On Predicting the Polarization of Low-frequency Emission by Diffuse Interstellar Dust

1. This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it must be from Dick.Where is Dick anyway? This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it must be from Dick.Where is Dick anyway?This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it must be from Dick.Where is Dick anyway?This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it must be from Dick.Where is Dick anyway?This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it must be from Dick.Where is Dick anyway?This is a slide from Dick Bond that packs a lot of information. A lot of information is on this slide, so it Martin -- Submillimetre Polarization

2. On Predicting the Polarizationof Low-frequency Emission by Diffuse Interstellar Dust IAS 12 September 2005 Martin -- Submillimetre Polarization

3. ID  Peter Martin  CITA Martin -- Submillimetre Polarization

4. Motivation – CMB Polarization As we have heard, and will hear, several of the recent and next-generation cosmic microwave background (CMB) experiments have polarimetric capability, promising to add to the finesse of precision cosmology. Among these are Archeops, Boomerang (B2K in 2003), and the Planck Surveyor. Martin -- Submillimetre Polarization

5. Archeops and Planck HFI __ __ __  Archeops: 10’ to 20’ @ 545 353 217 143 GHz Martin -- Submillimetre Polarization

6. BOOMERanG    Martin -- Submillimetre Polarization

7. Contaminating components Dust dominates above 100 GHz Higher latitude Figure from http://www.planck.fr/heading136.htmlGiard and Lagache Martin -- Submillimetre Polarization

8. Motivation – Cirrus One of the diffuse foregrounds contaminating the CMB signal near a few 100 GHz (mm to submillimetre range) is “cirrus” – thermal emission by diffuse interstellar dust. Martin -- Submillimetre Polarization

9. Cirrus IRAS 100 micron Faint diffuse emission everywhereeven at high latitude Martin -- Submillimetre Polarization

10. Cirrus Mitigation Not the topic of this talk. Plan A: mask out regions of bright cirrus. But wide sky coverage is needed for precision cosmology. Only 20% of the sky has H I column density below 10^20 / cm^2. Even that produces a non-negligible foreground (~ 1 MJy/sr at 100 microns). Plan B: measure properties of cirrus at high frequency where CMB is not important, and extrapolate to lower frequencies where one does have to address component separation. Martin -- Submillimetre Polarization

11. Motivation – Dust Polarization Since optical polarization is commonly seen, from differential extinction by aligned aspherical dust particles, it is expected that thermal emission from these grains will be polarized. Note: Galaxy is optically thin in submm. Therefore, we see the whole galaxy, or right out of it. Unlike star probes which rely on differential extinction along path. But at high latitude, not dissimilar if stars are sufficiently distant. Martin -- Submillimetre Polarization

12. Polarization: Optical and FIR Both depend on aligned grains. Orientation of E-vector of optical polarization is orthogonal to that of the emitted radiation. Figure from http://www.planck.fr/article263.html Pontieu and Lagache Martin -- Submillimetre Polarization

13. Alignment Theory “Alignment for Dummies” – coming soon to a discerning supermarket checkout counter near you. Martin -- Submillimetre Polarization

14. Polarization of Diffuse Emission Indeed, in the Galactic plane and in dark (molecular) clouds, dust emission in the infrared and submillimetre has been measured to be polarized. (next talk) It seems likely that the faint diffuse cirrus emission, of more relevance to CMB experiments, will be polarized too. Martin -- Submillimetre Polarization

15. Now that we’re motivated… Martin -- Submillimetre Polarization

16. What has been accomplished? (1) We discuss how well the degree of polarization of the diffuse cirrus component can be predicted. To do this we draw on what is known about alignment from optical (and infrared and ultraviolet) interstellar polarization. We emphasize the importance of the polarized intensity and its spectral dependence (needed also for extrapolation to CMB frequencies). Martin -- Submillimetre Polarization

17. What has been accomplished? (2) We comment on polarization (alignment) of small grains, possibly relevant to the anomalous emission. We do not assess the power spectrum, which depends on the spatial variation of the alignment. (other talks) Martin -- Submillimetre Polarization

18. Polarization of Emission Polarized intensity P and intensity I are summed over all grains species. The ratio is gives the degree of polarization of the submillimetre emission, p_emission. Non-aligned grains dilute the net polarization. Because of different weighting, the spectral dependence of the polarized intensity can be different than that of total emission. Martin -- Submillimetre Polarization

