# Magnetic Field Decay

```Magnetic Field Decay
An electric current produces the field
{Except in a bar magnet….}
In natural systems there usually is electrical resistance  decay of field.
Decay time =
 2σ
= 30,000 yrs - ⊗
2
c
= 4 &times; 10 9 yrs - 
Parker, 1979
= 10 24 yrs - Galaxy
⇒ ⊗, contain generator or dynamo.
1
Generation of Magnetic Fields
•
The key principle
In a conducting fluid, magnetic field lines are tied to the fluid elements.
A.  Recall: a loop of wire with an electric current makes a magnet.
Current
Magnetic field lines
Normally it takes a battery of some sort to maintain the current against resistance.
2
B.  Now imagine the loop to be superconducting and flexible. Squash it to a
smaller size.
The result: since the same number of field lines thread through loop, the field inside
loop is stronger.
C.  The extension to a fluid.
Stretch it
Stronger field
Initial configuration
3
D.  The principle remains true for a continuous fluid threaded by field.
Before
After
Field lines area carried with fluid
E.  T. Gold calls it the Spaghetti Theory.
But remember the spaghetti strands must be stretchable ones.
H.  This is the rule of thumb used in astrophysics to understand field behavior.
For the most part the fluids of interest are highly conducting.
4
2.  How the principle can explain amplification of fields.
Consider a single loop of fluid threaded by field.
Pull, bend into an eight, and lay back over itself.
Squash it all together.
N.B.
a PULL
and a
TWIST
are
needed
It now contains twice as much magnetic flux!
5
3.  Babcock’s Solar dynamo hypothesis
A.  Initial dipole field.
B.  Equator rotates faster than poles.
Field is pulled
into spiral.
Produces strong
east-west field
(toroidal).
C.  Section “floats” to surface and erupts.
It twists as it floats up  tilt of sunspots
6
D.  Due to the tilt of sunspots, the general dipole field is built up anew. But in the
opposite sense to the original one!
Sum of many loops
averages to a large dipole
E.  This explains the reversal, the dynamo effect itself, and the solar cycle.
F.  But, what drives the equator to rotate fastest???
UNKNOWN!
7
Helioseismology
8
Science, Howe et al.
9
Magnetic Fields - Summary
Object
Strength
Reversals
Sun (global dipole)
1 - 2 (gauss)
11 yr
&gt; 1000
Sunspots
~
0.002
?
0
-
0.3
~ 0.5 X 106 yr
0
-
4-6
?
0.1- 0.2
?
Tentative Conclusions
1.
,
, outer planets have vigorous dynamo action, internal electric currents.
Rotation &amp; Convection = Dynamo
2.
,
lack convection, fields died.
3.
lacks rotation.
4.
probably no dynamo but unclear.
10
11
Sun - Summary and Questions
1.  Sun is a typical lower main sequence star.
2.  Age ~ 5 b.y.
3.  Vigorous 22 yr magnetic cycle.
4.  Luminosity history - fainter when young?
5.  Does magnetic cycle influence
?
6.  Why the differential rotation?
7.  Explanation of neutrino spectrum?
12
```