Intermediate-mass black holes in dwarf galaxies out to redshift $\sim$
  2.4 in the Chandra COSMOS Legacy Survey
  We present a sample of 40 AGN in dwarf galaxies at redshifts $z \lesssim$
2.4. The galaxies are drawn from the \textit{Chandra} COSMOS-Legacy survey as
having stellar masses $10^{7}\leq M_{*}\leq3 \times 10^{9}$ M$_{\odot}$. Most
of the dwarf galaxies are star-forming. After removing the contribution from
star formation to the X-ray emission, the AGN luminosities of the 40 dwarf
galaxies are in the range $L_\mathrm{0.5-10 keV} \sim10^{39} - 10^{44}$ erg
s$^{-1}$. With 12 sources at $z > 0.5$, our sample constitutes the
highest-redshift discovery of AGN in dwarf galaxies. The record-holder is
cid\_1192, at $z = 2.39$ and with $L_\mathrm{0.5-10 keV} \sim 10^{44}$ erg
s$^{-1}$. One of the dwarf galaxies has $M_\mathrm{*} = 6.6 \times 10^{7}$
M$_{\odot}$ and is the least massive galaxy found so far to host an AGN. All
the AGN are of type 2 and consistent with hosting intermediate-mass black holes
(BHs) with masses $\sim 10^{4} - 10^{5}$ M$_{\odot}$ and typical Eddington
ratios $> 1\%$. We also study the evolution, corrected for completeness, of AGN
fraction with stellar mass, X-ray luminosity, and redshift in dwarf galaxies
out to $z$ = 0.7. We find that the AGN fraction for $10^{9}< M_{*}\leq3 \times
10^{9}$ M$_{\odot}$ and $L_\mathrm{X} \sim 10^{41}-10^{42}$ erg s$^{-1}$ is
$\sim$0.4\% for $z \leq$ 0.3 and that it decreases with X-ray luminosity and
decreasing stellar mass. Unlike massive galaxies, the AGN fraction seems to
decrease with redshift, suggesting that AGN in dwarf galaxies evolve
differently than those in high-mass galaxies. Mindful of potential caveats, the
results seem to favor a direct collapse formation mechanism for the seed BHs in
the early Universe.
