A search for 85.5- and 86.6-GHz methanol maser emission

We have used the Australia Telescope National Facility Mopra 22m millimetre telescope to search for emission from the 85.5-GHz and 86.6-GHz transitions of methanol. The search was targeted towards 22 star formation regions which exhibit maser emission in the 107.0-GHz methanol transition, as well as in the 6.6-GHz transition characteristic of class II methanol maser sources. A total of 22 regions were searched at 85.5 GHz resulting in 5 detections, of which 1 appears to be a newly discovered maser. For the 86.6-GHz transition observations were made of 18 regions which yielded 2 detections, but no new maser sources. This search demonstrates that emission from the 85.5- and 86.6-GHz transitions is rare. Detection of maser emission from either of these transitions therefore indicates the presence of special conditions, different from those in the majority of methanol maser sources. We have observed temporal variability in the 86.6-GHz emission towards 345.010+1.792, which along with the very narrow line width, confirms that the emission is a maser in this source. We have combined our current observations with published data for the 6.6-, 12.1-, 85.5-, 86.6-, 107.0-, 108.8- and 156.6-GHz transitions for comparison with the maser model of Sobolev & Deguchi (1994). This has allowed us to estimate the likely ranges of dust temperature, gas density, and methanol column density, both for typical methanol maser sources and for those sources which also show 107.0-GHz emission.Comment: 11 pages, accepted for publication in MNRAS, Latex, mn2e.cl

Masers and Outflows in the W3(OH)/W3(H2O) region

Methanol masers and molecular shock tracers were observed in the W3(OH)/W3(H$_2$O) region with the BIMA array and the Onsala 20m radiotelescope. Characteristics of the outflows in the region are discussed. A model of the W3(OH) methanol maser formation region is constructed.Comment: 4 pages, 2 figures, numerous journal misprints are correcte

Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators

We obtain a complete asymptotic expansion of the integrated density of states of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to a wide class of almost-periodic self-adjoint pseudo-differential operators of order less than 2w. In particular, we obtain such an expansion for magnetic Schr\"odinger operators with either smooth periodic or generic almost-periodic coefficients.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1004.293

Non-equilibrium excitation of methanol in Galactic molecular clouds: multi-transitional observations at 2 mm

We observed 14 methanol transitions near lambda=2 mm in Galactic star-forming regions. Broad, quasi-thermal J(0)-J(-1)E methanol lines near 157 GHz were detected toward 73 sources. Together with the 6(-1)-5(0)E and 5(-2)-6(-1)E lines at 133 GHz and the 7(1)-7(0)E line at 165 GHz, they were used to study the methanol excitation. In the majority of the observed objects, the Class I 6(-1)-5(0)E transition is inverted, and the Class II 5(-2)-6(-1)E and 6(0)-6(-1)E transitions are overcooled. This is exactly as predicted by models of low gain Class I masers. The absence of the inversion of Class II transitions 5(-2)-6(-1)E and 6(0)-6(-1)E means that quasi-thermal methanol emission in all objects arises in areas without a strong radiation field, which is required for the inversion.Comment: 23 pages paper (uses aasms4.sty), 12 pages tables (uses apjpt4.sty), 10 Jpeg figures, submitted to the ApJ

Primordial helium recombination III: Thomson scattering, isotope shifts, and cumulative results

Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background (CMB) at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of HeI and HeII recombination. Here we describe the effect of Thomson scattering, the $^3$He isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and $^3$He scattering modify the free electron fraction $x_e$ at the level of several $\times 10^{-4}$. The uncertainty in the $2^3P^o-1^1S$ rate is significant, and for conservative estimates gives uncertainties in $x_e$ of order $10^{-3}$. We describe several convergence tests for the atomic level code and its inputs, derive an overall $C_\ell$ error budget, and relate shifts in $x_e(z)$ to the changes in $C_\ell$, which are at the level of 0.5% at $\ell =3000$. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is $\sim 0.3$ in $x_e$.Comment: 19 pages, 15 figures, to be submitted to PR

Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrodinger operator

We prove the complete asymptotic expansion of the integrated density of states of a two-dimensional Schrodinger operator with a smooth periodic potentialComment: 46 pages, 4 figure

Discovery of new 19.9-GHz methanol masers in star-forming regions

We have used the NASA Tidbinbilla 70-m antenna to search for emission from the 21-30 E (19.9-GHz) transition of methanol. The search was targeted towards 22 star formation regions that exhibit maser emission in the 107.0-GHz 31-40 A+ methanol transition, and in the 6.6-GHz 51-60 A+ transition characteristic of class II methanol maser sources. A total of seven sources were detected in the 21-30 E transition, six of these being new detections. Many of the new detections are weak (≳0.5 Jy), however, they appear to be weak masers rather than thermal or quasi-thermal emission. We find a strong correlation between sources that exhibit 19.9-GHz methanol masers and those that both have the class II methanol masers projected against radio continuum emission and have associated 6035-MHz OH masers. This suggests that the 19.9-GHz methanol masers arise in very specific physical conditions, probably associated with a particular evolutionary phase. In the model of Cragg, Sobolev & Godfrey these observations are consistent with gas temperatures of 50 K, dust temperatures of 150-200 K and gas densities of 106.5-107.5 cm-3