MUSEQuBES: The relation between Ly$\alpha$ emitters and C IV absorbers at $z \approx 3.3$

We present a detailed study of the column density and covering fraction profiles of C IV absorption around 86 redshift $z \approx 3.3$ Ly$\alpha$ emitters (LAEs) detected in 8 Multi-Unit Spectroscopic Explorer (MUSE) fields of $1'\times 1'$ centered on 8 bright background quasars as part of the MUSEQuBES survey. Using Voigt profile fitting of all the C IV absorbers detected along these 8 sightlines, we generated a ``blind'' absorbers' catalog consisting of 489 C IV absorption components. We cross-matched this blind C IV catalog with the MUSE-detected LAE catalog and found a significant enhancement of C IV components within $\approx \pm$400 $\rm km\, s^{-1}$ of the systemic redshifts of the LAEs. Neither the C IV column density ($N$) nor the Doppler parameter ($b$) of individual C IV components shows any significant anti-correlation with impact parameter ($\rho$) of the LAEs in the 68 percentile range of $90\leq \rho \leq 230$ physical kpc (pkpc). We find a covering fraction of $\approx 60\%$ for a threshold $N$(C IV) of $10^{12.5}\, \rm \rm cm^{-2}$, which is roughly twice as high as in random regions. The C IV covering fraction remains constant at $\approx50\%$ for impact parameters in the range 150--250~pkpc ($\approx 3-6 R_{200}$). Using the covering fraction profile, we constrained the LAE--C IV absorber two-point correlation function, and obtained $r_0 = 3.4$ comoving Mpc (cMpc) and $\gamma = 1.2$ for a threshold $N$(C IV) of $10^{13.0}\, \rm cm^{-2}$. The C IV covering fraction is found to be enhanced for the LAEs that are part of a ``pair/group'' compared to the isolated ones.