on predicting the polarization of low-frequency emission by diffuse interstellar dust

16 June 2004, Winnipeg CASCA

Martin -- Submillimetre Polarization 1

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On Predicting

the Polarization

of Low-frequency Emission

by Diffuse Interstellar Dust

IAS 12 September 2005



Peter Martin

CITA

ID



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.



Archeops and Planck HFI

Archeops: 10’ to 20’ @ 545 353 217 143 GHz

__ __ __



BOOMERanG



Contaminating components

Dust dominates above 100 GHz

Higher latitude

Figure from http://www.planck.fr/heading136.html Giard and Lagache



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.



Cirrus

IRAS 100 micron

Faint diffuse emission everywhereeven at high latitude



Cirrus MitigationNot 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.



Motivation – Dust PolarizationSince 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.



Polarization: Optical and FIRBoth 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

http://www.planck.fr/article263.html



Alignment Theory“Alignment for Dummies”

– coming soon to a discerning supermarket checkout counter near you.



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.



Now that we’re motivated…



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).



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)



Polarization of EmissionPolarized 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.



Calculations: SubmillimetreIn 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:



Basic ModelFor 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?).



p_emission for Single GrainsP/I for astronomical silicate (and amorphous carbon)



Challenges

Wide range of grain sizes.

Different grain compositions.

Grain shape: how flattened/elongated?

Which grains are aligned? How well?



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?



Lessons from Extinction Curve

Fig. from Cardelli, Clayton, Mathis 1989

Continued rise in extinction into ultraviolet requires smaller and smaller grains.

“Bump” at 2200 A.

Separate grain components.



Extinction into IRFollows a power law of index about 2 (1.84 here).

Fig. from Martin and Whittet 1990

Silicate absorption at 10 microns (requires most of Si to be depleted in amorphous silicate grains).



Lessons from IRAS and ISOSpectrum components: Fig from Desert, Boulanger, Puget (1990)

1 mm

grains of size ~0.1 microns



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).



PAHs(simple ones)

Coronene C24H12Naphthalene

Phenanthrene Chrysene



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?



Spectral Index VariationsEvidence 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 wavelength over 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



Optical (and FIR) PolarizationBoth 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

http://www.planck.fr/article263.html



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



Wavelength Dependence of Polarization and Extinction

Polarization reaches a peak while extinction is still rising.

Fig. from Rogers and Martin 1979 Wavenumber



Polarization Curve

C

Fig. from Martin, Clayton and Wolff 1999

low polarization in the UV, whereas extinction keeps rising

power law rise in IR (not unlike extinction)



Implication of Low UV PolarizationDespite 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.

small grains not aligned

low polarization in the UV



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.

“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!

15 %

Fig. from Martin and Whittet 1990



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

grand foot 38

Fluffy silicate agglomerate IDP

Individual sub-grains the size of interstellar silicates (0.1 micron)

grand foot 39

GEMSGlass 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?



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



Summary so far…

Large grains dominate submillimetre emission.

Only large (silicate) grains are aligned.

But shape and alignment?



Shape and AlignmentBoth 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.



Polarization/Extinction at VObserved 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



Polarization/ExtinctionThis ratio varies systematically over the range infrared – optical – ultraviolet.



BootstrappingHildebrand and Dragovan 1995 find the effect of

disalignment by comparing p_e for their model at 2.2 micronsandp/tau observed at 2.2 microns.Problems: (i) 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.



p_emission for a MixtureP/I for astronomical silicate and graphite (both aligned)



Polarization/Extinctionp/tau ~ 6% at 2.2 microns.



Calculating p/tauNeed to carry out calculations of extinction (scattering + absorption) by particles comparable in size to wavelength (as in Mie theory for spheres, harder for spheroids).



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.



Results for Disalignment RRepeat: 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.



Apply to FIR and Submillimetre

For the same model (shape, axial ratio, grain components), self-consistently calculate the polarization of the low-frequency thermal emission, p_e.

Apply R from interstellar polarization model for that axial ratio (approximately correct).

Repeat for different axial ratios.

predict maximum p_emission expected.



Polarization of Emission of Aligned Grainspredict maximum p_emission expected from the aligned grains. Large.

Note how there is little dependence on shape and axial ratio.



