Transcript Anisotropy - IIT Kanpur

Is there a preferred direction in the Universe
P. Jain, IIT Kanpur
There appear to be several indications of the
existence of a preferred direction in the Universe
(or a breakdown of isotropy)
Optical polarizations from distant AGNs
Radio polarizations from distant AGNs
Low order multipoles of CMBR
On distance scales of less than 100 Mpc the Universe is not
homogeneous and isotropic
Most galaxies in our vicinity lie in a plane (the
supergalactic plane) which is approximately
perpendicular to the galactic plane.
The Virgo cluster sits at the center of this disc like
structure
On larger distance scales the universe appears isotropic
CFA Survey 1986
CFA Survey 1986
CMBR
What does CMBR imply about the isotropy of the universe?
WMAP released very high resolution data in march 2003
Total number of pixels = 512 x 512 x 12
The data is available at 5 frequencies
There is considerable contamination from foreground
emissions which complicate the interpretation of data
CMBR Probe WMAP
WMAP multi-frequency maps
Ka band 33 GHz
K band 23 GHz
Q band 41 GHz
W band 94 GHz
V band 61 GHz
T(,)  Temperature Fluctuations about the mean

l
T ( ,  )    almYlm ( ,  )
l 2 ml
Two Point Correlation Function
Statistical isotropy implies
If we assume that T (and alm) are Gaussian
random variables (with 0 mean) then all the
statistical information is contained in the two point
correlation function
or
Cl  l (l  1) alm a
*
lm
TT Cross Power Spectrum
The power is low at small l (quadrupole l=2)
The probability for such a low quadrupole to occur by a
random fluctuation is 5%
Oliveira-Costa et al 2003
The Octopole is not small but very planar
Surprisingly the Octopole and Quadrupole appear
to be aligned with one another with the chance
probability =1/62
Cleaned
Map
Quadrupole
Octopole
All the hot and cold spots of the Quadrupole and Octopole lie
in a plane, inclined at approx 30o to galactic plane
Oliveira-Costa et al 2003
Extraction of Preferred Axis
Imagine dT as a wave function y
Maximize the angular momentum dispersion

