The interstellar medium (ISM) is a complex nonlinear system governed by the interplay between gravity and magneto-hydrodynamics, as well as radiative, thermodynamical, and chemical processes. Our ...understanding of it mostly progresses through observations and numerical simulations, and a quantitative comparison between these two approaches requires a generic and comprehensive statistical description of the emerging structures. The goal of this paper is to build such a description, with the purpose of permitting an efficient comparison that is independent of any specific prior or model. We started from the wavelet scattering transform (WST), a low-variance statistical description of non-Gaussian processes, which was developed in data science and encodes long-range interactions through a hierarchical multiscale approach based on the wavelet transform. We performed a reduction of the WST through a fit of its angular dependencies. This allowed us to gather most of the information it contains into a few components whose physical meanings are identified and describe for instance isotropic and anisotropic behaviours. The result of this paper is the reduced wavelet scattering transform (RWST), a statistical description with a small number of coefficients that characterizes complex structures arising from nonlinear phenomena, in particular interstellar magnetohydrodynamical (MHD) turbulence, independently of any specific priors. The RWST coefficients encode moments of order up to four, have reduced variances, and quantify the couplings between scales. To show the efficiency and generality of this description, we applied it successfully to the following three kinds of processes that are a priori very different: fractional Brownian motions, MHD simulations, and Herschel observations of the dust thermal continuum in a molecular cloud. With fewer than 100 RWST coefficients when probing six scales and eight angles on 256 by 256 maps, we were able to perform quantitative comparisons, infer relevant physical properties, and produce realistic synthetic fields.
The magnetic field in the local interstellar medium does not follow the large-scale Galactic magnetic field. The local magnetic field has probably been distorted by the Local Bubble, a cavity of hot ...ionized gas extending all around the Sun and surrounded by a shell of cold neutral gas and dust. However, so far no conclusive association between the local magnetic field and the Local Bubble has been established. Here we develop an analytical model for the magnetic field in the shell of the Local Bubble, which we represent as an inclined spheroid, off-centred from the Sun. We fit the model to Planck dust polarized emission observations within 30° of the Galactic poles. We find a solution that is consistent with a highly deformed magnetic field, with significantly different directions towards the north and south Galactic poles. This work sets a methodological framework for modelling the three-dimensional (3D) structure of the magnetic field in the local interstellar medium, which is a most awaited input for large-scale Galactic magnetic field models.
The characterization of the dust polarization foreground to the cosmic microwave background (CMB) is a necessary step toward the detection of the B-mode signal associated with primordial ...gravitational waves. We present a method to simulate maps of polarized dust emission on the sphere that is similar to the approach used for CMB anisotropies. This method builds on the understanding of Galactic polarization stemming from the analysis of Planck data. It relates the dust polarization sky to the structure of the Galactic magnetic field and its coupling with interstellar matter and turbulence. The Galactic magnetic field is modeled as a superposition of a mean uniform field and a Gaussian random (turbulent) component with a power-law power spectrum of exponent αM. The integration along the line of sight carried out to compute Stokes maps is approximated by a sum over a small number of emitting layers with different realizations of the random component of the magnetic field. The model parameters are constrained to fit the power spectra of dust polarization EE, BB, and TE measured using Planck data. We find that the slopes of the E and B power spectra of dust polarization are matched for αM = −2.5, an exponent close to that measured for total dust intensity but larger than the Kolmogorov exponent − 11/3. The model allows us to compute multiple realizations of the Stokes Q and U maps for different realizations of the random component of the magnetic field, and to quantify the variance of dust polarization spectra for any given sky area outside of the Galactic plane. The simulations reproduce the scaling relation between the dust polarization power and the mean total dust intensity including the observed dispersion around the mean relation. We also propose a method to carry out multifrequency simulations, including the decorrelation measured recently by Planck, using a given covariance matrix of the polarization maps. These simulations are well suited to optimize component separation methods and to quantify the confidence with which the dust and CMB B-modes can be separated in present and future experiments. We also provide an astrophysical perspective on our phenomenological modeling of the dust polarization spectra.
