MODELING
OF THE INTERPLANETARY DUST CLOUD

S. S. HONG
Seoul National University, KOREA

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My long time collaborators with Zodiac Matters:• Jerry L. Weinberg• S.M. Kwon, J. Pyo, Y.M. Seo• Hero Tanabe, M. Ueno, M. Ishiguro, F. Usui, D. Ishihara,
T. Ootsubo, T. Matsumoto, AKARI IRC Team ;and Tadashi Mukai

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A ThreeThree-dimensional Model of the Interplanetary Dust Cloud
Seung Soo Hong , Seoul
Seoul National University

We are currently reducing the brightness of zodiacal emission (ZE) from the all sky IR survey
observations of the Japanese IR satellite, AKARI, which commands fine spatial resolution andsuperb sensitivity. The resulting maps will determine the ZE brightness, at solar elongation 90
degrees, over the entire ranges of the ecliptic longitude and latitude. This lecture explains how
one can make use of such fine resolution maps in probing three-dimensional structures of theinterplanetary dust (IPD) cloud. An emphasis will be given to the limitations of the currently
available 3-D models. For example, in building these empirical models of the IPD cloud, one often
employs specific functional forms to describe the vertical density structure of the cloud, whichleave unavoidable biases in the resulting 3-D models. Instead of relying on functional forms, wewill directly invert the profile of ZE brightness, at solar elongation 90 degree, over ecliptic
latitude from 0 through +/-90 degrees. This lecture will also explain how the pointing capabilityof the AKARI can be utilized in directly measuring the volumetric IR emissivities of theinterplanetary dust particles near the Earth’s orbit. We will analyze seasonal variations of thezodiacal emission brightness of the north and south ecliptic poles and locate the plane of
maximum IPD density as accurately as possible.

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金 我他

ON-AIR by Atta Kim (1958 ~ ) 現象の 重層性International Center of Photography, June 2006, N.Y.
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APOD : Aug 25, 2004
Taken in Namibia, May ‘04
by Stefan Seip
http://antwrp.gsfc.nasa.gov/apod/

Original schematic

http://antwrp.gsfc.nasa.gov/apod/ap040825.html

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How does the IPD cloud look like inside ?
1. how to construct a 3D model of the interplanetary dust
cloud from the ZL and ZE brightness distributions overthe sky
2. how to directly measure the volumetric emissivity of
the interplanetary dust particles near the Earth’s orbit
3. AKARI low resolution maps of the ZE brightness andpreliminary analysis of the maps
4. limitations of a single-component approach to the 3Dmodel construction

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Chap 1 Basic Concepts and Geometry
Chap 2 Degeneracy Cracking
Chap 3 Vertical Inversion
Chap 4 IPD Cloud Revealed to AKARI
Chap 5 In Retrospect

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Chap 1. BASIC CONCEPTS AND GEOMETRY

sunlight scattered by IPDs
⇒ Zodiacal VIS Light黃道 散亂光 ZL(ΛΛ, β)sunlight absorbed by IPDs
⇒ Zodiacal IR Emission 黃道 放出光 ZE(ΛΛ, β; λ)Dust in Space_090106

1) ZODIACAL LIGHT BRIGHTNESS INTEGRAL

2-D Distribution of ZL Brightness ⇐ OBSERVATION⇒ 3-D structure of the IPD cloud complex
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IN-ECLIPTIC ZL BRIGHTNESS INTEGRAL

It is possible to retrieve scattering phase function from theobserved elongation dependence of the ZL brightness in theecliptic.
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2) IN-ECLIPTIC ZE BRIGHTNESS INTEGRAL

It is possible to retrieve power-exponent ν from observed
elongation dependence of the ZE brightness in the ecliptic.
The grey exponent δ = ½ can be generalized to non-grey δ .
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3) SYMMETRY PLANE

Provided by M. Ishiguro

M. Ishiguro

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⇒ 3D shape of IPD cloud
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One needs to locate the plane of maximum IPD density interms of inclination and longitude of the ascending node.

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4) How does the IPD cloud look like ?
i) powe-law exponent νs for the volumetric scatteringcross-section n(r) σsca (r) of IPDsΘ) of IPDsii) scattering phase function Φ (ΘIii) power-law exponent νa for the volumetric absorption
cross-section n(r) σabs (r, λ) of IPDsiv) power-law exponent δ for the dust temperature T(r)v) location of the symmetry plane in terms of its
inclination is and the ascending node’s longitude Ωsvi) vertical structure function f(ββ`)

Crack n – sigma – nu – phi – delta – f Degeneracy`` A 3 - D Model of the IPD Cloud ``The IPD Cloud Structure & Optical Property of IPDs
Observations& Laboratory Experiments
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Chap 2. DEGENERACY CRACKING
1) A GLIMPSE OF ‘PROMISED LAND’
circular orbitRo

