Searching for redshifted 2.2 MeV neutron-capture lines from accreting neutron stars: Theoretical X-ray luminosity requirements and INTEGRAL/SPI observations

Accreting neutron stars (NSs) are expected to emit a redshifted 2.2 MeV line due to the capture of neutrons produced through the spallation processes of $^4$He and heavier ions in their atmospheres. Detecting this emission would offer an independent method for constraining the equation of state of NSs and provide valuable insights into nuclear reactions occurring in extreme gravitational and magnetic environments. Typically, a higher mass accretion rate is expected to result in a higher 2.2 MeV line intensity. However, when the mass accretion rate approaches the critical threshold, the accretion flow is decelerated by the radiative force, leading to a less efficient production of free neutrons and a corresponding drop in the flux of the spectral line. This makes the brightest X-ray pulsars unsuitable candidates for gamma-ray line detection. In this work, we present a theoretical framework for predicting the optimal X-ray luminosity required to detect a redshifted 2.2 MeV line in a strongly magnetized NS. As the INTEGRAL mission nears its conclusion, we have undertaken a thorough investigation of the SPI data of this line in a representative sample of accreting NSs. No redshifted 2.2 MeV line was detected. For each spectrum, we have determined the 3-sigma upper limits of the line intensity, assuming different values of the line width. Our findings suggest that advancing our understanding of the emission mechanism of the 2.2 MeV line, as well as the accretion flow responsible for it, will require a substantial increase in sensitivity from future MeV missions. For example, for a bright X-ray binary such as Sco X-1, we would need at least a 3-sigma line point source sensitivity of ~1E-6 ph/cm^2/s, that is, about two orders of magnitude better than that currently achieved. [Abridged]