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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 "CAT scan."

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 differences.

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).]

Redshift Averages versus Apparent Magnitude
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 them.]

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 drawn.

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 the sample.

QSO Z-Histograms for Apparent Mag 16.4. to 17.0 QSO Z-Histograms for Apparent Mag 17.2. to 17.8 QSO Z-Histograms for Apparent Mag 18.0. to 18.6
QSO Z-Histograms for Apparent Mag 18.8. to 19.4 QSO Z-Histograms for Apparent Mag 19.6 to 20.2 QSO Z-Histograms for Apparent Mag 20.4 to 21.0


There is a "sliding" progression in average redshift towards greater redshift of the histograms as dimmer samples are studied. (It is not clear at this point as to how experimental bias affects this progression.) The low-redshift peaks fade into the continua at around magnitude = 17.0 - 17.2. Pronounced redshift peaks, around z = 2.0, emerge in the faint-end samples. These begin at approximately magnitude = 19.8.

In a majority of cases the Southern samples have higher average redshifts and their peaks, when present, tend to be at higher redshifts than their Northern counterparts. The broad underlying continua, at mid-to-dimmer magnitudes, frequently vary considerably between the hemisphere paired samples. A cursory examination suggests that the Northern continua are slightly more symmetrical with respect to their maxima and are broader than those for the South.

The redshift histogram for the brightest Northern galactic QSO sample in this analysis (mag 16.4 - 16.6) is fairly similar to that of the Keck Hubble Deep Field (HDF) Redshifts histogram for galaxies. [Link to John Salzar's "Post Cards from the Edge of the Universe" (with a HDF Redshift Distribution) no longer works. 01 Aug 2011]

In a paper titled "On the existence of significant peaks in the quasar redshift distribution,"(4), K.G. Karlson finds that there is a periodicity present in the distribution of quasar redshifts and that when a redshift periodicity is found it is generally concluded that it indicates a non-cosmological origin to the redshifts. (He cautions his readers that this [periodicity] is not conclusive evidence against the cosmological interpretation.) [Added 23 May 2004.]

Reader comments are welcome. These may be included in future revisions of this page.

Related Articles and Web Pages

The Tautenburg - Calar Alto VPM Survey - A Quasar Search via Variablility and Zero Proper Motion [Added 08 Dec 2004.]


(1) Hewitt, A. and Burbidge, G., ApJ Sup 87, 451 (1993).- NADS
(2) Arp, H., private correspondence (1998).
(3) Hazard, C., McMahon, R., and Sargent,W.L.W., Nature, 322, 38, (1986)..
(4) Karlsson, K.G., Astronomy and Astrophysics, 58, 237-240 (1977) - NADS.

Send comments/questions to Bob Fritzius at fritzius@bellsouth.net