ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Citation I-Citation O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O B-Tag O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O
tokens: properties. This means that the stellar mass (or the dust luminosity when there is no stellar population included in the model) is not a free parameter even though it is technically possible to treat it as such. This would greatly expand the size of the parameter space by adding an extra dimension, while slowing the computation of the grid and the analysis by a similar amount, and degrade the accuracy of the estimation of the physical properties. Optionally, CIGALE can also handle fluxes for which only upper limits have been determined. We adopt the method presented in Appendix A2 of Sawicki (2012) . This affects the aforementioned computing steps in several ways. First, the computation of the χ 2 is divided between regular quantities (first three terms corresponding to Eq. ( 14 )) and those with only an upper limit (last three terms): with “erf” being the error function, f ul the flux upper limit, and the indices i , j , and k indicating respectively the fluxes, extensive properties, and intensive properties. See Eq. (A6)–(A10) of Sawicki (2012) for a full derivation 6 . The main difficulty is to determine α . For this we have to numerically solve ∂ χ 2 /∂ α = 0 for every model, which is equivalent to solving Eq. (A11) from Sawicki (2012) : We do so using the scipy.optimize.root root-finding method. Once the χ 2 are computed, the subsequent steps no longer depend on the presence or absence of upper limits. We have to note that objects in a catalogue do not all need to be fitted with the same set of data. CIGALE will automatically only consider the available data for a given object. The lack of certain data for some targets has a direct impact on some of the aforementioned computation steps. For steps 2 and 3, we simply do not include the data that have been marked as invalid in the input file (value lower than 0 or set to “nan”, by convention) in the computation of α and χ 2 . Another feature of this module is the possibility to assess whether or not physical properties can actually be estimated in a reliable way through the analysis of a mock catalogue. The idea is to compare the physical properties of the mock catalogue, which are known exactly, to the estimates from the analysis of the likelihood distribution. To build the mock catalogue we consider the best fit for each object. We then modify each quantity by adding a value taken from a Gaussian distribution with the same standard deviation as the uncertainty on the observation. This mock catalogue is then analysed in the exact same way as the original observations. Physical properties for which the exact and estimated values are similar can be estimated reliably. Applications of the pdf_analysis module to a sample of representative galaxies is presented in Sect. 5.3 . 5. Examples of <monospace>CIGALE</monospace> use cases As seen above, CIGALE has been designed to be flexible and versatile so that it may have various applications: estimation of the physical properties of an object