ner_tags: O O O O O O B-Formula I-Formula O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O 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-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O
tokens: ) 6 . Analysis suggests that FRB 121102’s DM local could be small ( Tendulkar et al. 2017 ). Such studies have potential implications for progenitor models, however FRB 121102 may not necessarily be representative of all FRBs. More accurate modelling of DM local may arise as further FRBs are localised. In this work we assume DM local = 0. 3 Excess electron model In this section we present the framework for combining the PDFs of DM exc components to retrieve a PDF, which describes the likelihood of an FRB at source redshift z s to have an observed extragalactic DM component DM exc , contributing to a measured time delay Δ t obs,exc between two observing frequencies ν 1,obs and ν 2,obs on Earth. We demonstrate this using our simulated IGM and progenitor models. Increasingly, accurate component models developed using FRB discoveries (or via other means) may allow these PDFs, which we refer to as excess electron models, to become increasingly useful tools for DM-redshift analysis. In Sect. 3.1 we describe our method and in Sect. 3.2 we apply Bayes’ theorem to the excess electron model and discuss advantages of doing so. 3.1 <italic>P</italic>(DM|<italic>z</italic>) methodology and results Following Eq. ( 1 ), an FRB emitted from a source at redshift z s has a DM exc formed from the sum of its extragalactic components. Assuming these components to be random independent variables drawn from their respective underlying PDFs, P (DM IGM | z s ) and P (DM host | z s ), the convolution of these PDFs, describes the likelihood of an FRB of given source redshift z s to have an observed extragalactic DM component DM exc . This DM exc results in a measured time delay Δ t obs,exc between two observing frequencies ( ν 1,obs and ν 2,obs ) on Earth. Example excess electron models generated using our IGM (Sect. 2.2 ) and host galaxy (Sect. 2.3 ) PDFs are shown in Fig. 4 . Comparisons between projections of these models for different values of z s and P (DM IGM | z s ) illustrate the initially significant (and diminishing with redshift) influence of the host galaxy on P (DM exc | z s ). These comparisons show that the potential host galaxy contribution to DM exc increases the likelihood of an FRB to have a DM exc in excess of that predicted by conventional analysis. This excess may be particularly large for sources at low redshifts. In some cases (see e.g. subplots (a) and (c), which trace YPSR distributions in spiral galaxies and elliptical distributions in elliptical galaxies, respectively), the influence of the host diminishes significantly by z s = 3, signified by the convergence of the P (DM exc ) curves with their IGM counterparts. In other cases (see e.g. subplots (c) and (f), where FRBs are confined to galactic regions of high electron density), the host’s potential influence is still significant at z s = 3. Differences between P (DM exc | z s ) profiles are also apparent between different progenitor models, particularly for sources with low redshifts.