Forecasting synchrotron spectral parameters with QUIJOTE-MFI2 in combination with Planck and WMAP

We present a parametric component separation forecast for the QUIJOTE-MFI2 instrument (10-20 GHz), assessing its impact on constraining polarised synchrotron emission at $1^\circ$ FWHM and $N_{\rm side}=64$. Using simulated sky maps based on power-law and curved synchrotron spectra, we show that adding QUIJOTE-MFI2 to existing WMAP+$Planck$+MFI data yields statistically unbiased parameter estimates with substantial uncertainty reductions: improvement factors reach $\sim$10 for the synchrotron spectral index ($\beta_s$), $\sim$5 for the curvature parameter ($C_s$), and $\sim$43 for polarisation amplitudes in bright regions. Deep QUIJOTE cosmological fields enable $\beta_s$ constraints even in intrinsically low SNR regions where WMAP+$Planck$ alone remain prior-dominated. Current combined sensitivities are insufficient to detect a synchrotron curvature of $C_s=-0.052$ on a pixel-by-pixel basis, but a $2\sigma$ detection is achievable for $|C_s|\gtrsim 0.14$ in the brightest regions of the Galactic plane. In those deep cosmological fields, combining QUIJOTE-MFI2 with WMAP and $Planck$ reduces the median synchrotron residual at 100 GHz by a factor of 6, to 0.033 $\mu$K$_{\rm CMB}$. These results demonstrate that QUIJOTE-MFI2 will provide critical low-frequency information for modelling Galactic synchrotron emission, offering valuable complementary constraints for future CMB surveys such as LiteBIRD and the Simons Observatory.