Standardized Luminosity of the Tip of the Red Giant Branch utilizing Multiple Fields in NGC 4258 and the CATs Algorithm

The Tip of the Red Giant Branch provides a luminous standard candle for calibrating distance ladders that reach Type Ia supernova (SN Ia) hosts. However, recent work reveals that tip measurements vary at the $\sim$ 0.1 mag level for different stellar populations and locations within a host, which may lead to inconsistencies along the distance ladder. We pursue a calibration of the tip using 11 Hubble Space Telescope fields around the maser host, NGC 4258, that is consistent with SN Ia hosts by standardizing tip measurements via their contrast ratios. We find $F814W$-band tips that exhibit a full 0.3 mag range and 0.1 mag dispersion. We do not find any correlation between HI column density and the apparent tip to 0.04 $\pm$ 0.03 mag/cm$^{-2}$. We search for a tip-contrast relation (TCR) and measure the TCR within the fields of NGC 4258 of $-0.015\pm0.008$ mag/$R$, where $R$ is the contrast ratio. This value is consistent with the TCR originally discovered in the GHOSTS sample (Wu et al. 2022) of $-0.023\pm0.005$ mag/R. Combining these measurements, we find a global TCR of $-0.021\pm0.004$ mag/R and a calibration of $M_I^{TRGB} = -4.025 \pm 0.035 - (R-4)\times0.021$ mag. We also use stellar models to simulate single age and metallicity stellar populations with [Fe/H] from $-2.0$ to $-0.7$ and ages from 3 Gyr to 12 Gyr and reconstruct the global TCR found here to a factor of $\sim$ 2. This work is combined in a companion analysis with tip measurements of nearby SN Ia hosts to measure $H_0$.
20 pages, 12 figures, 3 tables. Submitted to ApJ