Mid-infrared spectroscopy of zodiacal emission with AKARI/IRC
Aoi Takahashi, Takafumi Ootsubo, Hideo Matsuhara, Itsuki Sakon, Fumihiko Usui, Hiroki Chihara
MMid-infrared spectroscopy of zodiacal emission with AKARI/IRC
Aoi
Takahashi , , , , Takafumi Ootsubo , Hideo Matsuhara , ,Itsuki Sakon , Fumihiko Usui , Hiroki Chihara August 4 2019
1. Astrobiology center, 2-21-1 Osawa, Mitaka, 181-8588, Japan2. National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, 181-8588, Japan3. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara 252-5210, Japan4. Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOK-ENDAI), Shonan Village, Hayama 240-0193, Japan5. Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan6. Center for Planetary Science, Graduate School of Science, Kobe University, 7-1-48 Minatojima-Minamimachi,Chuo-Ku, Kobe 650-0047, Japan7. Department of General Education, Osaka Sangyo University, 3-1-1, Nakagaito, Daito, Osaka 560-0043,Japan* Corresponding author: [email protected]
Abstract
Interplanetary dust (IPD) is thought to be recently supplied from asteroids and comets. Grainproperties of the IPD can give us the information about the environment in the proto-solar system, andcan be traced from the shapes of silicate features around 10 µ m seen in the zodiacal emission spectra.We analyzed mid-infrared slit-spectroscopic data of the zodiacal emission in various sky directionsobtained with the Infrared Camera on board the Japanese AKARI satellite. After we subtractedthe contamination due to instrumental artifacts, we have successfully obtained high signal-to-noisespectra and have determined detailed shapes of excess emission features in the 9–12 µ m range in allthe sky directions. According to a comparison between the feature shapes averaged over all directionsand the absorption coefficients of candidate minerals, the IPD was found to typically include smallsilicate crystals, especially enstatite grains. We also found the variations in the feature shapes andthe related grain properties among the different sky directions. From investigations of the correlationbetween feature shapes and the brightness contributions from dust bands, the IPD in dust bandsseems to have the size frequency distribution biased toward large grains and show the indication ofhydrated minerals. The spectra at higher ecliptic latitude showed a stronger excess, which indicatesan increase in the fraction of small grains included in the line of sight at higher ecliptic latitudes. Ifwe focus on the dependence of detailed feature shapes on ecliptic latitudes, the IPD at higher eclipticlatitudes was found to have a lower olivine/(olivine+pyroxene) ratio for small amorphous grains.The variation of the mineral composition of the IPD in different sky directions may imply differentproperties of the IPD from different types of parent bodies, because the spatial distribution of theIPD depends on the type of the parent body. a r X i v : . [ a s t r o - ph . E P ] A ug Introduction
Asteroids and comets are primordial planetesimals, which have been formed in the proto-solar disk bygathering surrounding dust. Their constituents will surely retain the information about the environmentin the proto-solar system. However, the opportunity to observe comets is limited, and furthermore, nm-scaled structures in regolith on asteroids surfaces have well-experienced two types of space weathering [61,44]: micrometeoroid bombardment, on a timescale of 10 –10 years [51] and solar-wind irradiation, on atimescale of 10 –10 years [55] in case of the near-Earth asteroids.On the other hand, interplanetary dust (IPD) can be always observed and tell us the information onthe proto-solar phase. The IPD is the population of mineral dust grains with a size frequency distribu-tion expressed by a smoothly broken power-law with negative indices in the size range from sub- µ m tomillimeters ([23], [25]). It distributes in the interplanetary space globally and diffusely, and is thoughtto be supplied continuously from asteroids and comets. The IPD formed by the collisional cascades ofasteroids [56, 41, 42] is mainly supplied from the internal of asteroids, which has not seriously been af-fected by the space weathering. The IPD supplied by comets disruption [43] is also from the internal ofcomets, and the IPD liberated by comets sublimation [33, 48] is supplied from the comets surface, whichis refreshed every time they approach to the perihelion. Once the IPD has been liberated from the parentbodies, it accretes into the Sun along a spiral orbit due to the Poynting-Robertson drag. The accretiontimescale is typically 10 –10 years for 1 µ m-sized grains, although it increases proportionally to the grainsize [10, 62]. It is comparable to or shorter than the timescale of space weathering for internal structuresof the IPD, which is assumed to be similar to that for nm-scaled structures in asteroids regolith. Thus,at least small grains in the IPD can be thought to accrete into the Sun before their properties are alteredwell by space weathering. This means the IPD we currently observe, especially about small grains, hasnot significantly been affected by the space weathering, and the grain properties such as compositionsand crystal morphologies reflect dust properties in the formation regions of the parent planetesimals, likeasteroids or comets. Investigations of the grain properties of the IPD are, therefore, important for studiesof the formation process of the planetary system.The IPD absorbs sunlight in the ultraviolet–near-infrared and re-emits the absorbed energy as thermalemission in the mid-infrared. We observe it as zodiacal emission, which is the dominant source of diffusemid-infrared radiation all over the sky. Some spectral features have been detected in past spectroscopicobservations of the zodiacal emission. The mid-infrared camera on board the Infrared Space Observatory(ISOCAM) measured sky spectra over the wavelength range of 5–16 µ m and reported excess emission inthe 9–11 µ m range, with an amplitude of 6% of the continuum [49]. However, Leinert et al. (2002) [32]concluded that the zodiacal emission spectra obtained with the spectrophotometric sub-instrument ofthe ISO photometer, ISOPHOT, are smooth and featureless. The Mid-infrared Spectrometer on boardthe Infrared Telescope in Space (IRTS), the first Japanese infrared telescope, obtained zodiacal emissionspectra in the 4.5–11.7 µ m range and reported a 9–12 µ m excess [47]. These emission features originatefrom the Si-O vibration modes in small silicate grains of the IPD. The shapes of these features dependon the grain properties of the IPD, such as the mineral and chemical composition, crystallinity, andcrystal morphology, for example. These feature shapes can thus be used as tracers for investigating theproperties of small IPD grains and can help us to understand the environment in the proto-solar system.Past observations of the zodiacal emission, however, have not been sensitive enough to determine detailedshapes of the excess emission features.In the present paper, we derive the zodiacal emission spectra with high signal-to-noise ratios from74 observations toward various sky directions, and we present the detailed shapes of the silicate featuresfor the first time. The following two sections explain the observations and the data-reduction process.In section 4, we discuss the average feature shape and the variations in different sky directions, and wedemonstrate a possible link to the grain properties of the IPD. In section 5, we present the implicationsof these results, and we summarize our conclusions in the final section.2 Observations
