Friday 20 January 2012

Effect of varying separation in BMRs on the strength of Solar Cycle

The separation between the spots in a BMR has a significant effect on the strength of the Solar cycle.
R is the radius of individual sunspots, and 2 sunspots in a BMR are identical, except that they have magnetic field of opposite polarity. All the distances are between centers of sunspots.
1 unit distance=1000km
snomax=200
tilt=lat/2 with sd=19 degrees
Bmax as per Jiang et al.
Initial polar field= 3.5G, since this value gives stable(equal) oscillations for no change in parameters.

1. Separation= 2R-10


The magnetic field oscillates between +0.84 G and -2.55 G.
Difference= 3.39 G


2. Separation= 2R-5


The magnetic field oscillates between +1.6 G and -2.54 G.
Difference= 4.14 G

3. Separation=2R


The magnetic field oscillates between +2.65 G and -2.55 G.
Difference= 5.20 G

4. Separation= 2R+10


The magnetic field oscillates between +4.011 G and -2.50 G.
Difference= 6.51 G

5. Separation= 2R+20


The magnetic field oscillates between +5.56 G and -2.47 G.
Difference= 8.03 G

6. Separation= 2R+30


The magnetic field oscillates between +6.85 G and -2.45 G.
Difference= 9.30 G


Internal flux cancellation depends on the separation between the 2 spots in a BMR. The greater the separation, less is the cancellation, and more flux is transported towards the poles. Clearly affecting the strength of the cycle.

For every value of separation, there will be a different value of initial polar field, for which we will obtain an oscillation with same magnitude on either side of zero. But the difference between the peaks will stay the same, as previous simulations suggest.

Sunday 8 January 2012

Modified Separation

All the previous simulations were for  a larger separation between 2 sunspots in a BMR, so that maximum flux is differentially transported.

But now, to study the effect of varying the no. of sunspots per cycle, we need to fix the separation at some value.

For the next post, that will cover the variation of peak magnetic field with respect to variation in no. of errupting BMRs in a cycle, the separation will be fixed such that, the 2 sunspots in a BMR grace each other's boundaries. i.e. separation between their centres is twice their radius. For such a separation, stabilised oscillation is obtained for:
Initial field=3G
The field oscillates between +2.20 and -2.21G
Difference=4.41G

Note: This post should have been before the one below.
The post showing the effect of varying sunspot nos. is below.

Running the code with different number of BMRs per cycle


The code was run with different values of input BMRs per cycle, and the initial field was varied for each run to get a stable oscillation. The results are:

1. No. of BMRs per cycle = 7028,  with a peak of 200 BMRs@5.5 yrs.


Initial field = 3.5G
The field oscillates between +2.65G and -2.55G
Difference=5.20G

2. No. of BMRs per cycle = 10722, with a peak of 300 BMRs@5.5 yrs.

Initial field = 5G
The field oscillates between +3.81G and -3.64G
Difference=7.45G

3. No. of BMRs per cycle = 14412, with a peak of 400 BMRs@5.5 yrs.
Initial field = 7G
The field oscillates between +5.31 and -5.10
Difference= 10.41G

4. No. of BMRs per cycle = 18082, with a peak of 500 BMRs@5.5 yrs.
Initial field = 10G
The field oscillates between +6.58 and -7.25
Difference=15.85G

5. No. of BMRs per cycle = 21768, with a peak of 600 BMRs@5.5yrs.




Initial field = 12G
The field oscillates between +8.66 and -8.66G
Difference=17.32G


6. No. of BMRs per cycle = 25442, with a peak of 700 BMRs@5.5yrs.
Initial field = 13.5G
The field oscillates between +10.14 and -9.75G
Difference=19.89G


Ideally, the Sun's peak magnetic field near the poles has a magnitude of about 10G. So, keeping the separation between 2 spots in a BMR to be minimum, so that they just grace each other, we obtain a field of about 10 G in the last case.