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QSO Redshift Histograms
(for Incremental Apparent Magnitude Samples)
Robert S. Fritzius
305 Hillside Drive Starkville, MS
A Shade Tree Physics On Line Publication
Created 30 Aug 1998 - Latest update 01 Aug 2011.
If you assign quasi-stellar objects (QSOs) to incremental apparent
magnitude bins, arranged in a bright-to-dim sequence, then produce redshift
histograms for the bins, you might expect to see a set of broad
low-amplitude skewed bell-shaped curves whose maxima systematically slide
toward higher redshifts for dimmer and dimmer apparent magnitudes. The
set of adjoining histograms, thus produced, would be a kind of redshift
To see if the above idea is borne out by published data (or not), objects
listed in the CD-ROM version of the 1993 Hewitt & Burbidge QSO Catalog(1)
were analyzed using a computer program called Z-Mag-B. The program
assigned QSOs to redshift-apparent magnitude bins. One set of bins was
for North Galactic QSOs and the other set was for South Galactic QSOs.
Z-Mag-B selected 6574 objects from the QSO catalog. This number includes
165 unique low-redshift objects that are mostly called active
galactic nuclei (AGNs). These are characterized by the H I (4861) -
O III (4959, 5007) triplet. (Objects whose whose magnitudes had been
rounded off to the nearest integer, were not used.)
QSOs used in this analysis are as follows:
3096 North galactic QSOs with average redshift z = 1.45 +/- 0.80.
3478 South galactic QSOs with average redshift z = 1.65 +/- 0.78.
The figures for the AGNs, et.al., (which are included, above) are:
84 North - average redshift z = 0.30 +/- 0.16.
81 South - average redshift z = 0.36 +/- 0.17.
Once the redshift-apparent magnitude bins were filled, they were segregated
into magnitude limited samples. Each sample has an apparent magnitude
thickness of 0.2. The magnitude values shown with each histogram
correspond to the brighter edge of the sample.
The overall QSO redshift-magnitude diagrams (not shown in this web page)
turn out to not be statistically "normal" nor are the individual
magnitude-limited redshift histograms produced in this study. Many of the
latter appear to contain a broad (redshift-wise) continuum and often one
fairly well defined peak (sometimes two). No statement is made, at present,
about the statistical significance or insignificance of the differences
between paired North-South samples. In a planned update to this page,
Kolomogorov-Smirnov tests will be applied to them to quantify their
Before getting to the redshift histograms, the following diagram is shown
to depict the redshift averages for the sequential magnitude bins for North
and South galactic QSOs. It can be seen, that for the brighter samples,
the averages constitute more than a scatter diagram. They
increase in average redshift with decreasing apparent
magnitude. In general, the Southern samples are more redshifted than the
Northern samples. [Arp cautions that search mode bias, for example, radio
vs optical, may be a factor in the net redshift differences between
the galactic hemispheres.(2)] There is a relative redshift inversion
at magnitude v = 20.3, i.e., the Northern galactic QSOs become more
redshifted than the Southern QSOs. Both groups also appear to level off in
redshift with further decreases in magnitude. If these effects are more
than statistical fluctuations or search bias artifacts, they will be
important with regard to our overall understanding of QSOs. [There
is a reported shortage of detected very high redshift QSOs at
faint apparent magnitudes(3).]
QSO Redshift Averages for Apparent Magnitude Bins
Normalized redshift histograms for each apparent magnitude limited sample
were then produced. The normalization process reduces search mode bias
and facilitates comparisons between samples. The plots below are the
normalized redshift histograms for the magnitude limited samples in the
range v = 16.4 to 21.0. Northern galactic QSO histograms are on the
left and those for Southern galactic QSOs are on the right. [Histograms
shown are based on sample sizes (raw data) having at least 20 objects in
Natural smoothing, where added, is based on the following relations.
S(1) = ( 3 * N(1) + N(2) ) / 4
S(i) = ( N(i-1) + 3 * N(i) + N(i+1) ) / 5
Smoothed values for the junctions between adjacent bins are equal to their
arithmetic means. The curves which connect the smoothed points are hand
The y-axis for each histogram is "Normalized Number per delta v = 0.2."
The x-axis for each histogram is Redshift.
Downward pointing arrows, where shown, represent the average redshift for