Angle-dependent radiative grain alignment; Confirmation of a magnetic field - radiation anisotropy angle dependence on the efficiency of interstellar grain alignment
B-G Andersson, O. Pintado, S.B. Potter, V. Straizys, M. Charcos-Llorens
aa r X i v : . [ a s t r o - ph . GA ] S e p Astronomy & Astrophysics manuscript no. Andersson c (cid:13)
ESO 2018November 16, 2018
Angle-dependent radiative grain alignment
Confirmation of a magnetic field – radiation anisotropy angle dependence onthe efficiency of interstellar grain alignment
B-G Andersson ⋆, , O. Pintado , ∗ , S.B. Potter , V. Straiˇzys , and M. Charcos-Llorens USRA/SOFIA Science Center, NASA Ames Research Center, Mail Stop N211-3, Moffett Field, CA 94035, USA Instituto Superior de Corellaci´on Geol´ogica, CONICET, Miguel Lillo 205, 4000 San Miguel de Tucum´an, Argentina South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape Town, South Africa Institute of Theoretical Physics and Astronomy, Vilnius University, Goˇstauto 12, Vilnius LT-01108, Lithuania
ABSTRACT
Context.
Interstellar grain alignment studies are currently experiencing a renaissance due to the development of a newquantitative theory based on Radiative Alignment Torques (RAT). One of the distinguishing predictions of this theoryis a dependence of the grain alignment efficiency on the relative angle (Ψ) between the magnetic field and the anisotropydirection of the radiation field. In an earlier study we found observational evidence for such an effect from observationsof the polarization around the star HD 97300 in the Chamaeleon I cloud. However, due to the large uncertainties inthe measured visual extinctions, the result was uncertain.
Aims.
By acquiring explicit spectral classification of the polarization targets, we have sought to perform a more precisereanalysis of the existing polarimetry data.
Methods.
We have obtained new spectral types for the stars in our for our polarization sample, which we combine withphotometric data from the literature to derive accurate visual extinctions for our sample of background field stars. Thisallows a high accuracy test of the grain alignment efficiency as a function of Ψ.
Results.
We confirm and improve the measured accuracy of the variability of the grain alignment efficiency with Ψ, seenin the earlier study. We note that the grain temperature (heating) also shows a dependence on Ψ which we interpret asa natural effect of the projection of the grain surface to the illuminating radiation source. This dependence also allowsus to derive an estimate of the fraction of aligned grains in the cloud.
Key words.
Radiation mechanisms: general, Techniques: polarimetric, (ISM:) dust, extinction, ISM: magnetic fields
1. Introduction
Broadband optical/infrared interstellar polarization wasfirst detected in 1949 (Hall 1949; Hiltner 1949b,a) andwas already from the start assumed to be associated withdichroic extinction due to asymmetric dust grains alignedwith their long axis across the magnetic field direction(Hiltner 1949a; Spitzer & Tukey 1949). However, despiteover 60 years of efforts, the details of the grain align-ment process are still not fully understood. A quantita-tive understanding of the physical processes responsible forthe grain alignment and hence polarization will allow usnot only a better understanding of interstellar magneticfields, by e.g. putting the Chandrasekhar-Fermi method(Chandrasekhar & Fermi 1953) on a more solid footing, but ⋆ Visiting Astronomer, Complejo Astron´omico El Leoncito,operated under agreement between the Consejo Nacional deInvestigaciones Cientficas y T´ecnicas de la Rep´ublica Argentinaand the National Universities of La Plata, C´ordoba and SanJuan. will likely also provide new probes of the characteristics ofthe dust.The long standing ”text book” explanation for thealignment, via paramagnetic relaxation in rotating grains,was put forward in the seminal paper by Davis andGreenstein (Davis & Greenstein 1951: DG). Over the fol-lowing decades, various modifications were then proposedto enhance the efficiency of this mechanism, including pro-posals for enhancing the magnetic susceptibility of the ma-terial (Jones & Spitzer 