AKARI is a Japan-lead infrared astronomy satellite [39]. It carries a telescope with an effectiveaperture diameter of 68.5 cm and two focal plane instruments. One of them is the Infrared Camera (IRC;[46]). The IRC has three channels with different wavelength coverages: the NIR channel for 2–5 µ m, theMIR-S channel for 5–13 µ m, and the MIR-L channel for 12–27 µ m (although spectroscopy in the latteris limited to the region longer than 17.5 µ m, owing to an instrumental problem). All three channelsoperate simultaneously. Each channel is equipped with a slit aperture for spectroscopic observations ofdiffuse sources. The filter wheel in each channel includes a blank window as a shutter, and it enablesaccurate subtraction of dark-current images of the detector array, which is necessary for high-sensitiveobservations of diffuse sources.We have performed near- and mid-infrared spectroscopic observations of the zodiacal emission usingAKARI/IRC in the spectroscopic mode (IRC04 in the Astronomical Observation Template). As partof the mission program “SOSOS,” we obtained data during Phase 2 (November 2006–August 2007), inwhich the telescope and the instruments were cooled down to 5.8 K. Information about the observations islisted in Table 1. Thanks to its Sun-synchronous polar orbit, AKARI has the ability to observe the entiresky in six months, although its solar elongation angle is limited to 90 ± µ m; λ /∆ λ ∼ ×
256 pixels are installed.This wavelength coverage is optimum for investigating the silicate features around 10 µ m. These datawere taken separately using two grisms, SG1 (5.4–8.4 µ m) and SG2 (7.5–12.9 µ m). The IRC takesfour spectroscopic frames with the SG1 grism, then takes an imaging frame, and finally takes fourspectroscopic frames with the SG2 grism. Each frame consists of a short exposure (0.5844 sec) and threelong exposures (16.3632 sec). For each pointed observation, we analyzed the data from the long exposuresin the spectroscopic frames: 12 images in total (3 long exposures × µ m obtained with COBE/DIRBE [27],which is dominated by thermal emission from the interstellar dust in our Galaxy. The bright arc corre-sponds to the galactic plane. 3able 1: Log for 74 pointed observations. Pointing directions werewritten in 3 types of celestial coordinates: equatorial coordinates( α , δ ), geocentric ecliptic coordinates ( λ ⊕ , β ⊕ ), galactic coordi-nates ( l , b ). Solar elongations in all observations were in the rangeof 90 ± A from the dust bandsdefined by equation (6) was also shown in the last column.Observation ID Date (UT) α [deg] δ [deg] λ ⊕ [deg] β ⊕ [deg] l [deg] b [deg] A [%]1500701 2006/12/16 18:35:01 174.22 1.41 174.13 -1.00 264.99 58.68 4.901500703 2006/12/20 16:55:29 175.02 -7.11 178.27 -8.50 273.59 51.65 1.041500704 2006/11/22 18:56:11 150.22 3.09 151.20 -8.50 235.92 42.71 1.151500705 2007/02/04 16:40:21 226.81 -7.14 226.40 10.00 351.68 42.52 1.841500706 2007/02/05 19:08:19 228.04 -3.33 226.53 14.00 356.54 44.40 1.391500707 2007/02/05 13:21:40 46.69 6.59 46.13 -10.50 172.07 -43.01 0.821500708 2007/02/05 10:01:47 48.07 2.30 46.27 -15.00 177.62 -45.09 0.571500709 2006/12/15 05:23:58 349.86 6.51 353.27 10.00 86.08 -49.66 1.851500711 2007/02/05 14:00:26 239.22 31.05 227.00 50.00 49.93 49.59 0.791500712 2007/02/04 19:47:57 239.31 31.03 227.13 50.00 49.90 49.50 0.791500713 2006/12/16 09:28:29 355.14 -3.19 354.27 -1.00 84.58 -60.67 4.711500715 2006/12/15 07:03:14 349.86 6.51 353.27 10.00 86.08 -49.66 1.851500717 2006/12/17 05:50:18 226.05 60.54 176.40 70.00 98.30 49.76 0.791500718 2006/12/17 07:29:34 226.05 60.54 176.40 70.00 98.30 49.76 0.791500719 2006/11/10 11:15:25 90.00 -66.56 90.00 -90.00 276.38 -29.81 0.451500720 2006/11/10 19:31:34 90.00 -66.56 90.00 -90.00 276.38 -29.81 0.451500721 2007/02/04 21:21:44 248.99 49.66 227.27 70.00 76.65 41.96 0.771500722 2007/02/03 17:13:21 249.05 49.64 227.40 70.00 76.61 41.92 0.771500723 2006/12/28 13:11:21 230.95 57.48 188.00 70.00 92.19 49.56 0.811500724 2006/12/28 14:50:38 230.95 57.48 188.00 70.00 92.19 49.56 0.811500725 2007/02/05 14:50:05 59.22 -31.05 47.00 -50.00 229.93 -49.59 0.341500726 2007/02/05 06:27:59 68.92 -49.68 47.13 -70.00 256.68 -42.00 0.331500727 2006/12/19 04:59:29 46.71 -60.10 358.00 -70.00 277.46 -49.79 0.351500728 2006/12/19 06:38:46 46.71 -60.10 358.00 -70.00 277.46 -49.79 0.351500729 2006/12/20 07:27:51 46.76 -60.06 358.13 -70.00 277.39 -49.80 0.351500730 2006/12/20 09:07:08 46.76 -60.06 358.13 -70.00 277.39 -49.80 0.351500731 2006/12/28 14:01:00 50.95 -57.48 8.00 -70.00 272.19 -49.56 0.341500732 2006/12/28 15:40:16 50.95 -57.48 8.00 -70.00 272.19 -49.56 0.341500748 2007/05/02 14:28:54 141.03 36.33 131.80 20.00 187.57 45.50 0.761500751 2007/05/02 17:50:27 145.57 45.73 131.67 30.00 173.52 48.41 0.591500759 2007/05/05 21:07:43 320.39 -26.49 314.53 -10.50 21.13 -43.53 1.831500760 2007/05/05 19:26:06 317.83 -18.84 314.60 -2.50 29.97 -39.06 4.711501603 2007/06/17 08:56:51 174.34 -3.00 176.00 -5.00 269.39 54.98 3.091501607 2007/06/19 12:17:06 172.52 -12.03 178.00 -14.00 273.55 46.15 1.521501608 2007/06/19 13:56:33 172.52 -12.03 178.00 -14.00 273.55 46.15 1.521501609 2007/05/30 10:09:52 165.66 22.42 158.00 15.00 217.73 64.91 0.661501614 2007/05/31 15:55:55 161.83 9.86 159.50 2.00 237.54 56.04 5.091501615 2007/07/13 10:01:20 210.04 19.93 200.00 30.00 12.02 72.70 0.281501617 2007/06/01 10:14:34 169.80 26.21 160.00 20.00 210.22 69.40 0.531501618 2007/06/01 13:33:25 169.80 26.21 160.00 20.00 210.22 69.40 0.531501619 2007/08/09 17:03:30 239.22 31.05 227.00 50.00 49.93 49.59 0.271501620 2007/08/10 11:18:01 239.22 31.05 227.00 50.00 49.93 49.59 0.27Continue to the next page4ontinue from the previous pageObservation ID Date (UT) α [deg] δ [deg] λ ⊕ [deg] β ⊕ [deg] l [deg] b [deg] A [%]1501623 2007/06/23 11:39:56 2.11 -2.35 1.00 -3.00 98.55 -63.17 4.681501625 2007/07/02 13:40:07 193.31 5.70 190.00 10.50 304.17 68.57 0.711501627 2007/07/03 12:49:22 189.72 -5.27 191.00 -1.00 297.11 57.46 4.741501628 2007/07/03 14:28:50 189.72 -5.27 191.00 -1.00 297.11 57.46 4.741501629 2007/06/27 11:49:36 7.97 -5.82 5.00 -8.50 109.73 -68.18 2.331501631 2007/06/27 13:29:03 7.97 -5.82 5.00 -8.50 109.73 -68.18 2.331501633 2007/06/27 15:58:47 188.77 7.65 185.00 10.50 290.92 70.14 0.731501635 2007/06/28 10:13:36 190.89 10.01 186.00 13.50 296.38 72.78 0.531501639 2007/07/23 17:08:43 227.13 35.10 210.00 50.00 56.76 59.76 0.251501640 2007/07/23 23:46:38 227.13 35.10 210.00 50.00 56.76 59.76 0.251501645 2007/06/27 18:27:33 8.62 -6.08 5.50 -9.00 111.33 -68.57 2.221501646 2007/06/27 20:07:00 8.62 -6.08 5.50 -9.00 111.33 -68.57 2.221501647 2007/06/28 17:41:00 11.14 -9.35 6.50 -13.00 117.40 -72.15 1.621501648 2007/06/28 19:20:27 11.14 -9.35 6.50 -13.00 117.40 -72.15 1.621501649 2007/05/13 17:11:43 150.43 29.70 142.00 16.50 198.71 52.80 0.771501653 2007/07/02 12:42:56 2.41 19.08 10.00 16.50 109.45 -42.70 0.441501654 2007/07/02 14:22:32 2.63 18.62 10.00 16.00 109.59 -43.19 0.451501655 2007/07/03 18:33:12 3.34 19.47 11.00 16.50 110.72 -42.49 0.441501660 2007/05/16 16:17:52 143.10 -0.19 145.50 -14.00 234.23 34.98 1.371501661 2007/07/01 18:37:11 13.60 -8.84 9.00 -13.50 125.28 -71.70 1.581501662 2007/07/01 20:16:47 13.81 -9.30 9.00 -14.00 125.98 -72.15 1.531501663 2007/06/30 17:45:20 12.70 -9.23 8.00 -13.50 122.42 -72.10 1.581501664 2007/06/30 12:47:06 12.90 -9.69 8.00 -14.00 123.08 -72.56 1.531501669 2007/07/18 11:43:02 21.47 13.86 25.00 4.50 135.52 -48.17 1.161501670 2007/07/18 13:22:31 21.47 13.86 25.00 4.50 135.52 -48.17 1.161501671 2007/07/19 00:58:59 22.61 13.77 26.00 4.00 137.18 -48.02 1.291501672 2007/07/19 10:55:51 22.61 13.77 26.00 4.00 137.18 -48.02 1.291501673 2007/08/02 23:58:04 217.10 -16.24 220.00 -1.50 334.24 40.67 4.771501675 2007/08/04 00:51:59 219.84 -11.32 221.00 4.00 340.75 43.48 1.271501679 2007/08/19 12:27:54 240.55 9.97 236.00 30.00 21.43 41.99 0.341501680 2007/08/19 14:07:25 240.55 9.97 236.00 30.00 21.43 41.99 0.341501685 2007/08/08 11:01:27 225.47 -6.76 225.00 10.00 350.68 43.69 0.73End With a conventional reduction toolkit [45], the SG1 and SG2 spectra are not smoothly connected,owing to inconsistencies in the intensity levels in the overlapping wavelength range (i.e., 7.5–8.4 µ m).We have examined contamination due to various instrumental artifacts, and we have identified threetypes of artifacts that affect the slit-spectroscopic data: (1) light scattered from the detector pixels,(2) light scattered from the edge of the detector, and (3) the ghost of a small aperture window. Wehave determined empirically normalized profiles common to all the pointing data and have calculatedthe absolute values from the observed images for each pointing. More details about these artifacts areexplained in Appendix A.The data-reduction flow, including the subtraction of these artifacts, is summarized in Figure 2 anddescribed below. For each pointing, we started from the raw data for 12 two-dimensional images takenwith each grism: 3 exposures × λ = 0 . × ( Y −
12) + 0 .
