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Appendix A: Effective wavelengths and reddening coefficients

To ease future fitting (and plotting), we list in Table 5 the wavelengths at which one should evaluate the flux for spectra which are close to Rayleigh-Jeans, as well as relative reddening coefficients. These were calculated as follows

  

$$\langle\lambda\rangle=\left( \frac{\int\lambda^{-4}\lambda R_\lambda\,{\rm d}\lambda} {\int\lambda R_\lambda\,{\rm d}\lambda}\right)^{-1/4},$$ (A.1)

$$\left\langle\frac{A_\lambda}{A_V}\right\rangle= \frac{-2.5}{0.12}... ...mbda\,{\rm d}\lambda} {\int \lambda^{-4}\lambda R_\lambda\,{\rm d}\lambda}\cdot$$ (A.2)

Note that the wavelength $\langle\lambda\rangle$ is not the effective wavelength of the detected photons in a given filter, but is the wavelength at which a $\lambda^{-4}$ spectrum has the same flux as a $\lambda^0$ spectrum that produces the same number of counts in the filter considered.

RX J1856.5-3754