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Observations of the interstellar medium (ISM) show a complex density andvelocity structure which is in part attributed to turbulence. We here present aself-contained introduction to the multifractal formalism in a microcanonicalversion which allows us for the first time to compute precise turbulencecharacteristic parameters from a single observational map without the need foraverages in a grand ensemble of statistical observables. We focus on studyingthe 250 mu-m Herschel map of the Musca filament and make use of MHDsimulations. We find a clear signature of a multiplicative cascade in Muscawith an inertial range from 0.05 to 0.65 pc. We show that the proposedmicrocanonical approach provides singularity spectra which are truly scaleinvariant as required to validate any method to analyze multifractality. Theobtained, for the first time precise enough, singularity spectrum of Musca isclearly not as symmetric as usually observed in log-normal behavior. We claimthat the ISM towards Musca features more a log-Poisson shape of its singularityspectrum. Since log-Poisson behavior is claimed to exist when dissipation isstronger for rare events in turbulent flows in contrast to more homogeneous (involume and time) dissipation events, we suggest that this deviation fromlog-normality could trace enhanced dissipation in rare events at small scales,which may explain or is at least consistent with the dominant filamentarystructure in Musca. Moreover we find that sub-regions in Musca tends to showdifferent multifractal properties. It strongly suggests that different types ofdynamics exist inside the Musca cloud. These differences between sub-regionsappear only after eliminating noise features which have the tendency to"log-normalize" an observational map. Our study sets up fundamental tools whichwill be applied to other galactic clouds and simulations in forthcomingstudies.

astronomy and astrophysics

Description of turbulent dynamics in the interstellar medium:  multifractal/microcanonical analysis I. Application to Herschel observations  of the Musca filament