Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/conf/epp10/Mandal.pdf Äàòà èçìåíåíèÿ: Sat Sep 7 16:31:06 2013 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 02:21:18 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: active galaxy

Title-Page

Correlation of Linear Quasar Polarization : ALPs Revisited
XVI Lomonosov Conference On Elementary Particle Physics Ki-Young Choi Subhayan Mandal Chang-Sub Shin



Asia Pacific Center For Theoretical Physics

August 26, 2013

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

1 / 28


Quasars
Features Of AGN

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm
1

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

Accreting System

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

Accreting System Polarization Prop erties
3

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

Accreting System Polarization Prop erties 3 `Coherent Orientation Of The "Visible" Quasar Polarization On Cosmological Scale'

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

Accreting System Polarization Prop erties 3 `Coherent Orientation Of The "Visible" Quasar Polarization On Cosmological Scale' Different AGN's

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
2 Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28

1


Quasars
Features Of AGN Luminosity 1045 erg-cm Stability
2 1

Accreting System Polarization Prop erties 3 `Coherent Orientation Of The "Visible" Quasar Polarization On Cosmological Scale' Different AGN's
1 2 3 4 5
1 2

Quasar QSO Seyfert Blazar BL Lac

B.M. Peterson, An Introduction To Active Galactic Nuclei(CUP) Accretion p ower in astrophysics-J. Frank, A. R. King, Derek J. Raine (CUP) 3 D. Hutsem kers and H. Lamy, Astronomy and Astrophysics, 367, 381, (2001).
Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 2 / 28


Pictures
Here we include the artist impression of an AGN along with a physical schema.

Figure: Left Handed is Artists Impression & Right Handed is Physical Schema All the mentioned (or omitted) AGN types are just the same but orientaed differently along our line of sight - according to consensus(!) theory
Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 3 / 28


Alignment Effect
" `WE' 4 only consider objects which fulfil the criteria p = 0.6%, = 14 , and |bII | = 30 , where p is the p olarization degree and the uncertainty of the p olarization p osition angle. These constraints ensure that most objects are significantly and intrinsically p olarized with little contamination by the Galaxy, and that the p olarization p osition angles are measured with a reasonable accuracy"

4 D. Hutsem´kers, R. Cabanac, H. Lamy and D. Sluse, Astronomy and e Astrophysics, 441, 915, (2005) Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 4 / 28


Explanation
This curious effect has given way to several theories - such as -

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as 1

Instrumental Artefact

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

2

Contamination By Intersteller Polarization Inside Milky Way

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

3

Extinction By Dust Grains Aligned To Magnetic Field

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

3 4

Extinction By Dust Grains Aligned To Magnetic Field Conversion Of to

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

3 4 5

Extinction By Dust Grains Aligned To Magnetic Field Conversion Of to Correlated Magnetic Fields

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

3 4 5 6

Extinction By Dust Grains Aligned To Magnetic Field Conversion Of to Correlated Magnetic Fields Pro duction Of In The Accretion Disk

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Explanation
This curious effect has given way to several theories - such as -

3 4 5 6 7

Extinction By Dust Grains Aligned To Magnetic Field Conversion Of to Correlated Magnetic Fields Pro duction Of In The Accretion Disk Mixing Of to & Dust Extinction
5

5

arXiv:0910.3036
Quasar Polarization August 26, 2013 5 / 28

Subhayan Mandal (@APCTP)


Axion-Photon Mixing
This is how they mix

1 2

Dichroism Birefringence

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

6 / 28


Observations Provided Experimentally On Quasars

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed.

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed. Circular p olarization is absent or b elow appreciable level.

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed. Circular p olarization is absent or b elow appreciable level. The p olarization show regular alternence

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed. Circular p olarization is absent or b elow appreciable level. The p olarization show regular alternence The degree of linear p olarization is 1%

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed. Circular p olarization is absent or b elow appreciable level. The p olarization show regular alternence The degree of linear p olarization is 1% The same observation is also found with radio frequency.

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Observations Provided Experimentally On Quasars

They are nominally linearly p olarised as observed. Circular p olarization is absent or b elow appreciable level. The p olarization show regular alternence The degree of linear p olarization is 1% The same observation is also found with radio frequency.
1 2

Single field ALPs with two photon coupling may not explain all of these a t a ti m e . We need at least two fields.!