016 for SG1, (1) λ = 0 . × ( Y −
31) + 0 .
141 for SG2, (2)where λ is the corresponding wavelength in units of µ m, and Y is the pixel position along the direction ofspectral dispersion (1 ≤ Y ≤ < ± < ± . µ m and ± . µ m for SG1 and SG2, respectively)—as statistical errors in the responsecurve.In summary, we were able to subtract the three types of artifact components and derive reasonable6able 2: List of the data used for spectrum calibration.Object Object type Observation ID file spectroscopic modeNGC6543 planetary nebula 5020048 F33860-M.fits slit spectroscopyKF09T1 K0III-type star 5020032 F13450-M.fits slit-less spectroscopyHD42525 A0V-type star 5020023 F23384-M.fits slit-less spectroscopyspectra, smoothly connecting between the data from SG1 and SG2 for all pointing directions. The spectrainclude two types of statistical errors: those due to spatial dispersion during the extraction of the one-dimensional profile and those due to uncertainties in the response curves we used. The intensity levels areconsistent within 10% accuracy with those calculated from the zodiacal-emission model obtained fromDIRBE imaging observations (hereafter, the “DIRBE zodi-model:” [27]). Figure 3 shows the correlationof the intensities at 12 µ m between the AKARI observations used in this work and the DIRBE zodi-model. The AKARI intensities are about 10% higher than the model expectations uniformly at all skydirections. One of reasons for the 10% inconsistency may be an inappropriate color-correction factor usedfor the model construction from the DIRBE observational data. Kelsall et al. (1998) [27] assumed a color-correction factor appropriate for a single-temperature blackbody over the 8.8–15.2 µ m band. However,actual zodiacal spectra seem to have deviations from a blackbody due to excess emission in the range 9–12 µ m, which is found in this AKARI observation, and a deficit in emission at the side longer than 12 µ mon the contrary, which is expected from the decline of absorption coefficients (i.e., emission efficiencies)of small silicate grains [31, 11]. Since the DIRBE response in this wavelength band is more sensitive atthe longer side, the 12 µ m-intensity may be resulted in a lower one than the actual. Another possibilitycausing the 10% inconsistency is the contribution of an isotropic component with an brightness uniformall over the sky, which comes also from an external to the solar system. The DIRBE zodi-model ignoressuch isotropic component and is fitted so that it can reproduce the amplitude and phase of the temporalvariation from the average for each line of sight (equation (10) of [27]).
10 20 30 40 50DIRBE zodi-model at 12 µ m [MJy/str]1020304050 O b t a i n e d i n t e n s it y a t µ m [ M J y / s t r] Figure 3: Correlation of the 12 µ m intensity between the spectra obtained in this work and the DIRBEzodi-model [27]. 7 Results
We found the emission features around 10 µ m to be present in the spectra at all pointing directions.Hereafter, we use the spectral data obtained from the SG2 (7.5–12.9 µ m) to investigate the detailed featureshapes, while the SG1 data have been used to confirm the subtraction of the artifact components. TheSG2 spectral data show the first reliable feature shapes around 9–10 µ m. ISOCAM spectra contained thediscontinuity at 9.5 µ m across the boundaries of the spectra obtained from two different circular-variablefilters (see Figure 4 of [49]), and this resulted in the uncertainty of the feature shapes especially in theshorter-wavelength side. On the other hand, the SG2 in the AKARI/IRC covers the entire wavelengthregion (8–12 µ m) of the emission features and we can detect the feature shapes by using spectra obtainedonly from the single spectroscopic element.In order to extract the excess emission first of all, we divided observed spectra by the continuumspectrum in each direction. We calculated the continuum spectra from the DIRBE zodi-model mentionedabove.In the mid-infrared wavelength region, the intensity of the zodiacal emission can be written as follows: Z λ ( λ ⊕ , β ⊕ , t ) = (cid:88) c =1 (cid:90) n c ( λ ⊕ , β ⊕ , s, t ) E c,λ B λ ( T ( λ ⊕ , β ⊕ , s, t )) ds, (3)where the subscript c corresponds to the type of IPD component defined in the DIRBE zodi-model [27]: asmooth cloud ( c = 1), dust bands ( c = 2), and a circumsolar ring with a trailing blob ( c = 3), which havedistinct spatial distributions. The quantity n c is the spatial density of the geometrical cross-section foreach IPD component. Positions in the Solar System are specified by the geocentric ecliptic coordinatesof the pointing direction, ( λ ⊕ , β ⊕ ), the distance s along the line of sight, and the observation date t . Thequantity E c,λ is the emissivity-modification factor, which is a function of wavelength and correspondsto deviations from the blackbody function ( B λ ( T )). Here T is the typical temperature of IPD grains ateach position. Kelsall et al. (1998) [27] determined n c and the spatial distribution of T by fitting to theDIRBE imaging observational data using the color-correction factors.We obtained the continuum spectra from these results. The modeled absolute intensities of the zodia-cal emission, however, include about 10% uncertainties due to the inconsistency described in Figure 3. Wetherefore scaled the calculated continuum intensity to match the observed intensity at 12 µ m. Denotingthe scaling ratio by α , we express the continuum spectrum C λ as C λ ( λ ⊕ , β ⊕ , t ) = α × (cid:88) c =1 (cid:90) n c ( λ ⊕ , β ⊕ , s, t ) B λ ( T ( λ ⊕ , β ⊕ , s, t )) ds. (4)The value of α was typically in the range from 1.0 to 1.1.We divided the observed zodiacal emission spectra Z λ by the continuum C λ for each of the 74 observa-tions (see Appendix B). We discuss below the wavelength dependence of these observed/continuum ratios,i.e., the shapes of the spectral features. Although the shapes exhibit diversity, the excess emission—andeven some sharp emission peaks—can be seen clearly beyond the error range in all of the spectra inthe 8–12 µ m region. Such detailed shapes have been found here for the first time thanks to the highsensitivity of the IRC and the accurate subtraction of instrumental artifacts. We next link the shapes of the emission features to the grain properties of the IPD included in theline of sight, from a mineralogical point of view. 8he observed/continuum spectra we obtained can be written as follows, using equations (3) and (4): Z λ C λ = 1 α × (cid:80) c =1 (cid:82) n c E c,λ B λ ( T ) ds (cid:80) c =1 (cid:82) n c B λ ( T ) ds . (5)This means the observed/continuum ratios correspond to the emissivity-modification factor E c,λ , aver-aged over all the IPD grains included in the line of sight, which have various compositions and grainsizes. The value of E c,λ for each grain can be replaced by the grain absorption coefficient Q abs . Theobserved/continuum ratios are thus determined by the Q abs values of all the IPD grains included in theline of sight. Since Q abs for a grain can be expressed approximately as a superposition of the Q abs valuesfor the constituent materials in the grain [6, 7], comparison of the observed/continuum ratios to the Q abs values for candidate minerals helps us to estimate the fractional content of each type of mineral in thegrain.In this paper, we consider four types of silicates as candidates: amorphous with olivine composition,amorphous with pyroxene composition, Mg-end forsterite (Mg SiO , one of the olivine crystals) and Mg-end ortho-enstatite (MgSiO , one of the pyroxene crystals). We assume solid solutions of the two types ofamorphous minerals, with Mg/(Mg+Fe)=0.5. These candidate minerals are among the main constituentsof IPD samples collected in the stratosphere or on the ground [37, 26]. In addition, they have vibrationmodes in the wavelength region we have considered in this work. We calculated their Q abs spectra fromthe optical constants [17] or dielectric functions (Sogawa et al. 2006 [54] and private communicationswith H. Chihara) on the basis of Mie theory [7, 29], assuming spherical grains with a size variationfrom 0.1 µ m to 100 µ m. The top four panels in Figure 4 show the results. We also plotted the massabsorption coefficients (MACs) for two types of crystals measured in the laboratory [31, 11]. The MACswere measured on crystalline dust samples with a size range 0.1–10 µ m. These samples are assumed tohave the shape probability distribution of a continuous distribution of ellipsoids (CDE), which includesellipsoidal grains with equal probabilities of all possible aspect ratios and orientations of the crystal axes.Large grains ( ≥ µ m) contribute mainly to the absolute intensity level of the zodiacal emission andprovide a blackbody emission baseline [49], because their Q abs values are relatively constant—aroundunity—compared to those for smaller grains, as you can see in Figure 4. In addition to this baseline,small grains ( ≤ µ m) can produce excess emission at specific wavelengths depending on their vibrationmodes. The spectral shape does not depend on the grain size regarding such small grains. Therefore, ourstudy of the shapes of the excess emission features can reveal the properties of small IPD grains, whichhave not altered well by space weathering (see section 1). In order to understand the typical properties of the small IPD grains over the entire sky, we firstaveraged the observed/continuum spectra over all 74 observations and compared the results with the Q abs values of candidate minerals. In the average observed/continuum spectrum shown in the bottompanel of Figure 4, we found three main peaks—around 9.60, 10.65, and 11.30 µ m—with sub-peaks around8.45, 10.15, and 11.85 µ m. Such sharp peaks can be caused only by small grains ( ≤ µ m) of crystallinesilicates. We can therefore say that the IPD typically includes some fraction of such small grains ofcrystalline silicates. In particular, the main peaks around 9.60 and 10.65 µ m can be caused by enstatite,while the sub-peaks around 10.15 and 11.85 µ m seem to be mainly contributed by forsterite. Around11.30 µ m, both forsterite and enstatite show peaks. The sub-peak at 8.45 µ m may originate from materialsother than those shown in Figure 4. Since the peaks originating from enstatite are more prominent thanthose from forsterite and other materials, the IPD appears to typically include plenty of enstatite.We note that the wavelength position of the enstatite peak around 9.2 µ m needs to be shifted toaround 9.6 µ m, in order to reproduce the obtained observed/continuum spectrum. Several factors cancause wavelength shifts of this peak.For example, replacing Mg-ions with Fe-ions is one possible reason for the shift of a peak to a longerwavelength, although the trend is slightly different for different peaks [31, 11]. Using the experimental9 Q a b s Amorphous olivine