Λ=Λ
Dumont 1975

wavelength – dependence of the IR emissivity of local
IPDs ⇒ material property
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2) NON-ZERO ECCENTRICITY OF THE EARTH ORBIT
elliptical orbit

×Please note that T/To = ( r/ro)-δδ.

modulation by the elliptical motion of Earth with eccentricity
0.0176
additional modulation due to the tilt of maximum density plane of
IPD cloud with i and Ωs
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In summary, we may have the followings :⇒Dust in Space_090106

3) DEGENERCY CRACKING STRATEGYFirst take To as an analysis parameter ; derive δ from the emissvity
color with the given value of To ; calculate α from To ; and then fix
ν for the given wavelength ; and then use To-independency conditionfor δ and ν, which will fix all the unknowns !
seasonal modulation

emissivity color

Planck function⇒Hong et al 2004, JKAS,37, 159

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4) FEASIBILITY TEST :OBSERATIONAL DIFFERENTIATION

Hong et al. (2004)
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FEASIBILITY TEST :OBSERVING SESSIONS

Hong et al. (2004)
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FEASIBILITY TEST : Without Imposing Noise
simultaneous measurement of To and delta

Hong et al. (2004)
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FEASIBILITY TEST : Without Imposing Noise
To-parameter Approach

Hong et al. (2004)
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FEASIBILITY TEST : NOISE IMPOSED
Hong et al. (2004)

Errors corresponding to the
64x64 binnings are imposedon the ZE brightness itself,from which the differential
brightness is formed, andhence we have theemissivity variation like theone shown on the right.
Original schematicFEASIBILITY TEST : With Noise Imposed
64 x 64 binning, 12 µm/ 25 µm color
To-parameter Approach

Original schematic

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FEASIBILITY TEST ; With Noise Imposed
128 x 128 binning, 7 µm/ 12 µm/ 25 µm color
To-parameter Approach

Hong et al. (2004)
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FEASIBILITY CONFIRMATION
Hong et al. (2004)

inputs for model simulations : ν = 1.0, δ = 0.5, To = 278 K- successfully recovered the input data
- wavelength selection for color base is important for success- the color correction hasn’t been made yet- even 32 x 32 binning might make the analysis possible

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5) REALITY OF THE PROMISED LAND
A year long monitoring is necessary to lift
degeneracy.
Due to severe limitation in the AKARI’s attitude
maneuvering, we couldn’t have enough number ofpointing opportunities; but we have secured
observations at both peri- and ap-helion positions.
Currently, efforts are underway to improve AKARI
calibrations for diffuse source light; with the
improved calibration, we expect to measure thelocal IPD emissivities for the first time.

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Chap 3. VERTICAL INVERSION
1) PREVIOUS STUDIES

Original schematic
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Original schematic

Original schematic

The resulting vertical profile is controlled by theimposed function itself.
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2) DIRECT INVERSION

Original schematicis fixed at 90o .

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2) DIRECT INVERSION

Original schematicis fixed at 90o .

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Replacing the integral by quadrature sum, one may
construct a triangular system of simultaneous linearequations.
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Dust in Space_090106

3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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3) RESULTS AND COMPARISON

Pyo et al. (2009), submitted

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4) COLOR PROFILE OF ZE OVER LATITUDE Beta

COBE/ DIRBE
4.9um - 12um
AKARI/ IRC
9um - 18um
COBE/ DIRBE
12um - 25um

Pyo et al. (2009), submitted

Can we understand the beta-dependence of color
temperature with the single component model ?

Pyo et al. (2009), submitted

Pyo et al. (2009), submitted

Pyo et al. (2009), submitted

Pyo et al. (2009), submitted

The single component model has
failed to reproduce the observedcolor profile of ZE over ecliptic
latitude. This is an example ofits many failures though.

5) HOW DOES THE IPD CLOUD LOOK LIKE?
It does depend on the wavelength used.
• The IPD cloud revealed by ZL in the opticalhappens to be similar to the one by ZE in 60
micro-meters.
• This is a limit of the brightness integral ; one
may needs help from dynamical model, laboratory
measurements of dust optical properties, etc.

Why does the IPD cloud look different from wavelength
to wavelength?
Beta Pic answers the question very well.

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Chap 5. IN RETROSPECT

ON-AIR by Atta Kim
100 Countries/100 Men
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References•http://antwrp.gsfc.nasa.gov/apod/ap040825.html•Hong, S. S., et al. 2004, JKAS, 37, 159•Pyo, J., et al. 2009, EPS, submitted•Telesco, C. M., et al. 2005, Nature, 433, 133