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

7 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1

Lin. Pol. for linearly unp olarised + p olarised quasars

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later
6

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2 3

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later 6 If all quasar of the sample are assumed to b e of the first kind

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2 3

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later 6 If all quasar of the sample are assumed to b e of the first kind
It may not explain the the regular alternence

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2 3

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later 6 If all quasar of the sample are assumed to b e of the first kind
It may not explain the the regular alternence i.e. it will not show /6 rotation per redshift as observed.
7

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2 3

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later 6 If all quasar of the sample are assumed to b e of the first kind
It may not explain the the regular alternence i.e. it will not show /6 rotation per redshift as observed. 7 However, chances are they are of the second kind - as the sample space is handpicked.

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Single Field ALPs & Observational Conflicts
There are some inherent problems with single field ALPs
1 2 3

Lin. Pol. for linearly unp olarised + p olarised quasars It may not suppress circular p olarization for the later 6 If all quasar of the sample are assumed to b e of the first kind
It may not explain the the regular alternence i.e. it will not show /6 rotation per redshift as observed. 7 However, chances are they are of the second kind - as the sample space is handpicked.

4

It fails to produce similar linear p olarization for the case of mm wave radio frequencies as we know from recent data analysis. 8

6 7 8

circ-p http://arxiv.org/p df/1107.2013v1.p df http://arxiv.org/p df/astro-ph/0507274.p df radio http://arxiv.org/p df/1203.5299v1.p df

ol-I dichro

circ-pol-II

circ-pol-III

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

8 / 28


Our Model.

10

1 1 1 L = - Fµ Fµ + µ µ - m2 4 2 2 1 2 1 - m2 - g Fµ Fµ - 2 4 for the scalar equation 1 2 + m2 = - g a 4 For the pseudoscalar one

1 2 + µ µ 2 1 g Fµ ~µ F 4



(1)





Fµ Fµ

(2)

1 2 + m2 = - g µ Fµ F a 4 Similarly, the equation for the photon may b e written as, E
9 10

(3)

T ot

+

2 ET ot p

= g B

ext

2 +g t 2





B

ext

2 ^ ân t 2



9

(4)

n is the unit normal in the direction of arXiv:1307.5994
Quasar Polarization August 26, 2013 9 / 28

Subhayan Mandal (@APCTP)


Description Contd.
It will lead to mixing matrix in a block diagonal form 2 iM 0 0 p -iM m2 0 0 M = , 2 0 0 p iN 0 0 -iN m2 Leading to a solution of these forms (z) = A (z) = (z) = A (z) =
1 sin(2 ) 2

(5)

ei
z

z

2 +
-

-

- ei

z

2 +

+

A (0)
+

cos2 ( )ei



2 +

+ sin2 ( )ei



z

2 +

2 2 1 sin(2) eiz +- - eiz ++ A (0) 2 2 2 cos2 ()eiz +- + sin2 ()eiz ++ A (0)
Quasar Polarization

A (0)

(6)

(7)
10 / 28

Subhayan Mandal (@APCTP)

August 26, 2013


Mixing Angle & Eigenvalues
Where the mixing angle/s are given by = =


1 ta n 2

-1

2g





Bk


-2 + m2 p

(8) (9)
2

2g B 1 tan-1 2 -2 + m p

The eigenvalues are such to b e ± = ± =


1 2 1 2

2 + m2 p



±

2 - m2 p 2 - m2 p

2


+ 2g





Bk
2

2

(10) (11)

2 + m2 ± p

2

+ 2g B

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

11 / 28


Correlators
Here we shall calculate all the correlators 1 A (z)A (z) = 1 + cos2 2 + cos[z( )/(2)] sin2 2 (12) 2 1 1 + cos2 2 + cos[z()/(2)] sin2 2 A (z)A (z) = (13) 2
A (z)A (z) A (0)A (0)


=

cos2 cos2 exp (i- z/(2)) + sin2 sin2 exp (i+ z/(2))


+ cos2 sin2 exp (i± z/(2)) + sin2 cos2 exp (i z/(2)) (14) We quote, the rest of the symb ols for completeness = + - - - = - - - ± = + - -
Subhayan Mandal (@APCTP)

; ; ;

= + - - + = + - + = - - +
August 26, 2013







(15) (16) (17)
12 / 28

Quasar Polarization


Formulas - to be plotted
For Degree of Linear Polarization we need to plot p
lin

=

Q2 + U2 . I

(18)