The Sun is embedded in the so-called Local Bubble (LB) – a cavity of hot plasma created by supernova explosions and surrounded by a shell of cold, dusty gas. Knowing the local distortion of the ...Galactic magnetic field associated with the LB is critical for the modeling of interstellar polarization data at high Galactic latitudes. In this his paper, we relate the structure of the Galactic magnetic field on the LB scale to three-dimensional (3D) maps of the local interstellar medium (ISM). First, we extracted the geometry of the LB shell, its inner surface, in particular from 3D dust extinction maps of the local ISM. We expanded the shell inner surface in spherical harmonics, up to a variable maximum multipole degree, which enabled us to control the level of complexity for the modeled surface. Next, we applied an analytical model for the ordered magnetic field in the shell to the modeled shell surface. This magnetic field model was successfully fitted to the
Planck
353 GHz dust polarized emission maps over the Galactic polar caps. For each polar cap, the direction of the mean magnetic field derived from dust polarization (together with the prior that the field points toward longitude 90° ± 90°) is found to be consistent with the Faraday spectra of the nearby diffuse synchrotron emission. Our work presents a new approach to modeling the local structure of the Galactic magnetic field. We expect our methodology and our results to be useful both in modeling the local ISM as traced by its different components and in modeling the dust polarized emission, which is a long-awaited input for studies of the polarized foregrounds for cosmic microwave background.
Super star clusters (SSCs), likely the progenitors of globular clusters, are one of the most extreme forms of star formation. Understanding how SSCs form is an observational challenge. Theoretical ...studies establish that, to form such clusters, the dynamical timescale of their parent clouds has to be shorter than the timescale of the disruption of their parent clouds by stellar feedback. However, due to insufficient observational support, it is still unclear how feedback from SSCs acts on the matter surrounding them. Studying feedback in SSCs is essential to understanding how such clusters form. Based on ALMA and VLT observations, we study this process in a SSC in the overlap region of the Antennae galaxies (22 Mpc), a spectacular example of a burst of star formation triggered by the encounter of two galaxies. We analyze a unique massive (~107M⊙) and young (1–3.5 Myr) SSC, still associated with compact molecular and ionized gas emission, which suggest that it may still be embedded in its parent molecular cloud. The cluster has two CO velocity components, a low-velocity one spatially associated with the cluster, and a high-velocity one distributed in a bubble-like shape around the cluster. Our results on the low-velocity component suggest that this gas did not participate in the formation of the SSC. We propose that most of the parent cloud has already been blown away, accelerated at the early stages of the SSC evolution by radiation pressure, in a timescale ~1 Myr. The high-velocity component may trace outflowing molecular gas from the parent cloud. Supporting evidence is found in shock-heated H2 gas and escaping Brγ gas associated with this component. The low-velocity component may be gas that was near the SSC when it formed but not part of its parent cloud or clumps that migrated from the SGMC environment. This gas would be dispersed by stellar winds and supernova explosions. The existing data is inconclusive as to whether or not the cluster is bound and will evolve as a globular cluster. Within ~100 pc of the cluster, we estimate a lower limit for the SFE of 17%, smaller than the theoretical limit of 30% needed to form a bound cluster. Further higher spatial resolution observations are needed to test and quantify our proposed scenario.
