The Sun and the Stars
The Sun and the Stars
Dr Matt Burleigh
The Sun and the Stars
Limb darkening
The surface of the sun does not have uniform brightness, it appears bright toward the
centre, darker towards the edges, and the colour is redder, an effect known as Limb
darkening - why?
Ans.
i) The density of the sun decreases with increasing distance from the centre
ii) The temperature of the sun decreases with increasing distance (at least through the
photosphere)
Dr Matt Burleigh
Dr Matt Burleigh
The Sun and the Stars
When we look at the sun, we can only see to a depth at which the radiation escapes unhindered.
Optical depth
The optical depth is a measure of the transparency of a medium to the incident radiation.
Consider an incident radiation flux F on a slab of gas with density , and thickness dx.
Let the opacity (the amount of absorption at a given wavelength) of the gas be .
Part of the incident radiation is absorbed by the gas and so,
dF    F dx
In a uniform medium
F ( x)  F (0)e   x
So that the flux diminishes exponentially with increasing depth
Astronomers define the quantity
Note
So


as the optical depth, where
d     dx
is dimensionless
F     F (0)e  
Dr Matt Burleigh
The Sun and the Stars
Limiting cases:
   1
optically thin (transparent)
   1 optically thick (opaque)
An optical depth of unity represents the thickness of absorbing gas from which a fraction 1/e
photons can escape.
In Astronomy the photosphere of a star is defined as the surface where the optical depth is 2/3.
Each photon emitted from this surface has an average of less than 1 scattering before escaping.
Photosphere emits a continuous spectrum which is a close approximation to a blackbody
– optically thick thermal emission
The photosphere cools with increasing radius. Cool gas scatters incident photons by absorption
and re-emission) producing dark lines at discrete energies.
Although the temperature rises through chromosphere its optical depth is v. small,
 effectively transparent to optical photons (optically thin)
excited atoms, ions in chromosphere produce an emission-line spectrum.
Dr Matt Burleigh
The Sun and the Stars
The solar magnetic field
For the sun or planet to have a magnetic field require a dynamo
Dynamo conditions:
1) Rotation
2) Convection
3) Electrically conducting material
Start with bipolar field. Differential solar rotation
(faster at equator than at poles), stretches and
enhances magnetic field lines (stretched field
lines store energy), poloidal field becomes toroidal
Field. Rising convection zones, twists toroidal field
into poloidal field and so on.
Sunspots occur where concentrated magnetic field
lines erupt from photosphere. They occur in pairs,
and appear dark because they are cooler than the
surrounding area.
Dr Matt Burleigh
The Sun and the Stars
Sunspots
dark patches that appear on photosphere – appear dark as they are cooler ~3800K
Components – dark umbra, lighter surrounding penumbra
site of intense magnetic field (B~0.1T, c.f. 0.001T at top of coronal loop)
appear in pairs with opposite polarity (or diffuse region not observed as a spot)
linked to solar cycle
Intense B-field interferes with convection  convection interrupted  cooler
Sunspots appear at fixed latitudes
Sunspots indicate that suns outer layers
rotate differentially (Galileo)
P (equator) ~ 25 days
P (40deg) ~ 27 days
Dr Matt Burleigh
The Sun and the Stars
The sunspot cycle:
Daily observations began at Zurich observatory in1749, and with the addition of other
observatories, ~continuously from 1849.
SSN = 10(Ng) + Ns (since each group contains roughly 10 sunspots)
The number of sunspots is seen to vary on an 11 year cycle. We are currently around solar
maximum
Each new cycle starts with the
appearance of sunspots at high
latitudes forming 2 bands either side of
the equator. As cycle progresses bands
form at lower and lower latitudes
(butterfly diagram, left). Note polarity of
magnetic field reverses at the start of
each new cycle.
From 1645-1715, there were very few
sunspots observed (Maunder
minimum). Coincided with the mini Iceage in Northern Europe.
Dr Matt Burleigh
The Sun and the Stars
The sunspot cycle:
Maunder minimum (1645-1715). Coincided with the mini Ice-age in Northern Europe.
Dr Matt Burleigh
Dr Matt Burleigh
Active Regions
•
•
As spot numbers increase so does solar activity
Each sunspot group is associated with an active region
several x 105km across
Magnetic activity is concentrated in these
Usually bipolar (Bipolar Magnetic Regions – BMRs)
•
•
•
•
•
•
Bright areas associated with BMRs in various
zones
In photosphere – faculae
Chromosphere – plages
Corona – streamers
Dr Matt Burleigh
Prominences
•
•
Streams of chromospheric gas – dark when viewed against disk
Quiescent
–
•
Long lived (weeks) curtain-like gas along neutral line separating poles of BMR
Active
–
Few hours – loops closely associated with solar flares
Dr Matt Burleigh
The Sun and the Stars
Solar flares
– closely associated with sunspot activity,
activity related to solar cycle – v. few at solar minimum,
solar maximum rate : hourly for small flares
every few hours for large flares
Size ~ 10,000 – 300,000 km
Duration ~ rise to maximum ~ 5min – decay time 20 min (small flare)
large flares ~ hours
Temp ~ several million K
energy up to 1030 J for largest flares
Dr Matt Burleigh
Effects – radiate energy across whole of the E-M spectrum radio-gamma-rays
eject highly energetic particles (cosmic rays)
High energy photons disrupt terrestrial communications by disturbing ionosphere
Cosmic rays damage satellites and would be lethal to unprotected astronauts
(implications for manned mission to mars)
For a great NASA movie on flares, see:
http://upload.wikimedia.org/wikipedia/commons/5/56/X-class_flares.ogv
Dr Matt Burleigh
Dr Matt Burleigh
The Sun and the Stars
(1) Pre-flare
S
N
S
N
S
N
(3) Reconnection point moves outwards
accelerated particles radio emission
and cosmic rays
(2) Magnetic reconnection
Joule heating produces X-ray, EUV and radio emission
Current flows to photosphere  ribbon flare
(seen in H-alpha)
Dr Matt Burleigh
The Sun and the Stars
Formation :
Disturbance at base of magnetic field
Energy released at top of loop where
B-field reconnects
Electric currents oppose reconnection
Joule heating raises plasma temperature
X-rays UV and radio emission
Currents heat gas at photosphere –ribbon flare
Particles simultaneously accelerated outward
Radio emission and cosmic rays
Reconnection point moves outwards
Dr Matt Burleigh