A multi-wavelength observation and investigation of six infrared dark clouds

Context. Infrared dark clouds (IRDCs) are ubiquitous in the Milky Way, yet they play a crucial role in breeding newly-formed stars. Aims. With the aim of further understanding the dynamics, chemistry, and evolution of IRDCs, we carried out multi-wavelength observations on a small sample. Methods. We performed new observations with the IRAM 30 m and CSO 10.4 m telescopes, with tracers ${\rm HCO^+}$, HCN, ${\rm N_2H^+}$, ${\rm C^{18}O}$, DCO$^+$, SiO, and DCN toward six IRDCs G031.97+00.07, G033.69-00.01, G034.43+00.24, G035.39-00.33, G038.95-00.47, and G053.11+00.05. Results. We investigated 44 cores including 37 cores reported in previous work and seven newly-identified cores. Toward the dense cores, we detected 6 DCO$^+$, and 5 DCN lines. Using pixel-by-pixel spectral energy distribution (SED) fits of the $\textit{Herschel}$ 70 to 500 $\mu$m, we obtained dust temperature and column density distributions of the IRDCs. We found that ${\rm N_2H^+}$ emission has a strong correlation with the dust temperature and column density distributions, while ${\rm C^{18}O}$ showed the weakest correlation. It is suggested that ${\rm N_2H^+}$ is indeed a good tracer in very dense conditions, but ${\rm C^{18}O}$ is an unreliable one, as it has a relatively low critical density and is vulnerable to freezing-out onto the surface of cold dust grains. The dynamics within IRDCs are active, with infall, outflow, and collapse; the spectra are abundant especially in deuterium species. Conclusions. We observe many blueshifted and redshifted profiles, respectively, with ${\rm HCO^+}$ and ${\rm C^{18}O}$ toward the same core. This case can be well explained by model "envelope expansion with core collapse (EECC)".Comment: 24 pages, 11 figures, 4 tables. To be published in A&A. The resolutions of the pictures are cut dow

Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

On the accretion process in a high-mass star forming region - A multitransitional THz Herschel-HIFI study of ammonia toward G34.26+0.15

[Abridged] Our aim is to explore the gas dynamics and the accretion process in the early phase of high-mass star formation. The inward motion of molecular gas in the massive star forming region G34.26+0.15 is investigated by using high-resolution profiles of seven transitions of ammonia at THz frequencies observed with Herschel-HIFI. The shapes and intensities of these lines are interpreted in terms of radiative transfer models of a spherical, collapsing molecular envelope. An accelerated Lambda Iteration (ALI) method is used to compute the models. The seven ammonia lines show mixed absorption and emission with inverse P-Cygni-type profiles that suggest infall onto the central source. A trend toward absorption at increasingly higher velocities for higher excitation transitions is clearly seen in the line profiles. The $J = 3\leftarrow2$ lines show only very weak emission, so these absorption profiles can be used directly to analyze the inward motion of the gas. This is the first time a multitransitional study of spectrally resolved rotational ammonia lines has been used for this purpose. Broad emission is, in addition, mixed with the absorption in the $1_0-0_0$ ortho-NH$_3$ line, possibly tracing a molecular outflow from the star forming region. The best-fitting ALI model reproduces the continuum fluxes and line profiles, but slightly underpredicts the emission and absorption depth in the ground-state ortho line $1_0-0_0$. The derived ortho-to-para ratio is approximately 0.5 throughout the infalling cloud core similar to recent findings for translucent clouds in sight lines toward W31C and W49N. We find evidence of two gas components moving inwards toward the central region with constant velocities: 2.7 and 5.3 km$\,$s$^{-1}$, relative to the source systemic velocity. The inferred mass accretion rates derived are sufficient to overcome the expected radiation pressure from G34.26+0.15.Comment: 20 pages, 18 figures, accepted by A&A 3 October 201

On the Magic Matrix by Makhlin and the B-C-H Formula in SO(4)

A closed expression to the Baker-Campbell-Hausdorff (B-C-H) formula in SO(4) is given by making use of the magic matrix by Makhlin. As far as we know this is the {\bf first nontrivial example} on (semi-) simple Lie groups summing up all terms in the B-C-H expansion.Comment: Latex ; 11 pages ; 1 figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.5 or 6), 200

HI in four star-forming low-luminosity E/S0 and S0 galaxies

We present HI data cubes of four low-luminosity early-type galaxies which are currently forming stars. These galaxies have absolute magnitudes in the range M_B=-17.9 to -19.9 (H_o=50 km/s/Mpc). Their HI masses range between a few times 10^8 and a few times 10^9 M_sun and the corresponding values for M_HI/L_B are between 0.07 and 0.42, so these systems are HI rich for their morphological type. In all four galaxies, the HI is strongly centrally concentrated with high central HI surface densities, in contrast to what is typically observed in more luminous early-type galaxies. In two galaxies (NGC 802 and ESO 118-G34), the kinematics of the HI suggests that the gas is in a strongly warped disk, which we take as evidence for recent accretion of HI. In the other two galaxies (NGC 2328 and ESO 027-G21) the HI must have been part of the systems for a considerable time. The HI properties of low-luminosity early-type galaxies appear to be systematically different from those of many more luminous early-type galaxies, and we suggest that these differences are due to a different evolution of the two classes. The star formation history of these galaxies remains unclear. Their UBV colours and Halpha emission-line strengths are consistent with having formed stars at a slowly-declining rate for most of the past 10^10 years. However, the current data do not rule out a small burst of recent star formation overlaid on an older stellar population.Comment: To appear in AJ, LateX, figures in gif format, paper also available at http://www.nfra.nl/~morganti/LowLu

On inductively free Restrictions of Reflection Arrangements

Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection arrangements A(W). The aim of this note is to extend this work by determining all inductively free restrictions of reflection arrangements.Comment: 15 pages, final version to appear in Journal of Algebr

Degeneracy and decomposability in abelian crossed products

In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product division algebra of exponent $p$ and index $p^2$ for $p$ an odd prime. The algebra we construct is generic in the sense of Amitsur and Saltman and has the property that its underlying abelian crossed product is a decomposable division algebra defined by a non-degenerate matrix. This algebra gives an example of an indecomposable generic abelian crossed product which is shown to be indecomposable without using torsion in the Chow group of the corresponding Severi-Brauer variety as was needed in [Karpenko, Codimension 2 cycles on Severi-Brauer varieites (1998)] and [McKinnie, Indecomposable $p$-algebras and Galois subfields in generic abelian crossed products (2008)]. It also gives an example of a Brauer class which is in Tignol's Dec group with respect to one abelian maximal subfield, but not in the Dec group with respect to another.Comment: 17 page