MAC (normalized)MAC (normalized)MAC (normalized)MAC (normalized)MAC (normalized)MIE (0.1 µ m)MIE (0.1 µ m)MIE (0.1 µ m)MIE (0.1 µ m)MIE (0.1 µ m)MIE (1 µ m)MIE (1 µ m)MIE (1 µ m)MIE (1 µ m)MIE (1 µ m)MIE (10 µ m)MIE (10 µ m)MIE (10 µ m)MIE (10 µ m)MIE (10 µ m)MIE (100 µ m)MIE (100 µ m)MIE (100 µ m)MIE (100 µ m)MIE (100 µ m) Q a b s Amorphous pyroxene Q a b s Foresterite (Olivine crystal) Q a b s Enstatite (Pyroxene crystal) λ [ µ m]0.91.01.11.2 ob s e r v e d / c on ti nuu m Figure 4: Absorption coefficients of candidate minerals. Top to bottom: amorphous with olivine compo-sition, amorphous with pyroxene composition, Mg-end forsterite (Mg SiO , one of the olivine crystals),and Mg-end ortho-enstatite (MgSiO , one of the pyroxene crystals). For comparison, the bottom-mostpanel shows the observed/continuum spectrum of the zodiacal emission averaged over all directions.We assumed a solid solution, with Mg/(Mg+Fe)=0.5 for the two amorphous minerals. We calculatedabsorption coefficients from their optical constants or dielectric functions on the basis of Mie theory,assuming grain sizes of 0.1, 1, 10, and 100 µ m. We obtained the optical constants of the two amorphousminerals from Dorschner et al. (1995) [17], and the dielectric functions of forsterite and enstatite fromSogawa et al. (2006) [54] and from private communications with H. Chihara. The solid blue lines in themiddle two panels represent the mass absorption coefficients (MACs) measured in the laboratory [31, 11],with the peaks scaled to the maximum value of Q abs calculated from Mie theory, assuming 1 µ m-sizedgrains. 10esults for the MACs from Chihara et al. (2002) [11], we plot the wavelengths of a peak around 9.2 µ m invarious solid solutions of enstatite as panel (a) in Figure 5. The wavelength position shifts to the longerside as the Fe/(Mg+Fe) ratio increases. Fe-end ferrosillite (FeSiO ) shows a peak at 9.54 µ m, which isclose to the observed peak position.Grains coated by organic materials also can show peaks at shifted wavelength positions [30]. Thiseffect can occur at peaks for which the real part of the dielectric function shows a negative valley [7],as does the enstatite peak around 9.2 µ m (see Figure 6). We assumed grains with a carbon-matrix andspherical enstatite-inclusions and calculated the dielectric function of the mixture following the Maxwell-Garnett law (e.g., [7, 21, 1, 6]). We then derived the Q abs spectrum from such composite dielectricfunctions using Mie theory [7, 29]. Changing the fraction of inclusions, we investigated the shift of thepeak wavelengths. The result is shown in panel (b) of Figure 5. The carbon mantle certainly shifts thepeak wavelength up to 9.28 µ m, but it is not sufficient to explain the observed peak wavelength.Similarly, the wavelength position of the peak depends on the porosity of grains. We assumed aporous grain consisting of an enstatite matrix with spherical vacuum inclusions. We calculated the Q abs spectrum in the same way as for grains coated by carbon. The peak is shifted to longer wavelengths byincreasing the porosity, as in panel (c) of Figure 5. An extremely porous grain exhibits a peak at 9.33 µ m,but this is again insufficient to explain the observations.Figure 5: The wavelength shift of a peak around 9.2 µ m due to (a) replacing Mg-ions with Fe-ions, (b)coating by carbon, (c) increasing porosity, and (d) elongation along the crystal a-axis. Here, λ peak meansthe peak wavelength, and dotted lines at λ peak = 9.56 µ m indicate the peak position in the zodiacalemission spectra. The values in panel (a) were extracted from the MACs for solid solutions, which weremeasured for samples in the size range 0.1–10 µ m. In the calculations for panels (b) and (c), we assumedthe grain size to be 1 µ m. For panel (d), we fixed the grain lengths along the b- and c-axes ( r b,c ) at 1 µ m,and we changed the length along the a-axis ( r a ) from 0.1 µ m to 100 µ m.11 λ [ µ m]-40-2002040 ε R e a-axisa-axisa-axisb-axisb-axisb-axisc-axisc-axisc-axis λ [ µ m]0.010.101.0010.00100.00 ε I m Figure 6: Dielectric function of orthorhombic-enstatite. The top and bottom panels show the real andimaginary parts, respectively. The c-axis is parallel to the direction of the tetrahedral chains, and thea-axis corresponds to the stacking direction of the layers of tetrahedral chains.Another possibility is the effect of crystal morphology. Ortho-enstatite is an orthorhombic crystal,and each crystal axis (a, b, c) has an individual dielectric function (see Figure 6). If we consider anellipsoidal grain, the Q abs spectrum is determined by the dielectric functions of each crystal axis and theaspect ratio in the directions of the crystal axes, assuming the surface mode in the Lorentz model [7, 57].Therefore, the wavelength positions of some peaks can be shifted depending on the aspect ratio [57]. Thiseffect also can occur at peaks for which the real part of the dielectric function shows a negative valley [7].An example of enstatite grains flattened or elongated along the a-axis (the stacking direction of the layersof tetrahedral chains) is shown in panel (d) of Figure 5. We calculated the Q abs spectra of such ellipsoidalgrains on the basis of the Lorentz model. We fixed the grain lengths along the b- and c-axes at 1 µ m andchanged the length along the a-axis from 0.1 µ m to 100 µ m. As shown in Figure 5, there are two separatepeaks in the shorter half of 9 µ m band. One curve descending toward the right shows the wavelengthposition of a peak contributed by the b-axis, and another curve, which is increasing and asymptotic,shows that of a peak contributed by the a-axis. The wavelength position of the latter peak dramaticallyincreases as a grain is elongated along the a-axis and finally, asymptotically approaches 9.48 µ m.No single effect alone is sufficient to shift the peak wavelength to reproduce the observed peak posi-tion, but the wavelength shift may be attributed to a combination of several effects. These effects arereasonable, because they are consistent with the results of laboratory measurements on collected samplesof the IPD. A lot of the collected IPD samples were found to be porous and/or carbonaceous [37, 9], andmany whisker- or platelet-shaped crystals have actually been found in those samples [8].In addition, by comparing the observed/continuum spectrum and the Q abs spectra of enstatite, wefound that the enstatite peak at 11.6 µ m is suppressed. According to Figure 6, the dielectric functions ofthe a- and b-axes are flat at wavelengths longer than 11.5 µ m, although the c-axis does have a significantpeak in this wavelength range [16]. The observed suppression implies that the grain length along thec-axis (the direction of the tetrahedral chains) may be reduced, corresponding either to platelet-shapedenstatite that is symmetric around the c-axis or to whisker-shaped enstatite that is elongated along the12- or b-axes. Since the observed/continuum spectra in Appendix B show a variety of feature shapes, we also com-pared the feature shapes among the various sky directions. We first considered the effect on the featureshapes due to dust bands. The brightness contribution from dust bands in each direction was determinedfrom the spatial distribution of the IPD given by the DIRBE zodi-model. This model includes threedust bands—around ± ◦ . ± ◦ , and ± ◦ —as one of the IPD components [27]. For each observed lineof sight, we calculated the continuum intensity at 12 µ m originating from the dust band components,defining A as the ratio to the continuum intensity at 12 µ m originating from all the components. This isgiven by A = (cid:82) n B µ m ( T ) ds (cid:80) c =1 (cid:82) n c B µ m ( T ) ds ×
100 [%] , (6)where the definitions of all the variables are the same as in equation (3), and the component representedby c = 2 corresponds to the dust bands.As another indicator of the sky direction, we considered the ecliptic latitudes β ⊕ of the pointingdirections. Figure 7 is a two-dimensional histogram of A vs. | β ⊕ | for all the observed directions. Wedivided the dataset in the directions with | β ⊕ | < ◦ into five A -bins (in percentages): 0 . ≤ A < . . ≤ A < .
