Modeling of Rayleigh Scattering and Interstellar Polarization for Evolved Late-Type Stars

TL;DR

This work addresses interpreting polarization in evolved late-type stars when interstellar polarization (ISP) complicates the signal. It develops a hybrid model that combines intrinsic Rayleigh scattering from the star with the Serkowski ISP, and conducts a parameter study to map how the total polarization and position angle behave. The key finding is that the hybrid polarization deviates from the classic $\lambda^{-4}$ Rayleigh slope, with the PA becoming wavelength-dependent and anomalous slopes arising when the stellar and ISP position angles differ; short wavelengths enhance Rayleigh-dominated changes. Applying the model to the carbon star R Scl demonstrates that observable polarization variabilities can be consistent with Rayleigh scattering despite ISP, providing practical guidance for photopolarimetric analysis of unresolved cool stars.

Abstract

Evolved late-type stars are frequently identified as photometric and spectroscopic variables, such as Mira-type or semi-regular variable objects. These stars can also be polarimetrically variable, an indicator of non-spherical geometry for spatially unresolved sources. Departures from symmetry can arise in a number of ways, such as the presence of a binary companion (e.g., multiple illumination sources for scattered light), brightness variations in the stellar atmosphere (e.g., large convective cells), or aspherical circumstellar envelopes (e.g., disks or aspherical stellar winds). Common polarigenic opacities for cool stars include Rayleigh scattering and dust scattering. The classic wavelength dependence of lambda^-4 for Rayleigh single scattering is generally straightforward; however, that signature can be confounded by interstellar polarization (ISP). We explore strategies for interpreting polarimetric observations when the interstellar polarization (ISP) cannot be removed. We introduce a "hybrid" spectrum that includes both Rayleigh polarization for a stellar contribution and the Serkowski Law for an interstellar contribution. We find the polarization spectral slope can be more shallow than expected from Rayleigh scattering alone. For stellar variability, shorter wavelengths give higher amplitude changes when Rayleigh scattering dominates the interstellar signal. Quite anomalous slopes can occur over limited wavelength intervals if the stellar and interstellar position angles differ by 90 deg. Results of the models are discussed in the context of photopolarimetry methods, and an application is considered in terms of variable polarization from the carbon star, R Scl.

Figures (7)

• Figure 1: Models of continuum polarization spanning from FUV through NIR wavelengths, displayed in log-log plots for parameters identified in Tab. \ref{['tab1']}. In the two left panels, the position angles $\psi_\ast$ and $\psi_I$ are held constant while $p_{\rm max}$ is varied (upper left) or $p_\ast$ is varied (lower left). The blue curve at upper left is the fixed stellar polarization whereas the red curve at lower left is the fixed interstellar polarization. In the two right panels, the polarization scales $p_{\rm max}$ and $p_\ast$ are held constant. At upper right the stellar position angle $\psi_\ast$ varies, whereas at lower right it is $\psi_I$ that varies. Again blue and red are for the fixed stellar and interstellar polarizations, respectively. Also, because $p_{\rm max}$ and $p_\ast$ are fixed, the upper and lower right panels are redundant, since what actually matters is the relative position angle, $|\psi_\ast-\psi_I|$.
• Figure 2: Polarization position angles plotted with wavelength (c.f., the right-side panels for Fig. \ref{['fig1']} and Tab. \ref{['tab1']}). In the upper panel, the fact that $\psi_I$ is constant is signified by all PAs converging to zero at longer wavelengths. In the lower panel, the trend is opposite, where all PAs converge to zero at short wavelengths because $\psi_\ast$ is now held constant.
• Figure 3: The same models as in Fig. \ref{['fig1']} now plotted with polarization as linear against inverse wavelength, $1/\lambda$, with $\lambda$ in microns. This version portrays the models in a format sometimes adopted by observers.
• Figure 4: The calculations from Fig. \ref{['fig1']} for polarization now limited to optical wavelengths. Superposed in colored dotted curves are the standard passband responses for UBVRIZ filters as red, green, blue, magenta, cyan, and orange. These are peak normalized and scaled to the figure.
• Figure 5: The calculations from Fig. \ref{['fig2']} for polarization position angle now limited to optical wavelengths. Superposed in colored dotted curves are the standard passband responses for UBVRIZ filters. These are peak normalized and scaled to the figure.