  There are many ways to probe alternative theories of gravity, namely, via:
experimental tests at solar system scale, cosmological data and models,
gravitational waves and compact objects. In the present paper we consider a
model of gravity with torsion $f(T)$ applied to compact objects such as neutron
stars (NSs) for a couple of realistic equations of state (EOS). To do so we
follow our previous articles, in which we show how to model compact stars in
this $f(T)$ gravity by obtaining its corresponding Tolman-Oppenheimer-Volkof
equations and applying this prescription to model polytropic compact stars. In
these modelling of NS in $f(T)$ gravity presented here, we calculate, among
other things, the maximum mass allowed for a given realistic EOS, which would
also allow us to evaluate which models are in accordance with observations. The
results already known to General Relativity must be reproduced to some extent
and, eventually, we can find models that allow higher maximum masses for NSs
than Relativity itself, which could explain, for example, the secondary
component of the event GW190814, if this star is a massive NS.
