On determinant of certain pentadiagonal matrix

In this paper, using the LU factorization, the relation between the determinant of a certain pentadiagonal matrix and the determinant of a corresponding tridiagonal matrix will be derived. Moreover, it will be shown that determinant of this special pentadiagonal matrix can be calculated by applying the fourth order homogeneous linear difference equation

COMAP Early Science: VI. A First Look at the COMAP Galactic Plane Survey

We present early results from the COMAP Galactic Plane Survey conducted between June 2019 and April 2021, spanning $20^\circ<\ell<40^\circ$ in Galactic longitude and |b|<1.\!\!^{\circ}5 in Galactic latitude with an angular resolution of $4.5^{\prime}$. The full survey will span $\ell \sim 20^{\circ}$- $220^{\circ}$ and will be the first large-scale radio continuum survey at $30$ GHz with sub-degree resolution. We present initial results from the first part of the survey, including diffuse emission and spectral energy distributions (SEDs) of HII regions and supernova remnants. Using low and high frequency surveys to constrain free-free and thermal dust emission contributions, we find evidence of excess flux density at $30\,$GHz in six regions that we interpret as anomalous microwave emission. Furthermore we model UCHII contributions using data from the $5\,$GHz CORNISH catalogue and reject this as the cause of the $30\,$GHz excess. Six known supernova remnants (SNR) are detected at $30\,$GHz, and we measure spectral indices consistent with the literature or show evidence of steepening. The flux density of the SNR W44 at $30\,$GHz is consistent with a power-law extrapolation from lower frequencies with no indication of spectral steepening in contrast with recent results from the Sardinia Radio Telescope. We also extract five hydrogen radio recombination lines to map the warm ionized gas, which can be used to estimate electron temperatures or to constrain continuum free-free emission. The full COMAP Galactic plane survey, to be released in 2023/2024, will be an invaluable resource for Galactic astrophysics.Comment: Paper 6 of 7 in series. 28 pages, 10 figures, submitted to Ap

COMAP Early Science: IV. Power Spectrum Methodology and Results

We present the power spectrum methodology used for the first-season COMAP analysis, and assess the quality of the current data set. The main results are derived through the Feed-feed Pseudo-Cross-Spectrum (FPXS) method, which is a robust estimator with respect to both noise modeling errors and experimental systematics. We use effective transfer functions to take into account the effects of instrumental beam smoothing and various filter operations applied during the low-level data processing. The power spectra estimated in this way have allowed us to identify a systematic error associated with one of our two scanning strategies, believed to be due to residual ground or atmospheric contamination. We omit these data from our analysis and no longer use this scanning technique for observations. We present the power spectra from our first season of observing and demonstrate that the uncertainties are integrating as expected for uncorrelated noise, with any residual systematics suppressed to a level below the noise. Using the FPXS method, and combining data on scales $k=0.051-0.62 \,\mathrm{Mpc}^{-1}$ we estimate $P_\mathrm{CO}(k) = -2.7 \pm 1.7 \times 10^4\mu\textrm{K}^2\mathrm{Mpc}^3$, the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum in the literature.Comment: Paper 4 of 7 in series. 18 pages, 11 figures, as accepted in Ap

COMAP Early Science: II. Pathfinder Instrument

Line intensity mapping (LIM) is a new technique for tracing the global properties of galaxies over cosmic time. Detection of the very faint signals from redshifted carbon monoxide (CO), a tracer of star formation, pushes the limits of what is feasible with a total-power instrument. The CO Mapping Project (COMAP) Pathfinder is a first-generation instrument aiming to prove the concept and develop the technology for future experiments, as well as delivering early science products. With 19 receiver channels in a hexagonal focal plane arrangement on a 10.4 m antenna, and an instantaneous 26-34 GHz frequency range with 2 MHz resolution, it is ideally suited to measuring CO($J$=1-0) from $z\sim3$. In this paper we discuss strategies for designing and building the Pathfinder and the challenges that were encountered. The design of the instrument prioritized LIM requirements over those of ancillary science. After a couple of years of operation, the instrument is well understood, and the first year of data is already yielding useful science results. Experience with this Pathfinder will drive the design of the next generations of experiments.Comment: Paper 2 of 7 in series. 27 pages, 28 figures, submitted to Ap

