Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

JINGLE – IV. Dust, H I gas and metal scaling laws in the local Universe

Scaling laws of dust, Hi gas and metal mass with stellar mass, specific star formation rate and metallicity are crucial to our understanding of the buildup of galaxies through their enrichment with metals and dust. In this work, we analyse how the dust and metal content varies with specific gas mass (MHI/M?) across a diverse sample of 423 nearby galaxies. The observed trends are interpreted with a set of Dust and Element evolUtion modelS (DEUS) – including stellar dust production, grain growth, and dust destruction – within a Bayesian framework to enable a rigorous search of the multi-dimensional parameter space. We find that these scaling laws for galaxies with −1.0 . logMHI/M? . 0 can be reproduced using closed-box models with high fractions (37-89%) of supernova dust surviving a reverse shock, relatively low grain growth efficiencies (=30-40), and long dust lifetimes (1-2Gyr). The models have present-day dust masses with similar contributions from stellar sources (50-80%) and grain growth (20-50%). Over the entire lifetime of these galaxies, the contribution from stardust (>90%) outweighs the fraction of dust grown in the interstellar medium (<10%). Our results provide an alternative for the chemical evolution models that require extremely low supernova dust production efficiencies and short grain growth timescales to reproduce local scaling laws, and could help solving the conundrum on whether or not grains can grow efficiently in the interstellar medium

JINGLE, a JCMT legacy survey of dust and gas for galaxy evolution studies: II. SCUBA-2 850 μm data reduction and dust flux density catalogues

We present the SCUBA-2 850μm component of JINGLE, the new JCMT large survey for dust and gas in nearby galaxies, which with 193 galaxies is the largest targeted survey of nearby galaxies at 850 μm. We provide details of our SCUBA-2 data reduction pipeline, optimized for slightly extended sources, and including a calibration model adjusted to match conventions used in other far-infrared (FIR) data. We measure total integrated fluxes for the entire JINGLE sample in 10 infrared/submillimetre bands, including all WISE, Herschel-PACS, Herschel-SPIRE, and SCUBA-2 850 μm maps, statistically accounting for the contamination by CO(J = 3-2) in the 850 μm band. Of our initial sample of 193 galaxies, 191 are detected at 250 μm with a ≥5σ significance. In the SCUBA-2 850 μm band we detect 126 galaxies with ≥3σ significance. The distribution of the JINGLE galaxies in FIR/sub-millimetre colour-colour plots reveals that the sample is not well fit by single modified-blackbody models that assume a single dust-emissivity index (β). Instead, our new 850 μm data suggest either that a large fraction of our objects require β < 1.5, or that a model allowing for an excess of sub-mm emission (e.g. a broken dust emissivity law, or a very cold dust component ≲10 K) is required. We provide relations to convert FIR colours to dust temperature and β for JINGLE-like galaxies. For JINGLE the FIR colours correlate more strongly with star-formation rate surface-density rather than the stellar surface-density, suggesting heating of dust is greater due to younger rather than older stellar-populations, consistent with the low proportion of early-type galaxies in the sample

The JCMT BISTRO Survey: Magnetic Fields Associated with a Network of Filaments in NGC 1333

We present new observations of the active star formation region NGC 1333 in the Perseus molecular cloud complex from the James Clerk Maxwell Telescope B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. The BISTRO data cover the entire NGC 1333 complex (~1.5 pc × 2 pc) at 0.02 pc resolution and spatially resolve the polarized emission from individual filamentary structures for the first time. The inferred magnetic field structure is complex as a whole, with each individual filament aligned at different position angles relative to the local field orientation. We combine the BISTRO data with low- and high- resolution data derived from Planck and interferometers to study the multiscale magnetic field structure in this region. The magnetic field morphology drastically changes below a scale of ~1 pc and remains continuous from the scales of filaments (~0.1 pc) to that of protostellar envelopes (~0.005 pc or ~1000 au). Finally, we construct simple models in which we assume that the magnetic field is always perpendicular to the long axis of the filaments. We demonstrate that the observed variation of the relative orientation between the filament axes and the magnetic field angles are well reproduced by this model, taking into account the projection effects of the magnetic field and filaments relative to the plane of the sky. These projection effects may explain the apparent complexity of the magnetic field structure observed at the resolution of BISTRO data toward the filament network

