Transcript Activity in other Stars I

Doppler Imaging
For stars whose spectral line profiles are dominated by rotational
broadening there is a one to one mapping between location on the star and
location in the line profile:
V = –Vrot
V = +Vrot
V=0
Doppler image of a young star (weak T Tauri). This is what
the sun probably looked like as a young star.
The Sunspot number
In 1843 H. Schwabe discovered that the sunspot number
varies with the cycle of 11 years. Schwabe did these
observations to study sunspots but he wanted to
discover an planet the orbits inside Mercury.
We define as a sunspot number:
R= K(10g+f)
f the number of individual spots,
g the number of groups
K an individual correction factor
Sun-spot numbers
The Butterfly Diagram
At the beginning of the sunspot cycle spots are first observed
to emerge at high (± 30o). As the cycle progresses subsequent
spots emerge towards the equator. This was first observed by
Carrington and Spörer in 1858.
t=0
+30
+30
0
0
-30
-30
t=11 yrs
Spots from the next cycle can appear at high latitudes even when
spots of the previous cycle appear near the equator. Spots above
latitude = |30 deg| (at the poles) are rare.
Hale Nicholson Law
Note:Tilt 3o – 11o at ±30o
latitude
f-spot
5.6o
f-spot
+
-
+
Cycle = n
+ p-spot
-
- p-spot
+ p-spot
-
-
Direction of rotation
Cycle = n+1
p-spot
“Butterfly” diagram of the spot
emergence
The activity cycles on
the sun
•
•
•
•
•
•
•
•
•
11 year period of the sunspot number
“Butterfly” diagram of the spot emergence
The Hale-Nicholson Law of sunspot polarity
Reversal of the general field
Increased number of flares
Increased X-ray and ultraviolet emission
Increased chromospheric emission
Stronger Corona
Change in topology of the magnetic field on the sun from
open field lines to closed magnetic loops
The Sun in X-rays
Change in topology of magnetic fields on Sun
22 years
Die CaII H and K lines I
Strong lines like CaII, MgII amd LyAlpha show an emission core.
Qualitatively we can explain it in the following way: Let us
assume we observe the Sun with a turn-able filter. We start at
the the wings and than turn the filter subsequently towards the
line centre. That means we start close to the photosphere and
move upwards in the solar atmosphere.

Die CaII H and K lines II
As long as the temperature drops, the line gets deeper.
Than we reach the temperature minimum and the line does
not get deeper any longer.
If we continue, we reach levels above the temperature
minimum which are hotter again. That mean we get less
absorption and an emission core in the line centre.

At the very centre of the CaII H, and K lines is again an
absorption component. This is an none-LTE effect.
Activity in other Stars II
Stellar activity is best measured using the Ca II H & K emission
feature. Measuring stellar activity cycles using photometry is difficult
since the expected brightness fluctuation are expected to be fractions
of a percent.
The strong Ca II lines show an emission reversal in the core that is
due to chromospheric emission.
Emission from
active regions
Activity in other Stars IV
Maunder minima: Young stars show high levels of activity with no
Maunder-type minima. About 1/4 of the solar-like stars studied are
in such a low state.
Older stars like the sun show lower levels of activity with occasional
Maunder-type minima.
The observation of chromospheric CaII-emission of solar-type
stars yields activity periods between 3 and 30 yrs.
Up to 15% of the solar-type stars, however, do not show any
significant activity. This suggests that even the existence of the
Grand minima is a typical property of cool main sequence stars
like the Sun.
From ROSAT X-ray data Hempelmann et al. (1996) find
that up to 70% of the stars with a constant level of activity
exhibit a rather low level of coronal X-ray emission.
Differential rotation of the Sun I
The differential rotation results from the coupling of
rotation and convection. Meridional circulation causes
a transport of angular momentum from some parts of
the star to other regions. The differential rotation thus
depends on the rotation rate of the star and the depth
of the convection zone.
Differential rotation of the Sun II
A + B sin2 + C sin4 
•  the rotation rate (deg/day)
•  the latitude (equator =0)
Differential rotation of the Sun III
After analysing all
drawings that
were made during
this time, it was
found that rotation
period of the sun
was 2% smaller
during the
Maunder
minimum than
today.
The energy source of the
magnetic field is the rotation of
the star
The   Dynamo
In the astrophysical context, a dynamo is a fluid flow capable of sustaining a
magnetic field indefinitely against Ohmic decay.
However, the ohmic decay time is so long (d=4 109 yrs) that a primordial field could have
survived since the formation of the Sun but a dynamo is need to explain the magnetic
cycle.
-effect: The production of a strong toroidal (30kG) magnetic field (--) underneath the Sun's
surface from an initially poloidal field (|) line. The figure shows a sketch of the field line
after it has been stretched by the faster rotation near the equatorial region:
-effect
The dynamo number
The Dynamo number is:
Meaning: The dynamo number is the ratio of the between the time-scale at
which the magnetic field strength increases (g) and the time-scale on
which it decays (d=0L2) (Ohmic dissipation time-scale, with  the
electric conductivity and L a typical length-scale.)  is the magnetic
diffusivity (108 m2/s)
• Examples:
• Milky Way: d=5 108 yrs; D=10-15
• Sun: d=4 109 yrs; D=1000-200 (D>1120 an oscillatory mode is excited).
• T Tauri star: D=4 105
• Stars in general: DΩ3
• Planets: d=104 yrs
Cycle length computed from
a simple model
•  magnetic diffusivity (108 m2/s)
• α10−(1…2) uT
• uT as the characteristic turbulence velocity. With uT100 m/s the
alpha-effect becomes 1 m/s.
The chromosphere
The Chromosphere
A few seconds before the beginning and a few seconds after the end
of total solar eclipse, we can see a red ring at the edge of the sun.
This „ring“ is the Chromosphere („colour sphere“).
These observations already show that the Chromosphere is located
above the photosphere.
If we take a spectrum of the sun at this very moment, we obtain the
flash-spectrum.

