Dark gamma-ray bursts (GRBs) are sources with no or faint optical/near infrared (NIR) afterglow with respect to the X-ray one. Three possible explanations of this optical darkness have been proposed, namely: i) the GRB might be at high redshift, such that the Lyman α absorption prevents optical identifications; ii) dust in the GRB host galaxy may absorb the optical/NIR wavelengths; and iii) the optical faintness might have an intrinsic origin. We study two dark GRBs discovered by Swift, namely, GRB100614A and GRB100615A. These sources are bright in the X-rays, but no optical/NIR afterglow has been detected for either source, despite the efforts of several follow-up campaigns that have been performed since soon after the GRB explosion. We analyze the X-ray data and collect all the optical/NIR upper limits in literature for these bursts. We then build optical-to-X-ray spectral energy distributions (SEDs) at the times at which the reddest upper limits are available, and we model our SEDs with the attenuation curves of the Milky Way (MW), Small Magellanic Cloud (SMC), and one obtained for a sample of starburst galaxies. We find that to explain the deepest NIR upper limits assuming either a MW or SMC extinction law, the visual extinction towards GRB100614A is AV>47mag, while for GRB100615A we obtain AV>58mag using data taken within one day after the burst and AV>22mag even 9.2 days after the trigger. If these bursts were strongly extincted by dust, these results imply that a MW or SMC-like dust obscuration is unlikely to be able to explain their optical darkness. Since both GRBs are bright in X-rays, explanation iii) also cannot explain their dark classification, unless optical radiation and X-rays are not part of the same synchrotron spectrum. In particular, the X-ray emission during the first 100-10000 s after the burst, shows in ∼70% of the cases a ``shallow phase'' unexpected by the fireball model, typically not tracked at optical wavelengths, that could mimic a stronger optical dust extinction than the real one. An alternative, or complementary explanation of the previous possibility, involves greyer extinction laws. A starburst attenuation curve gives AV>11 (AV>15) for GRB100614A (GRB100615A) before 1 day after the burst, which is less extreme, despite still very high. Assuming high redshift in addition to extinction, implies that AV>10 at z=2 and AV>4-5 at z=5, regardless of the adopted extinction recipe. These lower limits are well above the AV computed for previous GRBs at known redshift, but not unlikely. A different, exotic possibility would be an extremely high redshift origin (z>17 given the missing K detections). Population III stars are expected to emerge at z∼20 and can produce GRBs with energies well above those inferred for our GRBs at these redshifts. However, high NH values (above the Galactic ones) toward our GRBs challenge this scenario. Mid- and far-IR late afterglow (>105s after trigger) observations of these extreme class of GRBs can help us to differentiate between the proposed scenarios.
gamma-ray burst: general - dust, extinction - stars: Population III - gamma-ray burst: individual: GRB 100614A - gamma-ray burst: individual: GRB 100615A