Isospin-violating dark matter and neutrinos from the Sun

We study the indirect detection of dark matter through neutrino flux from their annihilation in the center of the Sun, in a class of theories where the dark matter-nucleon spin-independent interactions break the isospin symmetry. We point out that, while the direct-detection bounds with heavy targets like xenon are weakened and reconciled with the positive signals in DAMA and CoGeNT experiments, the indirect detection using neutrino telescopes can impose a relatively stronger constraint and brings tension to such an explanation, if the annihilation is dominated by heavy quark or τ-lepton final states. As a consequence, the qualified isospin-violating dark matter candidate has to preferably annihilate into light flavors.