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**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS**

Multiscale Structure in Dust Reflection and Cold H i
Steven J. Gibson National Astronomy and Ionosphere Center
Abstract. I present 2-D angular optical dust reflection tracing the H analysis reveals a uniform p ower-law in scale, from tens of parsecs down to p ower sp ectra of cold H i emission and i in the Pleiades reflection nebula. This slop e of -2.8 over 5 orders of magnitude tens of astronomical units.

1.

Intro duction

Multiscale structure in the neutral atomic ISM is well known (e.g., Green 1993; Deshpande et al. 2000; Dickey et al. 2001). A quantitative examination of this structure over a wide range of scales may help us understand its physical causes (e.g. turbulent cascades), especially if the smaller scales can be probed. Such an examination is usually difficult with H i 21cm line observations, due to sightline confusion and sensitivity limits at high resolution. However, H i and dust should be well mixed in cold gas, so dust may trace H i structure at fine scales. Powerspectrum studies of dust infrared emission show power-law behavior similar to H i emission (e.g., Gautier et al. 1992), and one study of optical dust reflection in cirrus does as well (Guhathakurta & Cutri 1994). Here I present optical and H i maps of the ISM associated with the Pleiades, where dust grains in a passing cloud are illuminated as a reflection nebula (Gordon & Arny 1984; White 1984; Breger 1987). Since the cluster is nearby ( 130 pc; Percival et al. 2005) and there is minimal dust in front of the neb ula (Cernis 1987), optical features are easily related to specific spatial scales. The nebula's rich optical structure is illustrated in Figures 1 & 2. H i maps must be interpreted with more caution, since some emission may lie in the background, but the emission shown in Figure 3 has the same velocity as interstellar absorption associated with the nebula and matches the dust distribution. 2. Analysis

Each image was run through a 2-D Fast Fourier Transform (FFT) algorithm (Press et al. 1988), and a map of the FFT modulus was computed as the quadrature sum of the real and imaginary transform components. The modulus values were then binned by "radial frequency" fr fx 2 + fy 2 , and the 2-D angular power spectrum P (fr ) was constructed as the square of the median modulus in each fr bin. The median statistic is robust against most artifacts that arise from "wraparound discontinuities" between the right and left or top and bottom image edges. However, the 2 or 3 lowest-frequency bins may still have excess 1


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Figure 1. Pleiades optical nebula, negative logarithmic intensity scale. Top left: 40-field mosaic from the 0.6m Burrell Schmidt telescop e (Gibson & Nordsieck 2003a). The b oxed area is shown in the lower panel. Bottom left: nebular core in the same mosaic. The b oxed area is shown in Figure 2. Right panels: 2-D angular p ower sp ectra derived from the images at left.

power in some cases, particularly for the WIYN data. Image apodization alleviated this problem for the H i maps but did not help with the WIYN data; the Schmidt and HST images produced minimal edge artifacts. Stars were also removed from the WIYN image prior to the FFT, so its power spectrum is quite clean aside from edge effects. No significant stars were present in the HST image. Stars were not removed from the Schmidt mosaic, because the total map flux is dominated by the nebulosity near the brightest stars; however all saturated pixels were replaced by neighbor interpolation. The power spectra are shown individually in Figures 1 - 3 and together as a composite spectrum in Figure 4. Angular frequency is measured in cycles per arcsecond. The dashed lines indicate valid ranges of measurement, particularly where the resolution limits of different data sets occur; near the resolution frequency, photon noise flattens the WIYN and HST spectra, and H i power


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Figure 2. Pleiades optical nebula, negative logarithmic intensity scale. Top left: Wisconsin-Indiana-Yale-NOAO (WIYN) 3.5m image of nebular fine structure east of the 4th-magnitude star Merop e, extended to indicate the p osition of the star and of the panel b elow. Image courtesy of C. J. Conselice and J. S. Gallagher. Bottom left: Hubble Space Telescop e Planetary Camera (HST-PC) image of Barnard's Merop e Nebula, IC 349 (Herbig & Simon 2001), 30 south of Merop e. Image courtesy of T. Simon. Right panels: 2-D angular p ower sp ectra derived from the images at left.

drops precipitously. Over 62% of the large-scale H i map is Dwingeloo data, so the 1 LAB Nyquist limit sets the resolution frequency for that spectrum.

