Lecture 5 - 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 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 Number o Monthly sunspot number is given by the Wolf Number: R = k (10g + f ) Group A 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. Group B 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. R Lecture 5 - The Solar Cycle 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? During the Little Ice Age, London’s Thames River froze in winter in the o When can we expect another mini-ice-age? 17th Century, a very rare event. Maunder Minimum Lecture 5 - The Solar Cycle Sunspot Number (cont.) Lecture 5 - The Solar Cycle Sunspot Number - where are we now? o Solar maxima ~ 2001 and ~2012. o Solar minima ~ 1997 and ~2007. Lecture 5 - The Solar Cycle Sunspot Polarity 1st 11-year cycle o Hale (1912) discovered sunspot magnetic fields using the Zeeman Effect (splitting and polarization of emission lines in a magnetic field). o Found that in one hemisphere, one magnetic polarity leads and the other follows, while in the opposite hemisphere the situation is reversed. 2st 11-year o Also found that the polarities were reversed after cycle every 11-years, i.e., similar to the Wolf Number. This is Hale’s Law. o The effective period for the reversal of the Sun’s surface magnetic field was therefore found to be 22- years. Black = negative polarity White = positive polarity Lecture 5 - The Solar Cycle Sunspot Position o Spörer’s Law: Sunspots migrate from latitudes of <40o north/south of the equator at one solar minimum, to close to the equator (<10o) at the next solar 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 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. Follower spot Leader spot ~5.6o Direction of equator Solar rotation direction Lecture 5 - The Solar Cycle Lecture 5 - The Solar Cycle The !" Effect o First proposed by Babcock (1964). Sub-surface o Stage 1: Initial Dipolar Field. poloidal field Initial poloidal field located below the convection zone in a region called the tachocline. o Tachocline is located at boundary Sub-surface poloidal between solid -> differential rotation. field Latitude (#) o Assumed poloidal field is: o o B# = B0 sec(#) -30 < # < +30 solid differential Rotation frequency vs. depth and latitude Lecture 5 - The Solar Cycle The !" Effect 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$). Lecture 5 - The Solar Cycle The !" Effect o Stage 3a: Buoyancy. Solar Surface As the field strength increases, the internal magnetic pressure (B2/8$) becomes significant. P i Pe o Magnetic buoyancy causes fields to rise from tachocline to surface. o Pi = Pe gas magnetic Pi = Pi + Pi 2 = nikTi + B /8 $ Pe = nekTe = const 2 => nikTi + B /8 $ = const • As magnetic pressure increases, gas pressure decreases => blob gets buoyant. Lecture 5 - The Solar Cycle The !" Effect o Stage 3b: Twisting. Due to effect of Sun's rotation on the rising magnetic field from deep within the Sun - a solar Coriolis effect. Called the ! effect. o Twist makes sunspot groups that obey Joy's law, and makes the magnetic field reverse from one sunspot cycle to the next (Hale's law). o !-effect regenerates poloidal field from toroidal field. o Solar convections draws field from tachocline to surface. Coriolis effect then causes twist. Lecture 5 - The Solar Cycle The !" Effect o Stage 4: Meridional Curculation. Surface flow carries reverse poloidal field pole-ward. o Reverse poliodal fields eventially neutralise old poloidal fields. o Poloidal field having accumulated in the surface polar regions (A) at cycle n must first be advected down to the tachocline (dotted line) before production of the toroidal field for cycle n+1 can take place (BC). Buoyant rise of flux rope to the surface (CD) is a process taking place on a much shorter timescale. Lecture 5 - The Solar Cycle The !" Effect o Figure from http://www.nature.com/nature/journal/v441/n7092/full/441402a.html Lecture 5 - The Solar Cycle.