Individually, they are given as, Q = A (z)A (z) - A (z)A (z) U = 2 â Real V = 2 â Imag A (z)A (z) â U0 â U0 I The circular p olarisation is given by A (z)A (z) (21) (19) (20)

The Rotation Measure is given by A A (z) - 0 = arctan - arctan A A (z)
Subhayan Mandal (@APCTP) Quasar Polarization

A A (z ) 0 A A (z ) 0
August 26, 2013

(22)
13 / 28


Graphs-I: Linear Polarization
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 but is varied around this p = 4 â 10-24 GeV m = 1e - 24 GeV& m is varied around this
Linear Polarization For Optical Band 0.01 0.01 0.01 0.01 0.01 0.0104 L-Pol. 0.0102 0.01 0.0098 0.0096 2e-024 1.6e-024 1.3e-024 1e-024 Scalar-Mass [GeV] 4e-029 7e-025 5e-029

0.01 0.0099995 0.009999 0.0104 0.0099985 0.0102 L-Pol. 0.009998 0.01 0.0099975 0.0098 0.009997 0.0096

Linear Polarization For Radio(mm) Band 0.01 0.01 0.01 0.01 0.01

0.01 0.01 0.01 0.01 0.01 0.01 2e-024

2e-029 3e-029 2 Mag-Field [GeV ]

2e-029 3e-029 2 Mag-Field [GeV ] 4e-029

1.6e-024 1.3e-024 1e-024 Scalar-Mass [GeV] 7e-025 5e-029

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

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Graphs-II: Circular Polarization
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 but is varied around this p = 4 â 10-24 GeV m = 1e - 24 GeV& m is varied around this
Circular Polarization For Optical Band 8e-005 6e-005 4e-005 2e-005 9e-005 8e-005 7e-005 6e-005 C-Pol. 5e-005 4e-005 3e-005 2e-005 1e-005 0 2e-024 1.6e-024 1.3e-024 1e-024 Scalar-Mass [GeV] 4e-029 7e-025 5e-029

9e-005 8e-005 7e-005 1.2e-009 6e-005 1e-009 5e-005 8e-010 4e-005 C-Pol. 3e-005 6e-010 2e-005 4e-010 1e-005 0 2e-010 0

Circular Polarization For Radio (mm) Band 1e-009 8e-010 6e-010 4e-010 2e-010

1.2e-009 1e-009 8e-010 6e-010 4e-010 2e-010 0 2e-024

2e-029 3e-029 2 Mag-Field [GeV ]

2e-029 3e-029 2 Mag-Field [GeV ] 4e-029

1.6e-024 1.3e-024 1e-024 Scalar-Mass [GeV] 7e-025 5e-029

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Quasar Polarization

August 26, 2013

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Stokes parameters : Case I
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 p = 4 â 10-24 GeV m = 1e - 24 GeV& m = 2e - 24
1 |v| |u| |q| 0.1

0.1 0.01 0.001

|v| |u|

Stokes Parameters (Optical)

Stokes Parameters (Radio) 1 1.5 2 2.5 Distance [Gpc] 3 3.5 4

0.01

0.0001 1e-005 1e-006 1e-007 1e-008

0.001

0.0001

1e-005

1e-006

1e-009 1e-010 1 1.5 2 2.5 Distance [Gpc] 3 3.5 4

1e-007

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August 26, 2013

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Stokes parameters : Case II
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 p = 4 â 10-24 GeV m = 8e - 24 GeV& m = 8.3e - 24
1 0.01 0.0001 Stokes Parameters (Radio) 1e-006 1e-008 1e-010 1e-012 1e-014 1e-016 |v| |u| |q|

1

|v| |u|

0.01 Stokes Parameters (Optical)

0.0001

1e-006

1e-008

1e-010

1e-012 1 1.5 2 2.5 Distance [Gpc] 3 3.5 4 1 1.5 2 2.5 Distance [Gpc] 3 3.5 4

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Quasar Polarization

August 26, 2013

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Correlation Of Linear Polarization : Case I
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 p = 4 â 10-24 GeV m = 1e - 24 GeV& m = 2e - 24
Linear Polarization Orientation Angle Difference Between Bins (Optical) 9e-025 7e-005 6e-005 8e-025 Scalar-Mass [GeV] Scalar-Mass [GeV] 5e-005 4e-005 7e-025 3e-005 2e-005 1e-005 5e-025 2e-029 3e-029 Magnetic-Field [GeV ]
2

