The Solar Corona
Steven R. Spangler Department of Physics and
Astronomy
University of Iowa
Basic facts on the Sun
• Distance: 149.6 million km
(1 astronomical unit)
• Radius: 696,000 km (6378
km for Earth)
• Mass: 1.989E30 kg
(5.97E24 kg for Earth)
Let’s begin by considering the disk of
the Sun
What we see as the disk of the Sun is a layer in its
atmosphere called the photosphere
The Sun is a beautiful illustration of
Blackbody Radiation, including Wien’s Law
The solar spectrum is a good match (although not perfect)
to a blackbody spectrum
A calculation on the extent of the solar
atmosphere
Pressure scale height
Acceleration of gravity
Solar photospheric data
Result: l=175 km… the height of the solar
atmosphere should be very small compared with the
radius of the Sun
Yet, above the photosphere is the chromosphere,
which extends upward 1000 km or more
The Solar Corona
It can extend out into space several solar
radii
This unexplained large
“scale height” of the solar
atmosphere was
recognized by the
beginning of the 20th
century. Some scientists
attributed it to the
presence of a superlight
element, “coronium” in
the corona
The existence of “coronium” also
seemed indicated by unknown lines in
the spectrum of the corona
• The 1905 book “The Sun” by Abbott commented on the
unidentified green and red lines in eclipse spectra
• Mystery resolved by Grotian around 1940
• Red and green lines are FeX and FeXIV, indicating
temperatures of 1 - 2 million K
The main problem in solar physics, and one of the
main problems in astrophysics, is explaining why
the corona has a temperature of 1 - 2 million K
Most theories for coronal heating invoke a
mechanism involving the solar magnetic field
• How can a magnetic field heat
a gas?
• Spatial variations in magnetic
field produce currents, currents
produce Joule heating
• Ionized gases with magnetic
fields (plasmas) carry waves.
Waves can be generated in one
part of the solar atmosphere
and be damped in another
• For the right answer, we need
measurements of the solar
magnetic field
We know the magnetic field both below
and above the corona
Below: the photosphere. Measurement of the
Zeeman Effect
Above the corona: direct magnetometer
measurements in the solar wind
How do we measure B in the corona
itself?
Direct
measure
ments
out here
Zeeman
measure
ments
here
Probing the Solar Corona with Radio
Propagation Techniques
Physics of Faraday Rotation
Demonstration
Signal Generators and Detectors: Observations of
Extragalactic Radio Sources with Radio Interferometers
Very Large Array
•
•
•
•
Radio interferometer
27 antennas
B or A array
Observations taken at 1465 and 1665 MHz
We use “constellations” of radio sources to
do a sort of tomography of the corona
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Ingleby, Spangler, Whiting 2007
Fig. 3.— Illustration of data used to obtain the coronal Faraday rotation for one of the lines of sight, that to 2325−049 on March 12. In all three panels, the orientation and length of the plotted lines
correspond to the polarization position angle and the polarized intensity, respectively, at that position in the source. The contours are of total intensity (Stokes parameter I). (a) The 1465 MHz
polarization position angle map on March 12, when the line of sight passed through the corona. (b) Similar map of the source on May 29, when the corona was far from the source. (c) Position angle
difference between the two maps, Δχ, which is the Faraday rotation due to the corona. For both components of the source, the Faraday rotation is 14°, corresponding to an RM of 6 rad m−2. The
resolution of all three maps is about 5 $\arcsec$ (angular diameter FWHM of the restoring beam).
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Fig. 3.— Illustration of data used to obtain the coronal Faraday rotation for one of the lines of sight, that to 2325−049 on March 12. In all three panels, the orientation and length of the plotted lines
correspond to the polarization position angle and the polarized intensity, respectively, at that position in the source. The contours are of total intensity (Stokes parameter I). (a) The 1465 MHz
polarization position angle map on March 12, when the line of sight passed through the corona. (b) Similar map of the source on May 29, when the corona was far from the source. (c) Position angle
difference between the two maps, Δχ, which is the Faraday rotation due to the corona. For both components of the source, the Faraday rotation is 14°, corresponding to an RM of 6 rad m−2. The
resolution of all three maps is about 5 $\arcsec$ (angular diameter FWHM of the restoring beam).
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Fig. 3.— Illustration of data used to obtain the coronal Faraday rotation for one of the lines of sight, that to 2325−049 on March 12. In all three panels, the orientation and length of the plotted lines
correspond to the polarization position angle and the polarized intensity, respectively, at that position in the source. The contours are of total intensity (Stokes parameter I). (a) The 1465 MHz
polarization position angle map on March 12, when the line of sight passed through the corona. (b) Similar map of the source on May 29, when the corona was far from the source. (c) Position angle
difference between the two maps, Δχ, which is the Faraday rotation due to the corona. For both components of the source, the Faraday rotation is 14°, corresponding to an RM of 6 rad m−2. The
resolution of all three maps is about 5 $\arcsec$ (angular diameter FWHM of the restoring beam).
Plasma Contributions to the Faraday
Rotation Integral
We need enough observations to sort out various contributions to coronal
density and magnetic field
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Fig. 4.— Representation of measured RMs on sky charts. The four separate panels show the location of the radio sources relative to the Sun on each of the 4
days of observation. The asterisk indicates the position of the Sun, and the dashed line is the ecliptic. The size of the plotted circle is a rough indicator of the
absolute magnitude of the RM. Filled circles correspond to positive RMs, and open circles represent negative RMs.
What have we learned from these
observations?
• A good model for the
coronal magnetic field B
as a function of r
• Information on the
functional form of B
• Coronal B field is
stronger than
extrapolations from
photosphere
• More magnetic energy
to dissipate
Future Developments
• EVLA (Expanded
VLA): Enormous
increase in sensitivity
of the VLA.
Commissioning of the
EVLA now in
progress..
• EVLA at 5 GHz: Will
make measurements
closer to the Sun,
observations have
more impact.
Modeling the coronal field from Faraday
rotation measurements
Use of independent information on coronal density
and location of the neutral line
These measurements of magnetic field and density at ~ 3R can be used to
estimate B and n at greater distances probed by Faraday Rotation
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Fig. 7.— Comparison of model and observed RMs. The line through the origin is not a fit, but it indicates perfect agreement. The top panel shows all the data.
The bottom panel shows the inner part of the diagram, containing most of the measurements, for which $\vert \mathrm{RM}\,\vert \leq 20$ rad m−2. The sets of
triangles indicate measurements of the two RM‐variable sources, 2351−012 and 0046+062. In these cases, each plotted symbol indicates a measurement
integrated over a time‐limited subset of the data. The model RMs have been calculated with a value of the adjustment parameter $\Gamma =25$ (see eq. [8] for
a definition of Γ).
From The Astrophysical Journal 668(1):520-532.
@ 2007 by The American Astronomical Society.
For permission to reuse, contact journalpermissions@press.uchicago.edu.
Fig. 7.— Comparison of model and observed RMs. The line through the origin is not a fit, but it indicates perfect agreement. The top panel shows all the data.
The bottom panel shows the inner part of the diagram, containing most of the measurements, for which $\vert \mathrm{RM}\,\vert \leq 20$ rad m−2. The sets of
triangles indicate measurements of the two RM‐variable sources, 2351−012 and 0046+062. In these cases, each plotted symbol indicates a measurement
integrated over a time‐limited subset of the data. The model RMs have been calculated with a value of the adjustment parameter $\Gamma =25$ (see eq. [8] for
a definition of Γ).
Time variation in the coronal Faraday rotation as
Indications of coronal “transients”