Power spectra of de-projected images of late-type galaxies in gas and/or dust emission are very useful diagnostics of the dynamics and stability of their interstellar medium .
Previous studies have shown that the power spectra can be approximated as two power-laws , a shallow one at large scale ( larger than 500 pc ) and a steeper one at small scale , with the break between the two corresponding to the line-of-sight thickness of the galaxy disk .
The break separates the 3D behaviour of the interstellar medium at small scale , controlled by star formation and feedback , from the 2D behaviour at large scale , driven by density waves in the disk .
The break between these two regimes depends on the thickness of the plane which is determined by the natural self-gravitating scale of the interstellar medium .
We present a thorough analysis of the power spectra of the dust and gas emission at several wavelengths in the nearby galaxy M33 .
In particular , we use the recently obtained images at five wavelengths by PACS and SPIRE onboard Herschel .
The large dynamical range ( 2-3 dex in scale ) of most images allows us to determine clearly the change in slopes from -1.5 to -4 , with some variations with wavelength .
The break scale is increasing with wavelength , from 100 pc at 24 and 100 \mu m to 350 pc at 500 \mu m , suggesting that the cool dust lies in a thicker disk than the warm dust , may be due to star formation more confined to the plane .
The slope at small scale tends to be steeper at longer wavelength , meaning that the warmer dust is more concentrated in clumps .
Numerical simulations of an isolated late-type galaxy , rich in gas and with no bulge , like M33 , are carried out , in order to better interpret these observed results .
Varying the star formation and feedback parameters , it is possible to obtain a range of power-spectra , with two power-law slopes and breaks , which nicely bracket the data .
The small-scale power-law is indeed reflecting the 3D behaviour of the gas layer , steepening strongly while the feedback smoothes the structures , by increasing the gas turbulence .
M33 appears to correspond to a fiducial model with an SFR of \sim 0.7 M _ { \odot } /yr , with 10 % supernovae energy coupled to the gas kinematics .