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We present a new method to constrain the dark matter halo density profiles ofdisk galaxies. Our algorithm employs a Markov Chain Monte Carlo (MCMC) approachto explore the parameter space of a general family of dark matter profiles. Weimprove upon previous analyses by considering a wider range of halo profilesand by explicitly identifying cases in which the data are insufficient to breakthe degeneracies between the model parameters. We demonstrate the robustness ofour algorithm using artificial data sets and show that reliable estimates ofthe halo density profile can be obtained from data of comparable quality tothose currently available for low surface brightness (LSB) galaxies. We presentour results in terms of physical quantities which are constrained by the data,and find that the logarithmic slope of the halo density profile at the radiusof the innermost data point of a measured rotation curve can be stronglyconstrained in LSB ([Vstar/Vobs]max ~ 0.16) galaxies. High surface brightnessgalaxies ([Vstar/Vobs]max ~ 0.79) require additional information on themass-to-light ratio of the stellar population - our approach naturallyidentifies those galaxies for which this is necessary. We apply our method toobserved data for the dwarf irregular galaxy DDO 154 and recover a logarithmichalo slope of -0.39 +- 0.11 at a radius of 0.14 kpc. Our analysis validatesearlier estimates which were based on the fitting of a limited set ofindividual halo models, but constitutes a more robust constraint than waspossible using other techniques since it marginalises over a wide range of haloprofiles.

Dark matter in disk galaxies I: a Markov Chain Monte Carlo method and application to DDO 154