We develop techniques for generating accurate and precise internal covariances for measurements of clustering and weak lensing angular power spectra. These methods are designed to produce non-singular and unbiased covariances for Euclid's large anticipated data vector and will be critical for validation against observational systematic effects. We construct jackknife segments that are equal in area to high precision by adapting the binary space partition algorithm to work on arbitrarily shaped regions on the unit sphere. Jackknife estimates of the covariances are internally derived and require no assumptions about cosmology or galaxy population and bias. Our covariance estimation, called DICES (Debiased Internal Covariance Estimation with Shrinkage), first estimates a noisy covariance through conventional delete-1 jackknife resampling. This is followed by linear shrinkage of the empirical correlation matrix towards the Gaussian prediction, rather than linear shrinkage of the covariance matrix. Shrinkage ensures the covariance is non-singular and therefore invertible, critical for the estimation of likelihoods and validation. We then apply a delete-2 jackknife bias correction to the diagonal components of the jackknife covariance that removes the general tendency for jackknife error estimates to be biased high. We validate internally derived covariances, which use the jackknife resampling technique, on synthetic Euclid-like lognormal catalogues. We demonstrate that DICES produces accurate, non-singular covariance estimates, with the relative error improving by $33\%$ for the covariance and $48\%$ for the correlation structure in comparison to jackknife estimates. These estimates can be used for highly accurate regression and inference.
CO(1-0) and CO(2-1) are commonly used as bulk molecular gas tracers. The CO line ratios (especially CO(2-1)/CO(1-0) - $R_{21}$) vary within and among galaxies, yet previous studies on $R_{21}$ and alike often rely on measurements constructed by combining data from facilities with substantial relative calibration uncertainties that have the same order as physical line ratio variations. Hence robustly determining systematic $R_{21}$ variations is challenging. Here, we compare CO(1-0) and CO(2-1) mapping data from ALMA for 14 nearby galaxies, at a common physical resolution of 1.7 kpc. Our dataset includes new ALMA (7m+TP) CO(1-0) maps of 12 galaxies. We investigate $R_{21}$ variation to understand its dependence on global galaxy properties, kpc-scale environmental factors, and its correlation with star formation rate (SFR) surface density and metallicity. We find that the galaxy-to-galaxy scatter is 0.05 dex. This is lower than previous studies which reported over 0.1 dex variation, likely reflecting significant flux calibration uncertainties in single-dish surveys. Within individual galaxies, $R_{21}$ has a typical mean value of ~0.64 and 0.1 dex variation, with an increase to ~0.75 towards galactic centers. We find strong correlations between $R_{21}$ and various galactic parameters, particularly SFR surface density, which shows a power-law slope of 0.10-0.11 depending on the adopted binning/fitting methods. Our findings suggest that, for studies covering main sequence galaxy samples, assuming a fixed $R_{21}$=0.64 does not significantly bias kpc-scale molecular gas mass estimates from CO(2-1). Instead, systematic uncertainties from flux calibration and the CO-to-H$_2$ conversion factor account for more systematic scatter of CO-derived molecular gas properties.
Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron injection into DSA and quantify the evolution of the nonthermal tail in self-generated electromagnetic turbulence. By analyzing electron trajectories and their momentum gain during shock-recrossing cycles, we demonstrate that electrons start participating in DSA when their speed is large enough to overrun the shock. We develop a minimal model showing that speed-dependent injection reproduces nonthermal electron spectra observed in kinetic simulations. Our findings establish a new criterion for electron DSA, which has broad implications for the nonthermal emission of shock-powered space/astrophysical systems.
this https URL . Comments are welcome!
this https URL for the FEW code, and this https URL for a data release accompanying this work