Optical emission is detected from filaments around the central galaxies of clusters of galaxies. These filaments have lengths of tens of kiloparsecs. The emission is possibly due to heating caused by the dissipation of mechanical energy and by cosmic ray induced ionisation. CO millimeter and submillimeter line emissions as well as H$_{2}$ infrared emission originating in such filaments surrounding NGC~1275, the central galaxy of the Perseus cluster, have been detected. Our aim is to identify those molecular species, other than CO, that may emit detectable millimeter and submillimeter line features arising in these filaments, and to determine which of those species will produce emissions that might serve as diagnostics of the dissipation and cosmic ray induced ionisation. The time-dependent UCL photon-dominated region modelling code was used in the construction of steady-state models of molecular filamentary emission regions at appropriate pressures, for a range of dissipation and cosmic ray induced ionisation rates and incident radiation fields.HCO$^+$ and C$_2$H emissions will potentially provide information about the cosmic ray induced ionisation rates in the filaments. HCN and, in particular, CN are species with millimeter and submillimeter lines that remain abundant in the warmest regions containing molecules. Detections of the galaxy cluster filaments in HCO$^{+}$, C$_{2}$H, and CN emissions and further detections of them in HCN emissions would provide significant constraints on the dissipation and cosmic ray induced ionisation rates.
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