magnitude_error_rykoff

skypy.utils.photometry.magnitude_error_rykoff(magnitude, magnitude_limit, magnitude_zp, a, b, error_limit=inf)

Magnitude error according to the model from Rykoff et al. (2015).

Given an apparent magnitude calculate the magnitude error that is introduced by the survey specifications and follows the model described in Rykoff et al. (2015).

Parameters:

magnitude: array_like

Apparent magnitude. This and the other array_like parameters must be broadcastable to the same shape.

magnitude_limit: array_like

\(10\sigma\) limiting magnitude of the survey. This and the other array_like parameters must be broadcastable to the same shape.

magnitude_zp: array_like

Zero-point magnitude of the survey. This and the other array_like parameters must be broadcastable to the same shape.

a,b: array_like

Model parameters: a is the intercept and b is the slope of the logarithmic effective time. These and the other array_like parameters must be broadcastable to the same shape.

error_limit: float, optional

Upper limit of the returned error. If given, all values larger than this value will be set to error_limit. Default is None.

Returns:

error: ndarray

The apparent magnitude error in the Rykoff et al. (2015) model. This is a scalar if magnitude, magnitude_limit, magnitude_zp, a and b are scalars.

Notes

Rykoff et al. (2015) (see [1]) describe the error of the apparent magnitude \(m\) as

\[\begin{split}\sigma_m(m;m_{\mathrm{lim}}, t_{\mathrm{eff}}) &= \sigma_m(F(m);F_{\mathrm{noise}}(m_{\mathrm{lim}}), t_{\mathrm{eff}}) \\ &= \frac{2.5}{\ln(10)} \left[ \frac{1}{Ft_{\mathrm{eff}}} \left( 1 + \frac{F_{\mathrm{noise}}}{F} \right) \right]^{1/2} \;,\end{split}\]

where

\[F=10^{-0.4(m - m_{\mathrm{ZP}})}\]

is the source’s flux,

\[F_\mathrm{noise} = \frac{F_{\mathrm{lim}}^2 t_{\mathrm{eff}}}{10^2} - F_{\mathrm{lim}}\]

is the effective noise flux and \(t_\mathrm{eff}\) is the effective exposure time (we absorbed the normalisation constant \(k\) in the definition of \(t_\mathrm{eff}\)). Furthermore, \(m_\mathrm{ZP}\) is the zero-point magnitude of the survey and \(F_\mathrm{lim}\) is the \(10\sigma\) limiting flux. Accordingly, \(m_\mathrm{lim}\) is the \(10\sigma\) limiting magnitud associated with \(F_\mathrm{lim}\).

The effective exposure time is described by

\[\ln{t_\mathrm{eff}} = a + b(m_\mathrm{lim} - 21)\;,\]

where \(a\) and \(b\) are free parameters.

Further note that the model was originally used for SDSS galaxy photometry.

References

[1]

Rykoff E. S., Rozo E., Keisler R., 2015, eprint arXiv:1509.00870