Context. A chemical scenario was proposed for photon-dominated regions (PDRs) according to which UV photons from nearby stars lead to the evaporation of very small grains (VSGs) and the production of ...gas-phase polycyclic aromatic hydrocarbons (PAHs). Aims. Our goal is to achieve better insight into the composition and evolution of evaporating very small grains (eVSGs) and PAHs through analyzing the infrared (IR) aliphatic and aromatic emission bands. Methods. We combined spectro-imagery in the near- and mid-IR to study the spatial evolution of the emission bands in the prototypical PDR NGC 7023. We used near-IR spectra obtained with the IRC instrument onboard AKARI to trace the evolution of the 3.3 μm and 3.4 μm bands, which are associated with aromatic and aliphatic C−H bonds on PAHs. The spectral fitting involved an additional broad feature centered at 3.45 μm that is often referred to as the plateau. Mid-IR observations obtained with the IRS instrument onboard the Spitzer Space Telescope were used to distinguish the signatures of eVSGs and neutral and cationic PAHs. We correlated the spatial evolution of all these bands with the intensity of the UV field given in units of the Habing field G0 to explore how their carriers are processed. Results. The intensity of the 3.45 μm plateau shows an excellent correlation with that of the 3.3 μm aromatic band (correlation coefficient R = 0.95) and a relatively poor correlation with the aliphatic 3.4 μm band (R = 0.77). This indicates that the 3.45 μm feature is dominated by the emission from aromatic bonds. We show that the ratio of the 3.4 μm and 3.3 μm band intensity (I3.4/I3.3) decreases by a factor of 4 at the PDR interface from the more UV-shielded layers (G0 ~ 150,I3.4/I3.3 = 0.13) to the more exposed layers (G0> 1 × 104,I3.4/I3.3 = 0.03). The intensity of the 3.3 μm band relative to the total neutral PAH intensity shows an overall increase with G0, associated with an increase of both the hardness of the UV field and the H abundance. In contrast, the intensity of the 3.4 μm band relative to the total neutral PAH intensity decreases with G0, showing that their carriers are actively destroyed by UV irradiation and are not efficiently regenerated. The transition region between the aliphatic and aromatic material is found to correspond spatially with the transition zone between neutral PAHs and eVSGs. Conclusions. We conclude that the photo-processing of eVSGs leads to the production of PAHs with attached aliphatic sidegroups that are revealed by the 3.4 μm emission band. Our analysis provides evidence for the presence of very small grains of mixed aromatic and aliphatic composition in PDRs.
Context. Current dust models are challenged by the dust properties inferred from the analysis of Planck observations in total and polarized emission. Aims. We propose new dust models compatible with ...polarized and unpolarized data in extinction and emission for translucent lines of sight (0.5 < AV < 2.5). Methods. We amended the DustEM tool to model polarized extinction and emission. We fit the spectral dependence of the mean extinction, polarized extinction, total and polarized spectral energy distributions (SEDs) with polycyclic aromatic hydrocarbons, astrosilicate and amorphous carbon (a-C) grains. The astrosilicate population is aligned along the magnetic field lines, while the a-C population may be aligned or not. Results. With their current optical properties, oblate astrosilicate grains are not emissive enough to reproduce the emission to extinction polarization ratio P353∕pV derived with Planck data. Successful models are those using prolate astrosilicate grains with an elongation a∕b = 3 and an inclusion of 20% porosity. The spectral dependence of the polarized SED is steeper in our models than in the data. Models perform slightly better when a-C grains are aligned. A small (6%) volume inclusion of a-C in the astrosilicate matrix removes the need for porosity and perfect grain alignment, and improves the fit to the polarized SED. Conclusions. Dust models based on astrosilicates can be reconciled with Planck data by adapting the shape of grains and adding inclusions of porosity or a-C in the astrosilicate matrix.
