Gaia Data Release 1 Documentation release 0
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7.4.2.5 Proper motions Figure 7.16: TGAS proper motion medians by pixel as a function of sky density. Left: right ascension, right: declination. Di fferent strategies have been taken to test TGAS proper motions. We have looked for problematic sky regions with unusually many high proper motions and also for unrealistic individual proper motions. We have taken high proper motion components to mean the ones exceeding ±150 mas yr −1 and determined the fraction of such proper motions in each of the 3072 level 4 HEALPix (13.43 sq.degr.). We then flag as suspicious, the regions where this fraction is more than ten times the global average. As a result we flag seven plus one HEALPix pixels for the right ascension and declination proper motions, respectively. Individual, high proper motions have been evaluated by computing their tangential velocity components, provided their parallaxes had uncertainties below 20%. We confirmed that no component corresponds to a tangential velocity exceeding significantly the escape velocity at the Sun position, estimated as about 500 km /s. We also looked at the dependence of the median proper motions with the sky density, as illustrated in Figure 7.16. We have flagged regions where the median reaches extreme values given the sky density, but the figure also shows that the flagged regions in reality follow the general distribution. The size of the regions is again 13.43 sq.degr. 7.4.2.6 Magnitude precision With only one band and its quoted precision published, validating the photometry without external comparisons looks di fficult. We devised however a method to check the photometric standard uncertainties, or to provide at least some upper limits on it, based on what we will call “internally homogeneous photometric samples”. The basic principle is to compare some observed dispersion of a G magnitude distribution to the one which is predicted by their standard uncertainty (i.e. the precision σ G computed using the phot g mean flux and phot g mean flux error fields in the Catalogue). The input data was cleaned of all sources with an astro- metric excess noise significance above 200 which would be an indication of duplicity or data reduction problems. Because outliers may remain, all dispersions are robustly estimated with a MAD (median absolute deviation). 281 There is obviously no way of obtaining an unbiased value about G magnitude by selecting samples based on the G magnitude itself, so the principle is to make a selection of samples using other magnitudes, G BP and G RP . In practice, we use instead what we call G BR =(G BP +G RP )/2, for two reasons: first this makes a magnitude closer to G , second the precision on G BR is better than on G BP or G RP alone. Samples are thus selected around some G BR values, with a extremely thin width around this value (about one mmag width for the brightest stars), and using stars having a similar colour, choosing e.g. 0.78 < G BP − G RP < 0.80 as it provides samples large enough (other colour ranges have been used without significant changes). In such internally homogeneous samples, one can assume that the G magnitude has some central value with a very small dispersion due to (a) the di fferences between stars of varying type, distance, extinction or variability, and (b) to the measurement errors, the latter being what we are trying to estimate. Obviously, the stars in these samples should be selected with a G BR having a precision better or comparable to the small bin width chosen, which then strongly reduces the sample sizes. The central G value in such sub-samples remains unknown (although it could be modelled by photometric trans- formations, though probably not to the required precision), so we subtract the median value in order to keep the G residuals only, centred on 0. Then, for a given G BR central value, all the residuals obtained in the one thousand sub-samples of one mmag bin size are collected for each mmag from G BR -0.5 mag to G BR +0.5 mag and then added to build one single sample to study. One of the resulting sample, around BR = 13, is shown Figure 7.17a. The resulting dispersion appears small enough to allow to study the e ffect of the measurement errors at the mmag level. That indeed this can be done is shown 7.17b, as the observed dispersion is clearly increasing as expected with the G standard uncertainty, at least above 0.5 mmag (the one mmag bin size of the sub-samples preventing any study of smaller uncertainties). Figure 7.17: Histogram of G magnitudes residuals in a sample with G BP − G RP ≈ 0.8 and G BR ∈]12.5, 13.5[ mag collected by steps of one mmag in G BR (a). Observed dispersion of these G residuals in equal size bins of standard uncertainty in G, showing that the residuals are related, as expected, to the measurement errors (b). As indicated, the variance around 0 is the sum of some intrinsic variance (due to the G BR bin width and G BR measurement errors, the small variations between stars, variability, multiplicity, etc) and of the variance due to the measurement errors estimated by the σ G standard uncertainty. So, a robust weighted fit has been done by cutting in equal size bins of standard uncertainty, estimating in each bin the variance by the square of the MAD and fitting the linear model: observed variance = intrinsic variance + unit-weight variance × standard uncertainty squared. One of these fits is shown Figure 7.18a; here the unit-weight standard deviation found (square root of the unit-weight variance), representing the ratio of the “external” errors over the “internal” one is 1.74 ± 0.1. In this figure, the 282 Yüklə 5,01 Kb. Dostları ilə paylaş:
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