Quantitative Grain Size Estimationon Airless Bodies from the
Negative Polarization Branch:
The Case of Dawn Mission Targets,(4) Vesta and (1) Ceres using NHAO NIC
Yoonsoo P. Bach1,2,3, Masateru Ishiguro2,3, Jun Takahashi4,Jooyeon Geem2,3, Daisuke Kuroda5, Hiroyuki Naito6, Jungmi Kwon7
1. KASI, Korea; 2. Seoul Nat U, Korea; 3. Seoul Nat U, Astronomy Research Center, Korea; 4. Center for Astronomy, U Hyogo, Japan;
5. Japan Spaceguard Association, Japan; 6. Nayoro Observatory, Japan; 7. The U of Tokyo, Japan

Bach et al. (2022), StGal, 5, 4Bach et al. (2024a), A&A, 684, 80
Bach et al. (2024b), A&A, 684, 81
Nayuta UM, 2024-07-31

Contents
Ø Intro & Motivation◦

Insights from Experiments & Observations (Paper I: Bach+24a, A&A, 684, 80)

Ø Target selection
Ø Observations & Data reduction (Paper 0: Bach+22, StGal, 5, 4)
Ø Results (Paper II: Bach+24b, A&A, 684, 81)
Ø Discussions & Future work

Bach et al. (2022), StGal, 5, 4Bach et al. (2024a), A&A, 684, 80
Bach et al. (2024b), A&A, 684, 81Intro: Polarimetry in Solar System
Ø Polarimetric phase curve (PPC)◦ Pol. as phase angle 𝑃! = 𝑃! (𝛼)[%]◦ Phase angle α = 180° − scat. ang.

𝑃! =Fresnel, Rayleigh: 𝑰∥ < 𝑰⟂𝐼⟂

unpol.

𝐼∥
𝛼pol.
Scattering plane𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼Obs.

Sun

Intro: Polarimetry in Solar System
Ø Polarimetric phase curve (PPC)◦ Pol. as phase angle 𝑃! = 𝑃! (𝛼)[%]◦ Phase angle α = 180° − scat. ang.

𝑃! =𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼𝛼%&'Neg. Pol. Branch
NPB (𝜶 < 𝜶𝟎 )Fresnel, Rayleigh: 𝑰∥ < 𝑰⟂

𝐼⟂
𝐼∥

Sun
𝛼

Scattering plane

Pos. pol. Branch
PPB (𝜶 > 𝜶𝟎)
non-flatness
information
width 𝛼#depth 𝑃!"#Obs.

Motivation

𝑃! =𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼
width 𝛼#Ø We found two observables are important (Bach+24, A&A, 684, 80; Paper I):◦ Albedo

Umow 1905, Physikalische Zeitschrift, 6 (20), 674;
CellinoA+ 15, MNRAS, 451, 3473;
LupishkoD 18, SoSyR, 52, 98§ The Umov law◦ Size parameter (D/λ)

Lyot 29, Dollfus 55, Gehrels+64 AJ, Clark 65 MNRAS, Kenknight+67 AJ, Geake+70 GeCAS,Dollfus 71 PSMP, Dollfus+71a A&A, Dollfus+71b A&A, Dollfus_71c LPSC, Dollfus+75 LPSC,Zellner+77a&b LPSC, Dollfus+77 RSTPA, Dollfus+79 Asteroids, Le Bertre+80 Icar,Geake+86 MNRAS, Lupishko+89 Icar, Dollfus+89 Asteroids II, Geake+90 MNRAS,
Shkuratov+92 Icar, Shkuratov+ 94 E&MP, Volten+01 JGR, Shkuratov+02 Icar,
Shkuratov+04 JQSRT, Shkuratov+06 JQSRT, Belskaya+05 Icar, Hapke 12 Book,
Dabrowska+15 Icar, Nelson+18 Icar, Escobar-Cerezo+18 ApJS, Munoz+21 ApJS,Frattin+22 MNRAS, Spadaccia+22 A&A, Hadamcik+23 MNRAS, Sultana+23 Icar

Phase
angle αdepth 𝑃!"#And many (20+) more studies that we investigated but not directly used

Depth
𝑷𝐦𝐢𝐧

Depth
𝑷𝐦𝐢𝐧

width𝜶𝟎width
𝜶𝟎Bach+24, A&A, 684, 80; Paper I

Motivation

𝑃! =𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼
width 𝛼#Ø We found two observables are important (Bach+24, A&A, 684, 80; Paper I):◦ Albedo§ The Umov law

Phaseangle αUmow 1905, Physikalische Zeitschrift, 6 (20), 674;
CellinoA+ 15, MNRAS, 451, 3473;
LupishkoD 18, SoSyR, 52, 98

depth 𝑃!"#

◦ Size parameter (D/λ)

Smallptcls
Depth𝑷𝐦𝐢𝐧
Depth𝑷𝐦𝐢𝐧

Bach+24, A&A, 684, 80; Paper I
width𝜶𝟎width 𝜶𝟎Motivation

𝑃! =𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼width 𝛼#Ø We found two observables are important (Bach+24, A&A, 684, 80; Paper I):◦ Albedo§ The Umov law

Umow 1905, Physikalische Zeitschrift, 6 (20), 674;
CellinoA+ 15, MNRAS, 451, 3473;
LupishkoD 18, SoSyR, 52, 98

