Detecting Chameleons: The Astronomical Polarization Produced by Chameleon-like Scalar Fields

TL;DR

The paper analyzes chameleon-like scalar fields (including Olive-Pospelov variants) that couple to photons, leading to photon–scalar mixing in magnetic fields and producing both linear and circular polarization with characteristic frequency dependence. It develops a Stokes-vector formalism for propagation through many magnetic domains, deriving analytic results in weak and maximal mixing limits and providing a fitting expression for mean polarization across regimes. By applying these results to a broad set of astrophysical observations—starlight, quasars, GRBs, the Crab Nebula, and CMB considerations—it derives the strongest current bounds on the photon–chameleon coupling, with starlight and high-redshift quasars driving the most stringent limits. Notably, a tentative nonzero signal is reported in galactic starlight polarization, while the distinctive circular-polarization signature in the 1–1000 Å range emerges as a potential smoking-gun test for chameleon-like theories. If future short-wavelength circular polarization measurements do not reveal the predicted peak, much of the parameter space for such models would be strongly constrained, underscoring the practical impact of polarization astronomy for testing beyond-Standard-Model scalar fields.

Abstract

We show that a coupling between chameleon-like scalar fields and photons induces linear and circular polarization in the light from astrophysical sources. In this context chameleon-like scalar fields includes those of the Olive-Pospelov (OP) model describing a varying fine structure constant. We determine the form of this polarization numerically and give analytic expressions in two useful limits. By comparing the predicted signal with current observations we are able to improve the constraints on the chameleon-photon coupling and the coupling in the OP model by over two orders of magnitude. It is argued that, if observed, the distinctive form of the chameleon induced circular polarization would represent a smoking gun for the presence of a chameleon. We also report a tentative statistical detection of a chameleon-like scalar field from observations of starlight polarization in our galaxy.

Figures (6)

• Figure 1: Dependence of the mean linear polarization, $\bar{p}$, in the maximal mixing limit on the intrinsic polarization ($p_{0}$). The solid line is the exact value of $\bar{p}$ whereas the dashed line is the value calculated from the fitting formula Eq. (\ref{['fpbar3']}). The thin dotted line shows $\bar{p} = p_{0}$ as would be the case when chameleon photon mixing is weak or non-existent. We can see that for $p_{0} \lesssim 90\%$ maximal chameleon-photon mixing increases the average linear polarization, whereas for $p_{0} \gtrsim 90\%$ it slightly decreases it.
• Figure 2: Probability of measuring the linear polarization degree ($p$) less than some $p_{\rm m}$ for a random object if chameleon-photon mixing is maximal.
• Figure 3: Dependence of the total polarization degree, $p$, the linear polarization degree, $m_{l}$ and the circular polarization degree $q$ on wavelength for two hypothetical objects with $N = 100$ and $NP_{\rm max} \ll 1$. Here $\lambda_{\rm crit} = 4\pi^2/\vert m_{\rm eff}^2\vert L$ where $L$ is the coherence length of the magnetic field regions. The total path length of the light through the magnetic field is given by $L_{\rm path} = NL$. We define $\lambda_{\rm osc} = \lambda_{\rm crit}/N$. We have assumed that initially $p=0$ and that there is no initial chameleon flux.
• Figure 4: Dependence of the total average polarization degree, $\bar{p}$, and r.m.s. circular polarization degree, $\bar{q}$, when averaged over many sources, each with $N = 100$ and $N P_{\rm max} \approx N(BL/2M)^2 \ll 1$. Here $\lambda_{\rm crit} = 4\pi^2/\vert m_{\rm eff}^2\vert L$ where $L$ is the coherence length of the magnetic field regions. The total path length of the light through the magnetic field is given by $L_{\rm path} = NL$. We define $\lambda_{\rm osc} = \lambda_{\rm crit}/N$. Initially we have assumed that $p=0$ and that there is no initial chameleon flux.
• Figure 5: Simulated data for two objects whose light has passed through roughly $1\,{\rm Mpc}$ of the magnetic field of a typical galaxy cluster. We have assumed $m_{\phi} \ll 2.2 \times 10^{-12}\,{\rm eV}$ and $M = 10^{10} \,{\rm GeV}$; which corresponds to strong mixing for wavelengths of $\lambda_{\rm max} \approx 24 \lambda_{\rm crit}$. We have assumed that both objects have little or no intrinsic circular polarization, and are $50\%$ linearly polarized prior to chameleon mixing. Qualitatively similar behaviour is seen for different values of the intrinsic linear polarization, $m_{l0}$, and in particular the behaviour CP fraction does not depend greatly on $m_{l0}$.