Abstract
An analytical model for the Maxwell radiation field in an axisymmetric galaxy, proposed previously, is first checked for its predictions of the spatial variation of the spectral energy distributions (SEDs) in our Galaxy. First, the model is summarized. It is now shown how to compute the SED with this model. Then the model is adjusted by asking that the SED predicted at our local position in the Galaxy coincides with the available observations. Finally, the first predictions of the model for the spatial variation of the SED in the Galaxy are compared with those of a radiation transfer model. We find that the two predictions do not differ too much. This indicates that, in a future work, it should be possible with the present model to check if the “interaction energy” predicted by an alternative, scalar theory of gravitation, contributes to the dark matter.
Highlights
Advances in Astronomy analytical representation of the general solution of the source-free Maxwell equations in the axisymmetric case [14]
The Maxwell model of the interstellar radiation field [12] has been first checked for its predictions of the spatial variation of the spectral energy distributions (SEDs) in our Galaxy. e model has been adjusted by asking that the SED predicted at our local position in the Galaxy, equation (32) with ρ ρloc ≔ 8 kpc and z zloc ≔ 0.02 kpc, coincides with the observations collected through different spatial missions [7,8,9]. en the predictions of the model for other positions in the Galaxy have been compared with the predictions obtained by using a recent radiation transfer model [6]
E two predictions do not differ too much in magnitude, even though the predictions of the present model oscillate rather strongly as function of the wavelength, especially at short wavelengths and not very far (1 kpc) from the axis of the Galaxy
Summary
We give a new presentation of the model that was built in Ref. [12] and that uses results of Ref. [14] and references therein. is presentation uses an easy extension of the result [14]. ωω0j 2 an expiωj ω0 knz ωjtSnj Even though these formulae follow from a discretization and from using an integration rule that is only approximate for the starting integral, they provide (without the O(1/N4) remainder) an exact solution of the source-free Maxwell equations (see §3.3 in Reference [12]). E arguments of the Bessel functions J0 and J1 in equations (19) and (20)–(22), as well as the spatial part of the argument of the complex exponential in equations (19) and (23), are of the order of ρ/λ or z/λ For a galaxy, these are numbers of the order of 1025; the numerical implementation of the model needs to use a precision better than quadruple precision—which leads to long computation times [12]. The precise choice of the model, i.e., equations (10) or (11) or (12), is totally neutral
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