.. _runs_cosmos_lf_smf:

COSMOS validation: LF and SMF
==============================

.. warning::

   **Work in progress.** The SMF comparison curves are being corrected.
   The Ilbert+2013 reference model currently shown uses approximate digitized
   data points; the correct double-Schechter model from Table 2 of
   Ilbert et al. (2013) is being substituted. More work is needed before
   the curves are properly derived.

Script: ``scripts/measure_cosmos_lf_smf.py``

**Catalogue:** Ilbert+2009 photo-z (``photoz_vers2.0_010312.fits``), 1 195 952 galaxies.
Selection: ``flag_maskI == 0``, ``photoz > 0``.
Redshift range: :math:`0.2 \leq z \leq 3.0`. Bands: FUV, NUV, B, V, R (LePhare K-corrections).
Masses: ``logMs`` (Chabrier IMF, BC03). Cosmology: :math:`H_0 = 70`, :math:`\Omega_m = 0.30`.

Survey area per band (HEALPix nside = 2048):
FUV 2.01 deg², NUV 2.05 deg², B/V/R ≈ 2.11 deg².
Apparent magnitude limits from mode of N(m): FUV 26.9, NUV 25.1, B/V/R 26.1, I 26.4 (selection band).
Mass completeness limits (Pozzetti+2010 80th percentile): 8.3 dex at z = 0.35 → 11.3 dex at z = 2.5.

.. figure:: ../figures/runs/cosmos_mag_counts.png
   :width: 100%
   :alt: Galaxy number counts per band

   N(m) per band (0.25 mag bins) with estimated :math:`m_\mathrm{lim}` (red dashed).

.. figure:: ../figures/runs/cosmos_smf_comparison.png
   :width: 100%
   :alt: COSMOS SMF comparison

   1/Vmax SMF (blue) vs Ilbert+2013 (red band) and Driver+2022 local model (green dash-dot).
   Agreement is excellent at z = 0.2–1.1 above the mass completeness limit.
   At z > 1.5 the I-band selection misses low-mass galaxies detected by the NIR-selected
   Ilbert+2013 UltraVISTA sample.

.. figure:: ../figures/runs/cosmos_lf_mfuv_comparison.png
   :width: 80%
   :alt: FUV luminosity function

   FUV (~1500 Å) LF. Brightens strongly from z = 0.2 to z = 2, tracing the star-formation
   rate density evolution.

.. figure:: ../figures/runs/cosmos_lf_mnuv_comparison.png
   :width: 80%
   :alt: NUV luminosity function

   NUV (~2500 Å) LF. Shallower GALEX limit (25.1 AB) restricts coverage relative to optical bands.

.. figure:: ../figures/runs/cosmos_lf_mb_comparison.png
   :width: 80%
   :alt: B-band luminosity function

   Rest-frame B-band (~4400 Å) LF vs Ilbert+2005 VVDS (dashed). Agreement within
   uncertainties at z ≤ 1.1.

.. figure:: ../figures/runs/cosmos_lf_mv_comparison.png
   :width: 80%
   :alt: V-band luminosity function

   Rest-frame V-band (~5500 Å) LF. :math:`M_V^\star` brightens by ~0.7 mag from z = 0.35 to z = 2.5.

.. figure:: ../figures/runs/cosmos_lf_mr_comparison.png
   :width: 80%
   :alt: R-band luminosity function

   Rest-frame R-band (~6500 Å) LF vs Loveday+2015 local Schechter reference (orange dashed).

**Outputs:** ``data/COSMOS/cosmos_{smf,lf_BAND}_z{z1}_{z2}.fits``,
``cosmos_mag_limits.fits``, ``cosmos_completeness.fits``.