The flash-spectrum shows many emission lines, most notably the
Balmer-lines and CaII H and K.
The Chromosphere can also be observed out of eclipse with a narrowband filter, for example in H .

Flash-Spectrum
The Chromosphere is about 400 (temperature
minimum) to 2000 km above the photosphere.
Structures in the Chromosphere are
dominated by the magnetic field
The magnetic field strength on the Sun decreases with a scaleheight of 1000 km. In contrast to this the pressure-scale height
is only 100 km.
This means that the structures of the Chromosphere are
determined by the magnetic field not by the gas-pressure.
The density of the Chromosphere is between 2 10-11 and 2 10-14
gcm-3. For comparison, the density of the photosphere is about
2.7 10-7 g cm-3.
Important: the flow-speed of the material in the Chromosphere is so
huge that matter can flow through the whole Chromosphere,
before every reaching an equilibrium.
The temperature of the Chromosphere is 6000 to 25000 K.
Energy balance I
The largest contribution to the overall radiative losses of
5000 Wm-2 of the Chromosphere are from the CaII K
and L lines together with the so-called infrared
calcium triplet at 854.2, 849.8, and 866.2 nm,
followed by the Mg II resonance lines, and Lyman
Alpha.
The net radiative losses peak at a value of 0.01 Wm-3
around at height of 800 km. The radiative losses
decrease steadily by a factor 50 out to about 2000
km.
Energy balance II
These net lot must be balanced locally by some form of
heating.
The energy needed to heat the Corona is only
100 Wm-2!
The heating rate required to balance the losses of the
Chromosphere are 50 times larger than what is need
to heat the corona!
About 99% of the universe
exist in the state of plasma
Debye length, the scale over which electric fields are screened
out by a redistribution of the electrons (“Abschirmlänge, Länge
über die eine lokale Überschussladung auf 1/2 abgefallen ist.”)
Plasma frequency
The natural collective oscillation frequency of a charge species (electrons, ions, etc.) in a
plasma, in the absence of (or at least parallel to) a magnetic field. Also known as
Langmuir or Langmuir-Tonks frequency; see also electrostatic waves, plasma oscillations.
The CaII H and K lines I
Strong lines like CaII, MgII amd LyAlpha show an emission core.
Qualitatively we can explain it in the following way: Let us
assume we observe the Sun with a turn-able filter. We start at
the lie wings and than turn the filter subsequently towards the
line centre. That means we start close to the photosphere and
move upwards in the solar atmosphere.

The CaII H and K lines II
As long as the temperature drops, the line gets deeper.
Than we reach the temperature minimum and the line does
not get deeper any longer.
If we continue, we reach levels above the temperature
minimum which are hotter again. That mean we get less
absorption and an emission core in the line centre.

