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