.. _book_fig_chapter5_fig_lutz_kelker:


Eddington-Malmquist & Lutz-Kelker Biases
----------------------------------------
Figure 5.3

An illustration of the Eddington-Malmquist (left) and Lutz-Kelker (right)
biases for mock data sets that simulate upcoming LSST and Gaia surveys
(see text). The left panel shows a bias in photometric calibration when using
pairs of measurements of the same stars with realistic photometric error
distributions. Depending on the adopted faint limit (x-axis), the median
difference between two measurements (dashed line) is biased when this limit
is too close to the 5-sigma data limit (corresponding to errors of 0.2 mag);
in this example the 5-sigma magnitude limit is set to 24. The solid line shows
the assumed random measurement errors - if the number of stars in the sample
is large, the random error for magnitude difference may become much smaller
than the bias. The right panel shows the bias in absolute magnitude for
samples calibrated using trigonometric parallax measurements with relative
errors :math:`\sigma_\pi / \pi`, and two hypothetical parallax distributions
given by eq. 5.41 and p = 2, 4.



.. image:: ../images/chapter5/fig_lutz_kelker_1.png
    :scale: 100
    :align: center


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