Constraining spatial variations of the fine structure constant using clusters of galaxies and Planck data

We propose an improved methodology to constrain spatial variations of the fine structure constant using clusters of galaxies. We use the Planck 2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of 618 x-ray selected clusters. We then use a Monte Carlo Markov Chain algorithm to obtain the temperature of the cosmic microwave background at the location of each galaxy cluster. When fitting three different phenomenological parametrizations allowing for monopole and dipole amplitudes in the value of the fine structure constant we improve the results of earlier analysis involving clusters and the cosmic microwave background power spectrum, and we also find that the best-fit direction of a hypothetical dipole is compatible with the direction of other known anomalies. Although the constraining power of our current data sets do not allow us to test the indications of a fine structure constant dipole obtained though high-resolution optical/UV spectroscopy, our results do highlight that clusters of galaxies will be a very powerful tool to probe fundamental physics at low redshift.

Figure 1

Distribution on the sky of the clusters in our sample.

Figure 2

(a) Average of the temperature anisotropy as a function of frequency for the three selected clusters evaluated on the Planck 2013 nominal map on disks of radius ${\theta }_{500}$. (b) TSZ anisotropy measured on a disk of size ${\theta }_{500}$ on our foreground cleaned patches. (c) Average temperature anisotropy evaluated in a ring placed around the three clusters. Red circles and blue squares have been shifted by $\pm 5\mathrm{GHz}$ for easier viewing.

Figure 3

Best fit to the TSZ temperature anisotropies of the three clusters represented in Fig. 2. For each cluster we plot the best-fit model obtained considering the relativistic corrections to the frequency dependence.

Figure 4

Directions in galactic coordinates for the spatial variation of the fine structure constant from [1] and [2] in blue and cyan, respectively, for the dark energy dipoles from [9] in green, dark flow direction from [11, 14, 15, 16, 17] in red, for the CMB asymmetry from [10] in yellow, and for our results from the analysis (C) of models 1, 2 and 3 in orange, magenta and brown, respectively. Finally, we also indicate in blue and green dashed circles the direction of the Cold Spot anomaly and the intrinsic CMB dipole, respectively [12, 13, 18].

Figure 5

Comparison of our constraint with the ones reported in previous works. In (a) and (b) we show the results from model 2 and 1, respectively. See the main text for a discussion.