1967; Mathis 1986) and enhancedtorques on the grains due to particle ejections from thegrain surface (Purcell 1979). Generally, the driving mecha-nism for the grain spin-up in the various modifications tothe DG mechanism are fixed in the grain’s coordinate sys-tem (including the above so called ”Purcell rockets” if theparticle ejection sites are restricted to specific locations onthe grain surface).Another long-standing possibility to produce grainalignment is through mechanical alignment in situationswith relative motion between the gas and dust (Gold 1952;Lazarian & Efroimsky 1996). This flow will tend to cause the grains to align themselves with as small a collisionalcross-section as possible to the flow (Lazarian & Efroimsky1996). Because most large scale flows in the ISM (includingwinds from hot stars) tend to be ionized, these flows areusually constrained to be along the magnetic field lines andtherefore cause grain alignment with the long axis of thegrain along the magnetic field direction and polarizationperpendicular to the magnetic field direction.Starting in the 1990s several authors, includingLazarian & Draine (1999a,b) and Roberge (2004) put theparamagnetic relaxation paradigm into doubt by showingthat, due to the internal energy modes of the grains, a dustgrain will tend to change its orientation in space on rel-atively short time scales. Since such a ”flip” will cause atorque fixed in the grain to drive the grain rotation in theopposite direction (in a space-based coordinate system) thegrain never achieves a significant angular momentum, mak-ing paramagnetic relaxation alignment inefficient.Parallel to the discovery of these challenges forthe classical DG model, an alternative theory of in-terstellar grain alignment was being worked out byBruce Draine, Alexander Lazarian and their coworkers(e.g. Draine & Weingartner 1997; Lazarian & Hoang 2007).Based on early work by Dolginov & Mitrofanov (1976) theyshowed that an irregular grain with a net helicity will bespun up by the differential scattering of the left and right-hand circular components in an external light source. Overmany periods of Lamour precession, the light can then alsoalign the grain with their long axis perpendicular to themagnetic field, without any contribution from paramag-netic relaxation. Because helicity is invariant on reflection,this mechanism is not susceptible to the limitations by the”thermal flipping” of the grain. The sole environmentalrequirement for alignment by this mechanism is that theradiation field be anisotropic. In the interstellar medium,this is almost always the case. Hence, while the physicalmechanisms responsible for the grain alignment are quitedistinct, to first order extended DG alignment and radia-tive alignment provide the same observational prediction;namely polarization parallel to the projected magnetic fielddirection.Radiative Alignment Torque (RAT) theory has maturedover the last decade and is now providing a number of spe-cific, testable, predictions (Lazarian & Hoang 2007). Onesuch prediction, which is especially attractive for probingthe validity of the theory, since it is unique to RAT theory, isthat the alignment efficiency, but not the polarization angle,should vary with the angle between the magnetic field andthe radiation field anisotropy (Ψ; see Lazarian & Hoang2007). One way to observationally probe this prediction isto find dust grains for which the dominant radiation sourceis a localized source (a star) and measure the alignmentefficiency for background stars projected at different posi-tion angles around the source star. Figure 1 illustrates thegeometry of the situation.We found such a combination of star and nearby dust inthe Chamaeleon I cloud and showed in Andersson & Potter(2010), combining new polarimetry with the multi-band po-larimetry from Whittet (1992), that the grain alignment isindeed enhanced at small projected distances to the centralsource star (in this case HD 97300). A preliminary study ofthe angle dependence of the alignment was also carried outin Andersson & Potter (2010), but was limited by the factthat, for most of our field stars, the spectral classification BB b a Fig. 1.
