Thermophysical Modeling of 20 Themis Family Asteroids with WISE/NEOWISE Observations

Home , 171 Ophelia, 222 Lucia, 468 Lina, 526 Jena, 767 Bondia, 936 Kunigunde

Draft version May 18, 2021 Typeset using LATEX twocolumn style in AASTeX63

Haoxuan Jiang1 and Jianghui Ji1, 2

1CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China 2CAS Center for Excellence in Comparative Planetology, Hefei 230026, China

(Received March 2, 2021) Submitted to AJ

ABSTRACT Themis family is one of the largest and oldest asteroid populations in the main-belt. Water-ice may widely exist on the parent body (24) Themis. In this work, we employ the Advanced Thermophysical Model as well as mid-infrared measurements from NASA’s Wide-Field Infrared Survey Explorer to explore thermal parameters of 20 Themis family members. Here we show that the average thermal inertia and geometric albedo are 39.5 ± 26.0 Jm−2s−1/2K−1 and 0.067 ± 0.018, respectively. The family members have a relatively moderate roughness fraction on their surfaces. We ﬁnd that the relatively low albedos of Themis members are consistent with the typical values of B-type and C-type asteroids. As aforementioned, Themis family bears a very low thermal inertia, which indicates a ﬁne and mature regolith on their surfaces. The resemblance of thermal inertia and geometric albedo of Themis members may reveal their close connection in origin and evolution. In addition, we present the compared results of thermal parameters for several prominent families.

Keywords: minor planets, asteroid — — thermal — individual, Themis family

1. INTRODUCTION 7 Themis family asteroids, and found that the spectra The Themis family is located in the outer region of of carbonaceous chondrite meteorites can ﬁt the gen- the asteroid belt at a mean distance of 3.13 AU from eral spectral shapes and trends of their Themis fam- the Sun, and is one of the oldest asteroid family, hav- ily members. Based on NASA 3.0-m Infrared Telescope ing been predicted to be formed ∼ 2.5 ± 1.0 Gyr ago Facility (IRTF), Rivkin & Emery(2010) and Campins (Broˇzet al. 2013) by a collisional event from its parent et al.(2010) reported the spectroscopic detection of body (24) Themis. In Nesvorn´yHierarchical Clustering water-ice and organic material on the family’s parent Method (HCM) Asteroid Family Catalog, Themis fam- body (24) Themis, indicating the widespread presence of ily is one of the largest asteroid populations, which in- water-ice in asteroidal surfaces and interiors of Themis. cludes more than 4700 family members (Nesvorny 2012) IRTF’s spectra showed the presence of a constant depth in 3.1−µm absorption due to the existence of water-ice, with proper orbital elements 3.08 ≤ ap ≤ 3.24 AU, ◦ as well as absorptions between 3.3 and 3.6 µm that are 0.09 ≤ ep ≤ 0.22 and ip ≤ 3 , where ap, ep, and ip closely matched by organic compounds, implying that

