1. The solar continuum spectrum
Figure 1: Brightness temperature Tb of the solar continuum at disk center between 0.2
and 5 µm.
(a) Assume that LTE and the Eddington-Barbier approximation are valid for the
formation of the solar continuum for wavelengths λ > 100 nm. Explain both
assumptions.
(b) Give the definition of the brightness temperature Tb . Does this definition
assume LTE? Does it assume the validity of the Eddington-Barbier approximation? Does it assume that the object is optically thick? Figure 1 shows the
brightness temperature for the solar continuum. Why is it useful to use Tb
instead of the observed intensity Iλ ?
In the wavelength range 10 nm – 1 cm, the solar continuum is mainly due to H I bf,
H I ff, H− ff, H− bf, and bf transitions of metals.
(c) Briefly describe these extinction processes.
(d) Copy Figure 1 and draw at which wavelength range which of these processes
dominate the extinction.
(e) Explain why H− ff and H− bf can be considered as LTE processes in the solar
atmosphere.
(f) Draw the continuum extinction coefficient for the same wavelength range as
Figure 1 on a qualitative scale. Explain the curve. The minimum lies at
λ = 1.6µm, discuss what this implies.
(g) Figure 3 shows a sketch of the solar spectrum similar as Figure 1 but for a
much wider wavelength range than Figure 1. Explain the two minima.
(h) Why are the spectral lines with λ & 200 nm in absorption and at shorter
wavelengths in emission? What kind of behaviour of spectral lines do you
expect left and right of 160 µm? Explain.
(i) Is the H I 1–∞ edge in emission or absorption? Indicate its contribution to
Avrett’s curve in the figure.
1
Figure 2: Drawing of the solar spectrum by E.H. Avrett. Horizontal axis: wavelength,
increasing logarithmically to the left. Vertical axis: brightness temperature of the radiation
from the center of the solar disk. Spectral lines are drawn schematically as short vertical
lines.
(j) Explain why images of the full disk of the Sun at a wavelength of 500 nm
show a darker edge as compared to the center of the disk (i.e., explain limb
darkening).
(k) Use Figure 3 to indicate where the Sun shows limb darkening and limb brightening for all wavelengths λ > 100 nm.
(l) LTE does not hold for λ < 100 nm and the Eddington-Barbier approximation
is not valid at the right-hand side of Figure 3. The emission lines between λ =
10 nm and λ = 20 nm are not chromospheric but coronal in origin, and form
at temperatures of about T ≈ 106 K. Describe their emission mechanism and
explain that their photon production is thermal. Explain why their brightness
temperature is orders of magnitude lower than the coronal temperature at
which they form.
2