The Small-scale Structures in Interstellar HI: A resolvable puzzle? Avinash A. Deshpande Raman Research Institute, Bangalore (+ K.R. Anantharamaiah, K.S. Dwarakanath, W.M. Goss, J.A. Hodge, P.M. McCulloch, and V. Radhakrishnan)

Pre-puzzle picture Birth of the puzzleBirth of the puzzle What do we actually measure ? HI- opacity distribution, longitudinal integration, power-spectra (e.g., in the Cas-A direction) & implications Possible resolution (and the howevers) Implications for other components of ISM (e.g., Extreme scattering events, DM changes/variance)

Single-dish studies: cloud size ~ 1pc Aperture-synthesis studies : Greisen, 1973; Bregman et al, 1983; Schwarz et al, 1986 >> Structures detected down to the resolution limit of these observations (~1 arc-min) similar results from studies in other directions …e.g. Green (1989) … direct measurement of Fourier (visibility) components. >> HI gas in our galaxy is organized on, and maintains, a hierarchy of scales from 1 kpc to at least 1 pc.

(Subsequent) VLBI studies (triggered what has remained as a puzzle for a few decades.)  Dieter, Welch & Romney (1976): 3C147 Observed: variation in the HI opacity on scale <0”.16 Concluded: cloud size <70AU; n(HI) ~ 10 5 cm -3 ; M(HI)~ 3x10 -7 M_solar  Crovisier & Dickey (1983): cutoff below 0.2 pc??  Diamond et al (1989) Observed: sub-arc scale opacity variation (3 extra-gal sources) most striking changes in direction of 3C138 Concluded: clouds with linear diameters ~ 25 AU; n(HI) ~ cm -3

 Davis et al (1996), Faison et al (1998): imaging of 7 sources; Δτ ~ on 10s of AU (transverse) separation. Also,……  Pulsars: two/multi-epoch absorption measurements ( ν ~ 100 km/s …. midway movement 10AU/year) e.g., PSR (ad et al, 1992): marginal change in opacity noticed.  A detailed and more sensitive study in 6 pulsar directions by Frail et al (1994) : opacity variations ( Δτ ~0.1 ) with time.

Over-dense, over-pressure clouds of 10s of AU scale….when a cutoff at 0.2 pc was implied by other considerations! Naturally, a puzzle appeared to have born The observations were/are mostly okay….did not really create the puzzle. Did the interpretation create it ? ??

Problems with the small-scale structure in HI: Heiles(1996) The (over) pressure problem: P SC ~ 40T 2 50 P eq ism G G = L || L possible…high G & low T ?? Cylinders and disks seen as continuous curved filaments and curved sheets ( G cyl ~ 5, G disk ~10) for T~ 15K Recognition of a non-unity G was the real major step in beginning to resolving the puzzle.

But, are such preferentially aligned lower dimensional structures really essential for the “G” to be high ? No. A simple-minded linear increase in the opacity variance from the implicit integration along sightlines can be very significant, even in a typical velocity sliced opacity distribution. …..slow but steady gain ! sqrt(spatial_thickness_of_Vslice/contributing_scale)

What do we actually measure in VLBI and multi-epoch pulsar observations? VLBI a. structure of the background source b. structure of the absorbing gas c. spatial frequency filter function of the telescope Case 1. Uniform a 2. Uniform b a x b transfer fn. c richer in structure than a or b

Note : absorption “visibility” at large spatial frequency does not always imply small-scale structure in ‘b’  effect of ‘a’ should be carefully accounted. When ‘a’ is uniform (or, while measuring HI emission, Green1993 ), a single interferometer baseline gives a pure measure of a point in power spectrum. Real life situation is in between the two cases (1 & 2). Proper imaging is required (mapping) and then compare opacity in closely separated directions [also, need to study distribution over a range of scales].

What should we expect….? …cont. Consider, an opacity difference between two different sight-lines sampling a transverse separation, say, X o Is the opacity difference contributed by a longitudinal scale which is also equal to X o ? NO! …..All longitudinal scales contribute! Does it correspond to an opacity contribution from a single transverse scale X o ? NO! …..All transverse scales contribute!

(1-cos(2pi.Xo/X))/2 Xo

Fractional integral power V/s log(X/Xo)

Ironically, the scale X o does not contribute even the large scales contribute (“red” spectra), although with much reduced weightage. So, as a variance of the opacity differences, one is measuring the “structure function” (Δτ 2 (X o )) (related to FT power spectrum), and NOT a point in the power-spectrum itself. (i.e., NOT a contribution at ONE particular spatial frequency, BUT a SUM over all spatial frequencies).

What is the expected structure function for HI opacity ? Cas-A data: opacity distribution >> FT>> ….. Estimation of power-spectrum>> power-law slope ~ -2.8 (ad,Dwarakanath,Goss 2000) Consistent with Green’s (1993) range of estimates of spatial-power spectral slopes……for HI emission.

Cas-A opacity: spatial spectrum 0.02pc 4pc

Expectations for opacity variations at small transverse separations

The Howevers Cas-A data is only indicative…. Power-spectral slopes and fluctuation strengths may be quite different in different directions in the galaxy. (e.g. for HI emission: Green, 1993; Cyg-A…..ad+Dwarakanath,Goss,2000; ISM simulations….Poster by Hodge+ad) *** Change of slope by 0.1 leads to a factor of 2 different extrapolated expectation in opacity difference. Note that extrapolations is over many orders in scales. One hopes that the present/future measurements, when systematically combined and compared, will reveal the variety in the spatial distribution, and provide a clear picture of the details. Need for structure function/power-spectral measurements in more directions.

What about lower dimensional structures one observes and expects from other considerations? Yes, lower dimensional discrete structures like shells and filaments do exist in reality, but are not essential to invoke as wide-spread, or a part of diffuse component, to understand the presently observed so-called small-scale structure. But they can only increase the “expected” variance.

Is the same resolution relevant for ESEs ? …over-dense plasma lenses ? Yes, it is easy to explain both the strengths and the frequency of the ESEs as just another manifestation of random ionized medium. (ad+Radhakrishnan, 2006)

A simulated ESE…. At a low and high RF The structure function also gives expected DM Variance/changes_with_time

Conclusions Opacity differences observed so far over AU transverse separations are consistent with a single power-law description (e.g., with slope -2.8) of the distribution of HI opacity in the ISM.

It is wrong to directly associate the transverse separation to a longitudinal scale (for estimating the HI number density) because, the observed column density difference is contributed by a range of scales (large as well as small). Disks/ cylinders (i.e. filaments/sheets), as well as very low temperatures, are not essential. Recent observations [e.g. Faison, Goss 2001, Brogan et al 2005] seem consistent with the general predictions.

All may be well pressure equilibrium seems to hold good for the relevant range of structures. Above considerations relevant for Ca II, Na I observations. (τ differences) The ESE’s can also be easily explained as merely due to expected statistical fluctuations in density of ionized component.

Thank you.