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We present photometric and spectroscopic analyses of gravity (g-mode)long-period pulsating hot subdwarf B (sdB) stars. We perform a detailedasteroseismic and spectroscopic analysis of five pulsating sdB stars observedwith {\it TESS} aiming at the global comparison of the observations with themodel predictions based on our stellar evolution computations coupled with theadiabatic pulsation computations. We apply standard seismic tools for modeidentification, including asymptotic period spacings and rotational frequencymultiplets. We calculate the mean period spacing for $l = 1$ and $l = 2$ modesand estimate the errors by means of a statistical resampling analysis. For allstars, atmospheric parameters were derived by fitting synthetic spectra to thenewly obtained low-resolution spectra. We have computed stellar evolutionmodels using {\tt LPCODE} stellar evolution code, and computed $l = 1$ g-modefrequencies with the adiabatic non-radial pulsation code {\tt LP-PUL}. Derivedobservational mean period spacings are then compared to the mean periodspacings from detailed stellar evolution computations coupled with theadiabatic pulsation computations of g-modes. The atmospheric parameters derivedfrom spectroscopic data are typical of long-period pulsating sdB stars with theeffective temperature ranging from 23\,700\,K to 27\,600\,K and surface gravityspanning from 5.3\,dex to 5.5\,dex. In agreement with the expectations fromtheoretical arguments and previous asteroseismological works, we find that themean period spacings obtained for models with small convective cores, aspredicted by a pure Schwarzschild criterion, are incompatible with theobservations. We find that models with a standard/modest convective boundarymixing at the boundary of the convective core are in better agreement with theobserved mean period spacings and are therefore more realistic.

Asteroseismic analysis of variable hot subdwarf stars observed with TESS I. The mean g-mode period spacings in hot subdwarf B stars