The geometry used to probe the effects of the rel-ative orientation of the magnetic field and radiation fieldanisotropy is illustrated. In the two panels, the dashed linesillustrate an idealized magnetic field. (a; side view) A brightsource is located close to and in front of an underlying in-terstellar cloud surface, such that its radiation locally dom-inates over the diffuse radiation field. (b; en face view) Byprobing the polarization of background field stars we canprobe the effects of angle dependent Radiative AlignmentTorque (RAT) grain alignment (Adapted, with permissionof the AAS, from Andersson & Potter 2010)and therefore the determinations of the visual extinctionson each line of sight, had to be accomplished using near in-frared (NIR; 2MASS) photometry alone. Because the smallcolor excesses in the NIR and uncertainties in the reddeningvector slope, the spectral classifications typically had uncer-tainties of a full spectral class, translating to uncertaintieson the visual extinctions of ∼
2. Observations, data reduction and analysis
We used the REOSC spectrometer (Pintado & Adelman1996) on the 2.15 m telescope at the CASLEO on thenights of 2011, March 4–6. The spectrometer was used withthe 300 lines/mm grating, producing a measure wavelengthcoverage of λλ λ =3.4 ˚A/pixel. The detector used was a thinned TEK1024 × µ m pixels. Wavelength calibra-tion was achieved using exposures of Thorium-Argon hol-low cathode lamps. No attempt was made to achieve pho-tometric calibration of the data as the sky conditions didnot warrant it.The data reduction was achieved using standard pro-cedures and routines in the IRAF environment. Afterbias and flat-field corrections, the two-dimensional spec-tra were traced and integrated across the dispersion di-rection and extracted into one-dimensional form. The ex-tracted spectra were then wavelength calibrated, normal-ized and compared, interactively, to the standard sequencefrom Jacoby et al. (1984). The classifications were redoneindependently several times, by two of the authors. Theresulting spectral classifications are listed in Table 1. Alsolisted in Table 1 are the derived colour excesses, based onTycho (Høg et al. 2000) photometry and intrinsic coloursfrom Cox (2000). In a small number of cases Tycho pho-tometry is not available, and in those cases we have in-stead used NOMAD (Zacharias et al. 2005) photometry.Visual extinctions ( A V ) were calculated using total-to-selective extinction ( R V ) values derived, from A V = R V × E B − V , using the relation: R V = 1 . × E V − K /E B − V fromWhittet & van Breda (1978).As discussed in Andersson & Potter (2007), the wave-length of the maximum of the polarization curve ( λ max )is a sensitive probe of the grain alignment and one thatis immune to the magnetic field topology along the line ofsight. The absolute value of λ max depends on the over-allgrain size distributions and likely on the color and intensityof the local diffuse interstellar radiation field (ISRF), butas shown by Andersson & Potter (2007) the slope in the λ max vs. A V relation is universal. Hence we can measurethe relative grain alignment enhancement in a region byderiving the average relationship between λ max and A V forfield stars behind the cloud in question and then probingfor localized deviations from this average relationship. Wedid this in Andersson & Potter (2007, 2010) and found thatin Chamaeleon I, but beyond the region around HD 97300(where its radiation field dominates that of the diffuse ra-diation), a linear relationship is found: h λ max ( A V ) i = (0 . ± . . ± . × A V . (1)
3. Results and discussion
The uncertainties for the spectral classifications are basedon estimates from the two independent classifiers. Usuallythe results by the individual classifiers agreed to within theassigned uncertainties. The luminosity class assignmentsare less certain. For early-type star (up to F) we assumethat the stars are on the Main Sequence. For later stellartypes (G and beyond), we used the known distance to theChamaeleon I cloud ( d = 150 ±
