Robust Chauvenet Outlier Rejection

Sigma clipping is commonly used in astronomy for outlier rejection, but the number of standard deviations beyond which one should clip data from a sample ultimately depends on the size of the sample. Chauvenet rejection is one of the oldest, and simplest, ways to account for this, but, like sigma clipping, depends on the sample's mean and standard deviation, neither of which are robust quantities: Both are easily contaminated by the very outliers they are being used to reject. Many, more robust measures of central tendency, and of sample deviation, exist, but each has a tradeoff with precision. Here, we demonstrate that outlier rejection can be both very robust and very precise if decreasingly robust but increasingly precise techniques are applied in sequence. To this end, we present a variation on Chauvenet rejection that we call "robust" Chauvenet rejection (RCR), which uses three decreasingly robust/increasingly precise measures of central tendency, and four decreasingly robust/increasingly precise measures of sample deviation. We show this sequential approach to be very effective for a wide variety of contaminant types, even when a significant -- even dominant -- fraction of the sample is contaminated, and especially when the contaminants are strong. Furthermore, we have developed a bulk-rejection variant, to significantly decrease computing times, and RCR can be applied both to weighted data, and when fitting parameterized models to data. We present aperture photometry in a contaminated, crowded field as an example. RCR may be used by anyone at https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ

The fading of Cassiopeia A, and improved models for the absolute spectrum of primary radio calibration sources

Based on five years of observations with the 40-foot telescope at Green Bank Observatory (GBO), Reichart & Stephens (2000) found that the radio source Cassiopeia A had either faded more slowly between the mid-1970s and late 1990s than Baars et al. (1977) had found it to be fading between the late 1940s and mid-1970s, or that it had rebrightened and then resumed fading sometime between the mid-1970s and mid-1990s, in L band (1.4 GHz). Here, we present 15 additional years of observations of Cas A and Cyg A with the 40-foot in L band, and three and a half additional years of observations of Cas A, Cyg A, Tau A, and Vir A with GBO's recently refurbished 20-meter telescope in L and X (9 GHz) bands. We also present a more sophisticated analysis of the 40-foot data, and a reanalysis of the Baars et al. (1977) data, which reveals small, but non-negligible differences. We find that overall, between the late 1950s and late 2010s, Cas A faded at an average rate of $0.670 \pm 0.019$ %/yr in L band, consistent with Reichart & Stephens (2000). However, we also find, at the 6.3$\sigma$ credible level, that it did not fade at a constant rate. Rather, Cas A faded at a faster rate through at least the late 1960s, rebrightened (or at least faded at a much slower rate), and then resumed fading at a similarly fast rate by, at most, the late 1990s. Given these differences from the original Baars et al. (1977) analysis, and given the importance of their fitted spectral and temporal models for flux-density calibration in radio astronomy, we update and improve on these models for all four of these radio sources. In doing so, we additionally find that Tau A is fading at a rate of $0.102^{+0.042}_{-0.043}$ %/yr in L band.Comment: 17 pages, 12 figures, accepted to MNRA