Constraining spatial variations of the fine structure constant using clusters of galaxies and Planck data I. de Martino*, C.J.A.P. Martins, H. Ebeling, D. Kocevski arXiv:1605.03053 Foreground cleaned Planck 2013 Nominal data
Methodology Ingredients • X-ray cluster catalog with well measured positions and redshifts • Planck 2013 Nominal maps
.
We produced cleaned patches P(ν, x) centered on each cluster position x and on each maps of frequency ν as Σx∈RP(ν, x)P(857 GHz, x) P(ν, x) = P(ν, x) − w(ν)P(857 GHz, x) where w(ν) = , (R = [θcl , θpatch]) 2 Σx∈R[P(857 GHz, x)] Examples of cleaned galaxy clusters
A1656
Recent observational studies suggest that the fine structure constant could vary over the sky. Such spatial variation has been mainly studied using a large archival dataset of metal absorption lines in the redshift range z = [0.3 − 4.2] along the line-of-sight of bright quasar, and its dipole amplitude has been measured to be ∆α/α = (12±2)×10−6 with a best fit dipole direction (RA,DEC)=(17.3±1hours, −61◦ ±10◦) [1, 2]. It is important to explore additional independent tests that may verify or rule out the spectroscopic result. In the present work we focus on a complementary analysis, at lower redshifts, which can be carried out using current and forthcoming multi-frequency measurements of galaxy clusters. Clusters of galaxies contain a hot Intra-Cluster Medium (ICM) which reaches temperatures in the range Te ∼ 1 − 10keV. CMB photons are scattered off by the hot electrons of the ICM by means of the Sunyaev Zeldovich effect. This process produces secondary anisotropies on the CMB power spectrum which have two components: the thermal Sunyaev Zeldovich effect (TSZ) due to the thermal motion of the electron in ICM medium, and the kinematic one (KSZ) due to the peculiar velocity of the cluster with respect to the isotropic CMB frame. The TSZ anisotropies induced by clusters of galaxies along the line of sight l are usually expressed in terms of the Comptonization parameter Yc Z kB σT ∆TTSZ = T0G(x)Yc = T0G(x) 2 Te(l)ne(l)dl, (1) mc l where in the non relativistic limit G(x) = xcoth(x/2) − 4, where x = hν(z)/kB TCMB (z) is the reduced frequency and TCMB (z) is the CMB black-body temperature at the cluster location. In the concordance ΛCDM model TCMB,std (z) = T0(1 + z). However, in particular classes of models, the evolution of the CMB temperature can be related to that of other observables and thus, there will be both variations of the fine-structure constant and violations of the standard TCMB (z) law [3]: TCMB (z) ∆α . (2) ∼ (1 + z) 1 + T0 α Therefore, if one is able to determine the CMB temperature at the cluster location using the SZ effect, the relation in eq. (2) can be used as a phenomenological relation to observationally test the spatial variation of α.
PSZ1 G081.01-50.92
Introduction
Recipe STEP 1: Let us clean the Planck 2013 Nominal maps from foreground emission (i.e. thermal dust, CO lines, synchrotron and etc...) STEP 2: Let us measure the TSZ emission at cluster location and extract the CMB temperature. Let us note that the frequency dependence of the TSZ effect depends by the CMB temperature: g(ν) 7−→ g(ν, TCMB (z)).
Results Best fit parameters from the MCMC analysis for the Models 1 and 2
Model 1
STEP 3: Once we have extracted the TCMB (z) from the data, we are ready to estimate the variation of the fine structure constant at cluster location: ∆α TCMB (z) −1 = 1− , α obs T0(1 + z)
MCMC priors Test
m
(A) 0 (B) [−1, 1] (C) 0 (D) [−1, 1]
d [−1, 1] [−1, 1] [−1, 1] [−1, 1]
RA DEC Npar (◦ ) (◦) 261.0 −58.0 1 261.0 −58.0 2 [0, 360] [−90, +90] 3 [0, 360] [−90, +90] 4
References
Theoretical models Model 1. ∆α = m + d cos(Θ), α th
Model 2.