Linear Polarization Orientation Angle Difference Between Bins (Radio) 9e-025 1.4e-014 1.2e-014 8e-025 1e-014 8e-015 7e-025 6e-015 4e-015 2e-015 5e-025 2e-029 3e-029 Magnetic-Field [GeV ]
2

6e-025

6e-025

0 4e-029 5e-029

0 4e-029 5e-029

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Quasar Polarization

August 26, 2013

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Correlation Of Linear Polarization : Case II
T he y= = = following values have b een fed to the numerical code. z = 1.5e + 41GeV -1 2.5 â 10-9 /3.7 â 10-14 GeV 10+12 = g1 = g1 GeV-1


B = 1nG = 2 â 10-29 GeV2 p = 4 â 10-24 GeV m = 8e - 24 GeV& m = 8.3e - 24
Linear Polarization Orientation Angle Difference Between Bins (Optical) 8.3e-024 6e-006 5e-006 8.25e-024 Scalar-Mass [GeV] Scalar-Mass [GeV] 4e-006 3e-006 8.2e-024 2e-006 1e-006 0 8.1e-024 2e-029 3e-029 Magnetic-Field [GeV ]
2

Linear Polarization Orientation Angle Difference Between Bins (Radio) 8.3e-024 2e-015 1.8e-015 1.6e-015 8.25e-024 1.4e-015 1.2e-015 8.2e-024 1e-015 8e-016 6e-016 4e-016 2e-016 8.1e-024 2e-029 3e-029 Magnetic-Field [GeV ]
2

-1e-006 4e-029 5e-029

0 4e-029 5e-029

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Quasar Polarization

August 26, 2013

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Discussions
Salient Features are such to b e

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1

The absence of circular p olarisation

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

3

The effect found in other wavebands, too.

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

3 4

The effect found in other wavebands, too. Also, we note that fine tuning such as resonance etc. is not reqd. here.

Notable p oints here -

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

3 4

The effect found in other wavebands, too. Also, we note that fine tuning such as resonance etc. is not reqd. here. Higher masses than plasma frequency may still produce the same result

Notable p oints here -

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

3 4

The effect found in other wavebands, too. Also, we note that fine tuning such as resonance etc. is not reqd. here. Higher masses than plasma frequency may still produce the same result Higher Couplings may also b e investigated.

Notable p oints here -

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Discussions
Salient Features are such to b e
1 2

The absence of circular p olarisation The regular alternance of orientation of p olarisation in different bins Not Produced Here

3 4

The effect found in other wavebands, too. Also, we note that fine tuning such as resonance etc. is not reqd. here. Higher masses than plasma frequency may still produce the same result Higher Couplings may also b e investigated. Which however may b e restricted by other considerations
fifth force

Notable p oints here -

.

11

11 http://arxiv.org/p df/astro-ph/9806099.p df ; http://arxiv.org/p df/1206.1809.p df Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 20 / 28


Thank You
I thank the following p ersons for their useful suggestions & help during the preparation of this presentation. Ki-young-Choi Chang-Sub Shin Soo A. Kim

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

21 / 28


Framework of One component Mixing - I
W2 +
2 Y

(y) Ay (y)

+M

(y) Ay (y)

=0

(23) (24)
2

M= ± = 1 -m2 - 2 ± p 2

-m2 2gB 2Bg -2 p -m2 - 2 p
2

+ 4 -m2 2 + (2gB) p

The eigenvectors would b e given similarly as - The |+ |+ >= 1 (2gB) + (- |- >= 1 (2gB)2 + -2 - - p
Quasar Polarization

/-

(25) > is given as, (26)

2

m2

- + )

2

2gB -m2 - +
2 -p - - 2gB

2

(27)

Subhayan Mandal (@APCTP)

August 26, 2013

22 / 28


Framework of One component Mixing - II
The normalisation constants are given by - &
1 (2gB)2 +(-2 - p
-

)

2

as

1 N-

1 (2gB)2 +(-m2 -+ )2

as

1 N+

,

- then the transformation matrix would

b e given by S=
2gB N+ -m2 - N+

-
+

-

-2 - p N- 2gB N-

-



The explicit form of the final equations are, 2 eiy +- - eiy (y) = - 2 1 Ay (y) = eiy +- - eiy - The mixing angle would b e given by
Subhayan Mandal (@APCTP)

