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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=0L2) (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: DΩ3 • Planets: d=104 yrs Cycle length computed from a simple model • magnetic diffusivity (108 m2/s) • α10−(1…2) uT • uT as the characteristic turbulence velocity. With uT100 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 thephotosphere (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