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Lecture 5 - The Solar Cycle
LectureLecture 5 - The Solar Cycle5 - The Solar Cycle
o Topics in today’s lecture:
o The solar cycle
o Sunspot number
o Sunspot polarity
o Sunspot position.
o Sunspot inclination
Lecture 5 - The Solar Cycle
The Solar CycleThe Solar Cycle
o The main characteristics of the “Solar Cycle” are:
1. 11-year period of the sunspot cycle.
2. Equator-ward drift of the active latitude.
3. 22-year magnetic cycle.
4. Tilt of sunspot groups.
5. Reversal of polar magnetic fields near the time of cycle maximum.
Lecture 5 - The Solar Cycle
Sunspot NumberSunspot Number
o Monthly sunspot number is given by the Wolf Number:
R = k (10g + f )
where g is number of groups, f is number of individual spots,
and k is a correction factor that accounts for telescope size,
atmospheric conditions, etc.
o Eg: Diagram contains two groups. Group A contains 2 spots,
while group B contains 3 spots (i.e., g = 2 groups and f = 5
spots). Assuming K~1 => R=1*(10*2+5)=25.
o The Wolf Number show an ~11-year cycle.
Group A
Group B
R
Lecture 5 - The Solar Cycle
Sunspot Number (cont.)Sunspot Number (cont.)
o Maunder Minimum - period of decreased
sunspot numbers in ~1645-1715.
o Coincided with mini-ice-age in Europe, when
average temperatures of Earth fell by ~1 K.
o Did the solar dynamo turn off?
o When can we expect another mini-ice-age?
Maunder Minimum
During the Little Ice Age, London’sThames River froze in winter in the17th Century, a very rare event.
Lecture 5 - The Solar Cycle
Sunspot Number (cont.)Sunspot Number (cont.)
Lecture 5 - The Solar Cycle
Sunspot Number - where are we now?Sunspot Number - where are we now?
o Solar maxima ~ 2001 and ~2012.
o Solar minima ~ 1997 and ~2007.
Lecture 5 - The Solar Cycle
Sunspot PolaritySunspot Polarity
o Hale (1912) discovered sunspot magnetic fields usingthe Zeeman Effect (splitting and polarization ofemission lines in a magnetic field).
o Found that in one hemisphere, one magnetic polarityleads and the other follows, while in the oppositehemisphere the situation is reversed.
o Also found that the polarities were reversed afterevery 11-years, i.e., similar to the Wolf Number. Thisis Hale’s Law.
o The effective period for the reversal of the Sun’ssurface magnetic field was therefore found to be 22-years.
Black = negative polarity
White = positive polarity
1st 11-year
cycle
2st 11-year
cycle
Lecture 5 - The Solar Cycle
Sunspot PositionSunspot Position
o Spörer’s Law: Sunspots migrate from latitudes of <40o north/south of theequator at one solar minimum, to close to the equator (<10o) at the nextsolar minimum. This occurs with an ~11-year periodicity.
o Produces the “butterfly diagram”.
o There is an asymmetry between the northern and the southern hemisphere.
Lecture 5 - The Solar Cycle
Sunspot OrientationSunspot Orientation
o Joy’s Law: The magnetic axis of sunspot groups are tilted by ~5.6o to the
equator, with the leader spot located closer to the equator.
Solar rotation direction
Leader spot
Follower
spot
Direction of
equator
~5.6o
Lecture 5 - The Solar Cycle
Lecture 5 - The Solar Cycle
TheThe !"!" E Effectffect
o First proposed by Babcock (1964).
o Stage 1: Initial Dipolar Field.
Initial poloidal field located below the
convection zone in a region called the
tachocline.
o Tachocline is located at boundary
between solid -> differential rotation.
o Assumed poloidal field is:
B# = B0 sec(#) -30o < # < +30o
Sub-surface poloidal
field
Rotation frequency vs. depth
and latitude
solid differential
Latitude (#)
Sub-surface
poloidal field
Lecture 5 - The Solar Cycle
TheThe !"!" E Effectffect
o Stage 2: The " effect.
Submerged lines of force are drawn out
by differential rotation: " = "(#).
o Field is concentrated and converted from
poloidal to toroidal fields.
o Magnetic pressure builds (B2/8$).
Lecture 5 - The Solar Cycle
The The !"!" E Effectffect
o Stage 3a: Buoyancy.
As the field strength increases, theinternal magnetic pressure (B2/8$)becomes significant.
o Magnetic buoyancy causes fields to risefrom tachocline to surface.
o Pi = Pe
Pi = Pigas + Pi
magnetic
= nikTi + B2/8 $Pe = nekTe = const
=> nikTi + B2/8 $ = const
• As magnetic pressure increases, gaspressure decreases => blob gets buoyant.
Pi Pe
Solar Surface
Lecture 5 - The Solar Cycle
The The !"!" E Effectffect
o Stage 3b: Twisting.
Due to effect of Sun's rotation on the risingmagnetic field from deep within the Sun - a solarCoriolis effect. Called the ! effect.
o Twist makes sunspot groups that obey Joy's law,and makes the magnetic field reverse from onesunspot cycle to the next (Hale's law).
o !-effect regenerates poloidal field from toroidalfield.
o Solar convections draws field from tachocline tosurface. Coriolis effect then causes twist.
Lecture 5 - The Solar Cycle
The The !"!" E Effectffect
o Stage 4: Meridional Curculation.
Surface flow carries reverse poloidalfield pole-ward.
o Reverse poliodal fields eventiallyneutralise old poloidal fields.
o Poloidal field having accumulated inthe surface polar regions (A) at cycle nmust first be advected down to thetachocline (dotted line) beforeproduction of the toroidal field forcycle n+1 can take place (BC).Buoyant rise of flux rope to the surface(CD) is a process taking place on amuch shorter timescale.
Lecture 5 - The Solar Cycle
The The !"!" E Effectffect
o Figure from http://www.nature.com/nature/journal/v441/n7092/full/441402a.html