Does the gamma-ray signal from the central Milky Way indicate Sommerfeld enhancement of dark matter annihilation?

Recently, Daylan et al. (2014) show that the GeV gamma-ray excess signal from the central Milky Way can be explained by the annihilation of $\sim 40$ GeV dark matter through $b\bar{b}$ channel. Based on the morphology of the gamma-ray flux, the best-fit inner slope of the dark matter density profile is $\gamma =1.26$. However, recent analyses of Milky Way dark matter profile favor $\gamma =0.6-0.8$. In this article, we show that the GeV gamma-ray excess can also be explained by the Sommerfeld-enhanced dark matter annihilation through $b\bar{b}$ channel with $\gamma =0.85-1.05$. We constrain the parameters of the Sommerfeld-enhanced annihilation by using the data from Fermi-LAT. We also show that the predicted gamma-ray fluxes emitted from dwarf galaxies generally satisfy the recent upper limits of gamma-ray fluxes detected by Fermi-LAT.