Although the magnetospheric accretion model has been extensively applied to T Tauri Stars with typical mass accretion rates, the very low accretion regime is still not fully explored. Here we report multi-epoch observations and modeling of CVSO 1335, a 5 Myr old solar mass star which is accreting mass from the disk, as evidenced by redshifted absorption in the H$alpha$ profile, but with very uncertain estimates of mass accretion rate using traditional calibrators. We use the accretion shock model to constrain the mass accretion rate from the Balmer jump excess measured with respect to a non-accreting template, and we model the H$alpha$ profile, observed simultaneously, using magnetospheric accretion models. Using data taken on consecutive nights, we found that the accretion rate of the star is low, $4-9 times 10^{-10} ,$ M$_{odot},$ yr$^{-1}$, suggesting a variability on a timescale of days. The observed H$alpha$ profiles point to two geometrically isolated accretion flows, suggesting a complex infall geometry. The systems of redshifted absorptions observed are consistent with the star being a dipper, although multi-band photometric monitoring is needed to confirm this hypothesis.
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