The Sun's Eleven Year Magnetic Reversal Theory

download The Sun's Eleven Year Magnetic Reversal Theory

of 18

  • date post

    06-Apr-2018
  • Category

    Documents

  • view

    213
  • download

    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