More information on modsource

modsource computes the spectrum emitted by a uniform source. The spectrum consists of continuum emission and spectral line emission. The line emission is computed under the assumption of local thermodynamic equilibrium (LTE). modsource takes into account the optical depth of the lines, the finite angular resolution of the telescope, and the presence of the cosmic microwave background (CMB) to compute the radiative transfer. Depending on the continuum and line excitation temperatures, the lines can appear in emission or in absorption in the synthetic spectrum. Several molecules and/or components can be modeled at the same time. The spectra of these components are computed separately, and then added linearly. It is a correct treatment for components that do not overlap spectrally or spatially within the beam, or for components with optically thin emission. However, such a treatment is not correct in the case of spatially-overlapping components with optically thick emission. In such cases, the intensities of the lines will be overestimated.

The components belong by default to the ``main group'' of components. The components marked with the option /absorption belong to the ``foreground'' group of components. For the ``main group'' components, the background used to compute the radiative transfer is the sum of the CMB and the source continuum emission. For the ``foreground'' components, the spectrum is computed recursively and the background initially consists of the spectrum of the ``main group'' (that already contains the CMB and the source continuum).

The source continuum emission is assumed to be optically thin (i.e. transparent to the CMB) and spatially uniform, to fill the beam of the single-dish telescope or the synthesized beam of the interferometer, and to come from a location behind the medium that contains the molecules modeled with modsource (i.e. lines and continuum are not mixed). The assumption of a uniform continuum emission filling the beam will produce inacurrate results in the case of a centrally peaked continuum emission and a molecule component with a beam filling factor smaller than 1. In such a case, the molecule should ``see'' a stronger continuum than what modsource assumes. Given that different components may have different beam filling factors, properly taking into account the small-scale structure of the continuum emission would not be trivial and is beyond the scope of modsource.

Let's call $T_{{\rm cont},\,\nu}$ the effective radiation temperature of the source continuum emission. It corresponds to the level of the ``baseline'' in the spectrum if this ``baseline'' represents the true continuum level of the source (case of, e.g., interferometric or some single-dish wobbler spectra), or the user has to assume its value if the baseline cannot be trusted and has been removed (case of, e.g., single-dish position-switching spectra). $T_{{\rm cont},\,\nu}$ can be a frequency-dependent function.

For a component with a beam filling factor of 1, the brightness temperature of the spectrum is computed as:

$$T_{\rm B}(\nu) = J_\nu(T_{\rm ex}) (1-e^{-\tau_\nu}) + T_... ...} + J_\nu(T_{\rm cmb}) e^{-\tau_\nu} - J_\nu(T_{\rm cmb})\,\,,$$ (1)

where $\tau_\nu$ is the opacity of the transition, $T_{\rm ex}$ the excitation temperature of the transition, $T_{\rm cmb}$ the temperature of the CMB, and $J_\nu(T) = \frac{h\nu/k}{e^{h\nu/kT}-1}$, with $h$ the Planck constant, and $k$ the Boltzmann constant. The last term in Eq. 1 represents the subtraction of the spectrum of the off-source position in the case of single-dish observations or the spatial filtering of the uniform CMB radiation in the case of interferometric observations. This equation can be rewritten as:

$$T_{\rm B}(\nu) = T_{{\rm cont},\,\nu} + \left(J_\nu(T_{\r... ...\nu(T_{\rm cmb})-T_{{\rm cont},\,\nu}\right) (1-e^{-\tau_\nu})$$ (2)

For a component with an arbitrary beam filling factor, $\eta$, modsource computes the spectrum as:

$$T_{\rm B}(\nu) = T_{{\rm cont},\,\nu} + \eta\left(J_\nu(T... ...\nu(T_{\rm cmb})-T_{{\rm cont},\,\nu}\right) (1-e^{-\tau_\nu})$$ (3)

For $N_1$ components in the ``main group'' (mg), the output spectrum is:

$$T_{\rm B}^{\rm mg}(\nu) = T_{{\rm cont},\,\nu} + \sum_{i=... ...T_{\rm cmb})-T_{{\rm cont},\,\nu}\right) (1-e^{-\tau_{\nu,i}})$$ (4)

For $N_2$ additional components in the ``foreground group'', the output spectrum is computed with the following recursive equation:

$$T_{\rm B}^j(\nu) = T_{\rm B}^{j-1}(\nu)e^{-\tau_{\nu,j}} ... ..._{{\rm ex},j})-J_\nu(T_{\rm cmb})\right) (1-e^{-\tau_{\nu,j}})$$ (5)

with $j$ varying from 1 to $N_2$ and $T_{\rm B}^0(\nu) = T_{\rm B}^{\rm mg}(\nu)$. Note that this equation is correct only if all foreground components have a beam filling factor, $\eta_j$, of 1.

By default, the final output spectrum is

$$T_{\rm B}(\nu) = T_{\rm B}^{N_2}(\nu)-T_{{\rm cont},\,\nu}$$ (6)

or, if there is no ``foreground group'' component:

$$T_{\rm B}(\nu) = T_{\rm B}^{\rm mg}(\nu)-T_{{\rm cont},\,\nu}$$ (7)

If the user selects the option /keepcont, then the output spectrum is $T_{\rm B}(\nu) = T_{\rm B}^{N_2}(\nu)$ in the first case and $T_{\rm B}(\nu) = T_{\rm B}^{\rm mg}(\nu)$ in the second case. More details about modsource can be found in Maret, Hily-Blant, Pety et al., Astronomy & Astrophysics 526, A47 (2011).