=



(28)

2 + 2 +

+

Ay (0) Ay (0) (29)

+

M

=

1 ta n 2

-1

2gB m2 - 2 p
August 26, 2013

(30)
23 / 28

Quasar Polarization


Framework of One component Mixing - III
The probability expression stays the same PA


= sin2 (2M ) sin

2

y 2

(31)

Finally, we quote the mixing length formula in its extended form osc = 2 - p 4gBk m2 + 4g2 B2 2 (32)

1 I(z) = I0 - 2 (I0 + Q0 ) PA Q(z) = I(I0 Q0 )


M

U(z) = U0 (SM )2 cos (C -V V (z)
0

(SM )2 sin (C

y 2 M ) y

)2

+ (C - (C



M

)2 cos (SM ) )2 sin (SM )



M

2 y 2 y

sgn

= U(U0 V0 , V0 -U0 ),
Quasar Polarization August 26, 2013 24 / 28

Subhayan Mandal (@APCTP)


Dichroism

Abstract : Based on a new sample of 355 quasars with significant optical p olarization and using complementary statistical methods, we confirm that quasar p olarization vectors are not randomly oriented over the sky with a probability often in excess of 99.9%. The p olarization vectors app ear coherently oriented or aligned over huge ( 1 Gp c) regions of the sky located at b oth low (z 0.5) and high (z 1.5) redshifts and characterized by different preferred directions of the quasar p olarization. In fact, there seems to exist a regular alternance along the line of sight of regions of randomly and aligned p olarization vectors with a typical comoving length scale of 1.5 Gp c. ¯ Furthermore, the mean p olarization angle app ears to rotate with redshift p er Gp c . ----at the rate of 30

Subhayan Mandal (@APCTP)

Quasar Polarization

August 26, 2013

25 / 28


Alignment in Radio wave
ABSTRACT We present a detailed statistical analysis of the alignment of polarizations of radio sources at high redshift. We use the JVAS/CLASS 8.4-GHz surveys for our study. This study is motivated by the puzzling signal of alignment of polarizations from distant quasars at optical frequencies. We explore several different cuts on the polarization flux for our analysis. We find that the entire data shows a very significant signal of alignment on very large distance scales of order 500 Mpc. The alignment starts to decay only at much larger distances of order Gpc. If we only consider data with polarization flux greater than 1 mJy, we find alignment at distance scales less than 150 Mpc. We also find that data with polarization flux less than 0.5 mJy does not show significant alignment. Similar results are seen for data with degree of polarization less than 0.01, although here a mild signal of alignment is observed for a narrow range of angular separations. We argue that the signal cannot be explained in terms of bias due to systematic errors in removal of instrumental polarization. We also find that the degree of polarization shows a strong negative correlation with the total flux. The data appears to fall into two classes, one of which shows such a correlation. The remaining set, which has total flux greater than 100 mJy and degree of polarization lying between 0.01 and 0.1, shows a more random behaviour. The latter set is also found to show no alignment
Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 26 / 28


Long Range Forces
1 2 3

Both the Scalar & Pseudoscalar couplings may b e b ounded from ab ove by long range force exp eriments. However, pseudoscalars are b est constrained by astrophysical consideration. We shall compare here the product of the restrictive upp er b ounds of these two pitched against the exp erimental b ound on the same product.
10 10
10

1
12

2 3

10 10

24

N

s

26

Scalar baryon coupling g

10 10 10 10 10 10

14

1 2 3

10 g
16

28

4

e

p

10
N

30

g

18

s

5
20

10 6 10 8 10
4

32

5 4

34

22

7

4
36

24

10

8

10

6

10

4

10

2

10

0

10

2

10

10

6

10

8

10

8

10

6

10

4

10

2

10

0

10

2

10

4

10

6

10

8

m
Subhayan Mandal (@APCTP) Quasar Polarization

m
August 26, 2013 27 / 28


Full Data
600

12

'vectordata.txt' u 2:1 'vectordata.txt' u ($2):(($1)+180) 'vectordata.txt' u ($2):(($1)+360) 500

400

300

200

100

0 -3 -2 -1 0 1 2 3

12 For the original data cf. D. Hutsem´kers, R. Cabanac, H. Lamy and D. e Sluse, Astronomy and Astrophysics, 441, 915, (2005) Subhayan Mandal (@APCTP) Quasar Polarization August 26, 2013 28 / 28