First BISTRO Observations of the Dark Cloud Taurus L1495A-B10: The Role of the Magnetic Field in the Earliest Stages of Low-mass Star Formation

We present BISTRO Survey 850 μm dust emission polarization observations of the L1495A-B10 region of the Taurus molecular cloud, taken at the James Clerk Maxwell Telescope (JCMT). We observe a roughly triangular network of dense filaments. We detect nine of the dense starless cores embedded within these filaments in polarization, finding that the plane-of-sky orientation of the core-scale magnetic field lies roughly perpendicular to the filaments in almost all cases. We also find that the large-scale magnetic field orientation measured by Planck is not correlated with any of the core or filament structures, except in the case of the lowest-density core. We propose a scenario for early prestellar evolution that is both an extension to, and consistent with, previous models, introducing an additional evolutionary transitional stage between field-dominated and matter-dominated evolution, observed here for the first time. In this scenario, the cloud collapses first to a sheet-like structure. Uniquely, we appear to be seeing this sheet almost face on. The sheet fragments into filaments, which in turn form cores. However, the material must reach a certain critical density before the evolution changes from being field dominated to being matter dominated. We measure the sheet surface density and the magnetic field strength at that transition for the first time and show consistency with an analytical prediction that had previously gone untested for over 50 yr

Planck intermediate results. XXI. Comparison of polarized thermal emission from Galactic dust at 353 GHz with interstellar polarization in the visible

The Planck survey provides unprecedented full-sky coverage of the submillimetre polarized emission from Galactic dust. In addition to the information on the direction of the Galactic magnetic field, this also brings new constraints on the properties of dust. The dust grains that emit the radiation seen by Planck in the submillimetre also extinguish and polarize starlight in the visible. Comparison of the polarization of the emission and of the interstellar polarization on selected lines of sight probed by stars provides unique new diagnostics of the emission and light scattering properties of dust, and therefore of the important dust model parameters, composition, size, and shape. Using ancillary catalogues of interstellar polarization and extinction of starlight, we obtain the degree of polarization, p(V), and the optical depth in the V band to the star, tau(V). Toward these stars we measure the submillimetre polarized intensity, P-S, and total intensity, I-S,I- in the Planck 353 GHz channel. We compare the column density measure in the visible, E(B - V), with that inferred from the Planck product map of the submillimetre dust optical depth and compare the polarization direction (position angle) in the visible with that in the submillimetre. For those lines of sight through the di ff use interstellar medium with comparable values of the estimated column density and polarization directions close to orthogonal, we correlate properties in the submillimetre and visible to find two ratios, R-S/V = (P-S/I-S) = (p(V)/tau(V)) and R-P/p = P-S/p(V), the latter focusing directly on the polarization properties of the aligned grain population alone. We find R-S/V = 4.2, with statistical and systematic uncertainties 0.2 and 0.3, respectively, and R-P/p = 5.4 MJy sr(-1), with uncertainties 0.2 and 0.3 MJy sr(-1), respectively. Our estimate of R-S/V is compatible with predictions based on a range of polarizing dust models that have been developed for the di ff use interstellar medium. This estimate provides new empirical validation of many of the common underlying assumptions of the models, but is not yet very discriminating among them. However, our estimate of R-P/p is not compatible with predictions, which are too low by a factor of about 2.5. This more discriminating diagnostic, R-P/p, indicates that changes to the optical properties in the models of the aligned grain population are required. These new diagnostics, together with the spectral dependence in the submillimetre from Planck, will be important for constraining and understanding the full complexity of the grain models, and for interpreting the Planck thermal dust polarization and refinement of the separation of this contamination of the cosmic microwave background.Peer reviewe

Observations of Magnetic Fields Surrounding LkH alpha 101 Taken by the BISTRO Survey with JCMT-POL-2

