Statistical methods for the analysis of rotation measure grids in - - PowerPoint PPT Presentation

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Statistical methods for the analysis of rotation measure grids in - - PowerPoint PPT Presentation

Aug 16, 2023 26 likes •290 views

Statistical methods for the analysis of rotation measure grids in large scale structures Valentina Vacca Main collaborators: N. Oppermann, T. Enlin, M. Selig, M. Greiner, H. Junklewitz, J. Jasche, M. Reinecke Other people involved: E.

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SLIDE 1

Statistical methods for the analysis of rotation measure grids in large scale structures Valentina Vacca

Main collaborators:

  • N. Oppermann, T. Enßlin, M. Selig, M. Greiner, H.

Junklewitz, J. Jasche, M. Reinecke Other people involved:

  • E. Carretti, L. Feretti, C. Ferrari, G. Giovannini, F. Govoni, C.

Hales, C. Horellou, S. Ideguchi, M. Johnston-Hollitt, M. Murgia, R. Paladino, R. F. Pizzo, A. Scaife

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SLIDE 2

Introduction Approach Results Perspectives Conclusions

OUTLINE

1

Context and general description

2

Bayesian approach

3

Test of the code and results with real data

4

Future developements

5

Summary and conclusion

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SLIDE 3

Introduction Approach Results Perspectives Conclusions

CONTEXT

GOAL: Study the origin and evolution of cosmic magnetism

CREDIT: Klaus Dolag

LOFAR-UK station Guy Gratton (c) 2011, hosted by STFC. SKA spaceref.com

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SLIDE 4

Introduction Approach Results Perspectives Conclusions

FARADAY DEPTH

φi = a0 xi

dx ne Bx

(1 + z)2 φ2

i ∼

xi

dx

(1 + z)4 a2

0n2 eB2 x λx

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SLIDE 5

Introduction Approach Results Perspectives Conclusions

FARADAY DEPTH

  • galaxy cluster

filament voids

  • φi = a0

xi

dx ne Bx

(1 + z)2 φ2

i ∼

xi

dx

(1 + z)4 a2

0n2 eB2 x λx

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SLIDE 6

Introduction Approach Results Perspectives Conclusions

FARADAY DEPTH

  • galaxy cluster

filament voids

  • φ2

i ∼ σ2 i,gal + σ2 i,int + σ2 i,env

≈ σ2

i,gal +

eχ0

(1 + zi)4+χ2 + L(zi)

L0 eχ1

L(zi) =

zi

c H0

  • Wm(1 + zi)3 + Wc(1 + zi)2 + Wl

dz

(1 + zi)5

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SLIDE 7

Introduction Approach Results Perspectives Conclusions

AVAILABLE INFORMATION

FARADAY ROTATION CATALOG FOR 37543 SOURCES FROM NVSS Taylor et al. (2009)

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SLIDE 8

Introduction Approach Results Perspectives Conclusions

AVAILABLE INFORMATION

GALACTIC AND EXTRAGALACTIC CONTRIBUTION di = φg,i + φe,i + ni Oppermann et al. (2012, 2014) (see Torsten’s talk)

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SLIDE 9

Introduction Approach Results Perspectives Conclusions

AVAILABLE INFORMATION

REDSHIFT CATALOG

−3.5 −3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 log(z) 0.0 0.2 0.4 0.6 0.8 1.0 Number of Sources

real

LOFAR UK

Hammond et al. (2012)

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SLIDE 10

Introduction Approach Results Perspectives Conclusions

AVAILABLE INFORMATION

REDSHIFT CATALOG

1 2 3 4 5 6 z 0.0 0.2 0.4 0.6 0.8 1.0 Contribution

Intrinsic Environment

σ2

int ∝

eχ0

(1 + zi)4+χ2 σ2

env ∝ eχ1 L(zi)

