The pure pressure effects just discussed will be superposed upon the Stewart effect, which depends upon the photospheric depth. The latter will cause a general increase in the strength of all lines from dwarf to giant, as a result of the greater amount of matter lying above the photosphere in the giant. The two effects are observed together when direct intensity measures are employed, such as the estimates embodied in [Chapter VIII], while the pressure effect is given almost purely when differential estimates of intensity for the same spectrum are used, as in most investigations of spectroscopic parallax. The observational evidence from both sources will now be put forward, in order to examine the sufficiency of the theories that have been advanced to account for the absolute magnitude effects.
The empirical relations used in the estimation of spectroscopic parallax should provide material for examining the simple pressure effect, as they are derived from the ratio of two lines in the same spectrum. Unfortunately the line ratios actually in use were selected because they were convenient to measure, and gave (empirically) consistent results, not for reasons of theoretical tractability. Fourteen line ratios are used, for example, by Harper and Young,[421] but only four of these consist of pairs of unblended lines with known series relations. It is only for such lines that a useful test of theory can be made.
[TABLE XXIII]
| M | = | +7 | +8.8 | +9.2 | +11.0 | +13.2 | ||||
| +6 | +13.3 | |||||||||
| +5 | +3.5 | +5.0 | +7.4 | +9.6 | ||||||
| +4 | +10.0 | +10.8 | ||||||||
| +3 | -1.8 | +0.5 | +3.8 | +6.7 | ||||||
| +2 | +6.7 | +7.0 | +7.6 | +10.0 | ||||||
| +1 | -7.2 | -3.8 | +0.2 | +3.2 | ||||||
| 0 | +3.5 | +3.4 | +3.2 | +3.0 | ||||||
| 1 | -12.9 | -8.2 | -3.2 | -0.3 | ||||||
| -2 | +0.3 | -0.2 | -1.4 | -3.7 | ||||||
| -3 | -12.1 | -7.3 | -3.8 | |||||||
| -4 | -2.8 | -4.2 | -5.8 | -10.0 |
| M | = | +6 | -2.0 | -1.4 | ||||||
| +5 | -1.5 | -0.5 | 0.0 | +1.0 | ||||||
| +4 | +1.2 | +1.3 | ||||||||
| +3 | +1.8 | +3.3 | +4.4 | +4.5 | ||||||
| +2 | +5.0 | +3.0 | ||||||||
| +1 | +4.8 | +6.5 | +7.8 | +7.6 | ||||||
| 0 | +6.5 | +4.7 | ||||||||
| -1 | +8.6 | +9.3 | +11.0 | +11.0 | ||||||
| -2 | +12.0 | +8.6 | +8.6 | +8.2 |
| M | = | +6 | -18.1 | |||||||
| +5 | -3.7 | -5.8 | -9.6 | -14.7 | ||||||
| +4 | -15.3 | |||||||||
| +3 | -1.0 | -3.3 | -6.6 | -11.0 | ||||||
| +2 | -12.4 | |||||||||
| +1 | +1.7 | -0.6 | -3.7 | -7.5 | ||||||
| 0 | -9.4 | |||||||||
| -1 | +4.5 | +2.0 | -0.9 | -4.0 | ||||||
| -2 | -6.6 | |||||||||
| -3 | +7.2 | +4.7 | +2.0 | -0.2 |
| M | = | +6 | +7.4 | +6.2 | ||||||
| +5 | +6.2 | |||||||||
| +4 | +4.3 | +3.0 | ||||||||
| +3 | +3.0 | |||||||||
| +2 | +1.3 | 0.0 | ||||||||
| +1 | 0.0 | |||||||||
| 0 | 0.0 | -2.0 | ||||||||
| 1 | +2.6 | |||||||||
| -2 | +2.0 | +0.7 | ||||||||
| -3 | +5.2 |
The preceding table contains a transcription of the reduction-curve material given by Harper and Young for the four pairs of lines mentioned. Tabulated quantities are the “step differences” for the classes at the heads of the columns, and the absolute magnitudes contained in the first column.
Presumably the irregularities of the observed curves have been smoothed out in forming the reduction table, but the figures will certainly give an indication of the direction in which a given line is affected by absolute magnitude.
The predicted effect of lowered pressure upon the lines involved is contained in the table that follows: