We discuss physical properties and baryonic content of broad Ly \alpha absorbers ( BLAs ) at low redshift . These absorption systems , recently discovered in high-resolution , high-signal to noise quasar absorption line spectra , possibly trace the warm-hot intergalactic medium ( WHIM ) in the temperature range between 10 ^ { 5 } and 10 ^ { 6 } K. The central idea is that in ionization equilibrium WHIM filaments should contain a very small fraction of neutral gas ( f _ { H I } \sim 10 ^ { -5 } -10 ^ { -6 } , typically ) , giving rise to weak intervening H i Ly \alpha absorption . Due to the high temperature of the WHIM , these Ly \alpha absorbers must be thermally broadened to Doppler parameters ( b values ) \geq 40 km s ^ { -1 } . It is expected , however , that also non-thermal line broadening processes , line blends , and noise features can mimic broad spectral features , complicating the quantitative estimate of the baryon content of the BLAs . To extend previous BLA measurements we have reanalyzed archival STIS data of the two quasars H 1821+643 and PG 0953+415 and have identified 13 BLA candidates along a total ( unblocked ) redshift path of \Delta z = 0.440 . Combining our measurements with previous results for the lines of sight toward PG 1259+593 and PG 1116+215 , the resulting new BLA sample consists of 20 reliably detected systems as well as 29 additional tentative cases , implying a BLA number density of dN _ { BLA } / dz = 22 - 53 . Eight BLAs show associated absorption from H i Ly \beta and/or O vi . The comparison between Ly \alpha , Ly \beta , and O vi line widths suggests that non-thermal broadening and noise features substantially affect the observed BLA b value distribution . However , it remains unclear whether BLAs and O vi absorbers trace the same gas phase in the WHIM filaments . We estimate that the contribution of BLAs to the baryon density at z = 0 is \Omega _ { b } ( BLA ) \geq 0.0027 h _ { 70 } ^ { -1 } for absorbers with log [ N ( cm ^ { -2 } ) / b ( km s ^ { -1 } ) ] \gtrsim 11.3 . This number indicates that WHIM broad Ly \alpha absorbers contain a substantial fraction of the baryons in the local Universe .