Frequency Dependence of Polarized IntensityBecause of different weighting, the spectral dependence of the polarized intensity P can be different than that of total emission, I

Non-aligned grains dilute the net polarization. If the frequency dependence of emission for the diluting component is different, then this introduces a frequency dependence for p = P/I.

Measuring P (rather than p) offers a direct way of examining the spectral behaviour for the aligned grains.



Complication: DilutionNon-aligned grains contribute to the thermal emission and dilute the net polarization.

In the MRN/Draine and Lee/Kim and Martin model with silicate and (large) graphite, this causes a further reduction, by d ~ 1/3.

Note that the dilution of p/tau in the optical by extinction by unaligned graphite has resulted in a larger R, and so this is payback.



Dilution: Silicate + Graphite ModelSilicate is only part of the submillimetre emission.Fig. from Draine and Anderson 1985



Final Prediction of p_emissionKim & Martin 1995 interstellar polarization models+ maximum interstellar (p/tau)_V = 0.0267 + dilution in submillimetre d = 1/3

Uncertainty arising from using models, and R.



Further Dilution

Self-consistent model predicts a maximum p_emission = 7 +/- 2 %.

When averaged over large regions with • non-uniform alignment (beam dilution) • or less than perfect alignment (perhaps the direction of the magnetic field), • or with alignment which changes along the line of sight, typically half of this might be expected (recall SMF figure of p/E_B-V).



ObservationsArcheops observes ~5 %, even averaged over large regions near the plane. Note E-vector orientation is as expected too.



Discussion: alternative models

Desert et al. model uses one type of big grain. Therefore, less dilution in submm (only by VSGs; d ~ 0.9), but less in optical too, lowering R and so compensating in product d*R.

Also no refractive indices (or shape or axial ratio) specified, so no detailed calculation possible.



Alignment of Small Grains

p/tau very low in the UV, where extinction comes from small grains (VSGs, PAHs). What polarization there is is consistent with coming from big grains. Small grains, the ones that spin most rapidly and might produce anomalous emission, are not well aligned.



Polarization: UV extinction bump

This star is rho Oph AB. Fig. from Wolff et al. 1997



Polarization: UV bump (1)

Polarization feature is at the same position as the UV extinction bump, has a positive excursion, and shows no change in position angle.

But only seen in 2 of the 28 lines of sight in the Galaxy observed by WUPPE and HST (FOS), despite sufficient S/N (Martin, Clayton, and Wolff 1999).

Not a common phenomenon.



Polarization: UV bump (2)

The ratio delta_p/delta_tau is a measure of the polarization efficiency of the carriers of the extinction bump and polarization feature (if present).This ratio is small compared to the corresponding ratio for the continuum (often by an order of magnitude). It is at least 2 orders of magnitude smaller than the theoretical maximum for perfectly aligned graphite carriers (0.8; Martin et al. 1995).Thus, either the alignment is quite incomplete or only a small fraction of the grains is aligned.

.



BN polC tau = 3, p = 15 at 10 microns. p/t = .2 (.22) see martin 1975Would this, compared to 2 microns, make sense



Bare silicatesHildebrand and Dragovan 1995 uses bare silicates; argues ice (O’Connell) can’t be too thick. Does not mention organic refractories.



Martin 75It 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. (silicate to ice mass ratio 15 – 45).



CoatedDesert: BG are dominated in mass by the silicates, with coating of organicCG 89: volume dominated (90%) by organic refractories so optical properties are those of mantle (but if all Si is depleted, and only 26% C in mantles, then Si mass is significant (density is higher).Both: need to absorb starlight to warm up. (circumstellar silicates are warm without organic refractory mantles)Both simulate optical albedo, but don’t have reliable IR (2 micron) albedo.



DesertSizesPAH: 1 nm = 10 A = 0.001 micronVSG: 7 nm = 70 A = 0.007 micronBG: 15 to 110 nm = 150 to 1100 A = 0.015 to 0.11 micronMost mass in largest particles



templateC

grand foot 74

17O anomaly

A grain enriched in 17O.

Supernova condensate or massive star?



IR spectrum

For

on predicting the polarization of low-frequency emission by diffuse interstellar dust

Documents

lot of information

dick bond

submillimetre range

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frequency emission

cirrus thermal emission

diffuse foregrounds

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