CBR has the answer

I used -254 km/s for the (blue)shift of M110; another current catalog gives -241. M Geha et al (Astronomical Journal 131:332-342, 2006) give -243 based on a speed graph and including a 3 km/s correction for contamination with M31 stars. Also taking their 824 kpc distance, changes my value for M110 to -107=-72-35.

The "giant stream surrounding M31" (R Ibata et al, Mon. Not. R. Astron. Soc. 351:117-124, 2004) might be a rudimentary galactic disk at nearly right angles to M31 and to our line of sight, as if M31 were an elliptical galaxy. Light from M110 passes through this disk and incurs an Oort's law shift. Also, contamination from stars in this disk could explain the relatively large -254 vs. -241 discrepancy.

There is no 36 km/s redshift period. The spectral powers at 73.2 and 36.6 km/s (quanta studied because they are c/2^12 and c/2^13, resp.), were 4.2 and 8.3 (Tifft, Astroph. & Space Sci., 244:29-56, 1996, Table I). This 1:2 ratio signifies aliasing.

The 72.1 km/s period corresponds to 0.95 Mpc; a recent estimate of the distance to M31 is 0.89 Mpc, and 137*0.95 Mpc = 424 M lt yr, close to 450. Furthermore c/72.1 is near 137^(5/3). This suggests the adiabatic ideal gas laws, with the Tifft period analogous to pressure, and the long period to temperature, for a volume of 137.

Blueshifts (Ibata op. cit., Fig. 4 top center, p. 121) suggest that the "M31 stream" is a large, swiftly rotating, faint spiral galaxy blueshifted approx. 144 km/s w.r.t. M31. Tifft (Astroph. & Space Sci. 285:429-449, 2003, Fig. 1) found in 1989 that isolated double galaxies differ in redshift by about 0, 72, or 144 km/s, with no halfway peaks.

Monatomic ideal Gas #1, perhaps more than one of them, expands adiabatically to volume=137.036, the reciprocal of the fine structure constant. Pressure equals volume^(-5/3), and for Gas #1, z1 equals that pressure. This gives a redshift of 82.29 km/s. The head of Tifft's first family of harmonics is 72.1 km/s, so a correction factor 72.1/82.29 is applied. If volume=137/2, then using the same correction, the redshift is 229 km/s. This (232 km/s) is the head of Tifft's second family of harmonics (Astroph. & Space Sci. 244:29-56, 1996, Table 2, p. 39).

Two different compilations of quasars (op. cit., 2003, Figs. 4 & 6; also Fig. 3; pp. 433-435) agree in their four main redshift peaks (average of Figs. 4 & 6): z = 1.43, 0.95, 0.60, 0.34; the first three of these appear in Table I. Table I also lists peaks at 1.97 (confirmed by Figs. 3 & 6), 0.274 (Figs. 5 & 6 suggest 0.21 would be a better estimate), 0.131 and 0.064 (both confirmed by Figs. 7 & . Figs. 4, 7 & 8 show a peak at 0.155. Figs. 7 & 8 show a peak at 0.085. Fig. 7 shows a peak at 0.032. Fig. 3 shows a peak at 2.7.

Monatomic Gas #2 expands adiabatically to volume 137/2^n, n=0,1,... . Temperature equals volume^(-2/3), and for Gas #2, z2 equals that temperature, times the correction factor above. This gives predicted quasar redshifts, the smallest of which corresponds to the 429 M lt yr period of galaxy distribution, assuming a Hubble parameter of 75 km/Mpc.

Predicted peaks, 72.1/82.29*(137/2^n)^(-2/3) for n = 9,8,...,0:
z = 3.35, 2.11, 1.33, 0.84, 0.53, 0.33, 0.21,
0.132, 0.083, 0.052, 0.033

Observed quasar (including active galactic nuclei) redshift peaks:
z = 2.7, 1.97, 1.43, 0.95, 0.60, 0.34, 0.274, 0.21, 0.155,
0.131, 0.085, 0.064, 0.032

So Gas #2 explains most of the peaks. Large redshifts due to Gas #1 are few and far between, because its exponent is 5/3 instead of 2/3. Suppose all states of Gases #1 and #2 are equally likely, statistically independent, and z=z1+z2. The densest clusters (three to eight peaks each) below z=3, are centered around:

z = 2.6, 2.11, 1.33, 0.84, 0.54, 0.334, 0.289, 0.213,
0.135, 0.084, 0.056, 0.034

The best-defined observed peaks are those at z = 0.064, 0.60 and 1.43. The redshift between predicted and observed is (zobs-zpred)/(1+zpred). These correspond to distances of 100, 510, and 560 M lt yr, resp.

The diatomic adiabatic gas law, without correction, would give a smallest redshift of 3.10 km/s, close to Tifft's (op. cit., 1996) value of 2.88 km/s. The Lehto/Tifft volume doubling rule, combined with the adiabatic gas law, gives the quasar redshifts and redshift periodicities observed.

While diatomic "Gas #1b" gives Tifft's 2.88 km/s period, diatomic Gas #2b gives 2.88*137=395 km/s. Tifft (1996, Table 2) shows a narrow harmonic peak of this family at 100 km/s = approx. 395/4. The monatomic Gas #1 periods of 72 km/s and 229 km/s interact statistically to give a small peak at 229-2*72=85 km/s as observed (ibid.).

Of the 90 possible redshifts calculated above for quasars, 58 were included in the 12 clusters. The redshifts of 0.156 and 0.161 calculated, give a subthreshold peak corresponding to the observed 0.155.

Apparently no more than one copy each of Gases #1 and #2 exists in quasars. Without at least one copy of Gas #2, there would be a large peak near zero redshift. Perhaps such objects are not recognized as quasars. This possibility also would strengthen the predicted peak near 0.84.

Converting z=0.03 to z=3 to a natural logarithmic scale, I chose 13 peaks randomly, ordered them, and added the absolute values of the differences from the corresponding observed peak. In 10,000 trials, the average sum was 5.3; 0.7% of sums were less than 2, 0.2% were less than 1.75, and the smallest was 1.5. For the predicted values above (including the 1.585 value of the close cluster of two), the sum was 0.75, indicating p<<0.0001.

Tifft's smallest redshift quanta occur not only with galaxies, but with stars in the Milky Way. See the quantized redshift thread for more information.