The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints

Abstract: We present a measurement of the Hubble constant made using geometric distance measurements to megamaser-hosting galaxies. We have applied an improved approach for fitting maser data and obtained better distance estimates for four galaxies previously published by the Megamaser Cosmology Project: UGC 3789, NGC 6264, NGC 6323, and NGC 5765b. Combining these updated distance measurements with those for the maser galaxies CGCG 074-064 and NGC 4258, and assuming a fixed velocity uncertainty of 250 km s$^{-1}$ associated with peculiar motions, we constrain the Hubble constant to be $H_0 = 73.9 \pm 3.0$ km s$^{-1}$ Mpc$^{-1}$ independent of distance ladders and the cosmic microwave background. This best value relies solely on maser-based distance and velocity measurements, and it does not use any peculiar velocity corrections. Different approaches for correcting peculiar velocities do not modify $H_0$ by more than ${\pm}1{\sigma}$, with the full range of best-fit Hubble constant values spanning 71.8-76.9 km s$^{-1}$ Mpc$^{-1}$. We corroborate prior indications that the local value of $H_0$ exceeds the early-Universe value, with a confidence level varying from 95-99% for different treatments of the peculiar velocities.

• The paper provides a comprehensive reference for LaTeX symbols, including AAS and AMS Math specific sets, categorized for efficient typesetting of scientific documents.
• The organized structure enables users to quickly find correct commands, minimizing typographical errors and enhancing accuracy in typesetting complex mathematical expressions.
• The resource enhances workflow efficiency in scientific publishing and provides a basis for developing automated typesetting tools and AI-assisted formatting solutions.

Overview of 'AAS, AMS Math, and LaTeX Symbols'

The paper "AAS, AMS Math, and LaTeX Symbols" presents a comprehensive list of mathematical symbols and their corresponding LaTeX commands. This document is a pragmatic resource for researchers and authors who utilize LaTeX for preparing manuscripts, especially those working within the astrophysics and mathematics community. By collating symbols related to AAS (American Astronomical Society) and AMS (American Mathematical Society) standards, the author provides a meticulous reference aimed at enhancing the efficiency and effectiveness of typesetting complex mathematical equations and notations.

Content Synopsis

The document is structured around numerous tables, each succinctly cataloging symbols under a specific category. Here is a brief overview of the key inclusions:

1. Additional AAS Symbols: This section lists symbols frequently used in astronomical contexts, such as bounds, bond types, celestial units, and various measurement markers.
2. Text-mode Accents and National Symbols: These sections provide guidance for text accentuation necessary for correctly rendering names and terms with specific national or linguistic characters.
3. Math-mode Accents and Greek/Hebrew Letters: A prevalent feature in mathematical and scientific documents, these tables provide a reference to include accents on variables and Greek letters, which form the cornerstone of mathematical typographies.
4. Binary Operators and Relations: These tables encompass operators essential for expressing mathematical operations and relationships, including variations provided by AMS to manage set relations and operations effectively.
5. Miscellaneous Symbols and Arrows: A collection of less frequently used, but critical symbols and directional arrows that aid in detailing procedural flow and vector representations.
6. Variable-sized and Delimiters Symbols: These are pivotal for writing integrals, summations, and for defining boundaries within mathematical expressions, thereby facilitating clarity in complex mathematical configurations.
7. Function Names: A list of pre-defined LaTeX functions that simplifies the notation of common mathematical functions, enhancing readability and reducing typographical errors.

Numerical Results and Claims

While the paper does not present conventional numerical results or experimental claims, its strength lies in the organized presentation of symbols that reflects a thorough awareness of typographical needs within the scientific publishing domain. The efficacy of this document is evident in its potential to minimize errors and inconsistencies that may arise from manual symbol entry.

Implications and Future Developments

Practically, this collation aids in ensuring clarity and precision across documents, crucial in scientific discourse where misinterpretation can lead to significant misunderstandings. Theoretically, it posits a baseline for developing automated typographical tools that could leverage this repository for enhanced text processing.

Future developments might include integrating this resource within LaTeX editor plugins or cloud-based typesetting platforms, enabling real-time symbol suggestions, and corrections as authors compose their documents. With the growing dataset of symbols, there is tremendous scope for developing AI-based formatting and editing tools that adaptively learn and suggest appropriate symbols based on document context.

In conclusion, while the document serves as a static reference, its implications for improving typesetting accuracy and workflow efficiency are substantial, particularly in fields necessitating precise mathematical communication. Such meticulous documentation is invaluable for fostering clear communication and facilitating more rigorous scientific exploration.