The power spectrum of extended [C II] halos around high redshift galaxies

ALMA observations have detected extended ($\simeq 10$ kpc) [C II] halos around high-redshift ($z \gtrsim 5$) star-forming galaxies. If such extended structures are common, they may have an impact on the line intensity mapping (LIM) signal. We compute the LIM power spectrum including both the central galaxy and the [C II] halo, and study the detectability of such signal in an ALMA LIM survey. We model the central galaxy and the [C II] halo brightness with a S\'ersic+exponential profile. The model has two free parameters: the effective radius ratio $f_{R_e}$, and the central surface brightness ratio, $f_{\Sigma}$, between the two components. [C II] halos can significantly boost the LIM power spectrum signal. For example, for relatively compact [C II] halos ($f_\Sigma=0.4$, $f_{R_{\rm e}}=2.0$), the signal is boosted by $\simeq 20$ times; for more extended and diffuse halos ($f_\Sigma=0.1, f_{R_{\rm e}}=6.0$), the signal is boosted by $\simeq 100$ times. For the ALMA ASPECS survey (resolution $\theta_{\rm beam} = 1.13''$, survey area $\Omega_{\rm survey}=2.9\,\rm arcmin^{2}$), the [C II] power spectrum is detectable only if the deL14d [C II] - SFR relation holds. However, with an optimized survey ($\theta_{\rm beam} = 0.232''$, $\Omega_{\rm survey}=2.0\,\rm deg^{2}$), the power spectrum is detectable for almost all the [C II] - SFR relations considered in this paper. Such a survey can constrain $f_\Sigma$ ($f_{R_{\rm e}}$) with a relative uncertainty of $\sim 15\%$ ($\sim 10\%$). A successful LIM experiment will provide unique constraints on the nature, origin, and frequency of extended [C II] halos, and the [C II] - SFR relation at early times.