At the very centre of the CaII H, and K lines is again an
absorption component. This is an none-LTE effect.
Chromospheric thermometer
In the temperature range between 6000
and 10000 K, a small increase of the
temperature leads to a large increase of
the radiative cooling. That is why the
temperature in the Chromosphere is
almost constant.
Ca II line profile
Images taken in the core of CaII H and K show
basically two kinds of structures:
Plage regions appear as bright structures in
these images. The Plage regions in the
Chromosphere are closely related with the
active regions in the photosphere.
The chromospheric network: This is
basically the edges of the cells of the supergranulation.
Ca II line spectrum
Why does the edges of the super-granulation
appear bright in CaII K, K images?
The magnetic flux-tubes are moved to the edges of the
super-granulation by the turbulent motion in the
photosphere.
Since the flux-tubes heat up the Chromosphere, they
appear as bright pints in the Chromosphere.
Observations with the Michelson Doppler Imager of the
SOHO satellite show that statistically, the magnetic
field of the Sun is exchanged every 40 hours.
Activity in other Stars I
Stellar activity is best measured using the Ca II H & K emission
feature. Measuring stellar activity cycles using photometry is difficult
since the expected brightness fluctuation are expected to be fractions
of a percent.
The strong Ca II lines show an emission reversal in the core that is
due to chromospheric emission.
Emission from
active regions
Activity in other Stars II
The Mt. Wilson Ca II H & K project has been monitoring the Ca II emission
using a so-called S-index in a sample of 100 stars for the past 40
years. These measurements indicate activity cycles of a few years to
30 years.
Ca II line
Strong absorption lines are formed higher up in the stellar atmosphere. The core
of the lines are formed even higher up (wings are formed deeper). Ca II is formed
very high up in the atmospheres of solar type stars.
The CaII H and K lines
and the magnetic field
A very interesting property of the CaII lines is that the flux of the
core of the line is proportional to the magnetic field strength
of the star.
This relation is valid for thephotosphere (Schrijver, Cote,
Zwaan, Saar 1987), as well as for stars (see following
figures).
Spicules I
In Halpha images taken at the solar limb the spicules appear elongated (if seen on
the disk, they are known as "mottles" or "fibrils").
The spicules are located at the edges of the cells of the super-granulation.
They exist, because of a local enhancement of the magnetic field strength.
Usually, we say that the Chromosphere has a thickness of 2000 km but spicules
 they can reach up to 15000 km above the
are chromospheric structures and
solar surface.
The thickness of the spicules is typically 2000 km.
Spicules
Spicules II
Spicules are dynamic jets in which matters flows upwards with a velocity of
20-30 km/s during the expansion phase. They can reach several
thousand kilometres in height before collapsing and fading away.
Their mass flux mass is about 100 times that of the solar wind.
The typical life-time of spicules is 10-15 minutes.
Observations with turnable filters show that the chromospheric spicules are

closely related to the photospheric
flux-tubes.
Spicules are usually associated with regions of high magnetic flux.
Spicules form a dense pattern in the vicinity of sunspot. This pattern is
called super-penumbra.
Spicules III
Spicules are formed by sound waves, which have a period of about 5minutes.
Although the sound waves usually are damped, under certain
conditions, they leak into the low atmosphere, or Chromosphere,
spawning shock waves.
These waves propel the plasma, producing more than 100,000
spicules at any given time on our star's surface.
But note: The spicules cover only 1-2% of the solar surface, the
chromospheric volume thus is largely empty!
Acoustic and magnetic wave heating
of the Chromosphere in stars
•
The observations of the CaII H and K as well as
MgII h and k lines show the presence of core emission in all observed latetype stars. This emission is attributed to an outward temperature rise in the
chromospheres of these stars which is ultimately generated by mechanical
heating.
• Two categories of heating mechanisms:
 hydrodynamic (acoustic and pulsational waves) and
 magnetic mechanisms (MHD waves and magnetic field dissipation).
 Flares, reconnection events and other disturbances can generate Alfvén
waves.
 With almost any kind of footpoint motion you will generate Alfvén waves.
Alfvén velocity:
Sound speed:
=Cp/Cv; kB=1.38064852(79)×10−23 JK-1
Flux-tubes in different stars
(Note only 1.6% of the sun covered with flux
tubes)
The magnetic carpet
The Michelson Doppler Imager Experiment of the SOHO satellite
showed the magnetic carpet for the first time.
The magnetic carpet is formed by a large number of very small,
emerging, bipolar magnetic regions that form a magnetic network.
The foot-points of these flux-elements are moved around by the
granulation, and eventually end up at the edges of the supergranulation.

The flux-elements disappear if to flux-elements of opposite polarity
meet.
When the magnetic carpet presumably contributes significantly to the
heating of the corona.
Chromospheric structures
The transition region
The layer between the Chromosphere (T ≈ 104K) and the Corona
(T>106K) is called transition region.
Because the in homogeneity of this layer, the transition region is
not a layer of a specific height but a thin layer with a specific
temperature.
At the top part of the transition region, the temperature jumps
suddenly to coronal temperatures.

Because the pressure is proportional to the density*temperature,
the density of the material thus decreases correspondingly.
The transition region can be studied with highly excited lines and in
the UV-continuum (TRACE experiment).
Solar spectrum in the UV
Temperature and height
Images at different
wavelength
Continuum: Photosphere.
CaII H,K : Thermometer of the Chromosphere.
Halpha: Unfortunately Halpha is formed over an extended range
 to interpret Halpha data. In general
in altitude. It is thus difficult
we may say that Halpha shows “the structure of the magnetic
field in the Chromosphere“.
171 A continuum: The Emission at this wavelength comes from
regions with a temperature of about 100,000 K. This is the
transition region to the corona.
171AA continuum