COMAP Early Science: V. Constraints and Forecasts at z∼3z \sim 3

We present the current state of models for the $z\sim3$ carbon monoxide (CO) line-intensity signal targeted by the CO Mapping Array Project (COMAP) Pathfinder in the context of its early science results. Our fiducial model, relating dark matter halo properties to CO luminosities, informs parameter priors with empirical models of the galaxy-halo connection and previous CO(1-0) observations. The Pathfinder early science data spanning wavenumbers $k=0.051$-$0.62\,$Mpc$^{-1}$ represent the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum. Our 95% upper limit on the redshift-space clustering amplitude $A_{\rm clust}\lesssim70\,\mu$K$^2$ greatly improves on the indirect upper limit of $420\,\mu$K$^2$ reported from the CO Power Spectrum Survey (COPSS) measurement at $k\sim1\,$Mpc$^{-1}$. The COMAP limit excludes a subset of models from previous literature, and constrains interpretation of the COPSS results, demonstrating the complementary nature of COMAP and interferometric CO surveys. Using line bias expectations from our priors, we also constrain the squared mean line intensity-bias product, $\langle{Tb}\rangle^2\lesssim50\,\mu$K$^2$, and the cosmic molecular gas density, $\rho_\text{H2}<2.5\times10^8\,M_\odot\,$Mpc$^{-3}$ (95% upper limits). Based on early instrument performance and our current CO signal estimates, we forecast that the five-year Pathfinder campaign will detect the CO power spectrum with overall signal-to-noise of 9-17. Between then and now, we also expect to detect the CO-galaxy cross-spectrum using overlapping galaxy survey data, enabling enhanced inferences of cosmic star-formation and galaxy-evolution history.Comment: Paper 5 of 7 in series. 17 pages + appendix and bibliography (30 pages total); 15 figures, 6 tables; accepted for publication in ApJ; v3 reflects the accepted version with minor changes and additions to tex

COMAP Early Science: I. Overview

The CO Mapping Array Project (COMAP) aims to use line intensity mapping of carbon monoxide (CO) to trace the distribution and global properties of galaxies over cosmic time, back to the Epoch of Reionization (EoR). To validate the technologies and techniques needed for this goal, a Pathfinder instrument has been constructed and fielded. Sensitive to CO(1-0) emission from $z=2.4$-$3.4$ and a fainter contribution from CO(2-1) at $z=6$-8, the Pathfinder is surveying $12$ deg$^2$ in a 5-year observing campaign to detect the CO signal from $z\sim3$. Using data from the first 13 months of observing, we estimate $P_\mathrm{CO}(k) = -2.7 \pm 1.7 \times 10^4\mu\mathrm{K}^2 \mathrm{Mpc}^3$ on scales $k=0.051-0.62 \mathrm{Mpc}^{-1}$ - the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum. Based on these observations alone, we obtain a constraint on the amplitude of the clustering component (the squared mean CO line temperature-bias product) of $\langle Tb\rangle^2<49$ $\mu$K$^2$ - nearly an order-of-magnitude improvement on the previous best measurement. These constraints allow us to rule out two models from the literature. We forecast a detection of the power spectrum after 5 years with signal-to-noise ratio (S/N) 9-17. Cross-correlation with an overlapping galaxy survey will yield a detection of the CO-galaxy power spectrum with S/N of 19. We are also conducting a 30 GHz survey of the Galactic plane and present a preliminary map. Looking to the future of COMAP, we examine the prospects for future phases of the experiment to detect and characterize the CO signal from the EoR.Comment: Paper 1 of 7 in series. 18 pages, 16 figures, submitted to Ap

On determinant of certain pentadiagonal matrix

In this paper, using the LU factorization, the relation between the determinant of a certain pentadiagonal matrix and the determinant of a corresponding tridiagonal matrix will be derived. Moreover, it will be shown that determinant of this special pentadiagonal matrix can be calculated by applying the fourth order homogeneous linear difference equation

H.E.S.S. realtime follow-ups of IceCube high-energy neutrino alerts

International audienceThe evidence for multi-messenger photon and neutrino emission from the blazar TXS 0506+056 has demonstrated the importance of realtime follow-up of neutrino events by various ground- and space-based facilities. The effort of H.E.S.S. and other experiments in coordinating observations to obtain quasi-simultaneous multiwavelength flux and spectrum measurements has been critical in measuring the chance coincidence with the high-energy neutrino event IC-170922A and constraining theoretical models. For about a decade, the H.E.S.S. transient program has included a search for gamma-ray emission associated with high-energy neutrino alerts, looking for gamma-ray activity from known sources and newly detected emitters consistent with the neutrino location. In this contribution, we present an overview of follow-up activities for realtime neutrino alerts with H.E.S.S. in 2021 and 2022. Our analysis includes both public IceCube neutrino alerts and alerts exchanged as part of a joint H.E.S.S.--IceCube program. We focus on interesting coincidences observed with gamma-ray sources, particularly highlighting the significant detection of PKS 0625-35, an AGN previously detected by H.E.S.S., and three IceCube neutrinos