Estimate of the Warm Dark Matter Free-Streaming Cut-Off with Isolated Dwarf Galaxies in the Local Field

The standard cold dark matter ΛCDM cosmology model is a triumph of modern physics. However, it predicts an excess of isolated dwarf galaxies in the field. Warm dark matter is an alternative that reduces the predicted number density of dwarf galaxies. We obtain the warm dark matter free-streaming cut-off wavevector $k_{\text{fs}}$ from the number density of isolated dwarf galaxies in the Local Field with data of the Local Volume Database (LVDB) catalog. $k_{\text{fs}}$ is defined as follows: $P_{\Lambda \text{CDM}}\left(k\right)\text{exp}\left(？k^2/k_{\text{fs}}^2\right)$ is the linear density power spectrum, before first galaxies, i.e., before re-generation of small-scale perturbations, referred to the present time. We obtain $k_{\text{fs}}={2.5}_{？1.9}^{+1.8}\text{？}{\text{Mpc}}^{？1}$ , with 68% confidence. This result is in agreement with previous measurements, but in disagreement with published limits.