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 Issue A&A Volume 503, Number 2, August IV 2009 L13 - L16 Letters https://doi.org/10.1051/0004-6361/200912620 28 July 2009

Appendix A: The FUV luminosity

For the modeling in Sect. 4, the FUV luminosity is required. Assuming the protostar to emit a blackbody spectrum, this quantity depends on the bolometric luminosity and the effective temperature . While of the embedded protostar can be determined relatively well from photometry in the IR and is assumed to be given in the following, only rough estimations of are available, since photons are absorbed or redistributed to longer wavelengths by the high dust and gas column density toward the source.

 Figure A.1: Luminosity in the FUV band depending on for . The spectral classification is indicated by red circles. Open with DEXTER

The Stefan-Boltzmann law requires

 (A.1)

with the source radius R, the Stefan-Boltzmann constant , and the solar temperature, radius, and luminosity (, , and ). The FUV band is limited by the Ly edge (13.6 eV,  Å) at short wavelengths and the average dust working function at long wavelengths (6 eV,  Å). For temperatures between  K and  K, the peak of the blackbody intensity is within the FUV band (Wien's displacement law, ). The FUV luminosity is obtained from integrating between and   by

 = (A.2) = (A.3)

with and . For and , the integral in Eq. (A.3) is , and Stefan-Boltzmanns law is recovered. In Fig. A.1, the FUV luminosity depending on is given for . At a temperature of  K, where peaks, the ratio is 0.55. Considering temperatures below this peak, the FUV luminosity is within a factor of 3 for  K and a factor of 10 for  K. We note that this is valid independently of , since .

How does this temperature dependence affect the results of the models in Sect. 4? In the absence of any attenuation,  erg s-1 is required to provide the necessary FUV field of ISRF at position B for heating. Assuming the bolometric luminosity to be correct, the temperature needs to be higher than 6800 K. For a temperature of  K instead of  K, the FUV luminosity decreases by a factor of 2 and the required column density for attenuation (Sect. 4) reduces to . We conclude that the modeling results are not affected by as long as the temperature exceeds about 104 K.

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