Phase
angle αPark+08 JAE 21 266◦ Size parameter (D/λ)

depth 𝑃!"#Moon Obs. from∴ 𝐷 ~ 1 − 2 µm(Moon)

Shkuratov+92 Icar 95 283

Smallptcls
Depth𝑷𝐦𝐢𝐧
Depth𝑷𝐦𝐢𝐧
Widenging stops'at ( ~1 − 2λλ0.4–0.6

stops @ 1µm

Dollfus+Bowell 1971 A&A, 10, 29

Bach+24, A&A, 684, 80; Paper I
width𝜶𝟎width 𝜶𝟎

Targets
Criteria:• Brightest• Most studied• Likely to contain small (≲ 20µm) particles(4) Vesta
560 × 450 km"Airless Bodies"(1) Ceres
960 × 890 km

Observation

Special Thanks

Ø NHAO NIC, polarimetric-mode◦ J, H, Ks-band simultaneous pol.

Ø (1) Ceres: 5 obs.
◦ 2020-06-21, 2020-10-02, 2020-10-18, 2021-09-09, 2021-11-07

Ø (4) Vesta: 6 obs.
◦ 2019-10-22, 2019-11-08, 2019-11-21, 2019-12-18, 2020-01-10, 2020-02-13

3+ year of data reduction→ Published NICpolpy

Bach et al. 2022 (StGal)PPCØ Ceres: Matches well with Palomar
Ø Vesta: First NIR pol of V-type

𝑃! =200" (5.1-m) telescope (WIRC+Pol)(Masiero et al. 2022 PSJ)
The first NIR pol. for asteroids (!?)

𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼
width 𝛼#Phase
angle αdepth 𝑃!"#

Bach+24b A&A, 684, 81; Paper IIPPCØ Ceres: Matches well with Palomar
Ø Vesta: First NIR pol of V-type

𝑃! =200" (5.1-m) telescope (WIRC+Pol)(Masiero et al. 2022 PSJ)
The first NIR pol. for asteroids (!?)

𝐼⟂ − 𝐼∥
𝑄=−𝐼⟂ + 𝐼∥
𝐼
width 𝛼#Phase
angle αdepth 𝑃!"#

Bach+24b A&A, 684, 81; Paper II

Case of Vesta

Large rocks

Depth𝑷𝐦𝐢𝐧FineParticles(compared to λ)Data: Geake et al. (1986) MNRAS

Width𝜶𝟎Depth𝑷𝐦𝐢𝐧

Bach+24b A&A, 684, 81; Paper IIwidth𝜶𝟎

Case of Vesta

Large rocksØ 𝑷𝐦𝐢𝐧 - 𝜶𝟎 change for Vesta
Ø Particle size:𝐷~ 5 − 10 𝜆 ~ 2µm
𝜆𝑫 ~ 𝟏𝟎 − 𝟐𝟎 µ𝐦
Bach+24b A&A, 684, 81; Paper II
First quantitative estimation of D
from multi-λ pol to NIR

Vesta
𝐷≲ 5– 10𝜆

Depth
𝑷𝐦𝐢𝐧

Fine
Particles(compared to λ)Ceres
Data: Geake et al. (1986) MNRAS

Width𝜶𝟎Depth𝑷𝐦𝐢𝐧

Bach+24b A&A, 684, 81; Paper IIwidth
𝜶𝟎Consistent with- Optical pol.: Le Berte & Zellner 1980- Spectra : HiroiT+94, LiJY+11, MartikainenJ+19

Discussions – ImportanceAn independent way to measure particle size D

Ø Compensates thermal modeling based estimations.
Data from MacLennan & Emery (2022) PSJ
Figure from Bach, Y. P. (2023) PhDT
Methodology - seeGundlach & Blum 2012 & 2013

Thermal modeling🌛Discussions – ImportanceAn independent way to measure particle size D

Ø Compensates thermal modeling based estimations.
Data from MacLennan & Emery (2022) PSJ
Figure from Bach, Y. P. (2023) PhDT

Ø 100µm floor VS 10-20µm on Vesta?
◦ Bug found in M&E22§ (priv. comm. MacLennan 2023)

Methodology - seeGundlach & Blum 2012 & 2013

Thermal modeling◦ Our result is consistent with
their updated results!

Ø Summary:◦ First application of NIR polarimetry
to quantify grain size.
◦ Vesta 𝐷 ~ 10 − 20 µm◦ Ceres: further discussion needed (e.g., h value)Ø Future: Disk-resolved NIR pol for Vesta

Vesta

Prev.
workVSThiswork🌛Future Works – Vesta[1] Reddy V. et al. (2012) Science𝑷𝐫Ø Disk-resolved NIR polarimetry◦ Vesta is one of the "most heterogeneous asteroids"[1]◦ Albedo already known (Dawn mission)◦ With Pol. map, we may discuss grain size map (size VS craters, compositions, etc)

~ 560 kmlargerparticle

globalaverage(Bach+24b)
smallerparticle

𝜶Subaru IRCS with AO188 (K-band)(Best expected resol. = 70 km)
Vesta K-band 𝑷𝒓~ 400 kmcolor ~ composition

Small particle
high albedo region

Large particle
high albedo region

Small particle
low albedo region

Large particle
low albedo regionhttps://trek.nasa.gov/vesta/#

2023B proposal rejected
Planning to submit 2025A

Crater ejecta (high albedo, 50%)

Dark region (low alb