We report the first high spatial resolution measurement of magnetic fields surrounding LkHα 101, part of the Auriga–California molecular cloud. The observations were taken with the POL-2 polarimeter on the James Clerk Maxwell Telescope within the framework of the B-fields In Star-forming Region Observations (BISTRO) survey. Observed polarization of thermal dust emission at 850 μm is found to be mostly associated with the redshifted gas component of the cloud. The magnetic field displays a relatively complex morphology. Two variants of the Davis–Chandrasekhar–Fermi method, unsharp masking and structure function, are used to calculate the strength of magnetic fields in the plane of the sky, yielding a similar result of BPOS ~ 115 μG. The mass-to-magnetic-flux ratio in critical value units, λ ~ 0.3, is the smallest among the values obtained for other regions surveyed by POL-2. This implies that the LkHα 101 region is subcritical, and the magnetic field is strong enough to prevent gravitational collapse. The inferred δB/B0 ~ 0.3 implies that the large-scale component of the magnetic field dominates the turbulent one. The variation of the polarization fraction with total emission intensity can be fitted by a power law with an index of α = 0.82 ± 0.03, which lies in the range previously reported for molecular clouds. We find that the polarization fraction decreases rapidly with proximity to the only early B star (LkHα 101) in the region. Magnetic field tangling and the joint effect of grain alignment and rotational disruption by radiative torques can potentially explain such a decreasing trend

Planck intermediate results. XX. Comparison of polarized thermal emission from Galactic dust with simulations of MHD turbulence

Polarized emission observed by Planck HFI at 353GHz towards a sample of nearby fields is presented, focusing on the statistics of polarization fractions p and angles psi. The polarization fractions and column densities in these nearby fields are representative of the range of values obtained over the whole sky. We find that: (i) the largest polarization fractions are reached in the most diffuse fields; (ii) the maximum polarization fraction p(max) decreases with column density N-H in the more opaque fields with N-H > 10(21) cm(-2); and (iii) the polarization fraction along a given line of sight is correlated with the local spatial coherence of the polarization angle. These observations are compared to polarized emission maps computed in simulations of anisotropic magnetohydrodynamical turbulence in which we assume a uniform intrinsic polarization fraction of the dust grains. We find that an estimate of this parameter may be recovered from the maximum polarization fraction p(max) in diffuse regions where the magnetic field is ordered on large scales and perpendicular to the line of sight. This emphasizes the impact of anisotropies of the magnetic field on the emerging polarization signal. The decrease of the maximum polarization fraction with column density in nearby molecular clouds is well reproduced in the simulations, indicating that it is essentially due to the turbulent structure of the magnetic field: an accumulation of variously polarized structures along the line of sight leads to such an anti-correlation. In the simulations, polarization fractions are also found to anti-correlate with the angle dispersion function S. However, the dispersion of the polarization angle for a given polarization fraction is found to be larger in the simulations than in the observations, suggesting a shortcoming in the physical content of these numerical models. In summary, we find that the turbulent structure of the magnetic field is able to reproduce the main statistical properties of the dust polarization as observed in a variety of nearby clouds, dense cores excluded, and that the large-scale field orientation with respect to the line of sight plays a major role in the quantitative analysis of these statistical properties.Peer reviewe

Revealing the diverse magnetic field morphologies in Taurus dense cores with sensitive sub-millimeter polarimetry

We have obtained sensitive dust continuum polarization observations at 850 μm in the B213 region of Taurus using POL-2 on SCUBA-2 at the James Clerk Maxwell Telescope (JCMT), as part of the BISTRO (B-fields in STar-forming Region Observations) survey. These observations allow us to probe magnetic field (B-field) at high spatial resolution (∼2000 au or ∼0.01 pc at 140 pc) in two protostellar cores (K04166 and K04169) and one prestellar core (Miz-8b) that lie within the B213 filament. Using the Davis-Chandrasekhar-Fermi method, we estimate the B-field strengths in K04166, K04169, and Miz-8b to be 38±14 μG, 44±16 μG, and 12±5 μG, respectively. These cores show distinct mean B-field orientations. B-field in K04166 is well ordered and aligned parallel to the orientations of the core minor axis, outflows, core rotation axis, and large-scale uniform B-field, in accordance with magnetically regulated star formation via ambipolar diffusion taking place in K04166. B-field in K04169 is found to be ordered but oriented nearly perpendicular to the core minor axis and large-scale B-field, and not well-correlated with other axes. In contrast, Miz-8b exhibits disordered B-field which show no preferred alignment with the core minor axis or large-scale field. We found that only one core, K04166, retains a memory of the large-scale uniform B-field. The other two cores, K04169 and Miz-8b, are decoupled from the large-scale field. Such a complex B-field configuration could be caused by gas inflow onto the filament, even in the presence of a substantial magnetic flux