Euclid: Early Release Observations -- Interplay between dwarf galaxies and their globular clusters in the Perseus galaxy cluster

We present an analysis of globular clusters (GCs) of dwarf galaxies in the Perseus galaxy cluster that explores the relationship between dwarf galaxy properties and their GCs. Our focus is on GC numbers (N_̊m GC) and GC half-number radii (R_̊m GC) around dwarf galaxies, and their relations with host galaxy stellar masses (M_*), central surface brightnesses (μ_0), and effective radii (R_̊m e). This work is unique due to its large sample size and the absence of pre-selection based on μ_0 and R_̊m GC for dwarf galaxies. Interestingly, we find that at a given stellar mass, R_̊m GC is almost independent of the host galaxy μ_0 and R_̊m e, while R_ ̊m GC /R_ ̊m e depends on μ_0 and R_̊m e. Lower surface brightness and diffuse dwarf galaxies show R_ ̊m GC /R_ ̊m e ≈ 1, while higher surface brightness and compact dwarf galaxies show R_ ̊m GC /R_ ̊m e ≈ ,$1.5--2$. This means that for dwarf galaxies of similar stellar mass, the GCs have a similar median extent; however, their distribution is different from the field stars of their host. Additionally, low surface brightness and diffuse dwarf galaxies on average have a higher N_̊m GC than high surface brightness and compact dwarf galaxies at any given stellar mass. We also find that ultra-diffuse galaxies (UDGs) and non-UDGs in the sample have a similar R_̊m GC, while UDGs have a smaller R_ ̊m GC /R_ ̊m e (typically less than one) and a three to four times higher N_̊m GC than non-UDGs. Furthermore, when examining nucleated versus non-nucleated dwarf galaxies, we found that for M_* > 10^ M_⊙ nucleated dwarf galaxies seem to have a smaller R_̊m GC and R_ ̊m GC /R_ ̊m e with no significant differences seen between their N_̊m GC except at M_* < 10^ M_⊙ where the nucleated dwarf galaxies tend to have a higher N_̊m GC. Lastly, we explored the stellar-to-halo mass ratio (SHMR) of dwarf galaxies (halo mass based on N_̊m GC) and conclude that the Perseus cluster dwarf galaxies follow the expected SHMR at z=0 extrapolated down to M_* = 10^ M_⊙