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De Vries et al.
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FIG. 4. Residual rSDSS-F color differences after applying the
best stellar transformation to the quasar magnitudes, as function of
redshift. The lower panel shows the actual median of the distribu-
tion (~ 40 000 quasars). The top panel depicts the expected color
changes, based on a quasar template spectrum, and a mean stellar
spectrum of a K2V star (cf. Paper I). Note the excellent agreement
between the two curves, except for the lowest redshift range (which
is affected by the host galaxy contribution, cf. 3.3.5).
emission lines can account for upward of a few tenths of
a magnitude of the total brightness. Both these differ-
ences between the field stars and the quasars render the
stellar transformation less than ideal. It is something we
can correct for, however.
Figure 4 illustrates this calibration best. The bottom
panel shows the median rSDSS-F color for our quasar
sample as function of redshift. Ideally, these residuals
should be close to zero after calibration in the absence
of emission lines and quasar-stellar spectral differences.
This is clearly not the case. However, these color excur-
sions (of up to more than 0.2 in magnitude) are closely
matched by what one would expect using quasar and
stellar template spectra (top panel). As explained in
Paper I, we get the best agreement between the actual
residuals and the theoretical ones by assuming a mean
stellar template of a K2V star. This stellar type is con-
sistent with expectations based on population models for
our Galaxy (e.g., Bahcall & Soneira 1980, 1981). So, the
fact that these color excursions are well understood in
terms of quasar emission lines moving in and out of the
observing passband, makes it clear that we have to cor-
rect for it. If left "untreated" it will affect the variabil-
ity SF directly by artificially inflating the rms values at
certain time-lags. Given the epoch distribution of the
observations (time-lags preferentially at ~ 1, ~ 10, and
~ 50 years), the redshift maps more or less directly onto
a particular time-lag. The strong excursion at z ~ 3.6,
for example, would skew the SF signal preferentially at
10/(1+3.6) ~ 2, and 50/4.6 ~ 11 years. In this paper we
opted to use the actual median, as calculated across bins
with a width of 0.05 in redshift units, over the modeled
offsets. This accounts much better for the low (z < 0.4)
redshift quasars which are increasingly more contami-
nated (with decreasing redshifts) by their host galaxies.
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LL_ - _ a sm_ .__w__i_._ II w n i Ii
0 10 20 30 40 50
FIG. 5. Quasar variability distribution in the gsDss-band as
function of time-lag. This distribution has been calibrated as de-
scribed in the text. The thick solid line indicates the local median
value of the distribution, and its lack of significant deviation from
zero serves as an indication of our careful calibration. The top 4
histograms are for the time-lag bins [0, 10>, [10, 20>, [20, 30>,
and [30, 40> years respectively. The increase of the FWHM with
increasing time-lag is evident. The bin values are: 0.57, 0.94, 1.00,
and 1.05 magnitude. Note that the first histogram deviates by quite
a bit from a Gaussian distribution. The other three are accurately
described by one.
All of the other passband transformations are treated
similarly. The result is that each historic passband has
been brought onto their SDSS counterpart (either g or
r), with the important distinction that the color distri-
butions are centered around 0 as a function of redshift.
This method improves significantly over the procedure
outlined in Paper I. There, bulk corrections have been ap-
plied to the color distributions (irrespective of redshift).
Figure 2 of Paper I can therefore be considered a pro-
jection of Fig. 4 onto the y-axis. Only with the large
increase in sample size were we able to actually correct
for the redshift dependence in a meaningful way.
After all the photometric data have been transformed
onto the SDSS passbands, the measurements for each
individual quasar are permutated among each other, re-
sulting in about 4 time-lag measurements per band per
quasar. Obviously, none of the individual quasars have
been sampled photometrically anywhere near enough to
produce a meaningful structure function for each quasar
individually. The combined data-set, however, allows for
detailed variability studies provided one assumes that the
underlying cause of quasar variability is the same for all
of them. We will get back to this issue in 4.
This final data-set (one each for the gSDSS- and rsDss-
bands) contains sorted pairs of time-lag (in years) and
magnitude difference. For our sample of 41 391 quasars,
this amounts to 170 102 individual measurements for the
gSDSS-band, and 131 123 for the rSDSS-band. This exceeds
the total number of permutations in Paper I by more
than an order of magnitude. The difference in the totals
between the bands is because some GSC2 photometry
for the quasars have been repeated more in the J than
in the F band, boosting the permutation numbers for
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de Vries, W; Becker, R; White, R & Loomis, C. STRUCTURE FUNCTION ANALYSIS OF LONG-TERM QUASAR VARIABILITY, article, November 15, 2004; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1410080/m1/6/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.