3.

Discussion

All power spectra in Figures 1 - 4 are plotted against a power law with the same slope of -2.8, which was adopted from visual inspection. Within the dashed lines, most spectra are remarkably consistent with this power law. This includes the Schmidt spectra at scales < 1000 (log fr > -3), despite the presence of stars in the image. The consistency between the WIYN and Schmidt spectra


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Figure 3. Pleiades H i 21cm-line emission, negative scale. Bright stars and Schmidt mosaic b oundaries are shown for reference. Top left: 192-field mosaic using the D-configuration Very Large Array (VLA-D), with short spacings provided by the Green Bank 43m telescop e (Gibson et al. 1995). Linear intensity scale. Bottom left: Full Green Bank map (white contour) padded to 128x128 GB pixels with Dwingelo o/LAB 25m data (Kalb erla et al. 2005) for FFT analysis. VLA area is small square. Logarithmic intensity scale. Right panels: Angular p ower sp ectra. The lower sp ectra are for single channels with vlsr = +10 km s-1 ; the upp er sp ectra are integrated over the H i line.

here supports both being dominated by nebulosity. At scales > 1000 , the Schmidt spectrum deviates from the power law, probably because the stellar illumination pattern is becoming more important than dust density structure. For scales larger than the cluster core, the spectrum flattens in the absence of additional illumination structure. Similar "illumination bias" behavior is seen in power spectra of the smooth nebular models of Gibson & Nordsieck (2003b), at both optical and far-infrared wavelengths. The FIR model results indicate that, unfortunately, 100 µm maps from the Infrared Astronomical Satellite (IRAS) cannot be used to study multiscale structure in the Pleiades, because the 5 IRAS beam is too close to the illumination scale.


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Figure 4. Comp osite of the optical and H i angular p ower sp ectra shown in Figures 1-2. The relative scalings have b een adjusted to fit a uniform p ower law, but the slop e of each sp ectrum is unaltered. The dashed lines mark ranges of measurement for each data set. "Wavelength" = 1/spatial frequency. The maximum wavelength of any image is the image width, and the minimum is either twice the b eam width or twice the pixel width, whichever is greater.

The HST results are surprising. While some of the long, parallel streamers in the map are probably part of the larger nebular structure visible in the WIYN image, the bright structure in the HST map is from IC 349, an intense 20 clump whose dynamical relation to the larger Pleiades nebulosity is debated (Barentine & Esquerdo 1999; Herbig & Simon 2001; White 2003). IC 349 has the appearance of a lumpy, limb-brightened, optically-thick cloud, while most Pleiades optical nebulosity resembles smooth, optically-thin filaments. Thus it seems unlikely that IC 349 is typical of nebular structure elsewhere in the Pleiades at these scales. Yet the HST power spectrum is quite similar to the WIYN and Schmidt spectra. It is hard to understand this result unless the power spectrum is relatively insensitive to morphology.


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The H i power spectra are preliminary, as they have not yet been corrected for possible noise contamination. But if noise is not significant, as is probably true for at least the single-dish data, then the H i and dust slopes agree well enough to suggest a single power law for both, even at scales larger than that of the Pleiades nebulosity. This could indicate that the Pleiades ISM structure is the same as the more general ISM, which is consistent with the nebula merely being a chance illumination of ordinary interstellar material. On the other hand, there is no apparent difference in the slope of single-channel H i emission vs. that integrated over all relevant velocities, which does not agree with the theoretical predictions of Lazarian & Pogosyan (2000) for the general ISM. In any case, when combined, all of the Pleiades power spectra are consistent with a single, global power law over 5 orders of magnitude in angular and physical scale. 4. The Next Step: H i Self-Absorption Structure

Near the Galactic plane, where dust and H i emission are more confused, H i self-absorption (HISA) may serve as a useful cold gas tracer (e.g., Gibson et al. 2005). A HISA power spectrum investigation is underway. Acknowledgments. I would like to thank my long-term Pleiades collaborators Ken Nordsieck and Mark Holdaway. Work on this pro ject was supported by the Natural Sciences and Engineering Research Council of Canada and the U.S. National Science Foundation.
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