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Efficient searches for electromagnetic counterparts to gravitational wave,high-energy neutrino, and gamma-ray burst events demand rapid processing ofimage arithmetic and geometry set operations in a database to cross-matchgalaxy catalogs, observation footprints, and all-sky images. Here we introduceHEALPix Alchemy, an open-source, pure Python implementation of a set of methodsthat enables rapid all-sky geometry calculations. HEALPix Alchemy is built uponHEALPix, a spatial indexing strategy that is widely used in astronomicaldatabases as well as the native format of LIGO-Virgo-KAGRA gravitational-wavesky localization maps. Our approach leverages new multirange types built intothe PostgreSQL 14 database engine. This enables fast all-sky queries againstprobabilistic multimessenger event localizations and telescope surveyfootprints. Questions such as "What are the galaxies contained within the 90%credible region of an event?" and "What is the rank-ordered list of the fieldswithin an observing footprint with the highest probability of containing theevent?" can be performed in less than a few seconds on commodity hardware usingoff-the-shelf cloud-managed database implementations without server-sidedatabase extensions. Common queries scale roughly linearly with the number oftelescope pointings. As the number of fields grows into the hundreds orthousands, HEALPix Alchemy is orders of magnitude faster than otherimplementations. HEALPix Alchemy is now used as the spatial geometry enginewithin SkyPortal, which forms the basis of the Zwicky Transient Facilitytransient marshal, called Fritz.

HEALPix Alchemy: Fast All-Sky Geometry and Image Arithmetic in a Relational Database for Multimessenger Astronomy Brokers