A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements

Abstract

We describe a modification of the usual definition of astronomical magnitudes, replacing the usual logarithm with an inverse hyperbolic sine function; we call these modified magnitudes `asinh magnitudes'. For objects detected at signal-to-noise ratios of greater than about five, our modified definition is essentially identical to the traditional one; for fainter objects (including those with a formally negative flux) our definition is well behaved, tending to a definite value with finite errors as the flux goes to zero. This new definition is especially useful when considering the colors of faint objects, as the difference of two `asinh' magnitudes measures the usual flux ratio for bright objects, while avoiding the problems caused by dividing two very uncertain values for faint objects. The Sloan Digital Sky Survey (SDSS) data products will use this scheme to express all magnitudes in their catalogs.

11 pages, including 3 postscript figures. Submitted to AJ

References in corpus (1)

• High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning Data

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• The Environment of Lyman Break Analogues (ELBA) survey: Star-forming galaxies in small groups
• Photometric calibration in u-band using blue halo stars
• Probing the rapid formation of black holes and their galaxy hosts in QSOs
• Deblurring galaxy images with Tikhonov regularization on magnitude domain
• Multi-wavelength Observations of MWC 297: Constraints on Disk Inclination and Mass Outflow
• A six year image-subtraction light curve of SN 2010jl
• Z-Sequence: Photometric redshift predictions for galaxy clusters with sequential random k-nearest neighbours
• Recalibration of SDSS photometric zero-points based on the InfraRed Flux Method temperature scale
• Wide Field Multiband Imaging of Low Redshift Quasar Environments
• Specific features of the average magnitudes and luminosities of quasars and galaxies as a function of redshift and their interpretation in the modified cosmological model
• Impact of astrophysical effects on the dark matter mass constraint with 21cm intensity mapping
• IVOA Recommendation: IVOA Photometry Data Model
• Discovery of a dwarf planet candidate in an extremely wide orbit: 2017 OF201
• Where's Swimmy?: Mining unique color features buried in galaxies by deep anomaly detection using Subaru Hyper Suprime-Cam data
• Passive spiral galaxies deeply captured by Subaru Hyper Suprime-Cam
• Search for spatial coincidences between galaxy mergers and Fermi-LAT 4FGL-DR4 sources
• SIMS: Scale-Invariant Merit-Function-Based Scalarization for Multi-Task Learning
• The optical-infrared relation for active galactic nuclei: The role of contaminations
• pop-cosmos: Star formation over 12 Gyr from generative modelling of a deep infrared-selected galaxy catalogue
• Uncertain Photometric Redshifts with Deep Learning Methods
• Revealing a strongly reddened, faint active galactic nucleus population by stacking deep co-added images