The THRILS Factor: Investigating the properties of Little Red Dots (LRDs) at 3<z<6 with JWST/NIRSpec

JWST has uncovered a class of objects called LRDs, whose nature is still widely debated. In this work, we present a comprehensive spectroscopic analysis of nine LRDs in the Extended Groth Strip (EGS) field studied as part of THRILS and C3PO, both JWST Cycle 3 programs. These targets, photometrically selected based on their compact red appearance, are observed with deep spectroscopic exposures (at least8 hours), enabling robust detections of broad Balmer lines, He I emission, and other spectral features characteristic of AGN activity. Using the [SII] λ lambda6716,6731 doublet, we find electron densities (n e) between 2.33 < (n e) < 2.97 cm-3, comparable to those in narrow line regions (NLR) of local AGN and high- z galaxies. The spectroscopic depth further enables detailed characterization of broad Balmer line profiles. We fit both Gaussian and convolved exponential models to each source and find that five LRDs are statistically better described by the latter model. We measure optical depths τ sc = 0.56-0.91, scattering fractions f SC = 0.40-0.82 which correspond to column densities log(N e) about 23.93-24.14 cm-2, and covering fractions c f = 0.43-0.59. These results indicate a clumpier broad line region (BLR) geometry that deviates from conventional LRD models, which predict covering fractions close to unity. Furthermore, these Compton-thick gas columns may explain the X-ray weakness of LRDs. We also find that THRILS LRDs are narrow-line dominated compared to literature AGN-dominated LRDs, and show that exponential profile fitting corrects for systematic overestimation of black hole masses from Gaussian-based measurements.