Could the neutrino emission of TXS 0506+056 come from the accretion flow of the supermassive black hole?

High-energy neutrinos from the blazar TXS~0506+056 are usually thought to arise from the relativistic jet pointing to us. However, the composition of jets of active galactic nuclei (AGNs), whether they are baryon dominated or Poynting flux dominated, is largely unknown. In the latter case, no comic rays and neutrinos are expected from the AGN jets. In this work, we study whether the neutrino emission from TXS~0506+056 could be powered by the accretion flow of the supermassive black hole. Protons could be accelerated by magnetic reconnection or turbulence in the inner accretion flow. To explain the neutrino flare of TXS~0506+056 in the year of 2014-2015, a super-Eddington accretion is needed. During the steady state, a sub-Eddington accretion flow could power a steady neutrino emission that may explain the long-term steady neutrino flux from TXS 0506+056. We consider the neutrino production in both magnetically arrested accretion (MAD) flow and the standard and normal evolution (SANE) regime of accretion. In the MAD scenario, due to a high magnetic field, a large dissipation radius is required to avoid the cooling of protons due to the synchrotron emission.