Detecting chameleons: The astronomical polarization produced by chameleonlike scalar fields

We show that a coupling between chameleonlike scalar fields and photons induces linear and circular polarization in the light from astrophysical sources. In this context chameleonlike scalar fields include those of the Olive-Pospelov (OP) model, which describes 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 2 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 chameleonlike scalar field from observations of starlight polarization in our galaxy.

Figure 1

Dependence of the mean linear polarization, $\overline{p}$, in the maximal mixing limit on the intrinsic polarization ($p_0$). The solid line is the exact value of $\overline{p}$, whereas the dashed line is the value calculated from the fitting formula Eq. (32). The thin dotted line shows $\overline{p}=p_0$ as would be the case when chameleon-photon mixing is weak or nonexistent. 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 $p_m$ 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 $N{P}_{\max }\ll 1$. Here, ${\lambda }_{\mathrm{crit}}=4{\pi }^2/|m_{\mathrm{eff}}^2|L$, 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 $L_{\mathrm{path}}=NL$. We define ${\lambda }_{\mathrm{osc}}={\lambda }_{\mathrm{crit}}/N$. We have assumed that initially $p=0$ and that there is no initial chameleon flux.

Figure 4

Dependence of the total average polarization degree, $\overline{p}$, and root mean square circular polarization degree $\overline{q}$, when averaged over many sources, each with $N=100$ and $N{P}_{\max }\approx N(BL/2M{)}^2\ll 1$. Here, ${\lambda }_{\mathrm{crit}}=4{\pi }^2/|m_{\mathrm{eff}}^2|L$, 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 $L_{\mathrm{path}}=NL$. We define ${\lambda }_{\mathrm{osc}}={\lambda }_{\mathrm{crit}}/N$. 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 Mpc of the magnetic field of a typical galaxy cluster. We have assumed $m_{\varphi }\ll 2.2\times {10}^{-12}\mathrm{eV}$ and $M={10}^{10}\mathrm{GeV}$, which corresponds to strong mixing for wavelengths of ${\lambda }_{\max }\approx 24{\lambda }_{\mathrm{crit}}$. We have assumed that both objects have little or no intrinsic circular polarization, and are 50% linearly polarized prior to chameleon mixing. Qualitatively similar behavior is seen for different values of the intrinsic linear polarization $m_{l0}$, and, in particular, the behavior $CP$ fraction does not depend greatly on $m_{l0}$.

Figure 6

Simulated data for two objects whose light has passed through roughly 1 kpc of our galaxies magnetic field. We have assumed $m_{\varphi }\ll 6.4\times {10}^{-12}\mathrm{eV}$ and $M={10}^{10}\mathrm{GeV}$. We have assumed that both objects have little or no intrinsic circular polarization. Potentially detectable levels of $CP$ are seen between ${\lambda }_{\mathrm{osc}}\approx 12\AA$ and ${\lambda }_{\mathrm{crit}}\approx 608\AA$.