5, 1 . ≤ A < .
0, 2 . ≤ A < .
0, and 4 . ≤ A < .
0. The observed/continuum spectraaveraged over each A -bin are presented in Figure 8, and we compare the feature shapes among them.Similarly, we divided the dataset with A <
1% into four | β ⊕ | -bins: 0 ◦ ≤ | β ⊕ | < ◦ , 25 ◦ ≤ | β ⊕ | < ◦ ,40 ◦ ≤ | β ⊕ | < ◦ , and 60 ◦ ≤ | β ⊕ | < ◦ , excepting the data at | β ⊕ | = 90 ◦ , where the number of datapoints was too small. Figure 9 shows the observed/continuum spectra averaged over each | β ⊕ | -bin, andwe discuss below the differences in the feature shapes.As described in subsection 4.3, the Q abs values of the current initial candidates cannot preciselyreproduce the peak-wavelength positions in the observed spectra. We therefore cannot examine thegrain properties by fitting the superposition of these Q abs values to the observed spectra. Instead, forquantitative determinations of the feature shapes, we define the following four parameters: the equivalentwidth EW whole of the whole excess emission, the ratio EW . − . /EW . − . of the equivalent widthsat 10.0–10.5 µ m and 9.0–9.5 µ m, the wavelength shift ∆ λ peak of the peak excesses due to the crystallinesilicates, and the equivalent width ratio EW fo /EW en of the peak excesses due to the crystalline silicates.We remind that small grains ( ≤ µ m) cause excess emission and contribute to these parameters. Itmeans the first parameter EW whole is related to the fraction of small grains in the line of sight andthe other three parameters can be used for the investigation of the properties of small IPD grains. Wedescribe below the detailed definition of each parameter and its dependence on A and | β ⊕ | . The first parameter, the equivalent width of the whole excess emission, is defined by the equation: EW whole = (cid:90) µ m8 µ m Z λ − C λ C λ dλ [ µ m] . (7)Here Z λ and C λ are the zodiacal emission spectrum given by equation (3) and the continuum spectrumgiven by equation (4), respectively. This represents the excess strength in the 8–12 µ m range. Wecalculated this quantity for the observed/continuum spectra averaged over each bin, and we plot thedependence on A and | β ⊕ | in Figure 10. The parameter EW whole seems to be negatively correlated with A , although it is not well-expressed by a linear function, according to the extremely large reduced- χ value of the linear fit. On the other hand, EW whole does have a clear positive correlation with | β ⊕ | .This indicates that the IPD at higher | β ⊕ | (or higher A ) shows stronger (weaker) excess emission in the8–12 µ m range. 13igure 7: Two-dimensional histogram showing the brightness contribution A from the dust bands vs. theabsolute values | β ⊕ | of the ecliptic latitudes in the various pointing directions. We compared the featureshapes among the values of A in the datasets with | β ⊕ | < ◦ , enclosed by the red line in the figure, andinvestigated the dependence of the feature shapes on | β ⊕ | in the datasets with A < | β ⊕ | = 90 ◦ because the number of data points was too small.14 λ [ µ m]0.91.01.11.2 ob s e r v e d / c on ti nuu m ≤ A < 1.0 % (n=11)0.0 % ≤ A < 1.0 % (n=11)0.0 % ≤ A < 1.0 % (n=11)0.0 % ≤ A < 1.0 % (n=11)0.0 % ≤ A < 1.0 % (n=11)1.0 % ≤ A < 1.5 % (n=9)1.0 % ≤ A < 1.5 % (n=9)1.0 % ≤ A < 1.5 % (n=9)1.0 % ≤ A < 1.5 % (n=9)1.0 % ≤ A < 1.5 % (n=9)1.5 % ≤ A < 2.0 % (n=12)1.5 % ≤ A < 2.0 % (n=12)1.5 % ≤ A < 2.0 % (n=12)1.5 % ≤ A < 2.0 % (n=12)1.5 % ≤ A < 2.0 % (n=12)2.0 % ≤ A < 4.0 % (n=5)2.0 % ≤ A < 4.0 % (n=5)2.0 % ≤ A < 4.0 % (n=5)2.0 % ≤ A < 4.0 % (n=5)2.0 % ≤ A < 4.0 % (n=5)4.0 % ≤ A < 6.0 % (n=8)4.0 % ≤ A < 6.0 % (n=8)4.0 % ≤ A < 6.0 % (n=8)4.0 % ≤ A < 6.0 % (n=8)4.0 % ≤ A < 6.0 % (n=8)
Figure 8: The observed/continuum spectra averaged over each A -bin. The error bars represent thestandard errors in the averaging. We show the number n of data points in each bin in the legend.15 λ [ µ m]0.91.01.11.2 ob s e r v e d / c on ti nuu m ° ≤ | β Earth | < 25 ° (n=14)0 ° ≤ | β Earth | < 25 ° (n=14)0 ° ≤ | β Earth | < 25 ° (n=14)0 ° ≤ | β Earth | < 25 ° (n=14)25 ° ≤ | β Earth | < 40 ° (n=4)25 ° ≤ | β Earth | < 40 ° (n=4)25 ° ≤ | β Earth | < 40 ° (n=4)25 ° ≤ | β Earth | < 40 ° (n=4)40 ° ≤ | β Earth | < 60 ° (n=7)40 ° ≤ | β Earth | < 60 ° (n=7)40 ° ≤ | β Earth | < 60 ° (n=7)40 ° ≤ | β Earth | < 60 ° (n=7)60 ° ≤ | β Earth | < 80 ° (n=13)60 ° ≤ | β Earth | < 80 ° (n=13)60 ° ≤ | β Earth | < 80 ° (n=13)60 ° ≤ | β Earth | < 80 ° (n=13) Figure 9: The observed/continuum spectra averaged over each | β ⊕ | -bin. The error bars represent thestandard errors in the averaging. We show the number n of data points in each bin in the legend.16he derived excess strengths and the | β ⊕ | -dependence are roughly consistent with a previous studyby Reach et al. (2003) [49] of excess strengths at some β ⊕ and some solar elongations. This variation of EW whole can be interpreted as a difference in the IPD grain-size frequency distribution along the lines ofsight in different directions. Since an increase in the fraction of small grains seems to strengthen excessemission according to Figure 4, we can say that lines of sight at higher | β ⊕ | include a more fraction ofsmall grains, while the fraction of small grains exhibits a relative decrease in directions toward the dustbands. E W w ho l e [ µ m ] Slope: (-7.1 ± × -3 [ µ m/%]Intercept: (1.78 ± × -1 [ µ m]Correlation coefficient: -0.49 β Earth | [degree]0.100.150.200.250.30 E W w ho l e [ µ m ] Slope: (1.96 ± × -3 [ µ m/deg]Intercept: (1.27 ± × -1 [ µ m]Correlation coefficient: 0.46 Figure 10: The dependence of the equivalent width of the whole excess emission ( EW whole ) on thebrightness contribution from the dust bands ( A ; the top panel) and on the ecliptic latitude ( | β ⊕ | ; thebottom panel). Each filled circle is calculated from the observed/continuum spectrum averaged over eachbin and shown in Figures 8 and 9. The position on the horizontal axis corresponds to the mean value inthe bin. The solid lines are the linear functions that best fit the dependence, and the results of the fitsare summarized in Table 3. µ m and 9.0–9.5 µ m According to Figure 4, small grains ( ≤ µ m) of amorphous olivine and amorphous pyroxene pro-duce a smooth convex excess around 10 µ m and 9 µ m, respectively. As a tentative indicator of theolivine/(olivine+pyroxene) ratio in small amorphous grains, we define the ratio of equivalent widths inthe two wavelength regions, 10.0–10.5 µ m and 9.0–9.5 µ m: EW . − . /EW . − . = (cid:90) . µ m10 . µ m Z λ − C λ C λ dλ (cid:30) (cid:90) . µ m9 . µ m Z λ − C λ C λ dλ . (8)We selected these wavelength regions to avoid contamination by the peaks due to small crystalline silicatesas much as possible. The resulting correlation with A and | β ⊕ | is shown in Figure 11. The ratio17 W . − . /EW . − . shows a positive (negative) correlation with A ( | β ⊕ | ). This trend means thatsmall grains in the dust bands shows relatively strong olivine-like features, while the small IPD grains athigh | β ⊕ | appears to have more pyroxene-like features than typical small IPD grains do. E W . -- . / E W . -- . Slope: (4 ± × -2 [/%]Intercept: 1.16 ± β Earth | [degree]0.60.81.01.21.41.6 E W . -- . / E W . -- . Slope: (-5.4 ± × -3 [/deg]Intercept: 1.23 ± Figure 11: Dependence of the equivalent width ratio in 10.0 – 10.5 µ m and 9.0 – 9.5 µ m( EW . − . /EW . − . ) on the brightness contribution from the dust bands ( A ; the top panel) andon the ecliptic latitude ( | β ⊕ | ; the bottom panel). Other explanations are the same as in Figure 10. Theerrors in the y-axis at A =2.5 % and | β ⊕ | =30 ◦ and 50 ◦ were relatively large because of the small numbersof data points. The two remaining parameters are focused on more detailed feature shapes, which the AKARI ob-servations have enabled us to examine for the first time. We investigated the wavelength shifts andequivalent-width ratios of the peak excesses due to the small crystalline silicates: forsterite and enstatite.In order to compare such parameters among peaks from the same vibration modes in different directions,we need first to identify which peaks originate from the same vibration mode. We established a referencewavelength λ ref for each main peak that is common to all the observing directions, and we assumed thatthe peaks seen within the two neighboring wavelength bins around λ ref (corresponding roughly to theregion λ ref ± µ m) originate from the same vibration mode.The procedure we used to establish λ ref is the following.1. For the observed/continuum spectra in all 74 observations, we searched wavelength bins with apeak, which show a higher observed/continuum ratio than the neighboring bins.2. For all wavelength bins from 8 to 12 µ m, we counted the number of data points that have a peakat the bin. The resulting histogram is shown in Figure 12.18. We selected wavelength bins which have a peak most frequently among the five successive binsaround it, and we defined the center wavelengths of the selected bins as λ ref . Around 9.6 µ m,however, two neighboring wavelength bins had the same number of data points. For this case, wechose the center wavelength of the bin at the shorter wavelength as λ ref .In this way, we found seven peaks that are commonly seen in many directions, and we fixed the corre-sponding reference wavelengths at λ ref = 8.47, 8.96, 9.56, 10.15, 10.65, 11.34, and 11.84 µ m.Figure 12: The histogram of peak wavelengths. Each wavelength bin has a width of ∼ µ m. Wavelengthbins selected to serve as reference wavelengths are marked with a circle at the top. We used the data inthe seven peak regions indicated by the arrows.The position of a peak wavelength for each of the 74 observations is not always identical to λ ref . Fromeach of the seven regions of λ ref ± λ peak . The peak-wavelength shift inthe region around λ ref is then given by∆ λ peak = λ peak − λ ref [ µ m] . (9)Although the absolute values of these quantities do not have strong meanings because it depends onthe definition, the relative variations of ∆ λ peak among the different sky directions imply differences inthe grain properties, which affect the wavelength positions of their emission peaks. Figure 13 shows theresulting correlation of ∆ λ peak in each peak region with A and | β ⊕ | . ∆ λ peak seems not to change in mostregions, except for the region around 11.34 µ m and 8.96 µ m. This means that the grain properties suchas metal composition and crystal morphology do not dramatically change depending on the sky direction(see section 4.3). The region around 11.34 µ m is too complicated to be discussed deeply because twopeaks originating from both enstatite and forsterite contaminate this region.19 µ m -0.250.250.00 µ m -0.250.250.00 µ m -0.250.250.00 ∆ λ p ea k [ µ m ] µ m -0.250.250.00 µ m -0.250.250.00 µ m µ m -0.250.250.00 µ m -0.250.250.00 µ m -0.250.250.00 µ m -0.250.250.00 ∆ λ p ea k [ µ m ] µ m -0.250.250.00 µ m -0.250.250.00 µ m β Earth | [degree]-0.250.250.00 µ m Figure 13: Dependence of the wavelength shift ∆ λ peak of the peak excess due to small crystalline silicateson the brightness contribution from the dust bands ( A ; the top panels) and on the ecliptic latitude ( | β ⊕ | ;the bottom panels). Each panel indicates the result for the peak in the region around λ ref , which is notedat the upper right side of the panel and corresponds to the dotted line. Other explanations are the sameas in Figure 10. In the region around 8.96 µ m, some average observed/continuum spectra do not show apeak structure. 20 .4.4 Equivalent-width ratio of peak excesses due to small crystalline silicates The last feature-shape parameter we consider is the equivalent-width ratio, EW fo /EW en , of the peakexcesses due to small forsterite and enstatite grains. We took into account the peaks around 10.15 and11.84 µ m to calculate the equivalent width of the forsterite peak, while the peak around 9.56 and 10.65 µ mto calculate the equivalent width of the enstatite peak. We thus defined this parameter as EW fo EW en = EW peak (10 . µ m) + EW peak (11 . µ m) EW peak (9 . µ m) + EW peak (10 . µ m) , (10)where EW peak ( λ ref ) = (cid:90) λ peak ( λ ref )+0 . µ m λ peak ( λ ref ) − . µ m Z λ − C λ C λ dλ [ µ m] . (11)Here, λ peak ( λ ref ) is the peak wavelength in the region around λ ref at the individual A - or | β ⊕ | -bin. Thismeans that the wavelength intervals of these integrations change depending upon the wavelength shiftin each bin. As shown in Figure 14, EW fo /EW en exhibits a negative correlation with A , although thedispersion is significant. We could not find any correlation between EW fo /EW en and | β ⊕ | at least in thisstatistical processing, regarding the low correlation coefficient. E W f o / E W e n Slope: (-1.1 ± × -2 [/%]Intercept: (3.40 ± × -1 Correlation coefficient: -0.46 β Earth | [degree]0.200.250.300.350.40 E W f o / E W e n Slope: (-1 ± × -4 [/deg]Intercept: (2.90 ± × -1 Correlation coefficient: -0.16
Figure 14: Dependence of the equivalent-width ratio EW fo /EW en of the peak excesses due to smallcrystalline silicates on the brightness contribution from the dust bands ( A ; the top panel) and on theecliptic latitude ( | β ⊕ | ; the bottom panel). Other explanations are the same as in Figure 10. The errorsin the y-direction at A =2.5% and | β ⊕ | =30 ◦ , and 50 ◦ are relatively large because of the small numbers ofdata points. 21able 3: The slopes of the linear functions of A or | β ⊕ | that best fit EW whole , EW . −− . /EW . −− . ,and EW fo /EW en . The reduced- χ of each fit and correlation coefficient r are also shown. These slopevalues are plotted in Figures 10, 11, and 14, respectively.parameter A -dependence | β ⊕ | -dependencetype Slope reduced- χ r Slope reduced- χ rEW whole ( − . ± . × − . ± . × − EW . − . /EW . − . (4 ± × − − . ± . × − EW fo /EW en ( − . ± . × − − ± × − Units of [ µ m/%] for EW whole , [/%] for EW . − . /EW . − . and EW fo /EW en . The maximum amplitude of A is < Units of [ µ m/deg] for EW whole , [/deg] for EW . − . /EW . − . and EW fo /EW en . The possible maximum amplitude of | β ⊕ | is90 degree. In section 4, we presented the typical properties of the small IPD grains determined from the averagefeature shapes and we described the variations of the feature shapes and the related grain propertiesamong the different sky directions. We next describe the implications of these results.
