Aims. The process of gravitational fragmentation in the L1482 molecular filament of the California molecular cloud is studied by combining several complementary observations and physical estimates. We investigate the kinematic and dynamical states of this molecular filament and physical properties of several dozens of dense molecular clumps embedded therein. Methods. We present and compare molecular line emission observations of the J=2--1 and J=3--2 transitions of 12CO in this molecular complex, using the KOSMA 3-meter telescope. These observations are complemented with archival data observations and analyses of the 13CO J=1--0 emission obtained at the Purple Mountain Observatory 13.7-meter radio telescope at Delingha Station in QingHai Province of west China, as well as infrared emission maps from the Herschel Space Telescope online archive, obtained with the SPIRE and PACS cameras. Comparison of these complementary datasets allow for a comprehensive multi-wavelength analysis of the L1482 molecular filament. Results. We have identified 23 clumps along the molecular filament L1482 in the California molecular cloud. All these molecular clumps show supersonic non-thermal gas motions. While surprisingly similar in mass and size to the much better known Orion molecular cloud, the formation rate of high-mass stars appears to be suppressed in the California molecular cloud relative to that in the Orion molecular cloud based on the mass-radius threshold derived from the static Bonnor Ebert sphere. Our analysis suggests that these molecular filaments are thermally supercritical and molecular clumps may form by gravitational fragmentation along the filament. Instead of being static, these molecular clumps are most likely in processes of dynamic evolution.
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