The galaxy--electron cross-spectrum with ACT, SPT-3G and DESILS LRGs

The galaxy–electron cross-power spectrum $P_{ge}(k)$ measures the small-scale distribution of gas around galaxies, the quantity reshaped by feedback. We measure $P_{ge}$ from the kinetic Sunyaev–Zel’dovich (kSZ) signal of the photometric DESI Legacy Imaging Surveys luminous red galaxies, cross-correlating a velocity-weighted galaxy momentum template with the CMB temperature from ACT DR6 and, for the first time, SPT-3G. The absolute normalization of the cross-spectrum is fixed by a surrogate-field Monte Carlo that propagates the survey mask, lightcone evolution, and photometric-redshift weights, converting the measured pseudo-spectrum into $P_{ge}(k)$ in physical units. We detect $P_{ge}$ at $11.7\sigma$ with ACT and $8.4\sigma$ with SPT-3G, and at $12.3\sigma$ combining SPT-3G with the ACT northern cap, which it does not overlap. The two surveys have independent optics, beams, filtering and noise and share about two thirds of the SPT-3G galaxies; their amplitudes agree channel by channel, the largest difference being $0.7\sigma$. All $26$ null tests on the adopted night maps are consistent with zero signal, among them the six ACT frequency differences, the three SPT-3G frequency differences, and the four ACT cap differences of the main selection. Turning the amplitude into a gas fraction requires the host halo masses of the sample, which the cross-spectrum does not itself measure; taking them from its measured number density and from a published CMB-lensing calibration of the same galaxies, the gas within the virial radius is $25$–$33\mathrm{\%}$ of the cosmic baryon budget of the halo.