Deep R-band CCD linear polarimetry collected for fields with lines-of-sight toward the Lupus I molecular cloud is used to investigate the properties of the magnetic field within this molecular cloud. The observed sample contains about 7000 stars, almost 2000 of them with polarization signal-to-noise ratio larger than 5. These data cover almost the entire main molecular cloud and also sample two diffuse infrared patches in the neighborhood of Lupus I. The large scale pattern of the plane-of-sky projection of the magnetic field is perpendicular to the main axis of Lupus I, but parallel to the two diffuse infrared patches. A detailed analysis of our polarization data combined with the Herschel/SPIRE 350 um dust emission map shows that the principal filament of Lupus I is constituted by three main clumps acted by magnetic fields having different large-scale structure properties. These differences may be the reason for the observed distribution of pre- and protostellar objects along the molecular cloud and its apparent evolutive stage. On the other hand, assuming that the magnetic field is composed by a large-scale and a turbulent components, we find that the latter is rather similar in all three clumps. The estimated plane-of-sky component of the large-scale magnetic field ranges from about 70 uG to 200 uG in these clumps. The intensity increases towards the Galactic plane. The mass-to-magnetic flux ratio is much smaller than unity, implying that Lupus I is magnetically supported on large scales.
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