Observations of the post-common-envelope binaries EG UMa and PG 1026+002.

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 NaI 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[sup -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, V[sub rot] 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 V[sub rot] 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 V[sub rot] 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 ser of system parameters for EG UMa based upon our new measurement of K[sub 2] 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[sup -1], which, being in agreement with that measured from emission lines, adds... [ABSTRACT FROM AUTHOR]