∆α α th = m + dr(z) cos(Θ),
where m and d are the monopole and dipole amplitudes, Θ is the angle on the sky between the line of sight of each cluster and the best fit dipole direction, and r(z) is the look-back time in the concordance ΛCDM model. Conclusions
[1] Webb, J. K., et al. Phys. Rev. Lett., 107 (2011) 191101 [2] King, J. A., et al. MNRAS 422 (2012) 3370 [3] Avgoustidis, A., et al. JCAP 06 (2014) 62 [4] Mariano, A., Perivolaropoulos, L. Phys. Rev. D 86 (2012) 083517 [5] Mariano, A., Perivolaropoulos, L. Phys. Rev. D 87 (2013) 043511 [6] Kashlinsky, A., et al. ApJ Lett 686 (2008) L49 [7] Kogut, A., et al. ApJ, 419 (1993) 1 [8] Vielva, P., et al. ApJ, 609 (2004) 22
We use the Planck 2013 data to measure the TSZ effect at the location of 618 X-ray selected clusters. We then use a MCMC algorithm to obtain the temperature of the CMB at the location of each galaxy cluster. When fitting two different phenomenological parameterizations allowing for monopole and dipole amplitudes in the value of the fine structure constant we improve the results of earlier analysis involving clusters and CMB power spectrum, and we also found that the best-fit direction of a hypothetical dipole is compatible with the direction of other known anomalies.
Model 2
and to compare it with the theoretical predictions. We carry out 4 different MCMC analysis: (A) we assume the monopole amplitude to be zero and the direction of the dipole to be the best fit ones from quasar. The model has one free parameter (i.e. the dipole amplitude). (B) we still keep the direction of the dipole fixed at the best fit ones from quasar, but we leave the monopole and dipole amplitudes free to vary. In (C) and (D) we repeat the analysis as they are in (A) and (B) leaving the direction of the dipole free to vary.
(A) (B) (C) (D) (A) (B) (C) (D)
m
d
0.0 0.006 ± 0.004 0.0 0.021 ± 0.029 0.0 0.006 ± 0.005 0.0 0.019 ± 0.011
−0.002 ± 0.008 −0.008 ± 0.009 −0.030 ± 0.020 −0.030 ± 0.014 −0.003 ± 0.003 GLyr−1 −0.003 ± 0.005 GLyr−1 −0.042 ± 0.049 GLyr−1 −0.027 ± 0.051 GLyr−1
RA (◦) 261.0 261.0 255.1 ± 3.8 255.9 ± 4.2 261.0 261.0 261.6 ± 16.1 245.0 ± 12.9
DEC (◦) −58.0 −58.0 −63.2 ± 2.6 −55.3 ± 5.8 −58.0 −58.0 −61.3 ± 2.7 −56.0 ± 3.8
Visual representation of some known dipoles asymmetry directions Directions in galactic coordinates for some dipole anomalies: α-dipole from quasar [1, 2], the Dark Energy dipoles [4], Dark Flow direction [6], CMB asymmetry [5], Cold Spot anomaly [8], the intrinsic CMB dipole [7], and for our results from the analysis (C) of models 1 and 2.
Webb
et
al al
( 2011 )
King
et
Dark
Flow
Dark
Energy
CMB
asymmetry
CMB
Cold
CMB
Dipole
90
( 2012 )
Spot
Model
1 ( C )
Model
2
0
360
( C )
- 90
0 270
0 360
What’s next? Although galaxy clusters are not competitive with high-resolution optical/UV spectroscopy dataset, with next-generation of full sky CMB missions such as COrE/PRISM being able to detect & 10, 000 of SZ clusters in a much wider range of the redshifts, more detailed analyses as well as specific comparisons with particular classes of scalar field based models which include spatial and/or environmental dependencies will then become possible.
Ivan de Martino
[email protected] Departamento de Física Teórica e Historia de la Ciencia Facultad de Ciencia y Tecnología Universidad del País Vasco
270 - 30
360 - 30