15 pc, Whittet et al. 1997),spectroscopic parallaxes for luminosity classes III and V, and the measured colour excesses, derived for each lumi-nosity class, to set the luminosity class. The restriction tothese two luminosity classes could be a source of some er-ror, in a few cases where luminosity classes IV (or I) mighthave been more appropriate. Specifically, TYC 9410-1931-1and TYC 9414-0046-1 have been assigned a spectral classof G4 III. However, this spectral/luminosity class is locatedin the Herzsprung gap of the HR diagram where the num-ber of stars is quite small. As noted below some stars showcolour excess ratios that would indicate that they are partof binaries or show the effects of peculiar circumstellar ma-terial, or other effects yielding non-standard colours. Theformer of these two stars falls in this category.For five stars in our sample the colour excess E B − V isconsistent with zero and we have excluded these stars fromthe subsequent analysis. Similarly, for six stars the colourexcess ratio E V − K / E B − V is significantly smaller than thenominal value 2.74, assuming a standard interstellar extinc-tion curve and a R V value of 3.1 (Cox 2000). After checkingthe spectral classifications for these stars we conclude thatthe discrepancy is in the measured colours and may indi-cate binarity, or other non-standard spectral behaviour. Wehave therefore excluded also these stars from the analysisof the grain alignment variations.While a systematic increase in R V is expected for graingrowth, no clear correlation is seen between R V and columndensity (e.g. I ). This is likely because the total columndensities in our sample are still fairly small. Figure 2 shows the relative grain alignment efficiencies forthe stars in our sample as measured by the above techniquein filled (black) diamonds as a function of Ψ (see Figure 1):∆ λ i max = λ i max − h λ max ( A iV ) i . (2)The FIR ratio I /I is also shown, in open (red) dia-monds. The FIR data here are from the IRIS reprocessingof the IRAS data (Miville-Deschˆenes & Lagache 2005). Fordetails see Andersson & Potter (2007).In Figure 2 we have over-plotted the best fit of the func-tion ∆ λ max = A + B × cos(Ψ − Ψ ) where Ψ is the posi-tion angle from the star, relative to the average magneticfield direction in the area, as determined from the polariza-tion maps by McGregor et al. (1994); Andersson & Potter(2010) and Ψ is the symmetry angle of the function (inthis case the minimum). We have chosen a simple cosinerelation here, since the exact theoretical functional formfor the grain alignment depends on several unknown pa-rameters of the grains, the radiation field and the structureof the cloud along the line of sight. With the new and sig-nificantly improved visual extinctions for our backgroundstars, we find a statistically significant depression in ∆ λ max Ψ close to 0, in agreement with theoretical predictions.An F-test (Lupton 1993) yields a greater than 99% prob-ability that the two additional parameters in the cosinefunction are statistically warranted (as compare to a sim-ple average value). The parameters in the current best fitare all within the mutual uncertainties of the best fit inAndersson & Potter (2010). We now find a 9.5 σ deviationfrom a null result for the amplitude of the grain alignmentenhancement. ∆λ max =(0.073 0.004)-(0.067 0.007)cos( Ψ -(8.6 2.4))-0.13-0.0700.070.130.2 -0.100.10.20.3-100 -50 0 50 100 ∆ λ m ax [ µ m ] I /I Ψ [˚] Fig. 2.
The variations in grain alignment efficiency, asprobed by the location of the peak in the polarization curve,is shown as a function of the relative angle between the mag-netic field and radiation field anisotropy: Ψ (filled, black,diamonds. Also shown are the variations in the FIR ratio I /I (open, red, diamonds). Both show a variation withΨ. The change in the grain temperature can be understoodin terms of the surface area facing the illuminating star,while the variations in λ max are consistent with predictionsby RAT theory.The fractional polarization ( p max /A V ; Fig 3) for ourcombined sample shows a power-law slope b = − . ± . σ mutual uncertainty, from the resultsin Whittet et al. (2008): b = − . ± . Figure 2 also shows a systematic variation in the I /I ratio as a function of Ψ. To model this we envision thealignable grains as a system of simple parallelepipeds withtwo large sides of length a , and a smaller side of length b (like a pizza box; Figure 4). The radiative heating of thesegrains around the star then takes the form: I ∝ I r a [cos (Ψ) + ba sin (Ψ)] , (3)where I is the effective intensity of the central star and r is the distance between the star an dust grain. Figure 4illustrates the model geometry. We also need to allow forsymmetrical grains that will not show a dependence on theangle Ψ. As shown by Desert et al. (1990) the I /I ra-tio shows a roughly linear response to the radiation fieldstrength in the range 1-5 times the local interstellar radia-tion field. Hence, as a simple first order, heuristical, modelwe can fit the FIR colour temperature to the function: I I (Ψ) = c [(1 − ǫ ) + ǫ (cos (Ψ) + ( b/a )sin (Ψ))] , (4) p / A V [ % m a g - ] A V [mag] p/A V =(3.3 0.2) A V-(0.39 0.09)
Fig. 3.
The fractional polarization (p max / A V ) for the sam-ple is plotted as a function of the visual extinction. Thepower-law exponent is consistent, within the mutual error-bars, with the one found for deeper lines of sight byWhittet et al. (2008). JJJ Ψ B aab Fig. 4.
