates that the H$\alpha$-emitting phase is short-lived for the cold gas in galaxy clusters. On the other hand, the ubiquity of supersonic turbulence revealed by observed filaments strongly suggests that supersonic outflows are an integral part of AGN-ICM interaction, and that AGN activity plays a crucial role at driving turbulence in galaxy clusters.Comment: 9 pages, 4 figures, accepted for publication in ApJ

A machine learning approach to galactic emission-line region classification

International audienceDiagnostic diagrams of emission-line ratios have been used extensively to categorize extragalactic emission regions; however, these diagnostics are occasionally at odds with each other due to differing definitions. In this work, we study the applicability of supervised machine-learning techniques to systematically classify emission-line regions from the ratios of certain emission lines. Using the Million Mexican Model database, which contains information from grids of photoionization models using cloudy, and from shock models, we develop training and test sets of emission line fluxes for three key diagnostic ratios. The sets are created for three classifications: classic H ii regions, planetary nebulae, and supernova remnants. We train a neural network to classify a region as one of the three classes defined above given three key line ratios that are present both in the SITELLE and MUSE instruments’ band-passes: [O iii]λ5007/H β, [N ii]λ6583/H α, ([S ii]λ6717+[S ii]λ6731)/H α. We also tested the impact of the addition of the [O ii]λ3726, 3729/[O iii]λ5007 line ratio when available for the classification. A maximum luminosity limit is introduced to improve the classification of the planetary nebulae. Furthermore, the network is applied to SITELLE observations of a prominent field of M33. We discuss where the network succeeds and why it fails in certain cases. Our results provide a framework for the use of machine learning as a tool for the classification of extragalactic emission regions. Further work is needed to build more comprehensive training sets and adapt the method to additional observational constraints

High-spectral-resolution Observations of the Optical Filamentary Nebula Surrounding NGC 1275

Abstract We  present new high-spectral-resolution observations (R = λ/Δλ = 7000) of the filamentary nebula surrounding NGC 1275, the central galaxy of the Perseus cluster. These observations have been obtained with SITELLE, an imaging Fourier transform spectrometer installed on the Canada–France–Hawai Telescope with a field of view of 11 ′ × 11 ′ , encapsulating the entire filamentary structure of ionized gas despite its large size of 80 kpc × 50 kpc. Here, we present renewed fluxes, velocities, and velocity dispersion maps that show in great detail the kinematics of the optical nebula at [S ii] λ6716, [S ii] λ6731, [N ii] λ6584, Hα (6563 Å), and [N ii] λ6548. These maps reveal the existence of a bright flattened disk-shaped structure in the core extending to r ∼10 kpc and dominated by a chaotic velocity field. This structure is located in the wake of X-ray cavities and characterized by a high mean velocity dispersion of 134 km s−1. The disk-shaped structure is surrounded by an extended array of filaments spread out to r ∼ 50 kpc that are 10 times fainter in flux, remarkably quiescent, and have a uniform mean velocity dispersion of 44 km s−1. This stability is puzzling given that the cluster core exhibits several energetic phenomena. Based on these results, we argue that there are two mechanisms that form multiphase gas in clusters of galaxies: a first triggered in the wake of X-ray cavities leading to more turbulent multiphase gas and a second, distinct mechanism, that is gentle and leads to large-scale multiphase gas spreading throughout the core.</jats:p

Direct Detection of Black Hole-driven Turbulence in the Centers of Galaxy Clusters

Supermassive black holes (SMBHs) are thought to provide energy that prevents catastrophic cooling in the centers of massive galaxies and galaxy clusters. However, it remains unclear how this "feedback" process operates. We use high-resolution optical data to study the kinematics of multiphase filamentary structures by measuring the velocity structure function (VSF) of the filaments over a wide range of scales in the centers of three nearby galaxy clusters: Perseus, A2597, and Virgo. We find that the motions of the filaments are turbulent in all three clusters studied. There is a clear correlation between features of the VSFs and the sizes of bubbles inflated by SMBH-driven jets. Our study demonstrates that SMBHs are the main driver of turbulent gas motions in the centers of relaxed galaxy clusters and suggests that this turbulence is an important channel for coupling feedback to the environment. Our measured amplitude of turbulence is in good agreement with Hitomi Doppler line broadening measurement and X-ray surface-brightness fluctuation analysis, suggesting that the motion of the cold filaments is well-coupled to that of the hot gas. The smallest scales that we probe are comparable to the mean free path in the intracluster medium. Our direct detection of turbulence on these scales provides the clearest evidence to date that isotropic viscosity is suppressed in the weakly collisional, magnetized intracluster plasma