Wavefront Curvature in Optical Atomic Beam Clocks

Atomic clocks provide a reproducible basis for our understanding of time and frequency. Recent demonstrations of compact optical clocks, employing thermal atomic beams, have achieved short-term fractional frequency instabilities in the $10^{-16}$, competitive with the best international frequency standards available. However, a serious challenge inherent in compact clocks is the necessarily smaller optical beams, which results in rapid variation in interrogating wavefronts. This can cause inhomogeneous excitation of the thermal beam leading to long term drifts in the output frequency. Here we develop a model for Ramsey-Bord\'e interferometery using optical fields with curved wavefronts and simulate the $^{40}$Ca beam clock experiment described in [Olson et al., Phys. Rev. Lett. 123, 073202 (2019)]. Olson et al.'s results had shown surprising and unexplained behaviour in the response of the atoms in the interrogation. Our model predicts signals consistent with experimental data and can account for the significant sensitivity to laser geometry that was reported. We find the signal-to-noise ratio is maximised when the laser is uncollimated at the interrogation zones to minimise inhomogeneity, and also identify an optimal waist size determined by both laser inhomogeneity and the velocity distribution of the atomic beam. We investigate the shifts and stability of the clock frequency, showing that the Gouy phase is the primary source of frequency variations arising from laser geometry.Comment: 13 pages, 7 figure

Automatic Redshift Determination by use of Principal Component Analysis --- I: Fundamentals

With the advent of very large redshift surveys of tens to hundreds of thousands of galaxies reliable techniques for automatically determining galaxy redshifts are becoming increasingly important. The most common technique currently in common use is the cross-correlation of a galactic spectrum with a set of templates. This series of papers presents a new method based on Principal Component Analysis. The method generalizes the cross-correlation approach by replacing the individual templates by a simultaneous linear combination of orthogonal templates. This effectively eliminates the mismatch between templates and data and provides for the possibility of better error estimates. In this paper, the first of a series, the basic mathematics are presented along with a simple demonstration of the application.Comment: 23 pages, 9 Figures, minor revisions, accepted for publication in Astrophysical Journa

Far-Infrared OH fluorescent emission in Sagittarius B2

We present Infrared Space Observatory (ISO) observations of 16OH and 18OH toward Sgr B2 with a spectral resolution of 35 km/s. The OH J=5/2-3/2 and J=3/2-1/2 rotational lines of the 2Pi1/2 ladder are seen in emission while the cross-ladder transitions (from the 2Pi3/2 J=3/2 to the J=1/2, 3/2 and 5/2 levels of the 2Pi1/2ladder), and the 2Pi3/2 J=5/2-3/2 and J=7/2-5/2 lines are detected in absorption. The 18OH 2Pi3/2 J=5/2-3/2 Lambda-doublet at 120 mu is also observed in absorption. All OH Lambda-doublets are resolved (except the 98 mu) and show, in addition to the strong absorption at the velocity of Sgr B2, several velocity components associated to the gas surrounding Sgr B2 and to the foreground clouds along the line of sight. No asymmetries in the line intensities of each doublet have been observed. We have modeled the observations using a non-local radiative transfer code and found that the OH absorption/emission must arise in a shell around Sgr B2 not resolved by the ISO/LWS beam. The gas density is moderate, with upper limits of 10^4 cm^{-3} and 300 K in temperature. The OH abundance is high,(2-5)10^{-6}. We argue that a widespread photon dominated region explains the enhancement of OH abundance.Comment: 13 pages, 2 figures, accepted in ApJ Letter

HI Narrow Self-Absorption in Dark Clouds: Correlations with Molecular Gas and Implications for Cloud Evolution and Star Formation

We present the results of a comparative study of HI narrow self-absorption (HINSA), OH, 13CO, and C18O in five dark clouds. The HINSA follows the distribution of the emission of the carbon monoxide isotopologues, and has a characteristic size close to that of 13CO. This confirms that the HINSA is produced by cold HI which is well mixed with molecular gas in well-shielded regions. The ratio of the atomic hydrogen density to total proton density for these sources is 5 to 27 x 10^{-4}. Using cloud temperatures and the density of HI, we set an upper limit to the cosmic ray ionization rate of 10^{-16} s^{-1}. Comparison of observed and modeled fractional HI abundances indicates ages for these clouds to be 10^{6.5} to 10^{7} yr. The low values of the HI density we have determined make it certain that the time scale for evolution from an atomic to an almost entirely molecular phase, must be a minimum of several million years. This clearly sets a lower limit to the overall time scale for star formation and the lifetime of molecular clouds

Herschel observations of the hydroxyl radical (OH) in young stellar objects

Water in Star-forming regions with Herschel (WISH) is a Herschel Key Program investigating the water chemistry in young stellar objects (YSOs) during protostellar evolution. Hydroxyl (OH) is one of the reactants in the chemical network most closely linked to the formation and destruction of H2O. High-temperature chemistry connects OH and H2O through the OH + H2 H2O + H reactions. Formation of H2O from OH is efficient in the high-temperature regime found in shocks and the innermost part of protostellar envelopes. Moreover, in the presence of UV photons, OH can be produced from the photo-dissociation of H2O. High-resolution spectroscopy of the OH 163.12 micron triplet towards HH 46 and NGC 1333 IRAS 2A was carried out with the Heterodyne Instrument for the Far Infrared (HIFI) on board Herschel. The low- and intermediate-mass YSOs HH 46, TMR 1, IRAS 15398-3359, DK Cha, NGC 7129 FIRS 2, and NGC 1333 IRAS 2A were observed with the Photodetector Array Camera and Spectrometer (PACS) in four transitions of OH and two [OI] lines. The OH transitions at 79, 84, 119, and 163 micron and [OI] emission at 63 and 145 micron were detected with PACS towards the class I low-mass YSOs as well as the intermediate-mass and class I Herbig Ae sources. No OH emission was detected from the class 0 YSO NGC 1333 IRAS 2A, though the 119 micron was detected in absorption. With HIFI, the 163.12 micron was not detected from HH 46 and only tentatively detected from NGC 1333 IRAS 2A. The combination of the PACS and HIFI results for HH 46 constrains the line width (FWHM > 11 km/s) and indicates that the OH emission likely originates from shocked gas. This scenario is supported by trends of the OH flux increasing with the [OI] flux and the bolometric luminosity. Similar OH line ratios for most sources suggest that OH has comparable excitation temperatures despite the different physical properties of the sources.Comment: Accepted for publication in Astronomy and Astrophysics (Herschel special issue

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re

‘Stop-go’ policy and the restriction of post-war British house-building

From the mid-1950s to the early 1980s the Treasury and Bank of England successfully advocated a policy of restricting both private and public sector house-building, as a key but covert instrument of their wider ‘stop-go’ macroeconomic policy framework. While the intensity of restrictions varied over the economic cycle, private house-building was restricted (through limiting mortgage availability) for almost all this period. This was achieved by keeping building society interest rates low relative to other interest rates and thus starving the building society movement of mortgage funds. Mortgage restriction was never publicly discussed and sometimes operated alongside ambitious housing targets and well-publicised policy initiatives to boost housing demand. This paper outlines the evolution of house-building restriction, together with its impacts on the housing sector and the wider economy. We review the evolution of the policy framework and its consequences, compare the level and stability of British house-building during this period - historically and relative to other countries, and undertake time-series econometric analysis of its impacts on both house-building and house prices. Finally, implications for debates regarding stop-go policy, Britain’s housing problem, and the distributional consequences of government macroeconomic policy are discussed