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>A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements
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A Modified Magnitude System that Produces Well-Behaved Magnitudes, Colors, and Errors Even for Low Signal-to-Noise Ratio Measurements
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 5, 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 data products will use this scheme to express all magnitudes in their catalogs.
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机译：我们描述了对天文幅值的通常定义的修改，用反双曲正弦函数代替了对数。我们称这些修改后的幅度为“非正弦幅度”。对于以大于约5的信噪比检测到的物体，我们的修改后的定义与传统的基本相同。对于较弱的对象（包括形式为负磁通的对象），我们的定义表现良好，当磁通趋于零时，趋向于具有有限误差的确定值。当考虑微弱物体的颜色时，此新定义特别有用，因为两个“ asinh”幅值的差可测量明亮物体的通常通量比，同时避免了因将两个非常不确定的数值相除而导致的问题。 Sloan Digital Sky Survey数据产品将使用此方案在其目录中表达所有大小。
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