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The fundamental plane (FP) relation connects gamma-ray luminosity tointrinsic pulsar properties, offering the potential to estimate distances forradio-quiet (RQ) gamma-ray pulsars, where direct measurements are oftenunavailable. The Fermi Third Pulsar Catalog presents spectral data for 294gamma-ray pulsars, including 72 RQ pulsars, of which only 9 have knowndistances. This study investigates the FP relation's potential to predictdistances for RQ gamma-ray pulsars using machine learning (ML) approaches.Ordinary least-squares regression was employed alongside ML methods, includingrandom forest and support vector regression, to predict RQ gamma-ray pulsardistances. To ensure robustness, the analysis considered spectral cutoffsignificance and outlier data. Results confirm that the FP relation is validonly for pulsars exhibiting significant gamma-ray cutoffs, with FP exponentsclosely matching theoretical expectations. It was shown that gamma-ray emissionorigins significantly favor the curvature radiation regime over the synchrotronregime at the 4.2 sigma level. The distances for 62 RQ pulsars, for which notraditional measurements exist, are predicted for the first time. Theluminosity and spatial distributions of the considered RQ pulsar populationmatch known pulsar distributions. Predictions for RQ pulsars with knowndistances are consistent with measured data. This study provides a proof ofprinciple that the FP relation, combined with ML methods, is a promising toolfor distance estimation in RQ gamma-ray pulsars, using gamma-ray emissiondirectly for the first time in pulsar distance estimates. Future improvementscan be achieved with larger data sets, precise spectral cutoff determinations,and corrections for key factors like the beaming factor.

Prediction of radio-quiet gamma-ray pulsar distances using the Fundamental Plane relation