We present the H \alpha intensity map of the host galaxy of the repeating fast radio burst FRB 121102 at a redshift of z = 0.193 obtained with the AO-assisted Kyoto 3DII optical integral-field unit mounted on the 8.2-m Subaru Telescope .
We detected a compact H \alpha -emitting ( i.e. , star-forming ) region in the galaxy , which has a much smaller angular size [ < 0 ^ { \prime \prime } .57 ( 1.9 kpc ) at full width at half maximum ( FWHM ) ] than the extended stellar continuum emission region determined by the Gemini/GMOS z ^ { \prime } -band image [ \simeq 1 ^ { \prime \prime } .4 ( 4.6 kpc ) at FWHM with ellipticity b / a = 0.45 ] .
The spatial offset between the centroid of the H \alpha emission region and the position of the radio bursts is 0 ^ { \prime \prime } .08 \pm 0 ^ { \prime \prime } .02 ( 0.26 \pm 0.07 kpc ) , indicating that FRB 121102 is located within the star-forming region .
This close spatial association of FRB 121102 with the star-forming region is consistent with expectations from young pulsar/magnetar models for FRB 121102 , and it also suggests that the observed H \alpha emission region can make a major dispersion measure ( DM ) contribution to the host galaxy DM component of FRB 121102 .
Nevertheless , the largest possible value of the DM contribution from the H \alpha emission region inferred from our observations still requires a significant amount of ionized baryons in intergalactic medium ( the so-called ‘ missing ’ baryons ) as the DM source of FRB 121102 , and we obtain a 90 % confidence level lower limit on the cosmic baryon density in the intergalactic medium in the low-redshift universe as \Omega _ { \text { IGM } } > 0.012 .