Automated verification of refinement laws

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs

The structure of molecular clumps around high-mass young stellar objects

We have used the IRAM 30-m and FCRAO 14-m telescopes to observe the molecular clumps associated with 12 ultracompact (UC) HII regions in the J=6-5, 8-7 and 13-12 rotational transitions of methyl-acetylene (CH3C2H). Under the assumption of LTE and optically thin emission, we have derived temperature estimates ranging from 30 to 56 K. We estimate that the clumps have diameters of 0.2-1.6 pc, H_2 densities of 10^5-10^6 {cm^{-3}}, and masses of 10^2-2 10^4 M_\odot. We compare these values with those obtained by other authors from different molecular tracers and find that the H_2 density and the temperature inside the clumps vary respectively like n_{H_2} ~ R^{-2.6} and T ~ R^{-0.5}, with R distance from the centre. We also find that the virial masses of the clumps are ~3 times less than those derived from the CH3C2H column densities: we show that a plausible explanation is that magnetic fields play an important role to stabilise the clumps, which are on the verge of gravitational collapse. Finally, we show that the CH3C2H line width increases for decreasing distance from the clump centre: this effect is consistent with infall in the inner regions of the clumps. We conclude that the clumps around UC HII regions are likely to be transient (~10^(5) yr) entities, remnants of isothermal spheres currently undergoing gravitational collapse: the high mass accretion rates (~10^{-2} M_\odot yr^{-1}) lead to massive star formation at the centre of such clumps.Comment: 15 pages, 11 figures, A & A in pres

Carbon recombination lines in the Orion Bar

We have carried out VLA D-array observations of the C91alpha carbon recombination line as well as Effelsberg 100-m observations of the C65alpha line in a 5 arcmin square region centered between the Bar and the Trapezium stars in the Orion Nebula with spatial resolutions of 10 arcsec and 40 arcsec, respectively. The results show the ionized carbon in the PDR associated with the Orion Bar to be in a thin, clumpy layer sandwiched between the ionization front and the molecular gas. From the observed line widths we get an upper limit on the temperature in the C+ layer of 1500 K and from the line intensity a hydrogen density between 5 10^4 and 2.5 10^5 cm-3 for a homogeneous medium. The observed carbon level population is not consistent with predictions of hydrogenic recombination theory but could be explained by dielectronic recombination. The layer of ionized carbon seen in C91alpha is found to be essentially coincident with emission in the v=1-0 S(1) line of vibrationally excited molecular hydrogen. This is surprising in the light of current PDR models and some possible explanations of the discrepancy are discussed.Comment: 9 pages, 3 Postscript figures, uses aaspp4 and psfig, To Appear in ApJ Letters (accepted Jul. 24, 1997

X-Ray Emission from Young Stars in the Massive Star Forming Region IRAS 20126+4104

We present a $40\,$ks Chandra observation of the IRAS$\,$20126+4104 core region. In the inner $6^{\prime\prime}$ two X-ray sources were detected, which are coincident with the radio jet source I20S and the variable radio source I20Var. No X-ray emission was detected from the nearby massive protostar I20N. The spectra of both detected sources are hard and highly absorbed, with no emission below $3\,$keV. For I20S, the measured $0.5-8\,$keV count rate was $4.3\,$cts$\,$ks$^{-1}$. The X-ray spectrum was fit with an absorbed 1T APEC model with an energy of kT$\,=10\,$keV and an absorbing column of N$_H = 1.2\times 10^{23}\,$cm$^{-2}$. An unabsorbed X-ray luminosity of about $1.4\times 10^{32}\,$erg$\,$s$^{-1}$ was estimated. The spectrum shows broad line emission between 6.4 and 6.7\, keV, indicative of emission from both neutral and highly ionized iron. The X-ray lightcurve indicates that I20S is marginally variable; however, no flare emission was observed. The variable radio source I20Var was detected with a count rate of $0.9\,$cts$\,$ks$^{-1}$ but there was no evidence of X-ray variability. The best fit spectral model is a 1T APEC model with an absorbing hydrogen column of N$_H = 1.1\times 10^{23}\,$cm$^{-2}$ and a plasma energy of kT = 6.0$\,$keV. The unabsorbed X-ray luminosity is about $3\times 10^{31}\,$erg$\,$s$^{-1}$.Comment: 17pages, 4 figures to appear in Astronomical Journa

High Resolution Observations of the Massive Protostar in IRAS18566+0408

We report 3 mm continuum, CH3CN(5-4) and 13CS(2-1) line observations with CARMA, in conjunction with 6 and 1.3 cm continuum VLA data, and 12 and 25 micron broadband data from the Subaru Telescope toward the massive proto-star IRAS18566+0408. The VLA data resolve the ionized jet into 4 components aligned in the E-W direction. Radio components A, C, and D have flat cm SEDs indicative of optically thin emission from ionized gas, and component B has a spectral index alpha = 1.0, and a decreasing size with frequency proportional to frequency to the -0.5 power. Emission from the CARMA 3 mm continuum, and from the 13CS(2-1), and CH3CN(5-4) spectral lines is compact (i.e. < 6700 AU), and peaks near the position of VLA cm source, component B. Analysis of these lines indicates hot, and dense molecular gas, typical for HMCs. Our Subaru telescope observations detect a single compact source, coincident with radio component B, demonstrating that most of the energy in IRAS18566+0408 originates from a region of size < 2400 AU. We also present UKIRT near-infrared archival data for IRAS18566+0408 which show extended K-band emission along the jet direction. We detect an E-W velocity shift of about 10 km/sec over the HMC in the CH3CN lines possibly tracing the interface of the ionized jet with the surrounding core gas. Our data demonstrate the presence of an ionized jet at the base of the molecular outflow, and support the hypothesis that massive protostars with O-type luminosity form with a mechanism similar to lower mass stars

Long-term Variability of H2_2CO Masers in Star-forming Regions

We present results of a multi-epoch monitoring program on variability of 6$\,$cm formaldehyde (H$_2$CO) masers in the massive star forming region NGC$\,$7538$\,$IRS$\,$1 from 2008 to 2015 conducted with the GBT, WSRT, and VLA. We found that the similar variability behaviors of the two formaldehyde maser velocity components in NGC$\,$7538$\,$IRS$\,$1 (which was pointed out by Araya and collaborators in 2007) have continued. The possibility that the variability is caused by changes in the maser amplification path in regions with similar morphology and kinematics is discussed. We also observed 12.2$\,$GHz methanol and 22.2$\,$GHz water masers toward NGC$\,$7538$\,$IRS$\,$1. The brightest maser components of CH$_3$OH and H$_2$O species show a decrease in flux density as a function of time. The brightest H$_2$CO maser component also shows a decrease in flux density and has a similar LSR velocity to the brightest H$_2$O and 12.2$\,$GHz CH$_3$OH masers. The line parameters of radio recombination lines and the 20.17 and 20.97$\,$GHz CH$_3$OH transitions in NGC$\,$7538$\,$IRS$\,$1 are also reported. In addition, we observed five other 6$\,$cm formaldehyde maser regions. We found no evidence of significant variability of the 6$\,$cm masers in these regions with respect to previous observations, the only possible exception being the maser in G29.96$-$0.02. All six sources were also observed in the H$_2^{13}$CO isotopologue transition of the 6$\,$cm H$_2$CO line; H$_2^{13}$CO absorption was detected in five of the sources. Estimated column density ratios [H$_2^{12}$CO]/[H$_2^{13}$CO] are reported.Comment: 29 pages, 9 figure