328
THE OUTSIDE OF A STAR
The maximum ordinate of the spectral energy curve occurs near 5900 A.
Table 43 shows that the intensity is here rising faster than the black-
body curve as we go towards the violet; hence the maximum ordinate
will be displaced in this direction. Milne has calculated that the displace
ment amounts to 4-3 per cent., so that the effective temperature calculated
from (228-3) is 4-3 per cent, higher than that calculated from the total
intensity of the radiation. This is actually in good agreement with ob
servation; but reference to Fig. 5 shows that the accordance is accidental;
the trivial shift in the position of the maximum ordinate (inappreciable
on the scale of the diagram) achieves no real advance in explaining the
sun’s deviation from a black body.
By (227-2) the contrast in brightness between the centre and the
selected point near the limb (sec 6 = 3) is 0-6 for the integrated spectrum.
By Table 43 it is
iff = 0-46 for A4157; |f| = 0-77 for A12470.
This is mostly accounted for by the difference of effective temperatures
5326° and 6039°, a decrease of temperature having more effect on the
violet than on the red. According to Milne the observed contrast in all
wave-lengths agrees very closely with that predicted by this theory. He
considers this agreement to be very unwelcome; it is premature because
we have yet to take account of the variation of the absorption coefficient.
The close connection between centre-limb contrast and variation of k v is
shown by the occurrence of r„ sec 9 in (228-6); to double kjk is equivalent
to transferring to a new point on the disc where sec 6 is doubled. When
Fig. 5. Solar Energy Curve.
— Observed intensity.
Theoretical curve for constant absorption coefficient.
Theoretical curve for constant emission coefficient.