According to a comparison between the feature shapes averaged over all directions and the absorptioncoefficients of candidate minerals, we found that the IPD typically includes small silicate crystals such asenstatite.The most significant source of the IPD around 1 au is thought to be comets [43] and some of thecometary IPD particles collected in the stratosphere show clear enstatite peaks [36]. The results we haveobtained thus seem consistent with previous work.In the interstellar medium, the degree of crystallinity of silicate dust is less than 2 % [28]. Therefore,the silicate crystals seen in the IPD are likely to have been formed by re-condensation from gas in the solarnebula and/or by annealing of amorphous interstellar (i.e., pre-solar) dust. In the pressure environmentat the mid-plane of the proto-solar disk, the equilibrium condensation temperatures of enstatite andforsterite are 1300 K and 1400 K, respectively [19]. Hallenbeck et al. (2000) [24] have shown that theannealing temperature of silicates is about 950 K. However, such high temperature is possible only nearthe Sun (at least less than a few au), if we assume the global radial dependence of the disk temperaturein a stationary disk model [18, 3, 40]. This indicates radial mixing of the dust population and/or localheating in the proto-solar disk. A By comparing the feature shapes among different sky directions with the contribution, A , from thedust bands, we found several correlations between the feature shapes and A . This may imply differinggrain properties of the IPD originating from asteroids and comets. Sykes & Greenberg (1986) [56] andNesvorn´y et al. (2003) [41] propose that the dust bands were formed by the IPD from asteroids, whilethe main source of other IPD components is comets.According to the negative correlation between EW whole and A shown in Figure 10, the asteroidalIPD may have a size frequency distribution biased toward large grains. It may be because the dustcontinuously supplied by collisional cascades among asteroids can include a lot of large grains during thecascades, while the cometary IPD is ejected from melting icy mantles mainly as small grains [53]. Thus,differences in the supply processes may cause the different size frequency distributions.Other differences in the properties of the asteroidal and cometary IPD grains have been found inprevious work. A unique property of the asteroidal IPD is hydration. Schramm et al. (1989) [52] andGermani et al. (1990) [22] found hydrated minerals in the IPD particles thought to come from asteroids,while the cometary IPD seems to be anhydrous. The CM chondrites, which are a type of carbonaceous22eteorite thought to originate from C-type asteroids, are also well-known to contain hydrated materi-als [34, 35]. In addition, Usui et al. (2018) [60] discovered hydrated minerals in most C-complex asteroids.Common hydrated minerals are phyllosilicates like serpentine and talc, which are produced by aqueousalteration from forsterite or enstatite [20, 5, 58]. They show a smooth excess feature with a peak around10 µ m, similar to that of amorphous olivine [2]. We suggest the possibility that the feature caused byphyllosilicate may be responsible for increasing the ratio EW . − . /EW . − . at the directions towardthe dust bands, as shown in Figure 11, without an increase in the fraction of amorphous olivine. In such acase, the peaks originating from both forsterite and enstatite will appear to be reduced, because aqueousalteration changes the forsterite and enstatite into serpentine and talc, respectively. Considering that thephyllosilicate peak can replenish the excess strength around 10 µ m but not in the olivine peak around11.84 µ m, this scenario may also explain the negative correlation between A and EW fo /EW en shown inFigure 14. Since the most significant dust band at β ⊕ = ± ◦ . | β ⊕ | As mentioned in section 4.4, the | β ⊕ | -dependence of EW whole , the equivalent width of the wholeexcess emission in 8–12 µ m band, indicates an increase in the fraction of small grains at higher | β ⊕ | .This can be explained by the radial dependence of the size frequency distribution of the IPD grains.Jehn (2000) [25] found that large grains exist more frequently at a few au from the Sun as compared withnear the Earth, on the ecliptic plane where the IPD distributes convergently. Since the IPD at radialdistances far from the Earth is included only in lines of sight at low | β ⊕ | , the size frequency distributionof the IPD grains at high | β ⊕ | is relatively biased toward small grains. The radial dependence of the sizefrequency distribution is thought to be caused by the collfisional cascade during the accretion of IPDparticles toward the Sun owing to Poynting-Robertson drag [23].We also found differences in the mineral composition of the small IPD grains as a function of | β ⊕ | .This may imply differences in the grain properties of the IPD originating from different types of comets.According to Nesvorn´y et al. (2010) [43], the IPD from the Jupiter Family Comets (JFCs) is the mostsignificant and is distributed mainly around the ecliptic plane, barely spreading toward the ecliptic poles.On the other hand, the IPD from Oort Cloud Comets (OCCs) is known to have an isotropic distribution,owing to the wide range of inclinations of the OCCs. This means that the fraction of the IPD originatingfrom the OCCs becomes relatively larger at higher | β ⊕ | . One of reasons for the negative | β ⊕ | -dependenceof EW . − . /EW . − . may be because the IPD from the OCCs has a lower olivine/(olivine+pyroxene)ratio than the IPD from the JFCs regarding at least small amorphous grains. Such differences indicatethe different forming regions of the JFCs and the OCCs. Using mid-infrared slit-spectroscopic data of the zodiacal emission obtained with AKARI/IRC, wehave succeeded in detecting details of the shapes of the excess emission features in the 9–12 µ m range.The feature shape averaged over all directions indicates that the IPD typically includes small silicatecrystals such as enstatite, suggesting the existence of radial mixing and/or local heating of the dustin the proto-solar disk. We also found variations in the feature shapes among different sky directions.From investigations of EW whole , we found that the spectra at higher | β ⊕ | showed a stronger excess, whichindicates an increase in the fraction of small grains included in the line of sight at higher ecliptic latitudes.On the other hand, the negative correlation with A indicates that the size frequency distribution of theIPD in the dust bands is biased toward relatively large grains. The positive and negative correlations with A of EW . − . /EW . − . and EW fo /EW en , respectively, can be qualitatively explained by aqueousalteration from forsterite and enstatite to phyllosilicates in the asteroidal IPD. From the negative | β ⊕ | -dependence of EW . − . /EW . − . , we found the possibility that the IPD at higher ecliptic latitudes23ay have lower olivine/(olivine+pyroxene) ratio for small amorphous grains. Such variation of the mineralcomposition of the IPD at different ecliptic latitudes may imply the difference of the mineral compositionbetween the IPD from the JFCs and OCCs, because their distributions in ecliptic latitudes are different.This research is based on observations with AKARI, a JAXA project with the participation of ESA.We would like to thank all the members of the AKARI project. This work was supported by two JSPSKAKENHI Grant-in-Aid for Scientific Research (C): Grant Number JP17K05381 and JP17K05636, andpartly by the Astrobiology center and the National Astronomical Observatory of Japan. Since this paperis based on the PhD-thesis work of Aoi Takahashi, we greatly appreciate referees of the PhD-defense:Takahiro Iwata, Yuko Inatomi (ISAS/JAXA) and Hirokazu Kataza (University of Tokyo). Finally, weare sincerely thankful for pertinent comments from a reviewer and editorial works.24 Elimination of artifacts
Figure 15: A schematic view of three artificial components: (1) light scattered from detector pixels, (2)light scattered from the edge of the detector, and (3) ghost of a small aperture window. In actuality, someoptical elements—like a beam splitter, two lenses, and a grism—are also included between the aperturemask and the detector. The Y direction is the direction of wavelength dispersion. A.1 Light scattered from the detector pixels
A small fraction of the light incident on a detector pixel is scattered into other pixels in the samerow and column of the pixel array, even if the pixel is not saturated. From careful investigations ofpoint-source imaging data obtained in the MIR-S channel, it has been empirically found that the lightwith intensity S [ADU] incident at the pixel position ( X , Y ) is scattered into the pixel position ( X , Y ) with the fraction of G ( X − X ) = C X − X . ) [ADU] , (12)where C = 7 . × − (6 . × − ) for SG1 (SG2). This formula can be used also for the scattering alongthe Y-axis. The actual brightness of this component at each position is determined by the convolutionof the light scattered from all pixels in the same row and column: S ( X, Y ) = (cid:90) S ( X , Y ) × G ( X − X ) dX + (cid:90) S ( X, Y ) × G ( Y − Y ) dY [ADU] . (13)If we care about their effect on the slit-spectroscopic region, the light leaking from the main field of viewalong the X-axis is dominant [see (1) in Figure 15 and Appendix 2 of Sakon et al. (2007) [50]]. We calcu-lated the two-dimensional brightness distribution of the leaking light for each pointing data. After initialprocessing of the observed image (dark subtraction, linearity correction, and median determination), weassumed the brightness distribution in the processed image itself to be approximately the distribution of S , because the fraction of the scattered light that is included is as small as 10 − of the incident light [theorder of magnitude of C in equation (12)]. Using the distribution of S , we calculated the distribution of25
