Methanol masers : Reliable tracers of the early stages of high-mass star formation

The GLIMPSE and MSX surveys have been used to examine the mid-infrared properties of a statistically complete sample of 6.7 GHz methanol masers. The GLIMPSE point sources associated with methanol masers are clearly distinguished from the majority, typically having extremely red mid-infrared colors, similar to those expected of low-mass class 0 young stellar objects. The intensity of the GLIMPSE sources associated with methanol masers is typically 4 magnitudes brighter at 8.0 micron than at 3.6 micron. Targeted searches towards GLIMPSE point sources with [3.6]-[4.5] > 1.3 and an 8.0 micron magnitude less than 10 will detect more than 80% of class II methanol masers. Many of the methanol masers are associated with sources within infrared dark clouds (IRDC) which are believed to mark regions where high-mass star formation is in its very early stages. The presence of class II methanol masers in a significant fraction of IRDC suggests that high-mass star formation is common in these regions. Different maser species are thought to trace different evolutionary phases of the high-mass star formation process. Comparison of the properties of the GLIMPSE sources associated with class II methanol masers and other maser species shows interesting trends, consistent with class I methanol masers tracing a generally earlier evolutionary phase and OH masers tracing a later evolutionary phase.Comment: 45 pages, 19 figures, accepted for publication in Ap

New class I methanol masers

We review properties of all known collisionally pumped (class I) methanol maser series based on observations with the Australia Telescope Compact Array (ATCA) and the Mopra radio telescope. Masers at 36, 84, 44 and 95 GHz are most widespread, while 9.9, 25, 23.4 and 104 GHz masers are much rarer, tracing the most energetic shocks. A survey of many southern masers at 36 and 44 GHz suggests that these two transitions are highly complementary. The 23.4 GHz maser is a new type of rare class I methanol maser, detected only in two high-mass star-forming regions, G357.97-0.16 and G343.12-0.06, and showing a behaviour similar to 9.9, 25 and 104 GHz masers. Interferometric positions suggest that shocks responsible for class I masers could arise from a range of phenomena, not merely an outflow scenario. For example, some masers might be caused by interaction of an expanding HII region with its surrounding molecular cloud. This has implications for evolutionary sequences incorporating class I methanol masers if they appear more than once during the evolution of the star-forming region. We also make predictions for candidate maser transitions at the ALMA frequency range.Comment: 8 pages, 2 figures, to appear in proceedings for IAUS 287: Cosmic Masers - from OH to H

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

We consider a periodic self-adjoint pseudo-differential operator $H=(-\Delta)^m+B$, $m>0$, in $\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in \bx, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schr\"odinger operator with a periodic magnetic potential in all dimensions.Comment: 61 page

Planar infall of CH3OH gas around Cepheus A HW2

Aims: In order to test the nature of an (accretion) disk in the vicinity of Cepheus A HW2, we measured the three-dimensional velocity field of the CH3OH maser spots, which are projected within 1000au of the HW2 object, with an accuracy of the order of 0.1km/s. Methods: We made use of the European VLBI Network (EVN) to image the 6.7GHz CH3OH maser emission towards Cepheus A HW2 with 4.5 milli-arcsecond resolution (3au). We observed at three epochs spaced by one year between 2013 and 2015. During the last epoch, on mid-march 2015, we benefited from the new deployed Sardinia Radio Telescope. Results: We show that the CH3OH velocity vectors lie on a preferential plane for the gas motion with only small deviations of 12+/-9 degrees away from the plane. This plane is oriented at a position angle of 134 degrees east of north, and inclined by 26 degrees with the line-of-sight, closely matching the orientation of the disk-like structure previously reported by Patel et al.(2005). Knowing the orientation of the equatorial plane, we can reconstruct a face-on view of the CH3OH gas kinematics onto the plane. CH3OH maser emission is detected within a radius of 900au from HW2, and down to a radius of about 300au, the latter coincident with the extent of the dust emission at 0.9mm. The velocity field is dominated by an infall component of about 2km/s down to a radius of 300au, where a rotational component of 4km/s becomes dominant. We discuss the nature of this velocity field and the implications for the enclosed mass. Conclusions: These findings bring direct support to the interpretation that the high-density gas and dust emission, surrounding Cepheus A HW2, trace an accretion disk.Comment: 9 pages, 4 figures, 2 tables, accepted by Astronomy & Astrophysic

