Polarimetric constraints on axion-like particlesaxion-wimp2013.desy.de/e201031/e213180/Payez.pdf ·...

Polarimetric constraints on axion-like particles

from linear and circular polarisation measurements of quasar light

Alexandre Payez

in collaboration with J.R. Cudell and D. Hutsemékers

Interactions Fondamentales en Physique et en AstrophysiqueUniversité de Liège

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Searching for ALPs using their coupling with light

− 2

− 4

− 6

− 8

− 10

− 12

− 14

− 16

log

g

[G

eV

]10

− 14 − 12 − 10 − 8 − 6 − 4 − 2 0 2 4 6 8 10log m [eV]

10

−1

Adapted from

D. Cadamuro, PhD thesis

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Axion-like particles couple to one direction of polarisation

Pseudoscalar φ: Lφγγ =1

4gφFµν F̃

µν = −gφ(~E · ~B) = −gφ(~Er · ~B) = −gφ(~Er,‖ · ~B)

Dichroism:⇒ Changes linear polarisation

Birefringence:⇒ Changes circular polarisation

[Sikivie (1983)], [Maiani et al (1986)], [Ra�elt, Stodolsky (1988)], ...

⇓rich phenomenology

Remarks:

- any Stokes parameter: evolution → θ and ∆µ2

ωz (in a given ~B region)

- averaging over bandwidths → reduce circular polarisation (vs. monochromatic)[Payez, Cudell, Hutsemékers, PRD (2011)]

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Polarimetry is a useful tool

The mixing can be very e�cient at producing polarisation

& contradict precise quasar polarisation data

⇒ derive constraints

Recent example

→ rotation of UV polarisation angle (↔ quasar morphology)[Horns et al. (2012)], [di Serego Alighieri et al. (2010)]

This work

→ consider quasar classes with smallest intrinsic polarisations in visible

⇒ compare amount due to the mixing with observations (plin and pcirc)

[Payez, Cudell, Hutsemékers, JCAP (2012)]

rarely measured4|12

Quasar circular polarisation measurements in visible lightEuropean Southern Observatory, La Silla

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Towards the North Galactic Pole directionMost observed objects are located in that direction; z ∈ [0.4, 2.2]

[Courtois et al. (2013)]

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De�ning our sample

Quasar circular polarisation data in visible light

[Hutsemékers et al. (2010)]

Bessell V �lter; typical uncertainties < 0.1%

Subsample for our contraints on ALPs

only V-�lter data (�more monochromatic�)

only the least polarised classes

ω (eV)

V-filter

response

2.82.62.42.221.8

1

0.5

0

0.80.70.60.50.40.30.20.10

12

10

8

6

4

2

0

Circular polarisation degree (%)

Frequency

In factno evidence for non-vanishing pcirc @ 3σ(except for 2 blazars with plin > 20%)

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Linear polarisation data for quasars in that direction (from catalogs)


Filter not as crucial for plin


876543210

20

15

10

5

0

19 non-BAL in V-filter55 non-BAL

Linear polarisation degree (%)

Frequency

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47 BAL in V-filter53 BAL

Linear polarisation degree (%) 8|12




Filter not as crucial for plin


876543210

20

15

10

5

0



Frequency

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Last relevant magnetic �eld encountered

Towards center of local supercluster

Magnetic �eld

Faraday Rotation [Vallée (2002, 2011)]:Domain structure≈ 100 kpc random cells with ≈ 2 µG adding up to ≈ 10 Mpc

NB @ supercluster scale: 5�10 times smaller

Only detection available for local supercluster

gB always appear together: one can rescale

Electron density

In superclusters, ne ∼ 10−6 cm−3; ωp ∝√ne

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Conservative method

Start with unpolarised light (very conservative, especially for pcirc)

For each couple (m, g):

1 Generate random con�guration

2 Solve axion-photon mixing → polarisation generated

3 Probability to be smaller than the observed one?

P = N(pobs ≥ pth)/Ntot

4 Repeat and average over many con�gurations

con�guration

def=

{domain sizes, magnetic �eld directions (3D), electron densities

}

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New constraints on axion-like particles

[Payez, Cudell, Hutsemékers, JCAP (2012)]See next edition of the Review of Particle Properties (Particle Data Group)

3σ2σ1σ

CAST

SN1987A

m (eV)

g|~ B

dom

ain|

|~ Bdom

ain

,0|(G

eV−1)

10−1210−1410−1610−1810−2010−22

10−10

10−11

10−12

10−13

10−14

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New constraints on axion-like particlesIllustration of distributions corresponding to a 2σ C.L. exclusion; m = 10−20 eV


