Abstract
Aims. We use stellar line-of-sight velocities of Antlia B, a faint dwarf
galaxy in the NGC 3109 association, to derive constraints on the fundamental
properties of scalar field dark matter originally proposed to solve the
small-scale problems faced by cold dark matter models. Methods. We use the
first spectroscopic observations of Antlia B, a distant (d $\sim$ 1.35 Mpc)
faint dwarf ($M_\text{V} = -9.7$, M$_\star \sim 8\times10^5$M$_\odot$), from
MUSE-Faint - a survey of ultra-faint dwarfs with the Multi Unit Spectroscopic
Explorer. Through measurement of line-of-sight velocities for stars in the
$1'\times 1'$ field-of-view, we identify 127 stars as members of Antlia B,
allowing us to model its dark matter density profile with the Jeans modelling
code GravSphere. We implement a model for scalar field dark matter into
GravSphere and use this to place constraints on the self-coupling strength of
this model. Results. We find a virial mass of ${M_{200} \approx
1.66^{+2.51}_{-0.92}\times 10^9}$ M$_\odot$ and a concentration parameter of
${c_{200}\approx 17.38^{+6.06}_{-4.20}}$ for Antlia B. These results are
consistent with the mass-concentration relations in the literature. We
constrain the characteristic length scale of the repulsive self-interaction
$R_{\text{TF}}$ of the scalar field dark matter model to $R_{\text{TF}}
\lesssim 180$ pc (68% confidence level), which translates to a self-coupling
strength of $\frac{g}{m^2c^4}\lesssim 5.2 \times 10^{-20}$ eV$^{-1}$cm$^3$. The
constraint on the characteristic length scale of the repulsive self-interaction
is inconsistent with the value required to match the observations of cores of
dwarf galaxies in the Local Group, suggesting that the cored density profiles
of those galaxies are not caused by scalar field dark matter.