We observed a nearby millisecond pulsar J2124-3358 with the Hubble Space Telescope in broad far-UV (FUV) and optical filters. The pulsar is detected in both bands with fluxes F(1250-2000 A)= (2.5+/-0.3)x10^-16 erg/s/cm^2 and F(3800-6000 A)=(6.4+/-0.4)x10^-17 erg/s/cm^2, which correspond to luminosities of ~5.8x10^27 and 1.4x10^27 erg/s, for d=410 pc and E(B-V)=0.03. The optical-FUV spectrum can be described by a power-law model, f_nu~nu^alpha, with slope alpha=0.18-0.48 for a conservative range of color excess, E(B-V)=0.01-0.08. Since a spectral flux rising with frequency is unusual for pulsar magnetospheric emission in this frequency range, it is possible that the spectrum is predominantly magnetospheric (power law with alpha<0) in the optical while it is dominated by thermal emission from the neutron star surface in the FUV. For a neutron star radius of 12 km, the surface temperature would be between 0.5x10^5 and 2.1x10^5 K, for alpha ranging from -1 to 0, E(B-V)=0.01-0.08, and d=340-500 pc. In addition to the pulsar, the FUV images reveal extended emission spatially coincident with the known Halpha bow shock, making PSR J2124-3358 the second pulsar (after PSR J0437-4715) with a bow shock detected in FUV.
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