3σ2σ1σ

CAST

SN1987A

m (eV)

g|~ B

dom

ain|

|~ Bdom

ain

,0|(G

eV−1)

10−1210−1410−1610−1810−2010−22

10−10

10−11

10−12

10−13

10−14

121086420

below this valueall data are


Frequency

876543210



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New constraints on axion-like particlesIllustration of distributions corresponding to a 3σ C.L. exclusion; m = 10−20 eV


3σ2σ1σ

CAST

SN1987A

m (eV)

g|~ B

dom

ain|

|~ Bdom

ain

,0|(G

eV−1)

10−1210−1410−1610−1810−2010−22

10−10

10−11

10−12

10−13

10−14

121086420



Frequency

876543210



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New constraints on axion-like particlesEvolution of the plateau with the average electron density


3σ2σ1σ

CAST

SN1987A

ne,0 (×10−6 cm−3)

g|~ B

dom

ain|

|~ Bdom

ain

,0|(G

eV−1)

10210110010−110−2

10−10

10−11

10−12

10−13

10−14

11|12

Summary

Mixing predicts more polarisation than observed for least polarised quasars→ Improve current bounds on axion-like particles using plin and pcirc

Conservative method (unpolarised, only inside supercluster)

Stable constraints

How well do we know the magnetic �eld?→ make explicit the dependence on typical magnetic �eld strength

and mean electron density

Prospects

Future: X-ray polarimetry = extremely interesting for astrophysical region→ could lead to new constraints or a discovery

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- 21 measurements in white light (compilation)

- 21 measurements using a Bessell V �lter; typical uncertainties < 0.1%

⇒ Optical circular polarisation compatible with zero at 3σ for all objects**except 3 (1+2) highly linearly polarised blazars (plin > 20%)




⇒ 18 objects, 16 in the same direction

ω (eV)

V-filter

response

2.82.62.42.221.8

1

0.5

0

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- 21 measurements in white light (compilation)

- 21 measurements using a Bessell V �lter; typical uncertainties < 0.1%

⇒ Optical circular polarisation compatible with zero at 3σ for all objects**except 3 (1+2) highly linearly polarised blazars (plin > 20%)




⇒ 18 objects, 16 in the same direction0.80.70.60.50.40.30.20.10

12

10

8

6

4

2

0


Frequency

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Towards the North Galactic Pole directionThese 16 quasars have z ∈ [0.4, 2.2]

[Courtois et al. (2013)]

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only su�ciently precise measurements

plin/σplin ≥ 2 if plin ≥ 0.6%

σplin≤ 0.3% if plin ≤ 0.6%

debiased data at low signal-to-noise ratio


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15

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Frequency

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Frequency

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Linear polarisation degree (%) 15|12









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The reason why it can be reduced

Considering:

- �xed-energy solutions

- a single ~B region.

NB: ~E⊥,‖ = iω~A⊥,‖(temporal gauge)

In the basis (~e⊥, ~e‖):

A⊥(z) does not feel the interaction (decoupled);

Equation of motion for A‖(z) and φ(z):[(ω2 +

∂2

∂z2

)−M(ω)

](A‖(z)φ(z)

)= 0;

⇒ �C(z)� & �D(z)� = mixtures of A‖ and of φ, with eigenvalues µC,D(ω).

⇒ Phase-shift depends on ω, so does circular polarisation

Wave packets = �averaging over ω�

⇒ % 〈v(z)〉ω, as circular polarisation v(z , ω) can be positive or negative

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Axion�photon coupling and Primako� e�ect

~E = ~Er + ~E , ~B = ~Br + ~B; ~Er , ~Br : orthogonal �elds of the radiationreminder: ~Er de�nes the direction of polarisation

~E , ~B: possible external transverse �eldsfor astrophysical applications: usually ~B 6= 0, ~E = 0

γ polarised // to ~B in the case of pseudoscalar φ:

Lφγγ,ps =1

4gφFµν F̃

µν = −gφ(~E · ~B) = −gφ(~Er · ~B) = −gφ(~Er,‖ · ~B)

γ polarised ⊥ to ~B in the case of scalar φ:

Lφγγ,sc =1

4gφFµνF

µν =1

2gφ(~B2 − ~E 2)

and in (~̂B)2 there is ~B · ~Br ( 6= 0 for non-zero coupling)

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Polarimetric constraints on axion-like particlesaxion-wimp2013.desy.de/e201031/e213180/Payez.pdf ·...

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