19. Calculations: Submillimetre In the submillimetre range of interest, the size of the grains is much smaller than the wavelength  simple analytical formulae can be used for absorption (= emission) cross section per unit volume; e.g., for spheroids: Martin -- Submillimetre Polarization

20. Basic Model For a single grain composition (silicate) and axial ratio, independent of size, There is a slight wavelength dependence across the submillimetre range of interest, due to changes in m, but the large nu^beta dependence cancels out. Depends on composition too (but grains of other materials not aligned?). Martin -- Submillimetre Polarization

21. p_emission for Single Grains P/I for astronomical silicate (and amorphous carbon) Martin -- Submillimetre Polarization

22. Challenges Wide range of grain sizes. Different grain compositions. Grain shape: how flattened/elongated? Which grains are aligned? How well? Martin -- Submillimetre Polarization

23. Grain sizes (and compositions) Grains come in many sizes (perhaps a function of composition). Which grains produce the submillimetre emission? Which grains produce the extinction in the optical and ultraviolet? Which grains polarize in the optical and ultraviolet? Does this result in significant submm polarization? Martin -- Submillimetre Polarization

24. Continued rise in extinction into ultraviolet requires smaller and smaller grains. “Bump” at 2200 A. Separate grain components. Lessons from Extinction Curve Fig. from Cardelli, Clayton, Mathis 1989 Martin -- Submillimetre Polarization

25. Follows a power law of index about 2 (1.84 here). Extinction into IR Silicate absorption at 10 microns (requires most of Si to be depleted in amorphous silicate grains). Fig. from Martin and Whittet 1990 Martin -- Submillimetre Polarization

26. Lessons from IRAS and ISO Spectrum components: Fig from Desert, Boulanger, Puget (1990) grains of size ~0.1 microns   1 mm Martin -- Submillimetre Polarization

27. Origin of the Emission • Components/Mechanisms • > 100 microns: thermal emission by larger grains (size ~ 0.1 microns) • 60 and 25 microns: non-equilibrium emission by smaller grains, 0.007 micron = 70 A = 7 nm • 12 microns: non-equilibrium emission by tiny grains/PAHs, 1 nm • All of these components of course radiate at longer wavelengths too. • Tiny grains also spin rapidly and emit microwave radiation which could be another foreground contaminant of the CMB (anomalous emission). Martin -- Submillimetre Polarization

28. Coronene C24H12 Naphthalene PAHs(simple ones) Phenanthrene Chrysene Martin -- Submillimetre Polarization

29. Submillimetre Spectrum In the submillimetre the thermal emission is characterized by T and often a single beta, the spectral index of the dust emissivity: Total intensity is volume weighted, since C/V is size independent. In ISM, large grains carry most of the volume. Is beta constant (~ 2) with frequency? Is T constant with size? Is epsilon constant with T? Martin -- Submillimetre Polarization

30. Spectral Index Variations • Evidence for excess emission at 217 GHz (1.5 mm) (Archeops experiment: Bernard et al. – talk) • Comments • was attributed to cold dust at 5 – 7 K. But diffuse dust being that cold seems unphysical • effect is seen everywhere (so a property of dust, not environment) • Conclusion • beta is not constant with wavelengthover the range of interest • 1.8 for lambda < 600 microns (> 500 GHz) • 0 at 1 mm • 2.2 at lambda > 2 mm (< 150 GHz) • due to intrinsic processes in amorphous grains Martin -- Submillimetre Polarization

31. Optical (and FIR) Polarization Both depend on aligned grains. E-vector of optical polarization is perpendicular to the projected direction of magnetic field. Figure from http://www.planck.fr/article263.html Pontieu and Lagache Martin -- Submillimetre Polarization

32. Interstellar Polarization: Basics • extinction = scattering + absorption • grains are aspherical • aligned, so that in plane of sky the ensemble average grain profile is elongated • long axis of profile is oriented perpendicular to the magnetic field B • differential extinction according to orientation of electric vector with respect to this profile •  net polarization of transmitted light • greater extinction for E parallel to long axis •  E parallel to short axis, hence parallel to B Martin -- Submillimetre Polarization

33. Wavelength Dependence of Polarization and Extinction Polarization reaches a peak while extinction is still rising. Fig. from Rogers and Martin 1979 Martin -- Submillimetre Polarization Wavenumber 

