How can we measure turbulent microscales in the Interstellar Medium? Steven R. Spangler, University of Iowa

The Warm Ionized Medium (WIM): where do stellar structures end and turbulence begin? An overall view of the plasma we are studying(WHAM; Haffner et al 2003, ApJS 149, 405)

Turbulent spectra can be measured directly in the solar wind R. Bruno, B. Bavassano, Ad Sp. Res. 35, 939, 2005 Magnetic power spectrum Density spectrum Outer scale Inner scale

New result in solar wind turbulence…measurement and theoretical interpretation of dissipation range Sahroui et al, PRL 102, Damping understood as Landau damping of kinetic Alfven waves (e.g. Howes et al JGR 113, A05103, 2008)

An important feature of density turbulence in the solar wind: enhanced compressibility at the dissipation scale Density spectrum power law with “ bulge ” at ion inertial length (Coles and Harmon, ApJ 227, 1023,1989; Harmon and Coles, JGR A 110, A03101, 2005 )

How can we determine properties of microscale fluctuations in the ISM? … radio scintillations

Types of Scintillation Phenomena (i)Frequency scintillation (ii) Intensity cross- correlation

Technique of choice: angular broadening A crash course in radio astronomy What interferometers measure: the mutual coherence function Mutual coherence function as a continuous function: the complex visibility function Interferometers can also image sources viewed through a turbulent plasma

: a source broadened by interstellar turbulence Spangler and Cordes, ApJ 332, 346, 1988

Application of angular broadening theory yielded spectral index of interstellar turbulence Analysis yielded alpha = / (Kolmogorov = 3.67)

How do properties of visibility function relate to properties of the turbulence? Cordes et al, ApJ 288, 221, 1985; Spangler and Gwinn, ApJ 353, L29, 1990 Model for turbulent power spectrum Resultant phase structure function Reminder: alpha=11/3 is Kolmogorov Integrand tells which wavenumbers contribute most to measurement

What wavenumbers make primary contribution to measurement? qr Interferometric visibility measurements are dominated by irregularities with size of order the baseline length (Spangler, AIP Conf. Proc. 174, 66, 1988)

Interferometer angular broadening measurements are good for bumps or breaks in the spectrum on the dissipation scale The effect of a spectral “feature” Other spectral “features” at high wave numbers would produce similar departures from pure power law behavior

Evidence for a dissipation scale in interstellar plasma turbulence Spangler and Gwinn, ApJ 353, L29, 1988

Identification of the spectral break in interstellar turbulence … ion inertial length

Independent indicators of a spectral break in interstellar turbulence on the ion inertial scale Molnar et al, ApJ 438, 708, 1995…measurement of break in structure function in angular broadening measurements. Inner scale of 300 km. Rickett et al, MNRAS 395, 1392, 2009…estimate of turbulence characteristics from pulse broadening of scattered pulsars; shape of pulse at late arrival times. Inner scale km All results pertain to plasmas in HII regions

The possible significance of the Rickett et al (2009) results: a break, not a bottleneck Pure Kolmogorov Kolmogorov with break

Does the “Harmon-Coles Bulge” exist in interstellar turbulence? Density spectrum power law with “ bulge ” at ion inertial length (Coles and Harmon, 1989; 2005) Pure Kolmogorov power law Kolmogorov power law with spectral break

Progress in radioastronomical instrumentation means these measurements can be done better now

Zusammenfassung Recent developments in the theory of turbulence indicate that important processes are occurring on the ion inertial scale Radioastronomical measurements give us quantitative information on these scales New observations with existing radiotelescopes could address important issues in interstellar plasma physics Thanks

An inspirational figure for European-American scientific cooperation