RX J1856.5-3754 is one of the brightest nearby isolated neutron stars, and considerable observational resources have been devoted to it. However, current models are unable to satisfactorily explain the data. We show that our latest models of a thin, magnetic, partially ionized hydrogen atmosphere on top of a condensed surface can fit the entire spectrum, from X-rays to optical, of RX J1856.5-3754, within the uncertainties. In our simplest model, the best-fit parameters are an interstellar

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... density N H ≈ 1 × 10 20 cm −2 and an emitting area with R ∞ ≈ 17 km (assuming a distance to RX J1856.5-3754 of 140 pc), temperature T ∞ ≈ 4.3 × 10 5 K, gravitational redshift z g ∼ 0.22, atmospheric hydrogen column y H ≈ 1 g cm −2 , and magnetic field B ≈ (3-4) × 10 12 G; the values for the temperature and magnetic field indicate an effective average over the surface.