The mass distribution and the law of gravity in the Local Group dwarf irregular galaxy IC 1613

IC 1613 is a dwarf galaxy in the Local Group with an absolute magnitude M_B_ = 14.3 (L_B_ = 8.3 x 10^7^ L_sun_). The distance (725 kpc) is well determined from its Cepheids. The galaxy is gas rich, with M_Gas_/L~0.75. We imaged the H I distribution and velocity field using the VLA. The H I is lumpy in the inner parts, but the contours are regular at larger radii. The velocity field is regular and the line of nodes is coincident with the major axis of the gas distribution. The mean streaming velocity as a function of radius is corrected for asymmetric drift to determine the rotation curve. The peak velocity of ~25 km s^-1^ occurs at the outermost radius measured (~2.6 kpc). The acceleration at this point is ~5 x 10^-10^ cm s^-1^. At such low accelerations, modification of Newtonian gravity has been proposed by Milgrom (1983a,b), but we find no evidence for any such effect. With generous allowances for uncertainties in the inclination, velocity dispersion, gas mass, stellar M/L, and distance, the critical acceleration in Milgrom's theory must be a_0_ <~ 10^-9^ cm s^-1^. With all the uncertainties stretched to extremes, a_0_ <~ 3 x 10^-9^ cm s^-1^. Analysis of the rotation curves of bright galaxies has determined that this parameter should be ~1 x 10^-8^ h_50_ cm s^-1^, and the dynamics of the Coma Cluster limit the value to be a_0_ >~ 4 x 10^-8^ h^2^_50_ cm s^-1^. These differences are significant and the parameter constraints clearly depend on the mass of the system, subverting Milgrom's proposal. The rotation curve of IC 1613 shows evidence for dark matter in the outer parts. The maximum density of a dark halo that can be tolerated, p <~ 6 x 10^-26^ g cm^-3^, is an order of magnitude lower than that needed to explain the velocity dispersions of the extreme dwarf spheroidals.