20 40 60 80 100 120X [pixel]0.0000.0020.0040.006 N o r m a li ze d b r i gh t n e ss S7S11
Figure 16: The brightness profile of light scattered from the edge of the detector. The absolute value isnormalized by the brightness of the source causing the scattered light. The filters S7 and S11 are usedfor the imaging observations, because their wavelength coverages correspond to those of SG1 and SG2,respectively. We used the profile obtained with S7 for SG1 and with S11 for SG2. S from equation (13). Panel (a) in Figure 17 shows an example of the estimated brightness distributionof this component. We subtracted it from the processed image. A.2 Light scattered from the edge of the detector
The aperture mask we used was shared with the Near-Infrared (NIR) channel, and it had a smallwindow for the spectroscopy of point sources in the NIR channel. Since the detector surface in the MIR-Schannel is smaller than that in the NIR channel, some light that passes through this window is scatteredby the edge of the detector in the MIR-S channel and contaminates the slit-spectroscopic region [see (2)in Figure 15]. When we checked the imaging data in the MIR-S channel, we found some datasets withtwo images in different observations. One image of each dataset accidentally showed a clear line of thisscattered light caused by a bright point source illuminating the detector edge, while in the counterpart,the pointing direction was slightly dithered and the point source was properly imaged in the main field ofview. We subtracted the counterpart image from the image with the scattered light after correcting forthe position shift. This subtraction extracted the brightness due to the scattered light. We determinedthe brightness profile as a function of the distance from the edge of the detector. The intrinsic brightness, S , of the point source can be measured in the counterpart image. Figure 16 shows the brightness profile, S ( X ), of the scattered light normalized by S .According to data obtained from the NIR channel, which was pointed in the same direction as theMIR-S channel and for which the images covered the field of view of the small aperture window, no brightpoint source contaminated the field of view of the small window in any of the data we used. We thereforeassumed the brightness to be uniform in the field of view of the small window. Fortunately, the spectrumof the incident light passing through the edge of the small aperture window illuminates only a few pixelcolumns at the edge of the detector sensitive area. We replaced the brightness in such pixel columns by26igure 17: Two-dimensional images of (a) the light scattered in detector pixels from the main field ofview scaled by a factor 20, (b) the light scattered at the edge of a detector after going through the smallwindow aperture scaled by a factor of 100, and before and after the subtraction of these scattered light,(c) and (d), respectively. This is an example in the case of data pointed at ( λ s , β s ) = (174.13 deg, -1.00deg) in observation ID of 1500701.1 and obtained with SG2.the brightness illuminating the detector edge, S ( Y ), and then calculated the brightness distribution of S ( X, Y ) as in panel (b) of Figure 17. Note that we optimized some parameters of the profile S ( X )described in Figure 16 for the diffuse source of the scattered light. A.3 The ghost of the small aperture window
Some fraction of the light that passes through the small aperture window makes ghost componentsin the slit-spectroscopic region after tracing a ray like (3) in Figure 15. We assumed that this didnot contaminate the spectroscopic region of the small aperture window itself. As mentioned above,spectra from the small aperture window are partly seen at the edge of the detector sensitive area in thespectroscopic images. By combining the spectra of the small aperture window and the slit, we estimatedthe brightness profile of the ghost by the following steps, after first subtracting the artifacts described inthe previous two subsections.1. After extracting the one-dimensional spectra from the slit (slit spectra), we convolved them withthe width of the small window (corresponding to 25 pixels, while the slit width is ∼ Y is the direction of the wavelength dispersion, as definedin Figures 15 and 17. This corresponds to the quantity G ( Y ) in equation (14).3. We de-convolved the profile with the width of the small aperture window.The shape of the derived profile seems to be common in all the data, and the absolute value is roughlyproportional to the typical value of the mid-infrared brightness incident through the small aperturewindow. Figure 18 shows the normalized ghost profile obtained from the typical brightness in the smallaperture window.Using this common profile, we determined the absolute value appropriate for each pointing dataset.Since we could not determine the typical brightness in the small aperture window directly from theimage obtained in the MIR-S channel, we instead fitted the absolute value of the profile to the observeddata. If the artifacts are completely removed, the brightness in the regions where the optical system hasno response should be zero. However, the brightness in such regions was actually non-zero, even aftersubtracting the other two artifact components, (1) and (2). We assumed this non-zero brightness tooriginate from the ghost of the small aperture window. We therefore fitted the following function S ( Y )to the non-zero brightness seen in the regions without a system response: S ( Y ) = a + b Y + c G ( Y ) [ADU] , (14)where G ( Y ) is the brightness profile shown in Figure 18. The linear terms a + b Y represents thelinear offset needed to correct the residual. This offset may correspond to the ghost component of themain field of view, although we could not conclude this definitively. The constants a , b , and c are freeparameters that we optimized individually for each pointing dataset. Thus, S ( Y ) becomes identical tothe non-zero brightness in the regions without a system response. As such regions, we selected the pixel28igure 19: Brightness profiles in the slit-spectroscopic region. The brightness originates from zodiacalemission, denoted by ZE, with all artifacts (black); with only the ghost component after subtracting theother two artifact components of the scattered lights (blue); and with no artifacts after subtracting all theartifacts (red). The green line represents the brightness profile of the ghost component and corresponds tothe difference between the blue and red curves. The quantity Y is the pixel position along the direction ofspectral dispersion, as defined in Figures 15 and 17. At the top, we show the corresponding wavelengthscalculated using our wavelength calibration method. The 0th- and 2nd-order light is seen at Y ∼ ≤ Y ≤ λ s , β s ) = (174.13 deg, -1.00 deg). The observation ID is 1500701.1.ranges 25 ≤ Y ≤
80 or 180 ≤ y ≤
240 for SG1, and 45 ≤ Y ≤
90 or 200 ≤ Y ≤
240 for SG2, in orderto avoid the contribution of the target brightness in the 0th, 1st, and 2nd dispersion order. Examplesof the brightness profiles before and after subtracting the ghost component, and the profile of the ghostcomponent itself, are shown in Figure 19.After subtracting of these three types of artifacts, we succeeded in deriving spectra that are connectedreasonably smoothly between the data from SG1 and SG2 for all pointing data. Figure 20 shows anexample of a spectrum obtained before and after the subtraction. It is clear that the subtraction ofartifacts corrects for the inconsistency in the intensity levels of SG1 and SG2 in the overlapping wavelengthrange. 29 µ m]020406080 I n t e n s it y [ M J y / s t r] ZE + all artifacts (SG1)ZE + all artifacts (SG1)ZE + all artifacts (SG1)ZE + all artifacts (SG1)ZE + all artifacts (SG1)ZE + all artifacts (SG2)ZE + all artifacts (SG2)ZE + all artifacts (SG2)ZE + all artifacts (SG2)ZE + all artifacts (SG2)ZE (SG1)ZE (SG1)ZE (SG1)ZE (SG1)ZE (SG1)ZE (SG2)ZE (SG2)ZE (SG2)ZE (SG2)ZE (SG2)ZE (DIRBE ‘ s model)ZE (DIRBE ‘ s model)ZE (DIRBE ‘ s model)ZE (DIRBE ‘ s model)ZE (DIRBE ‘ s model) Figure 20: Spectra obtained with SG1 and SG2 before and after subtracting the three types of artifacts.This is an example of data obtained while pointing in the direction ( λ s , β s ) = (174.13 deg, -1.00 deg).The observation ID is 1500701.1. 30 Obtained observed/continuum ratio at each direction
We show observed/continuum ratios in all 74 sky directions from the next page. They are obtainedby following the reduction flow described in section 3 and dividing by the continuum calculated from theequation (4). 312345678 eferenceseferences