EPOCHS III: Unbiased UV continuum slopes at 6.5<z<13 from combined PEARLS GTO and public JWST NIRCam imaging

We present an analysis of rest-frame UV continuum slopes, $\beta$, using a sample of 1011 galaxies at $6.5<z<13$ from the EPOCHS photometric sample collated from the GTO PEARLS and public ERS/GTO/GO (JADES, CEERS, NGDEEP, GLASS) JWST NIRCam imaging across $178.9~\mathrm{arcmin}^2$ of unmasked blank sky. We correct our UV slopes for the photometric error coupling bias using $200,000$ power law SEDs for each $\beta=\{-1,-1.5,-2,-2.5,-3\}$ in each field, finding biases as large as $\Delta\beta\simeq-0.55$ for the lowest SNR galaxies in our sample. Additionally, we simulate the impact of rest-UV line emission (including Ly$\alpha$) and damped Ly$\alpha$ systems on our measured $\beta$, finding biases as large as $0.5-0.6$ for the most extreme systems. We find a decreasing trend with redshift of $\beta=-1.51\pm0.08-(0.097\pm0.010)\times z$, with potential evidence for Pop.~III stars or top-heavy initial mass functions (IMFs) in a subsample of 68 $\beta+\sigma_{\beta}<-2.8$ galaxies. At $z\simeq11.5$, we measure an extremely blue $\beta(M_{\mathrm{UV}}=-19)=-2.73\pm0.06$, deviating from simulations, indicative of low-metallicity galaxies with non-zero Lyman continuum escape fractions $f_{\mathrm{esc, LyC}}\gtrsim0$ and minimal dust content. The observed steepening of $\mathrm{d}\beta/\mathrm{d}\log_{10}(M_{\star}/\mathrm{M}_{\odot})$ from $0.22\pm0.02$ at $z=7$ to $0.81\pm0.13$ at $z=11.5$ implies that dust produced in core-collapse supernovae (SNe) at early times may be ejected via outflows from low mass galaxies. We also observe a flatter $\mathrm{d}\beta/\mathrm{d}M_{\mathrm{UV}}=0.03\pm0.02$ at $z=7$ and a shallower $\mathrm{d}\beta/\mathrm{d}\log_{10}(M_{\star} / \mathrm{M}_{\odot})$ at $z<11$ than seen by HST, unveiling a new population of low mass, faint, galaxies reddened by dust produced in the stellar winds of asymptotic giant branch (AGB) stars or carbon-rich Wolf-Rayet binaries.