Context. Large-scale motions in galaxies (supernovae explosions, galaxy collisions, galactic shear etc.) generate turbulence, which allows a fraction of the available kinetic energy to cascade down ...to small scales before it is dissipated. Aims. We establish and quantify the diagnostics of turbulent dissipation in mildly irradiated diffuse gas in the specific context of shock structures. Methods. We incorporated the basic physics of photon-dominated regions into a state-of-the-art steady-state shock code. We examined the chemical and emission properties of mildly irradiated (G0 = 1) magnetised shocks in diffuse media (nH = 102 to 104 cm-3) at low- to moderate velocities (from 3 to 40 km s-1). Results. The formation of some molecules relies on endoergic reactions. Their abundances in J-type shocks are enhanced by several orders of magnitude for shock velocities as low as 7 km s-1. Otherwise most chemical properties of J-type shocks vary over less than an order of magnitude between velocities from about 7 to about 30 km s-1, where H2 dissociation sets in. C-type shocks display a more gradual molecular enhancement with increasing shock velocity. We quantified the energy flux budget (fluxes of kinetic, radiated and magnetic energies) with emphasis on the main cooling lines of the cold interstellar medium. Their sensitivity to shock velocity is such that it allows observations to constrain statistical distributions of shock velocities. We fitted various probability distribution functions (PDFs) of shock velocities to spectroscopic observations of the galaxy-wide shock in Stephan’s Quintet and of a Galactic line of sight which samples diffuse molecular gas in Chamaeleon. In both cases, low velocities bear the greatest statistical weight and the PDF is consistent with a bimodal distribution. In the very low velocity shocks (below 5 km s-1), dissipation is due to ion-neutral friction and it powers H2 low-energy transitions and atomic lines. In moderate velocity shocks (20 km s-1 and above), the dissipation is due to viscous heating and accounts for most of the molecular emission. In our interpretation a significant fraction of the gas in the line of sight is shocked (from 4% to 66%). For example, C+ emission may trace shocks in UV irradiated gas where C+ is the dominant carbon species. Conclusions. Low- and moderate velocity shocks are important in shaping the chemical composition and excitation state of the interstellar gas. This allows one to probe the statistical distribution of shock velocities in interstellar turbulence.
Within four nearby (d < 160 pc) molecular clouds, we statistically evaluated the structure of the interstellar magnetic field, projected on the plane of the sky and integrated along the line of ...sight, as inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz and from the optical and near-infrared polarization of background starlight. We compared the dispersion of the field orientation directly in vicinities with an area equivalent to that subtended by the Planck effective beam at 353 GHz (10′) and using the second-order structure functions of the field orientation angles. We found that the average dispersion of the starlight-inferred field orientations within 10′-diameter vicinities is less than 20°, and that at these scales the mean field orientation is on average within 5° of that inferred from the submillimetre polarization observations in the considered regions. We also found that the dispersion of starlight polarization orientations and the polarization fractions within these vicinities are well reproduced by a Gaussian model of the turbulent structure of the magnetic field, in agreement with the findings reported by the Planck Collaboration at scales ℓ > 10′ and for comparable column densities. At scales ℓ > 10′, we found differences of up to 14.̊7 between the second-order structure functions obtained from starlight and submillimetre polarization observations in the same positions in the plane of the sky, but comparison with a Gaussian model of the turbulent structure of the magnetic field indicates that these differences are small and are consistent with the difference in angular resolution between both techniques. The differences between the second-order structure functions calculated with each technique suggests that the increase in the angular resolution obtained with the starlight polarization observations does not introduce significant corrections to the dispersion of polarization orientations used in the calculation of the molecular-cloud-scale magnetic field strengths reported in previous studies by the Planck Collaboration.
The characterization of the spectral energy distribution (SED) of dust emission has become a critical issue in the quest for primordial
B
-modes. The dust SED is often approximated by a modified ...black body (MBB) emission law but the extent to which this is accurate is unclear. This paper addresses this question, expanding the dust SED at the power spectrum level. The expansion is performed by means of moments around the MBB law, related to derivatives with respect to the dust spectral index. We present the mathematical formalism and apply it to simulations and
Planck
total intensity data, from 143 to 857 GHz, because no polarized data are yet available that provide the required sensitivity to perform this analysis. With simulations, we demonstrate the ability of high-order moments to account for spatial variations in MBB parameters. Neglecting these moments leads to poor fits and a bias in the recovered dust spectral index. We identify the main moments that are required to fit the
Planck
data. The comparison with simulations helps us to disentangle the respective contributions from dust and the cosmic infrared background to the high-order moments, but the simulations give an insufficient description of the actual
Planck
data. Extending our model to cosmic microwave background
B
-mode analyses within a simplified framework, we find that ignoring the dust SED distortions, or trying to model them with a single decorrelation parameter, could lead to biases that are larger than the targeted sensitivity for the next generation of CMB
B
-mode experiments.
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