gravitational collapse in saiph (kappa orionis) star

8/3/2019 Gravitational Collapse in saiph (Kappa Orionis) star

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GRAVITATIONAL COLLAPSE IN SAIPH STAR (ORION

KAPPA): A NOVEL THEORY

A.B.RAJIBHAZARIKA

DEPT. OFMATHEMATICS

DIPHU GOVT. COLLEGE, DIPHU

KARBI ANGLONG, ASSAM (INDIA)

PIN-782462

E-mail:

[email protected]

[email protected]

[email protected]

[email protected]

[email protected]

ABSTRACT

The present study is done theoretically to get the gravitational collapse phenomena

and a search for new concept towards the insight into the behavior of Double trios, Saiph

star(Orion Kappa) which are symmetrical set of six stars (globs) of the luminosityintensity of 50-52 magnitude found in concurrent doubles at Aldebaran and Betelgeuse

galaxies where the Saiph stars illuminates with such magnitude .This theory is novel

approach towards providing certain new results such as fusion process in the double triosstars , confinement time calculated as there are at present no such theory existing.

Key words: self- gravitating system, transport phenomena, collision, diffusion, skindepth, and space plasma physics, stellar clusters and association, early type stars (O andB),Orion population, binary and multiple stars, supernovae remnants in external galaxies.

PACS No: 4.40-b, 5.60Cd, 5.60-k, 5.60+w, 5.60-a, 82.56Lz, 94.05-a, 97.20Ec, 97.21+a,98.20-d, 97.80-d, 98.58Mj

INTRODUCTION

Bhatia and Hazarika (1995,1996) did some work on gravitational instability using theviscosity term showing influence on the gravitational collapse ,in the later paper the two

superposed fluid(plasma) flow past each other in horizontal magnetic field with rotation

and viscosity playing vital role for the collapse rotating neutrons stars Schwarzchildradius is derived. Jeans instability leading to gravitational collapse of stars is studied
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earlier by many authors Jeans (1902), Chandrasekhar (1981), El-Sayed and Mohamed

(2011) tried to prove the gravitational collapse with finite conductivity playing crucial

role.

PRESENT WORKBased on low beta plasma having low frequency fluctuation which is being stabilized by

skin depth, current diffusivity and with other parameters. The induced gravitational

instability by above mentioned parameters and as a whole the classical transportphenomenon is taken into consideration. The heat conduction term is calculated ,Banana

regime (Bootstrap) , ware effect is calculated where an important result Hazarikas

regime for Saiph star (Kappa orionis) which is R(1+4 -sin3 sin -2sin -2sin ) times of solar radius is found to be correct as 10.8503(approx. 11 ),with right ascession

(RA) of 05h 47m 45.4s(72.79594 degrees) and declination of -09deg 40m 11sec(-

9.669723 deg). The above facts compels one to study the phenomena of gravitational

collapse and thereby the suppression by different parameters.

Hazarikas constant for Saiph star (Kappa Orionis) is

1. sin2sin2sin3sin41 +++=hC =10.8503

BASIC EQUATION

h

h

h

h

E RC

FRCp

RC

FpRCR

eNE

2

)(

2

1 22 +==

..(1)

[ ]

=

22

222

2

h

th

t

i

CR

BCR

B

..(2)

eeee nq

d t

d Tn+ =

2

3..(3)

( )

2

s i n22

)s i n22(

122

22

t

e

BR

R

q

+

+

= X{

+

+22 )sin22(

1)sin22(

RR } ..(4)

( )

+=

iie

i pen

EB

Bv .

