On the [CII]-SFR relation in high redshift galaxies
  After two ALMA observing cycles, only a handful of [CII] $158\,\mu m$
emission line searches in z>6 galaxies have reported a positive detection,
questioning the applicability of the local [CII]-SFR relation to high-z
systems. To investigate this issue we use the Vallini et al. 2013 (V13) model,
based on high-resolution, radiative transfer cosmological simulations to
predict the [CII] emission from the interstellar medium of a z~7 (halo mass
$M_h=1.17\times10^{11}M_{\odot}$) galaxy. We improve the V13 model by including
(a) a physically-motivated metallicity (Z) distribution of the gas, (b) the
contribution of Photo-Dissociation Regions (PDRs), (c) the effects of Cosmic
Microwave Background on the [CII] line luminosity. We study the relative
contribution of diffuse neutral gas to the total [CII] emission ($F
_{diff}/F_{tot}$) for different SFR and Z values. We find that the [CII]
emission arises predominantly from PDRs: regardless of the galaxy properties,
$F _{diff}/F_{tot}\leq 10$% since, at these early epochs, the CMB temperature
approaches the spin temperature of the [CII] transition in the cold neutral
medium ($T_{CMB}\sim T_s^{CNM}\sim 20$ K). Our model predicts a high-z
[CII]-SFR relation consistent with observations of local dwarf galaxies
($0.02<Z/Z_{\odot}<0.5$). The [CII] deficit suggested by actual data
($L_{CII}<2.0\times 10^7 L_{\odot}$ in BDF3299 at z~7.1) if confirmed by deeper
ALMA observations, can be ascribed to negative stellar feedback disrupting
molecular clouds around star formation sites. The deviation from the local
[CII]-SFR would then imply a modified Kennicutt-Schmidt relation in z>6
galaxies. Alternatively/in addition, the deficit might be explained by low gas
metallicities ($Z<0.1 Z_{\odot}$).
