Time dependence of the ultraviolet radiation field in the local interstellar medium

Far-ultraviolet (FUV, 6 eV < h nu < 13.6 eV) radiation has been suggested as the main source of heating of the neutral interstellar gas, and, in this case, it determines whether the thermal balance of the neutral gas results in cold (T similar to 50-100 K) clouds ( cold neutral material [CNM]), warm (T similar to 10(4) K) clouds (warm neutral material [WNM]), or a combination of the two. For gas at fixed mean density, high FUV fields convert the neutral gas to WNM, while low fields result in CNM. The main sources of interstellar FUV radiation are short-lived massive stars in associations that form in giant molecular clouds. Using McKee & Williams distribution of birthrates for OB associations in the Galaxy, we determine the expected behavior of the time-dependent FUV field for random positions in the ISM at the solar circle. The FUV field is calculated in two bands (912-1100 and 912-2070 Angstrom) and at the wavelength 1400 Angstrom. In terms of U(-17)= U/ (10(-17) ergs cm(-3) Angstrom(-1)), where U is the energy density of the radiation field in some band, we find ( mean, median) values at the solar circle of U(-17) = (15.7, 7.4) and (14.2, 7.2) for the 912-1100 and 912-2070 Angstrom bands, respectively. At 1400 Angstrom we find (mean, median) values of U(-17) = (14.4; 7.5). Our median value for the 912-2070 Angstrom band is G(0) = 1.6 times Habing's value for the radiation field at the solar circle in this band and quite close to Draine's value, G(0) = 1.7. Habing and Draine's values are based on observations of sources of FUV radiation in the solar neighborhood, so all three values are close to observed values. Because of attenuation by dust, only associations within about 500 pc contribute significantly to the energy density at a given point. Large-angle scattering produces a diffuse field that is about 10% of the field produced by the sum of direct and small-angle ( < 5) scattering from discrete sources ( the associations), as observed. At a point exposed to the median radiation field, the brightest association typically produces about 20% of the total energy density. At a point exposed to an above average radiation field, the brightest association produces most of the energy density. Therefore, the FUV field is asymmetric at a given point, and the asymmetry grows for higher fields. The FUV field fluctuates with a variety of amplitudes, the larger ones being less frequent. The mean field is about twice the median field because of these fluctuations, or spikes, in the radiation field. These spikes, which last similar to 30 Myr, are caused by the infrequent birth of nearby associations. For spikes that are significantly higher than the mean field, the time interval between spikes is similar to 2U(-15)(3/2) Gyr. We also model shorter duration spikes caused by runaway OB stars. The presence of a fluctuating heating rate created by the fluctuating FUV field converts CNM to WNM and vice versa.