RELATION BETWEEN NUCLEAR LUMINOSITIES AND DIAMETERS
Visual magnitudes have been determined by Hopmann for the nuclei of 37 of the nebulae included in the present discussion. These data, together with types and diameters of the nebulae, are listed in [Table XIII]. When the magnitudes are plotted directly against the logarithms of the diameters, they show little or no correlation. When, however, the nebulae are reduced to the standard type (by applying corrections for differences in diameter along the sequence), a decided correlation is found whose coefficient is 0.76. This is shown in [Figure 9] The simple mean of the two regression curves is
| (6) |
where the slope differs by about 1 per cent from that in [formula (2)]. The list contains 16 elliptical nebulae, 15 normal, and 6 barred spirals. The nebulae are fairly representative, except that few late-type spirals are included. This is an effect of selection due to the fact that nuclei become less and less conspicuous as the sequence progresses.
The same result can be derived from a study of the differences, mn – mT, for the individual nebulae. The mean value is 1.55 ± 0.08, and the average residual is 0.60 mag. Means for the separate types are to be found in [Table XIV].
TABLE XIII
Diameters and Nuclear Magnitudes
| N.G.C. | Type | log d | mn Hopmann | mn Reduced |
|---|---|---|---|---|
| 221 | E2 | +0.42 | 9.84 | 11.85 |
| 1023 | SBa | .78 | 11.86 | 11.86 |
| 2841 | Sb | 0.78 | 12.08 | 11.19 |
| 3031 | Sb | 1.20 | 10.94 | 10.05 |
| 3115 | E7 | 0.60 | 10.83 | 11.09 |
| 3351 | SBb | .48 | 12.31 | 12.15 |
| 3368 | Sa | .85 | 11.68 | 11.43 |
| 3379 | E0 | .30 | 11.55 | 14.27 |
| 3412 | SBa | .40 | 11.59 | 11.59 |
| 3489 | Sb | .40 | 11.54 | 10.65 |
| 3626 | Sa | .28 | 12.37 | 12.12 |
| 3627 | Sb | .90 | 12.03 | 11.14 |
| 4125 | E4 | .30 | 11.74 | 13.04 |
| 4216 | Sb | .85 | 11.65 | 10.76 |
| 4278 | E1 | .0 | 12.02 | 14.38 |
| 4374 | E1 | .08 | 11.43 | 13.79 |
| 4382 | E4 | .48 | 11.77 | 13.07 |
| 4435 | E6 | .11 | 11.65 | 12.26 |
| 4438 | Sb | .54 | 11.83 | 10.94 |
| 4486 | E0 | .30 | 11.23 | 13.95 |
| 4546 | E6 | .18 | 11.75 | 12.36 |
| 4552 | E0 | .23 | 11.59 | 14.31 |
| 4569 | Sc | .65 | 12.05 | 10.57 |
| 4579 | SBc | .45 | 11.48 | 10.07 |
| 4621 | E5 | .30 | 11.60 | 12.56 |
| 4636 | E1 | .08 | 11.97 | 14.33 |
| 4649 | E2 | .30 | 11.57 | 13.58 |
| 4697 | E6 | .48 | 10.90 | 11.51 |
| 4699 | SBb | .57 | 10.72 | 10.56 |
| 4725 | SBb | .70 | 11.97 | 11.81 |
| 4736 | Sb | .70 | 10.36 | 9.47 |
| 5005 | Sc | .70 | 12.04 | 10.56 |
| 5033 | Sc | 0.78 | 12.38 | 10.90 |
| 5194 | Sc | 1.08 | 11.38 | 9.90 |
| 5322 | E3 | 0.15 | 12.10 | 13.76 |
| 5866 | Sa | .48 | 11.76 | 11.51 |
| 7331 | Sb | +0.95 | 11.82 | 10.93 |
| Means | +0.509 | 11.60 | 11.90 |
The low value for Sa-SBa is due to N.G.C. 5866, for which the magnitude difference of 0.06 is certainly in error, and the high value for Sc and SBc, to M 51, for which the difference of 3.98 mag. is not representative. The latter is accounted for in part by the fact that the mT refers to the combined magnitude of the main spiral and the outlying mass, N.G.C. 5195. When these two cases are discarded, the final mean becomes 1.52 ± 0.05, and the average residual, 0.52 mag., is consistent with the probable errors of the magnitude determinations. The small numbers of objects within each class are insufficient for reliable conclusions concerning slight variations along the sequence. From the constancy of mn – mT, the relation expressed by [formula (6)] necessarily follows, the small difference in the constant being accounted for by the different methods of handling the data.
Fig. 9.—Relation between nuclear magnitudes and diameters. The nebulae have been reduced to the standard type by applying corrections to the magnitudes.