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We present a new analysis of the profile data from the 47 millisecond pulsars comprising the 12.5-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), which is presented in a parallel paper (Alam et al. 2021a; NG12.5). Our reprocessing is performed using "wideband" timing methods, which use frequency-dependent template profiles, simultaneous time-of-arrival (TOA) and dispersion measure (DM) measurements from broadband observations, and novel analysis techniques. In particular, the wideband DM measurements are used to constrain the DM portion of the timing model. We compare the ensemble timing results to NG12.5 by examining the timing residuals, timing models, and noise model components. There is a remarkable level of agreement across all metrics considered. Our best-timed pulsars produce encouragingly similar results to those from NG12.5. In certain cases, such as high-DM pulsars with profile broadening, or sources that are weak and scintillating, wideband timing techniques prove to be beneficial, leading to more precise timing model parameters by 10-15%. The high-precision, multi-band measurements of several pulsars indicate frequency-dependent DMs. Compared to the narrowband analysis in NG12.5, the TOA volume is reduced by a factor of 33, which may ultimately facilitate computational speed-ups for complex pulsar timing array analyses. This first wideband pulsar timing data set is a stepping stone, and its consistent results with NG12.5 assure us that such data sets are appropriate for gravitational wave analyses., Comment: 62 pages, 55 figures, 5 tables, 3 appendices. Data available at http://nanograv.org/data/ and via DOI 10.5281/zenodo.4312887

We present time-of-arrival (TOA) measurements and timing models of 47 millisecond pulsars (MSPs) observed from 2004 to 2017 at the Arecibo Observatory and the Green Bank Telescope by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). The observing cadence was three to four weeks for most pulsars over most of this time span, with weekly observations of six sources. These data were collected for use in low-frequency gravitational wave searches and for other astrophysical purposes. We detail our observational methods and present a set of TOA measurements, based on "narrowband" analysis, in which many TOAs are calculated within narrow radio-frequency bands for data collected simultaneously across a wide bandwidth. A separate set of "wideband" TOAs will be presented in a companion paper. We detail a number of methodological changes compared to our previous work which yield a cleaner and more uniformly processed data set. Our timing models include several new astrometric and binary pulsar measurements, including previously unpublished values for the parallaxes of PSRs J1832-0836 and J2322+2057, the secular derivatives of the projected semi-major orbital axes of PSRs J0613-0200 and J2229+2643, and the first detection of the Shapiro delay in PSR J2145-0750. We report detectable levels of red noise in the time series for 14 pulsars. As a check on timing model reliability, we investigate the stability of astrometric parameters across data sets of different lengths. We report flux density measurements for all pulsars observed. Searches for stochastic and continuous gravitational waves using these data will be subjects of forthcoming publications., Comment: 54 pages, 52 figures, 7 tables, 1 appendix. Data are available at http://nanograv.org/data/ and via the DOI 10.5281/zenodo.4312297

High-reflectivity fused silica mirrors are at the epicentre of current advanced gravitational wave detectors. In these detectors, the mirrors interact with high power laser beams. As a result of finite absorption in the high reflectivity coatings the mirrors suffer from a variety of thermal effects that impact on the detectors performance. We propose a model of the Advanced LIGO mirrors that introduces an empirical term to account for the radiative heat transfer between the mirror and its surroundings. The mechanical mode frequency is used as a probe for the overall temperature of the mirror. The thermal transient after power build-up in the optical cavities is used to refine and test the model. The model provides a coating absorption estimate of 1.5 to 2.0 ppm and estimates that 0.3 to 1.3 ppm of the circulating light is scattered on to the ring heater., Comment: 14 pages, 9 figures

Advanced laser interferometer gravitational-wave detectors use high laser power to achieve design sensitivity. A small part of this power is absorbed in the interferometer cavity mirrors where it creates thermal lenses, causing aberrations in the main laser beam that must be minimized by the actuation of "ring heaters," which are additional heater elements that are aimed to reduce the temperature gradients in the mirrors. In this article we derive the first, to the best of our knowledge, analytical model of the temperature field generated by an ideal ring heater. We express the resulting optical aberration contribution to the main laser beam in this axisymmetric case. Used in conjunction with wavefront measurements, our model provides a more complete understanding of the thermal state of the cavity mirrors and will allow a more efficient use of the ring heaters in the Advanced Laser Interferometer Gravitational-wave Observatory., Comment: 7 pages, 5 figures, v2: minor changes to match published version