L0

χ0 = 0. χ1 = −2. χ2 = −2.5

z≤3: 3947 sources z>3: 56 sources

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SLIDE 11

Introduction Approach Results Perspectives Conclusions

AVAILABLE INFORMATION

REDSHIFT CATALOG

1 2 3 4 5 6 z 0.0 0.2 0.4 0.6 0.8 1.0 Contribution

Intrinsic Environment

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Number of sources

σ2

int ∝

eχ0

(1 + zi)4+χ2 σ2

env ∝ eχ1 L(zi)

L0

χ0 = 0. χ1 = −2. χ2 = −2.5

z≤3: 3947 sources z>3: 56 sources

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SLIDE 12

Introduction Approach Results Perspectives Conclusions

Algorithm: Gibbs sampling

RM catalog redshift zi Oppermann Galactic re- construction algorithm φe,i sample Metropolis- Hasting sampling Contributions: χ0, χ1, χ2, ... Galactic profile + power spectrum prior σ2

e(zi, χj)

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SLIDE 13

Introduction Approach Results Perspectives Conclusions

Test: 500 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 14

Introduction Approach Results Perspectives Conclusions

Test: 500 LOS

− 4 − 2 2 4 0.0 0.2 0.4 0.6 0.8 1.0

χ1

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SLIDE 15

Introduction Approach Results Perspectives Conclusions

Test: 500 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 16

Introduction Approach Results Perspectives Conclusions

Data selection

σpost < 5.0 rad/m2

−1.0 −0.5 0.0 0.5 1.0 sin(b) 5 10 15 20 posterior standard deviation rad/m2

# los ∼ 500 Oppermann et al. (2014)

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SLIDE 17

Introduction Approach Results Perspectives Conclusions

Real data: 500 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 18

Introduction Approach Results Perspectives Conclusions

Lofar: 3500 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 19

Introduction Approach Results Perspectives Conclusions

Lofar: 3500 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 20

Introduction Approach Results Perspectives Conclusions

SKA: 4000 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 21

Introduction Approach Results Perspectives Conclusions

SKA: 40000 LOS

0.0 0.2 0.4 0.6 0.8 1.0 −40 −20 20 40 −40 −20 20 40 − 4 − 2 2 4 −5.0 −2.5 0.0 2.5 5.0 − 4 − 2 2 4 − 4 − 2 2 4 − 5 . − 2 . 5 . 2 . 5 5 .

χ0 χ1 χ2 χ3 χ3 χ2 χ1 φ2

e,i = 100

  • eχ0

(1+zi)4+χ3 + L(zi) L0 eχ1 + p(b)eχ2

  • rad2/m4

intrinsic environment b-depend. z-depend.

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SLIDE 22

Introduction Approach Results Perspectives Conclusions

Second step

  • galaxy cluster

filament voids

  • {

l

{

l li3

i1 i4 i

li2

{

{

  • i

φ2

i ∼ σ2 i,int +

xi

dx

(1 + z)4

  • lij

a2

0n2 eB2 x λx

  • χj

, ≈ eχi0 + li1eχ1 + li2eχ2 + li3eχ3 + li4eχ4 + li5eχ5

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SLIDE 23

Introduction Approach Results Perspectives Conclusions

ADDITIONAL AVAILABLE INFORMATION

Jasche et al. (2010)

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SLIDE 24

Introduction Approach Results Perspectives Conclusions

ADDITIONAL AVAILABLE INFORMATION

φ2

e,i ∼ exp(χ0) + ΣN j=1lijexp(χj)

Cosmic web structure, redshift catalog → length matrix lij Jasche et al. (2010)

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SLIDE 25

Introduction Approach Results Perspectives Conclusions

Conclusions

  • Present data do not allow yet the detection of the

intrinsic and environment contribution but with Lofar we could infer information if the contributions are ∼ few rad/m2, and with SKA even if they are ∼ 0.5 rad/m2;

  • Proper reconstruction of the large scale structure up to

high redshift as well as a proper modeling of the magnetic Universe is needed to test the algorithm for investigating magnetic fields in the different environments and make predictions.

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SLIDE 26

Introduction Approach Results Perspectives Conclusions

THANK YOU!