  The $\mathrm{X}^+\ ^2\Sigma_u^+$ ground electronic state of the Mg$_2^+$ ion
has been studied by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE)
photoelectron spectroscopy. Rotationally cold Mg$_2$ molecules produced in a
laser-ablation supersonic-expansion source were ionized by resonant two-photon
absorption from the $\mathrm{X}\ ^1\Sigma_g^+(v"=0)$ ground vibronic state. The
photoelectron spectra of the $v^+=3-14$ vibrational levels of the
$\mathrm{X}^+$ state were recorded with rotational resolution and their
analysis led to the determination of accurate term values and rotational
constants for these levels. Improved values of the adiabatic ionization energy
of $^{24}$Mg$_2$ ($51\,503.9(4)$ cm$^{-1}$) and of the ground-state
dissociation energy of $^{24}$Mg$_2^+$ ($10 572.3(6)$ cm$^{-1}$) were
determined from experimental data.