12

..(5)


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GENERAL MHD MODEL :

[ ] =

+

2

0

2

0

0 ,B

c

tB

cmn i

( ) zGnmzmGnBcnm

RzrpXj

cB ii .1..cos2 00

0

4

0

0

0 ++++

(6)

jjtc

A 2

+=

..(7)

[ ] ppB

c

t

p 2

0

, =+

(8)

where Ac

j 2

4=

, [ ] BAXzBA = ., ,Poissons bracket

Eigen mode equation is obtained by linearizing the eqn.(6)-(8) in toroidal coordinates(r,, )for RTI as

( ) ( )( ) ( ) +++=

= 0

1

0 s i n2e x p2),,( qi nrri n qlrqi nlr m n

l

..

(9)The eigen value equation reduces to a differential equation

( ) 0)(

1 222

2

2

2

=+

++

sC

s

d

dh ..

(10)

( )2222

)(

1

sCs

G

h +

+

=

... (11)

On further solving eqn.(11) we get the growth as follows

( )

2/1

22222

1

+

+

=

s

C

ss

G h .. (12)


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where

( )

[ ]

( )

( )

[ ]( )

( )

( )

sin2sin2sin3sin41,

ln

,ln

,,4

,,ln

,,

12

4

3

,4,ln

,8

,,sin22

,,,

2

01

012

04

2

2

02

0

05

1

5

45

4

5

35

4

02

0

2

02

2

0

02

222222244

+=

=

=

====

==+

+

===

===+

====

R

cg

dr

ndLn

dr

pdLp

Ln

rnn

r

c

rB

c

gLngLnrmn

BrAAtt

ls

aB

rmngLngLnrmn

B

ppqn

R

rqnqnqn

s

mn

mnmn

pa

mn

pa

mni

pa

mnpa

mni

pa

mni

pa

pa

DISCUSSION

The growth rate as a function of finite conductivity we can find the first order derivative

to find that the function increases or decreases as :

( ){ }

( ){ }

0

12

2

1

2222

12

22

1222

22

=

+

+

+

+

=

sC

s

s

ssC

s

Gd

d

h

h

.(13)

as the above term is positive we can say that it decreases or the function stabilizes.

If the above term goes to 0 it gives us the root of the equation .i.e.,either the collapsing

growth rate of Saiph(Kappa Orion) is

( )2/1

222/12/1

2

++=

ss

CGh

Here we see that the function which is dependent on current diffusivity and skin depth ispositive i.e.,stabilizes the growth rate of star .if current diffusivity is more than 1000 the

potential collapses,similarly the skin depth values (1-10) shows the collapse of the


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potential of Kappa Orion(Saiph).It stabilizes for >1 always for if

and s remain constant, roots lies between 30 and 40.If we plot growth against the current

diffusivity and skin depth we can see the implosion and collapse of potential.

Gravitational red shift

For mass of the star including in the stellar spectra with those in spectra obtained in thelaboratory,the ratio M/R is too small for a gravitational redshift to be apparent. A white

dwarf is an old star whose interior consists of atoms whose electron structure have

collapsed and so it is very small


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Rc

GMsaiph

=

2

12

Rc

GMsaiphwith this condition no photons can even leave the star as it cannot radiate

i.e,a black hole.

111

152

Rc

GMsun

Schwarzchilds radius of Saiph star(Kappa Orionis)

2215

2

c

GM

c

GMR sun

saiph

s ==

ss RR 15=

Schwarzchilds radius of Saiph star (Kappa Orionis) is 15 times the Schwazchilds radiusof sun.


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REFERENCES

1.Bhatia P.K and Hazarika,A.B.Rajib: Physica Scripta 52,775(1995)

2.Bhatia,P.K and Hazarika,A.B.Rajib: Physica Scripta 53,57(1996)3.Jeans,J.H:Philosiphical transactions of Royal society of LondonA 199,1-53 (1902)

4.El-Sayed,M.F and Mohamed,R.A:ISRN Mechanical Engineering,Vol.2011,Art. ID

597172 (2011)5.Chandrasekhar,S:Hydrodynamic and hydromagnetic stability,Dover pub.,NY(1981)


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gravitational collapse in saiph (kappa orionis) star

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