This work presents a possible detection mechanism for close, detached, neutron star–red dwarf binaries, which are expected to be the evolutionary precursors of low‐mass X‐ray binaries (LMXBs). Although this pre‐low‐mass X‐ray binary (pre‐LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X‐ray luminosity of neutron star wind accretion in a pre‐LMXB system can be expected to exceed the intrinsic X‐ray luminosity of the red dwarf secondary star. Furthermore, the temperature of the radiation emitted from the neutron star wind accretion process is expected, within the confines of a reasonable set of conditions, to lie within the detection range of X‐ray satellites. Sources with X‐ray luminosities greater than that expected for a red dwarf star, but the positions of which coincide with that of a red dwarf star, are then candidate pre‐LMXB systems. These candidate systems should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a high‐mass compact object.

We present spectra in the range 8000–8665 Å of the close, detached M‐dwarf–white‐dwarf binaries EG UMa and PG 1026+002. The Na i absorption doublet (8183, 8195 Å) is detected along with a number of other absorption lines including intrinsically narrow metal Fe i and Ti i lines and the Ca ii infrared (IR) triplet (8498, 8542, 8662 Å). We update the ephemeris and orbital period of EG UMa. The radial velocity semi‐amplitude for the secondary star in EG UMa was found to be 125.9±0.4 km s−1. The excellent agreement between this value and that measured from emission lines, in conjunction with the lack of orbital‐phase variation of the absorption line strengths, confirms that the secondary‐star emission in EG UMa is chromospheric in nature and not influenced by irradiation. We determine a range of rotational velocities, Vrot sin i, for EG UMa as measured over the Na i absorption doublet and the Fe i and Ti i metal lines using three template stars. Although a broad range of Vrot sin i values are obtained, the narrow metal lines were found to give consistantly lower values than that given by the Na i absorption doublet. In addition, the measured values of Vrot sin i were inconsistent with other measured parameters and were therefore deemed too unreliable to be the basis for full system parameter calculations. We do, however, derive a complete set of system parameters for EG UMa based upon our new measurement of K2 and previous observational data. We present R‐band relative photometry of EG UMa, which shows relative flux variations at around the 5 per cent level and the occurrence of a flare event. These observations are again interpreted as being the result of the intrinsic chromospheric activity of the M dwarf in this system. We measure the semi‐amplitude of the radial‐velocity curve for PG 1026+002 to be 163.7±7.3 km s−1, which, being in agreement with that measured from emission lines, adds further support to the suggestion that the secondary‐star emission in PG 1026+002 is also largely chromospheric in nature. Rotational velocities for PG 1026+002 were determined by measurement over the Na i absorption doublet only. The Vrot sin i values obtained for PG 1026+002 using the three available template stars were all greater than expected from the assumption of synchronous rotation.

We employ high‐resolution echelle spectroscopy to measure the projected rotational velocity, Vrot sin i, in the post‐common‐envelope binaries EG UMa, HZ 9 and RE J1629 + 780. For EG UMa we obtain consistent Vrot sin i measurements from the Na i doublet at 8183, 8195  Å (31.2 ± 3.7 km s−1), the Fe and Ti intrinsically narrow metal (INM) lines in the region 8374–8430  Å (26.6 ± 2.7 and 27.8 ± 3.0 km s−1) and the K i line at 7698.9  Å (26.2 ± 3.5 km s−1). This is in contrast to previous measurements of Vrot sin i from the Na i doublet and INM features derived using lower‐resolution spectra, which were not consistent. Possible origins for the disagreement observed previously are discussed, including the inaccurate removal of telluric absorption. The values of Vrot sin i measured from the high‐resolution EG UMa spectra are also consistent with that expected from system parameters derived from previous observational data. We also update the ephemeris and orbital period of EG UMa. We obtained rotation rate measurements of 34.3 ± 3.8 km s−1 for HZ 9 and 25.1 ± 2.3 km s−1 for RE J 1629 + 780, as measured from the Na i doublet at 8183, 8195  Å and the INM lines. In both systems there is agreement between the Vrot sin i values measured from the two regions. The value of Vrot sin i measured in HZ 9 is similar to that measured for EG UMa. This is expected, as these systems share a similar orbital period and secondary star spectral type. The measurement of Vrot sin i in RE J 1629 + 780 indicates that this system, which lacks radial velocity shifts due to orbital motion, is a wide binary as opposed to a low‐inclination system.