Mapping circumstellar magnetic fields of late-type evolved stars with
  the Goldreich-Kylafis effect: CARMA observations at $\lambda 1.3$ mm of R Crt
  and R Leo
  Mapping magnetic fields is the key to resolving what remains an unclear
physical picture of circumstellar magnetic fields in late-type evolved stars.
Observations of linearly polarized emission from thermal molecular line
transitions due to the Goldreich-Kylafis (G-K) effect provides valuable insight
into the magnetic field geometry in these sources that is complementary to
other key studies. In this paper, we present the detection of spectral-line
polarization from both the thermal $J=2-1$ CO line and the $v=1, J=5-4$ SiO
maser line toward two thermal-pulsating (TP-) AGB stars, R Crt and R Leo. The
observed fractional linear polarization in the CO emission is measured as
$m_l\sim 3.1\%$ and $m_l\sim9.7\%$ for R Crt and R Leo respectively. A
circumstellar envelope (CSE) model profile and the associated parameters are
estimated and used as input to a more detailed modeling of the predicted linear
polarization expected from the G-K effect. The observed thermal line
polarization level is consistent with the predicted results from the G-K model
for R Crt; additional effects need to be considered for R Leo.
