Reinventing the slide rule for redshifts: the case for logarithmic wavelength shift. (arXiv:1812.05135v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Baldry_I/0/1/0/all/0/1">I. K. Baldry</a>
Redshift is not a shift, it is defined as a fractional change in wavelength.
Nevertheless, it is a fairly common misconception that Delta-z c represents a
velocity where Delta-z is the redshift separation between two galaxies. When
evaluating large changes in a quantity, it is often more useful to consider
logarithmic differences. Defining zeta = ln lambda_obs – ln lambda_em results
in a more accurate approximation for line-of-sight velocity and, more
importantly, this means that the cosmological and peculiar velocity terms
become additive: Delta-zeta c can represent a velocity at any cosmological
distance. Logarithmic shift zeta, or equivalently ln(1+z), should arguably be
used for photometric redshift evaluation. In addition, population distributions
in zeta, rather than z, are close to being evenly distributed in comoving
distance and have a more aesthetic spacing when considering galaxy evolution.
Some pedagogic notes on these quantities are presented.
Redshift is not a shift, it is defined as a fractional change in wavelength.
Nevertheless, it is a fairly common misconception that Delta-z c represents a
velocity where Delta-z is the redshift separation between two galaxies. When
evaluating large changes in a quantity, it is often more useful to consider
logarithmic differences. Defining zeta = ln lambda_obs – ln lambda_em results
in a more accurate approximation for line-of-sight velocity and, more
importantly, this means that the cosmological and peculiar velocity terms
become additive: Delta-zeta c can represent a velocity at any cosmological
distance. Logarithmic shift zeta, or equivalently ln(1+z), should arguably be
used for photometric redshift evaluation. In addition, population distributions
in zeta, rather than z, are close to being evenly distributed in comoving
distance and have a more aesthetic spacing when considering galaxy evolution.
Some pedagogic notes on these quantities are presented.
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