Constraints on cosmic rays in the Milky Way circumgalactic medium from OVIII observations

We constrain the cosmic ray (CR) population in the circumgalactic medium (CGM) of Milky Way by comparing the observations of absorption lines of OVIII ion with predictions from analytical models of CGM : precipitation (PP) and isothermal (IT) model. For a CGM in hydrostatic equilibrium, the introduction of CR suppresses thermal pressure, and affects the OVIII ion abundance. We explore the allowances given to the ratio of CR pressure to thermal pressure ($\rm{P}_{\rm{CR}}/\rm{P}_{\rm{th}}=\eta$), with varying boundary conditions, CGM mass content, photoionization by extragalactic ultraviolet background and temperature fluctuations. We find that the allowed maximum values of $\eta$ are : $\eta\lesssim10$ in the PP model and $\eta\lesssim6$ in the IT model. We also explore the spatial variation of $\eta$ : rising ($\eta=Ax$) or declining ($\eta=A/x$) with radius, where A is the normalization of the profiles. In particular, the models with declining ratio of CR to thermal pressure fare better than those with rising ratio with suitable temperature fluctuation (larger $\sigma_{\rm ln T}$ for PP and lower for IT). The declining profiles allow $A\lesssim8$ and $A\lesssim10$ in the case of IT and PP models, respectively, thereby accommodating a large value of $\eta \,(\simeq 200)$ in the central region, but not in the outer regions. These limits, combined with the limits derived from $\gamma$-ray and radio background, can be useful for building models of Milky Way CGM including CR population. However, the larger amount of CR can be packed in cold phase which may be one way to circumvent these constraints.