  Using an accurate Gaia TGAS 25pc sample, nearly complete for GK stars, and
selecting common proper motion (CPM) candidates from UCAC5, we search for new
white dwarf (WD) companions around nearby stars with relatively small proper
motions. For investigating known CPM systems in TGAS and for selecting CPM
candidates in TGAS+UCAC5, we took into account the expected effect of orbital
motion on the proper motion as well as the proper motion catalogue errors.
Colour-magnitude diagrams (CMDs) $M_J/J-K_s$ and $M_G/G-J$ were used to verify
CPM candidates from UCAC5. Assuming their common distance with a given TGAS
star, we searched for candidates that occupied similar regions in the CMDs as
the few known nearby WDs (4 in TGAS) and WD companions (3 in TGAS+UCAC5). CPM
candidates with colours and absolute magnitudes corresponding neither to the
main sequence nor to the WD sequence were considered as doubtful or subdwarf
candidates. With a minimum proper motion of 60mas/yr, we selected three WD
companion candidates, two of which are also confirmed by their significant
parallaxes measured in URAT data, whereas the third may also be a chance
alignment of a distant halo star with a nearby TGAS star (angular separation of
about 465arcsec). One additional nearby WD candidate was found from its URAT
parallax and $GJK_s$ photometry. With HD 166435 B orbiting a well-known G1 star
at ~24.6pc with a projected physical separation of ~700AU, we discovered one of
the hottest WDs, classified by us as DA2.0$\pm$0.2, in the solar neighbourhood.
We also found TYC 3980-1081-1 B, a strong cool WD companion candidate around a
recently identified new solar neighbour with a TGAS parallax corresponding to a
distance of ~8.3pc and our photometric classification as ~M2 dwarf. This raises
the question whether previous assumptions on the completeness of the WD sample
to a distance of 13pc were correct.
