  From the smallest scales of quantum systems to the largest scales of
intergalactic medium, turbulence is ubiquitous in nature. Often dubbed as the
last unsolved problem of classical physics, it remains a time tested paradigm
of dynamics far from equilibrium. The phenomenon even transcends to
self-propelled fluids such as dense bacterial suspensions that can display
turbulence at mesoscale even though the constituent particles move at Reynolds
number below unity. It is intensely debated whether such fluids possess an
effective temperature and obey fluctuation-dissipation relations (FDR) as they
are generally marred by a lack of detailed balance. In this letter, we answer
this question and report an exact expression of the effective temperature for a
distribution of interacting particles that are advected by a mesoscale
turbulent flow. This effective temperature is linear in particle diffusivity
with the slope defining the particle mobility that is higher when the
background fluid exhibits global polar ordering, and lower when the fluid is in
isotropic equilibrium. We believe our work is a direct verification of the
Einstein relation -the simplest FDR, for interacting particles immersed in a
mesoscale turbulence.