Oliveira-Costa et al 2003
Extraction of Preferred Axis
Alternatively Define
k = 1 …3, m = -l … l
Preferred frame eka is obtained by Singular Value Decomposition
ea represent 3 orthogonal axes in space
The preferred axes is the one with largest eigenvalue La
Ralston, Jain 2003
The preferred axis for both
Quadrupole
and
Octopole
points roughly in the direction
(l,b)  (-110o,60o) in Virgo Constellation
Hence WMAP data suggests the existence of a preferred
direction (pointing towards Virgo)
We (Ralston and Jain, 2003) show that there is considerable
more evidence for this preferred direction
CMBR dipole
Anisotropy in radio polarizations from distant AGNs
Two point correlations in optical polarizations from AGNs
Also point in this direction
CMBR Dipole
The dipole is assumed to arise due to the local (peculiar)
motion of the milky way, arising due to local in-homogeneities
The observed dipole also points in the direction of Virgo
Physical Explanations
Many explanations have been proposed for the
anomalous behavior of the low order harmonics
Non trivial topology
(Luminet, Weeks, Riazuelo, Leboucq
and Uzan, 2003)
Anisotropic Universe
(Berera, Buniy and Kephart, 2003)
Sunyaev Zeldovich effect due to local supercluster
(Abramo and Sodre, 2003)
Anisotropy in Radio Polarizations
Radio Polarizations from distant AGNs show
a dipole anisotropy
 Offset angle b  c  y
 (l2 )  c  (RM) l2
 RM : Faraday Rotation
Measure
 c = IPA (Polarization at
source)
b shows a Dipole
ANISOTROPY
Birch 1982
Jain, Ralston, 1999
Jain, Sarala, 2003
b = polarization
offset angle
Likelihood Analysis  The Anisotropy
is significant at 1% in full (332 sources) data set and
0.06% after making a cut in RM (265 sources)
|RM - <RM>| > 6 rad/m 2
<RM> = 6 rad/m 2
Distribution of RM
The cut eliminates the data near the central peak
The radio dipole axis also points towards Virgo
Jain and Ralston, 1999
Anisotropy in Extragalactic Radio Polarizations
beta = polarization offset angle
Using the cut |RM - <RM>| > 6 rad/m2
Anisotropy in Extragalactic Radio Polarizations
Using the cut |RM - <RM>| > 6 rad/m2
Galactic Coordinates
Anisotropy in Extragalactic Radio Polarizations
A generalized (RM dependent) statistic indicates that the
entire data set shows dipole anisotropy
Equatorial Coordinates
Possible Explanation
An anisotropically distributed background pseudoscalar field
 of sufficiently large strength can explain the observations
Pseudoscalar field at
source
To account for the RM dependence
Rotation in polarization =ggg ( )
  change in the pseudoscalar field along the path
ggg < 10 -11
GeV-1
Hutsemékers Effect
Optical Polarizations of QSOs appear to be locally
aligned with one another. (Hutsemékers, 1998)
1<z<2.3
A very strong alignment is seen in the direction of Virgo cluster
Hutsemékers Effect
1<z<2.3
Equatorial Coordinates
Statistical Analysis
• A measure of alignment is obtained by comparing
polarization angles in a local neighborhood
The polarizations at different
angular positions are
compared by making a parallel
transport along the great circle
joining the two points
Statistic
k, k=1…nv are the
polarizations of the nv
nearest neighbours of the
source i
 ki = contribution
due to parallel
transport
•Maximizing di() with respect to  gives a measure
of alignment Di and the mean angle 
Statistic
Jain, Narain and
Sarala, 2003
Alignment Results
We find a strong signal of redshift dependent
alignment in a data sample of 213 quasars
The strongest signal is seen in
Low polarization sample (p < 2%)
High redshift sample (z > 1)
Significance Level
Significance Level
Significance Level
Large redshifts (z > 1) show alignment
over the entire sky
Alignment Statistic (z > 1)
Alignment Results
Strongest correlation is seen at low polarizations ( p < 2%)
at distance scales of order Gpc
Large redshifts z > 1 show alignment over the entire sky
Jain, Narain and Sarala, 2003
Possible Explanation
Optical Alignment can also be explained
by a pseudoscalar field.
As the EM wave passes through large
scale magnetic field, photons (polarized
parallel to transverse magnetic field)
decay into pseudoscalars
The wave gets polarized perpendicular to the transverse
magnetic field
But we require magnetic field on cosmologically
large distance scales
Jain, Panda and Sarala, 2002
Preferred Axis
Two point correlation
Define the correlation tensor
Define
where
is the matrix of sky locations
S is a unit matrix for
an isotropic
uncorrelated sample
Preferred Axis
Optical axis is the eigenvector of S with maximum
eigenvalue
Alignment Statistic
Preferred axis points towards (or opposite) to Virgo
Degree of Polarization < 2%
Prob. for pairwise coincidences
dipole quad
dipole
quad
octo
radio
0.020
octo
radio
optical
0.061
0.042
0.024
0.015
0.023
0.004
0.059
0.026
0.008
Ralston and Jain, 2003
Concluding Remarks
There appears to be considerable evidence that there is a
preferred direction in the Universe pointing towards Virgo
However the CMBR observations may also be explained in
terms of some local distortion of microwave photons due to
supercluster.
The physical mechanism responsible for this is not known so far.
Radio anisotropy may also arise due to some local unknown effect
However it is not possible to attribute optical alignment to a
local effect
Future observations will hopefully clarify the situation
Anisotropy in Extragalactic Radio Polarizations
sin(2b) < 0 +
sin(2b) > 0 
Using the cut |RM - <RM>| > 6 rad/m2
Significance Level of Radio
Anisotropy
Radiation propagating over cosmological
distances also probes isotropy of the Universe
CMBR
Radiation from distant AGNs
On Large scale it is assumed that Universe is
Isotropic and Homogeneous
The 3-dim space appears the same in all
directions and at all locations
One way to test for isotropy and homogeneity
is by observing the density of matter (galaxies)
in different directions and positions
Angular correlation function


w( )  d (n1 )d (n2 ) 
or 3-D correlation function
APM Survey
100 degrees by 50 degrees around the South Galactic Pole
Intensities scaled to the number of galaxies
blue, green and red for bright, medium and faint galaxies
The APM survey has about 5 million galaxies
It gives an accurate measure of the angular two point
correlation function to about 10 degrees
The results agree reasonably well with the LCDM model
with
WL  0.7
Dodelson (2003)
Maddox et al (1990)