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tokens: catalog of the whole area covered by Herschel (HELP, Shirley et al. 2019 ) can be taken into consideration for the analysis. Moreover, new submillimeter surveys like TolTEC ( DeNigris Wilson 2019 ) or the future mid/near-infrared James Webb Space Telescope (JWST, Gardner et al. 2006 ) will certainly increase the area and/or the density of the background sources. Appendix A: The ingredients of the model The dark matter transfer function has been computed using Eisenstein and Hu’s fitting formula ( Eisenstein Hu 1998 ), which takes baryonic effects into account in a ΛCDM model. Having chosen an analytical computation of the power spectrum over the traditional numerical one using CAMB ( Lewis et al. 2000 ) is mainly due to computation time. The galaxy-dark matter cross-power spectrum has been computed through Eqs. ( 7 ) and ( 8 ), where the linear dark matter power spectrum is evolved to redshift z via the linear growth factor approximation of Carroll et al. (1992) . The HMF has of course been parametrized according to ( 1 ) for the two different fits we have described in Sect. 2.1 . The deterministic bias associated with each model has been derived using the peak background split as in Sheth Tormen (1999) . Furthermore, we have expressed the mean number of galaxies in a halo of mass M as where ⟨ N c g ⟩ M and ⟨ N s g ⟩ M are the mean number of central and satellite galaxies in a halo of mass M , respectively, expressed in terms of three HOD parameters ( α , log M 1 , log M min ) as and following Zehavi et al. (2005) and Zheng et al. (2005) . In essence, M min is the minimum mean halo mass required to host a (central) galaxy and M 1 > M min is the mean halo mass at which exactly one satellite galaxy is hosted. The mean number density of galaxies at redshift z is then given by The halo density profile has been assumed to match a Navarro-Frenk-White (NFW) profile ( Navarro et al. 1997 ). The normalized Fourier transform of the dark matter distribution within a halo of mass M is then given by ( Cooray Sheth 2002 ) where and ρ s are a scale radius and density that parametrize the profile, concentration parameter of a halo of mass M at redshift z , which satisfies for an NFW profile. The virial radius R vir has been computed through the virial overdensity at redshift z , using the fit by Weinberg Kamionkowski (2003) . It should be noted that we have not defined halos at a certain redshift as overdense regions of a constant factor (say 200) times the background or critical density, but using the virial overdensity instead, which depends on redshift. In practice, for a halo of mass M , we have adopted the concentration parameter by Bullock et al. (2001) , computed r s through ( A.1 ) and, subsequently, calculated ρ s using ( A.2 ). Appendix B: Additional tables and figures Fig. B.1. One- and two-dimensional (contour) posterior distributions from run 5 (in red) and run 1 (in blue), that is, a three-parameter and a two-parameter ST fit with 0 p 1 0.5,