34. Polarization Curve C low polarization in the UV, whereas extinction keeps rising power law rise in IR (not unlike extinction) Fig. from Martin, Clayton and Wolff 1999 Martin -- Submillimetre Polarization

35. Implication of Low UV Polarization Despite a wide range of grain sizes for extinction, only the larger grains are aspherical and aligned. Figs. from Kim and Martin 1994 Aligned grain mass distr. low polarization in the UV  small grains not aligned Martin -- Submillimetre Polarization

36. “It will be interesting to see if the 3.1 micron ice band is polarized as it would be if the aligned silicate grains were ice-coated.” (Martin 1975) – it is! Polarization of IR Features This is a line of sight to an embedded source, the Becklin-Neugebauer object in OMC 1. Still, the silicate to ice mass ratio is 15 – 45: thin frost. 15 % Fig. from Martin and Whittet 1990 Martin -- Submillimetre Polarization

37. Lessons from IR Extinction Features • 10 micron polarization •  silicate component is aligned • details of p/tau across the feature constrain the band strength and the shape and axial ratio •  Hildebrand and Dragovan 1995 find oblate with axial ratio ~ 1.5 Martin -- Submillimetre Polarization

38. Fluffy silicate agglomerate IDP Individual sub-grains the size of interstellar silicates (0.1 micron) foot

39. GEMS Glass with embedded metals and sulfides. Mg rich silicate. Mid-IR spectrum like comets. Fe and FeS inclusions. Lack of S depletion in gas a problem if GEMS interstellar? foot

40. Lessons from Interstellar Polarization • only the larger grains are aspherical and aligned • 10 micron polarization  silicate component is aligned • axial ratio not extreme; oblate • certainly “adequate” to model with silicates alone Martin -- Submillimetre Polarization

41. Summary so far… Large grains dominate submillimetre emission. Only large (silicate) grains are aligned. But shape and alignment? Martin -- Submillimetre Polarization

42. Shape and Alignment Both influence the degree of polarization. The degree of interstellar polarization is also made larger by larger column densities, but this is just as for extinction. Thus the column density can be normalized out by taking the ratio of polarization to extinction, p/tau. The observed envelope in p vs. tau constrains the shape and the best achieved alignment. Martin -- Submillimetre Polarization

43. Polarization/Extinction at V Observed amount of optical polarization per unit extinction provides the required measure of the asphericity and degree of alignment. Fig. from Serkowski, Mathewson, and Ford 1975 Martin -- Submillimetre Polarization ^

44. Polarization/Extinction This ratio varies systematically over the range infrared – optical – ultraviolet. Martin -- Submillimetre Polarization

45. Bootstrapping • Hildebrand and Dragovan 1995 find the effect of disalignment by comparing • p_e for their model at 2.2 microns • and • p/tau observed at 2.2 microns. • Problems: • former assumed pure absorption, whereas the latter involves grains of size comparable to wavelength, so scattering as well. Model p_e does not really apply at 2.2 microns. • (ii) p_e at 2.2 microns for silicates is very sensitive to how “dirty” they are, which has little effect on submm p_e. Hard to scale. Martin -- Submillimetre Polarization

46. p_emission for a Mixture P/I for astronomical silicate and graphite (both aligned) Martin -- Submillimetre Polarization

47. Polarization/Extinction p/tau ~ 6% at 2.2 microns. Martin -- Submillimetre Polarization

48. Calculating p/tau Need to carry out calculations of extinction (scattering + absorption) by particles comparable in size to wavelength (as in Mie theory for spheres, harder for spheroids). Martin -- Submillimetre Polarization

49. Detailed Models: Recipe • For a given axial ratio, and perfect alignment, find the aligned grain size distribution by fitting the wavelength dependence of interstellar polarization. • Compare to model of interstellar extinction, keeping track of mass of all components (unaligned grains contribute to tau and not p, and so cause dilution). Use models of Kim and Martin 1995. • Calculate p/tau. • Compare this to observed p/tau and deduce a reduction factor R (<1) due to imperfect alignment. Martin -- Submillimetre Polarization

50. Results for Disalignment R Repeat: axial ratios, oblate and prolate shapes. For example, for perfectly aligned oblate silicate particles (R ~ 1 in this case), the axial ratio needs to be no higher than 1.4 to produce the maximum p/tau observed. For larger axial ratios, grains must be somewhat disaligned by a quantifiable amount (reduction factor R < 1) to produce the same p/tau. Martin -- Submillimetre Polarization