High-velocity feature of the class I methanol maser in G309.38-0.13

The Australia Telescope Compact Array (ATCA) has been used to map class I methanol masers at 36 and 44 GHz in G309.38-0.13. Maser spots are found at nine locations in an area of 50''x30'', with both transitions reliably detected at only two locations. The brightest spot is associated with shocked gas traced by 4.5 micron emission. The data allowed us to make a serendipitous discovery of a high-velocity 36-GHz spectral feature, which is blue-shifted by about 30 km/s from the peak velocity at this frequency, but spatially located close to (within a few arcseconds of) the brightest maser spot. We interpret this as indicating an outflow parallel to the line of sight. Such a high velocity spread of maser features, which has not been previously reported in the class I methanol masers associated with a single molecular cloud, suggests that the outflow most likely interacts with a moving parcel of gas.Comment: 6 pages, 2 figures, accepted by MNRAS Letter

Methanol in W3(H2O) and Surrounding Regions

We present the results of an interferometric study of 38 millimeter-wave lines of CH3OH in the region around the water maser source W3(H2O) and a region extending about 30" to the south and west of the hydroxyl maser source W3(OH). The methanol emitting region around W3(H2O) has an extent of 2.0" x 1.2" (4400 x 2600 AU). The density is of order 1.e7 cm-3, sufficient to thermalize most of the methanol lines. The kinetic temperature is approximately 140 K and the methanol fractional abundance greater than 1.e-6, indicative of a high degree of grain mantle evaporation. The W3(H2O) source contains sub-structure, with peaks corresponding to the TW source and Wyrowski's B/C, separated by 2500 AU in projection. The kinematics are consistent with these being distinct protostellar cores in a wide binary orbit and a dynamical mass for the region of a few tens of Mo. The extended methanol emission to the southwest of W3(OH) is seen strongly only from the lowest excitation lines and from lines known elsewhere to be class I methanol masers, namely the 84.5 GHz 5(-1)-4(0)E and 95.2 GHz 8(0)-7(1)A+ lines. Within this region there are two compact clumps, which we denote as swA and swB, each about 15" (0.16 pc projected distance) away from W3(OH). Excitation analysis of these clumps indicates the presence of lines with inverted populations but only weak amplification. The sources swA and swB appear to have kinetic temperatures of order 50-100 K and densities of order 1.e5 - 1.e6 cm-3. The methanol fractional abundance for the warmer clump is of order 1.e-7, suggestive of partial grain mantle evaporation. The clumping occurs on mass scales of order 1 Mo.Comment: 28 pages including 6 figures and 4 tables, accepted by Ap

The Australia Telescope campaign to study southern class I methanol masers

The Australia Telescope Compact Array (ATCA) and the Mopra facility have been used to search for new southern class I methanol masers at 9.9, 25 (J=5) and 104 GHz, which are thought to trace more energetic conditions in the interface regions of molecular outflows, than the widespread class I masers at 44 and 95 GHz. One source shows a clear outflow association.Comment: 2 pages, 1 figure (composed from 3 files), to appear in proceedings of IAU Symposium 242 "Astrophysical masers and their environment" (eds. J. Chapman and W. Baan

Multi-transition study and new detections of class II methanol masers

We have used the ATNF Mopra antenna and the SEST antenna to search in the directions of several class II methanol maser sources for emission from six methanol transitions in the frequency range 85-115 GHz. The transitions were selected from excitation studies as potential maser candidates. Methanol emission at one or more frequencies was detected from five of the maser sources, as well as from Orion KL. Although the lines are weak, we find evidence of maser origin for three new lines in G345.01+1.79, and possibly one new line in G9.62+0.20. The observations, together with published maser observations at other frequencies, are compared with methanol maser modelling for G345.01+1.79 and NGC6334F. We find that the majority of observations in both sources are consistent with a warm dust (175 K) pumping model at hydrogen density ~10^6 cm^-3 and methanol column density ~5 x 10^17 cm^-2. The substantial differences between the maser spectra in the two sources can be attributed to the geometry of the maser region.Comment: 13 pages, 6 figures, Accepted for publication in MNRA

K. Schwarzschild's problem in radiation transfer theory

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem - to be more precise the calculation of the source function within the slab - was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo = 1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce 1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it, 2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere.Comment: 21 pages, 2 figures, JQSRT, accepted 16 May 200

Scott correction for large atoms and molecules in a self-generated magnetic field

We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z\al^2\le \kappa_0 for a sufficiently small $\kappa_0$, where \al denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, \al\to 0 such that \kappa =Z\al^2 is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion