The Sun at Radio Frequencies
Joachim Köppen -- Kiel -- Sept 2019
Some brief explanations
This simulation shows how the Sun looks in various radio frequencies. The solar
atmosphere consists of several layers of plasma with different temperatures
and densities: The lowest is the photosphere, a thin layer of about 400 km
thickness and with a temperature near 6000 K which produces the visible light.
It is the deepest layer we can inspect with electromagnetic waves, and may thus
be called the surface of the Sun. Above it lies the chromosphere, about 1000 km
thick and with a temperature of about 10000 K. Above a few 1000 km there lies
the corona with a few million K temperature which extents out to a few solar radii.
Radio emission of different frequencies is produced by these plasma regions in
different amounts. Since the radio waves travel through a charged plasma - notably
electrons - their paths do not follow straight lines, but are bent because of the
refraction caused by the electrons. This is especially strong at frequencies
below about a few MHz.
For the temperature and density stratification in the solar atmosphere one of
several models can be chosen:
- Waldmeier & Müller (1948, Astron.Mitt.Zürich 155; 1950, Z.f.Astrophysik 27, 58)
either with the coronal temperatures from hydrostatic equilibrium (Waldmeier, 1948,
Astron.Mitt.Zürich 154) or a constant value of 1.5 106 K. This work
considered the radio emission from the corona only, and it did not yet take into
account the refraction of radio waves which is important for frequencies below
about 1 GHz.
Note that as refraction is not taken
into account, the results are reliable only for frequencies above about 500 MHz.
- Smerd (1950, Australian Journal of Scientific Research A Physical Sciences, 2, 34)
represented the chromosphere and corona as layers of constant temperature, but also
treated the refraction of radio waves. In this script the user may change the
temperatures and the height of the border between the two layers.
(REFRACTION NEGLECTED for the moment)
- Hagen (1951, Astrophys.J. 113, 547) used a detailed model for the corona
and the underlying chromosphere to compute the fluxes and centre-to-limb variations
for 50, 10.6, 3.14, and 0.85 cm wavelength.
Note that as refraction is not taken
into account, the results are reliable only for frequencies above about 500 MHz.
- The model C by Vernazza, Avrett and Loeser (1981, Astrophys.J.Suppl. 45, 635) is
used for the photosphere, chromosphere, and lower corona. For the outer corona I
assume a constant temperature. (REFRACTION NEGLECTED for the moment)
S.F.Smerd was the first person to compute the radio emission from the Sun
and how radio waves travel through the solar atmosphere. This model is quite simple
but it captures the essential elements of the solar atmosphere. The results which
we may obtain with this schematic model should not be overinterpreted.
Temperature and density can be shown in the left hand plot as a function of distance
from the Sun's centre as well as a function of the height above the photosphere.
The radio brightness temperatures can be computed for a given position on the solar
disk, offset from the disc centre. This is done by following a line of sight which
starts with the observer, which in the sideways view of the Sun (right hand plot)
would be far away to the right. At every part of the line of sight - which may be
bent because of refraction - the simulation adds up the emission produced by each
location. The resulting sum is displayed in the plot on the left hand side.
There are additional plots of opacity and optical depths (for the specialists :-)
The controls are:
- Solar model: here the user selects the underlying model for the
temperature and density structure in the solar atmosphere.
- Plot: here the user selects which type of plot
are shown:
- profiles of temperature and electron density: as a function of distance from the centre
of the Sun (in solar radii; the radius of the Sun is 700 000 km) or of height above the
photosphere (in km). In some of the plots with height a vertical green line marks the
layer where the optical depth becomes equal to 1 at the specified frequency, i.e. the
depth from which an external observer receives the radiation.
- temperature as a function of optical depth: since an external observer looks into the
Sun down to the depth where the atmosphere gets opaque at the given frequency (i.e.
where optical depth = 1), the green vertical line indicates the temperature of this
layer and thus the radio brightness temperature.
- radio brightness temperature on a single line of sight
- radio brightness temperature from a scan across the solar disc, normalized to
the value from the centre of the solar disk.
- ... more work is being done ...
- View:: allows the choice between a large view which also
covers the outer parts of the corona ... or a small view which shows the
solar disc in a close-up.
- If the display of the radio brightness temperature is chosen:
- frequency [GHz]: is the frequency in we look at the Sun
- single offset: for a single line of sight at a position offset from
the disk centre (specified in solar radii) the simulation computes the path
of the radio wave through the plasma (displayed on the right) and adds a
red dot in the left plot to show the brightness temperature. Entering
another frequency or another offset and hitting the Enter key or clicking
the start button adds the corresponding result to the left plot.
- Scan: we can compute the relative profile of the radio brightness at
a number of lines of sight with the specified range for the offset values,
and display this profile as a curve, which represents the radio image
of the Sun. At the same time, the paths of the radio waves are shown
in the right hand plot for ten offset positions, which are also marked
with small dots on the curve in the left hand plot.
- start, stop, resume control the simulation.
- clear, auto clear ON/OFF normally, each change of parameters or model clears
the plot to show the new curve only. With "OFF" all the curves are superposed, to
make comparisons easier. "clear" allows the user to manually clear the plot,
in case of need.
- Mouse position: displays the coordinates of the present position of the
mouse in a plot.
- ... more work in progress ...