The heating of asymmetrical grains, aligned withthe magnetic field (thin, gray, lines) will vary with the an-gle Ψ. If only a fraction of the grains are alignable, we canuse the variations in the dust temperature to estimate thefraction of aligned grains or the axes ratio of these asym-metric grainswhere ǫ is the fraction of aligned, asymmetrical grains and b/a is the axes ratio of the asymmetrical grains.The two parameters ǫ and ( b/a ) are degenetrate in thefits. We therefore ran a number of fits using ǫ as a free pa-rameter with ( b/a ) − set to √
2, 2, 4 and 6. For these choicesof ( b/a ) we find ǫ =(0.58 ± ± ± ± b/a ) − =4.Kim & Martin (1995) present, in their Table 1, thepolarization-to-extinction ratio for perfectly aligned oblatespheroids with the axes ratios we used in our fits. Theyalso quote the maximum of the measured value of this ra-tio as p max /τ =0.028. If we use the ratio of the observed tocalculated value in their paper as signifying the requireddilution of the aligned oblate spheroidals (by unaligned, or fully symmetrical grains), we find that the fractions ofaligned grains they predict are 0.56, 0.31, 0.18 and 0.17,very close to the best fit values in our model.The fitting constant c in equation 4 contains the dis-tance from the illuminating star to each line of sight. Oursample is not large enough to conclusively show this depen-dence for different distance annuli, but splitting the samplein two and fitting the targets nearest to HD 97300 doesproduce an increased value of c , compared both to the fullsample and the more distant half-sample.Repeating this analysis on the full maps of IRAS datain the Chamaeleon region produces consistent results al-beit with larger scatter in the FIR ratio as a function ofposition angle (in particular, for the annuli d =0.3–0.4 degand d =0.4–0.5 deg, the best fit values for ǫ agree, withinthe error bars, with the ones found for our polarimetry starsample). Further analysis, in particular repeating the ex-periment for other cloud regions dominated by a near-bystar, will be needed to ascertain whether this effect is realor whether it is a statistical aberration in the current dataset.
4. Conclusions
With the improved observational data, we confirm the pre-liminary result from Andersson & Potter (2010) that thegrain alignment seems to depend on Ψ, as predicted by RATtheory. This provides an important observational constrainton, and in this case support for, the currently best devel-oped theory for interstellar grain alignment. With furthersupportive observational tests of the theory, the second-longest standing mystery of interstellar medium astro-physics may be within reach of resolution.We also find a dependence on Ψ in the I /I ra-tio. Since the aligned grains causing the polarization havetheir major axis perpendicular to the magnetic field, thisenhancement in the FIR ratio should be expected simplyas a projection effect of the grain surface to the radiationfrom the central star. Our best fit models of the FIR ratiofind that the fraction of aligned grains is very close to thatfound for theoretical models of the extinction and polariza-tion curves by Kim & Martin (1995).It is possible that an underlying corrugation of the cloudsurface could partly be responsible for the Ψ dependence.This could happen if a ridge centered on HD 97300 is ori-ented parallel to the average magnetic field. However, thelow estimated magnetic field of the Chamaeleon I cloud, B k = 3 ± µG (Bourke et al. 2001) makes this unlikely.Repeating the experiment in other regions where a local-ized radiation source dominates the grain illumination willallow such caveats to be addressed. The longest-standing mystery of ISM astrophysics is the na-ture of the carriers of the Diffuse Interstellar Bands, detected(see Friedman et al. 2011) in 1919 (Heger 1922) and identifiedas being of interstellar origin in 1936 (Merrill 1936) 5 - G A nd e r ss o n e t a l.: A n g l e - d e p e nd e n t r a d i a t i v e g r a i n a li g n m e n t Table 1.
Spectral types and photometry for stars in the region.
ID RA Dec
V B – V Sp. Class a Source b R V c A V (2000) (2000) [mag] [mag] [mag]TYC 9414-0186-1 10:59:06.97 -77:01:40.30 11.66 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( a ) The number in parenthesis gives the estimated uncertainty of the spectral class, in sub-classes; ( b ) Source of spectralclassification: A – This work, B – Michigan Spectral Survey (Houk & Swift 1999), C – SIMBAD database; ( c ) In a few casesunphysical results were obtained for R V . These likely indicate non-standard spectral classes. Those values have been omitted andmarked by — and the resulting visual extinctions were not used in the analysis. -G Andersson et al.: Angle-dependent radiative grain alignment Acknowledgements.
We gratefully acknowledge the time allocationand support of the staff of the CASLEO observatory. OIP contributionto this paper was partially supported by PIP0348 by CONICET.We are grateful to Bill Reach for helpful discussions about theFIR response to grain heating as well as the anonymous referee andthe A&A editor for helpful suggestions improving the clarity of themanuscript.
References