# The Sun's Eleven Year Magnetic Reversal Theory

date post

06-Apr-2018Category

## Documents

view

213download

0

Embed Size (px)

### Transcript of The Sun's Eleven Year Magnetic Reversal Theory

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

1/18

The Suns Eleven Year Magnetic Reversal Theory

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

2/18

1. Introduction

The presented theory in this draft document uses the speed of the rotating magnetic fields of the

Sun in order to calculate the magnetic field activity of the Sun and the number of sunspots which

appear on the Suns surface. A sunspot is a place on the Suns surface which is characterized by a very

strong magnetic field. Therefore, the number of the sunspots on the Sun is a good indicator of the

intensity of the overall Suns magnetic activity. It is well-known that the magnetic field of the Sun

peaks every eleven years, a cycle known as the sunspot cycle. At the peak of magnetic activity, the sun

records maxima of sunspot numbers on its surface. It should be noted that the length of the sunspot

cycle is not always exactly eleven years, to the contrary, it varies as discussed by Mursula and Ulich

(1).

The presented theory tries to achieve the following (non-exhaustive) goals:

- To successfully calculate the length of the sunspot cycle based on the variability of the

speeds of the Suns magnetic fields as found by Callebaut (2)

- To be able to calculate the speeds of the polar magnetic fields based on the sunspot cycle

length and the equatorial speed

- To successfully calculate the varying hemispherical number of sunspots during each

sunspot cycle

- To calculate the positive and negative polarity of the sunspots

- To depict the polar magnetic reversal event

A correlation between the intensity of the Suns magnetic activity and the variability of the

speeds of its magnetic fields is presented in Long Term Variations of the Torsional Oscillations of the Sun

(2). The authors state that the differential rotation of the Sun is least differential during the magnetic

maxima and most differential during the magnetic minima. In other words, the speeds of the equatorial

and the two polar speeds (North and South polar speeds of rotation) have the most similar values

during the period when a maximal number of sunspots are recorded. The presented theory tries to go

along with this finding and tries to calculate speeds of the equatorial and polar fields which fit the

behavior described in reference (2).

This draft document is structured as follows: In Section 2, the magnetic field theory is

described, in Section 3 the calculated values are presented and finally this document is concluded with

the essential findings of the new theory.

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

3/18

2. The Magnetic Field Theory of the Sun

As it has been previously stated, the theory bases its calculation on the variability of the speeds of

the magnetic fields of the Sun. The theory uses the model depicted in Fig. 1.

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

4/18

Figure 1. The observers model

S marks the polar view of the Sun. Let Ae represent the angular rotation of the equatorial field, An the

angular rotation of the north polar magnetic field and A s the angular rotation of the south polar

magnetic field. O represents an individual observer which travels around the Sun with constant

angular speed of Aob.The observer travels the length of the mean of the north polar and equatorial

field in one day. Although aware that the speed and the length of the south magnetic field is slightly

different from the speed and the length of the north field, we use the length of the north field only for

simplicity. Practical evidence has shown that the obtained results do not differ to a great scale. As a

consequence of the polar fields change at the end of each sunspot cycle, we observe different travel

lengths of the observer if two consecutive sunspot cycles are simulated. For instance, when the north

polar magnetic field switches with the south magnetic field and the length and speed of the north

magnetic field are lower than the length and speed of the south field, we observe shortened travel

length and consequently increased travel time of the observer.

The object m represents the direction of the magnetic fields of the Sun. The angular rotation speeds aremeasured in degrees per day.

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

5/18

The number of sunspots is calculated at each equilibrium point of rotational position (degrees)

between the equatorial field and the North or South polar field. Therefore, {fi} represents the position

(degrees) of the ith equilibrium point recorded (for North or South polar magnetic field). The number

of the sunspots is obtained from Eq. (1):

obeqsouthnorth PosPosMSSN =| (1),

where Poseq is the position of the equatorial field (degrees) and Pos ob is the position of the individual

observer. MSSNnorth|south is the number of sunspots on the North and South hemisphere of the Sun

respectively. It should be noted that Eq. (1) is performed at each equilibrium point of position between

equatorial and polar north field and between equatorial and polar south field, in order to calculate

MSSNnorth and MSSNsouth respectively.

The length of each sunspot cycle is calculated as sum of the periods (days) between the

equilibrium points of position of the equatorial and the polar fields (the equilibrium points will be

referred to as taking-over events further on).

Since the theory is based on an external individual observer, this theory is referred to as The

Observers Magnetic Field Theory of the Sun.

3. The Results

Two types of evaluation of the observers magnetic field theory were performed:

a) A static approach; the input parameter of the static approach is the average speed of theequatorial magnetic field. This approach is called static since the A eq, An and As are simulated with

constant values during the known length of the cycle. Considering the differential rotation of the Sun,

An and As are calculated as in Eq. (2) and Eq. (3):

An =Aeqx FactPN (2)

As= Aeqx FactPS (3)

where FactPN and FactPS represent the factors of difference in speed of rotation between the

equatorial magnetic field and the north and south magnetic fields respectively (see reference 3, The

Internal Rotation of the Sun).

.

b) A dynamic approach; in this approach a more realistic scenario is simulated. The input

parameters in this scenario are the length of the sunspot cycle and the monthly equatorial speed.

Therefore, the value of the speed of the equatorial field is not constant anymore, it is changed every

month. The values of the changing equatorial speed of the Sun in the period of the year 1920 till the

year 1990 are depicted in Fig. 2.

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

6/18

Figure 2. The dynamic equatorial speed.

From Long Term Variations of the Torsional Oscillations of the Sun (2).

At each taking-over event, a speed of the North and South polar field is searched in the

interval of 36 to 38 days for the North polar field, and in the interval of 36.5 to 38.5 days for the South

polar field. The chosen polar speed for that taking-over event is the speed which gives a minimal

difference between the real hemispheric sunspot number and the calculated hemispheric sunspot

number according to Eq. (1).

The simulation efforts were made with specially crafted software application created for this

purpose.

3.1.The Static Approach

The static approach is an approach which concentrates on the ability of the observers magnetic

field theory to successfully calculate the length of the cycle, not the magnetic intensity. Hence, by thealgorithm of the static approach presented in Section 3, it can be easily concluded that the simulation

of constant averaged values of the equatorial and polar fields cannot successfully calculate the real

hemispherical number of sunspots since the movement of the equatorial and therefore polar fields is

certainly not constant (Fig. 2).

The intensity of a sunspot cycle (s) used for calculation of the length of the cycle only, is depicted

in Fig. 3 and Fig. 4, for North and South polar fields respectively. The calculated sunspot numbers are

calculated from averaged equatorial speed of 25.75 days. On the Y-axis of both Fig. 3 and Fig. 4 are

presented the sunspot numbers calculated at each taking-over event. On the X-axis a time scale is

represented, where the time is measured in bits. One bit represents the time interval measured in days

8/3/2019 The Sun's Eleven Year Magnetic Reversal Theory

7/18

0

50

100

150

200

250

300

350

1 3 5 7 91113151719212325272931333537394143454749515355575961636567697173757779818385878991939597

Time (bits)

NumberofSunspots

0

50

100

150

200

250

300

350

1 3 5 7 91113151719212325272931333537394143454749515355575961636567697173757779818385878991939597

Time (bits)

NumberofSunspots

between each taking-over event. Since all fields of the sun have constant values, accompanied by the

constant value of the observer, one bit for the North field has value of 83.78 days and 82.63 for the

South field for equatorial speed of 25.75 days and values of FactPN and FactPS 1.443744 and

1.4527033 respectively.

As it has