arXiv:2105.08017v1 [astro-ph.EP] 17 May 2021 are proper semi-major axis, eccentricity and inclination, respectively. This population is known as one of the the ice and organic are widespread and may be evenly most statistically reliable asteroid family in the main distributed over the surface of (24) Themis (Campins belt (Fornasier et al. 2016). et al. 2010). If (24) Themis had experienced cometary Most of the Themis family members are recognized as activities or impact event, the surface ice may be replen- C-type asteroids (Mothé-Dinizet al. 2005). Ziffer et al. ished by a sub-surface reservoir (Campins et al. 2010). (2011) presented near-infrared spectra (0.8 − 2.4 µm) of Moreover, Fornasier et al.(2016) presented the outcomes of visible and near-infrared spectroscopic survey of 22 Themis family members, and found these asteroids have Corresponding author: Jianghui Ji diverse spectral behaviors including blue/neutral and [email protected], [email protected] moderately red spectra, which 4 of them showed absorp- 2 Jiang & Ji tion bands centered at 0.68 − 0.73 µm, indicating the mal inertia. Thus, we need to employ a more sophisti- presence of aqueous alteration. Besides, Marsset et al. cated thermal model to understand thermal features of (2016) analysed near-infrared spectral properties of 15 Themis family. In this work, we investigate 20 Themis- Themis family members, which are found to be consis- tians from the perspective of thermal physics. Thus we tent with that of chondritic porous interplanetary dust aim to derive their geometric albedos, thermal inertia, particles, and ultra-fine grained materials are found to effective diameters, roughness fraction, and obtain their be the dominant constituents, thereby inferring a par- distribution characteristics. The results may be consid- ent body accreted from a mixture of ice and anhydrous ered to assess whether the asteroids are ”interlopers”, silicates. thereby revealing the homogeneity/heterogeneity of the Furthermore, water-ice was also discovered on two family members. More recently, by using the data of main belt comets (MBCs), 133P/Elst-Pizarro and Subaru and Herschel telescopes, O’Rourke et al.(2020) 176P/LINEAR, which connected with Themis family showed that the thermal inertia and geometric albedo +25 −2 −1/2 −1 from viewpoints of dynamical evolution and spectral re- of (24) Themis to be ΓThemis = 20−10 Jm s K , flectance (Licandro et al. 2012; Hsieh & Jewitt 2006). pv,Themis = 0.07 ± 0.01 , respectively, with a diameter +10 Dynamical analysis showed that MBCs are more likely DThemis = 192−7 km. Moreover, the asteroid families to have formed in situ in the main belt, rather than are formed from the impact events in a wide variety of originate from the outer solar system (Fernándezet al. ages and heliocentric distances, thereby making spacial 2002). In particular, if they are the fragments of a environment of the families diversified, which may in collisional family, the activities of MBCs are driven by turn have induced an evolution of thermal process. The water-ice sublimation, implying that a plenty of aster- physical nature of the family members are also deter- oids from Themis family may have water-ice under the mined by the materials of parent body and the impactor. surface. As a matter of fact, after water-ice on (24) Therefore, by comparing the variations in thermal pa- Themis was detected by Rivkin & Emery(2010) and rameters of individual family, one may infer the colli- Campins et al.(2010), there are also similar water- sional scenario of the families and the characteristics of ice detections for other MBAs, along with 4 Themis the parent body. In addition, thermal inertia distribu- family members (Takir & Emery 2012; Hargrove et al. tion among individual asteroid family may be a crucial 2015). Moreover, the visible spectra of 133P/Elst- evidence for the existence of asteroidal differentiation Pizarro and 176P/LINEAR have resemblance to those (Matter et al. 2013). As iron meteorites have higher of three Themistians, indicating the two MBCs may be thermal conductivity than ordinary and carbonaceous the member of Themis family (Licandro et al. 2011). chondrites (Opeil et al. 2010), a metal iron-rich regolith With the data of Spitzer Space Telescope, Hsieh et al. is expected to have larger thermal inertia, thus thermal (2009) determined the geometric R-band albedos and inertia can help us distinguish iron-rich or iron-poor as- effective diameters of two MBCs, pR,133P = 0.05 ± 0.02, teroids (Delbo et al. 2015). Table1 lists the target aster- D133P = 3.8±0.3 km and pR,176P = 0.06±0.02, D176P = oids in this work, where includes the orbital and physical 4.0 ± 0.2 km. Recently, Yu et al.(2020) derived the parameters as well as the spectral type. From Table1, geometric albedo and effective diameter of 133P/Elst- we note that except (1633) Chimay and (1687) Glarona, +0.4 Pizarro to be 0.074 ± 0.013 and 3.9−0.3 km , respec- the remaining bodies are B-type or C-type asteroids, and tively, and evaluated the thermal inertia of 133P/Elst- (2592) Hunan is a slow rotator with a rotation period of Pizarro to be 25 Jm−2s−1/2K−1. The geometric albedos approximately 50 hours when compared to others. of two MBCs correspond roughly to the typical values This paper is structured as follows. In Section 2 we in- of Themistians. Therefore, the Themis family members troduce the Advanced Thermophysical Model (ATPM), may contain crucial clue to catastrophic event and inte- which can be used to calculate the theoretical flux of the rior characteristics of their parent body. target asteroids. The radiometric results for 20 Themis- The cometary activities of Themistians may be partly tians under study and their analysis are presented in involved in the surface temperature, which can be deter- Section 3. In Section 4, we show the distribution of ther- mined by certain thermophysical models. Masiero et al. mal parameters and compare those with other asteroid (2013) applied the Near Earth Asteroid Thermal Model families. Section 5 summarizes the results. (NEATM) (Harris 1998) to investigate thermal characteristics for a wide variety of asteroid families. However, 2. ADVANCED THERMOPHYSICAL MODEL AND the NEATM model can simply obtain the albedo and di- WISE OBSERVATIONS ameter of the asteroid, whereas the heat conduction and As mentioned in Delbo et al.(2015), asteroid ther- temperature variation procedure is dominated by thermophysical modeling aims to calculate the temperature Thermophysical modeling of Themis Family 3 of asteroids’ surface by using specific thermophysical where t is time, x is the depth below the asteroid surface, model, then the theoretical flux emitted by the asteroid κ, ρ and C are given as in Eq.1. Considering the upper can be obtained from Planck function. The tempera- and lower boundary conditions: ture is determined by several thermal process such as the absorption of sunlight, multiple scattering and reflected thermal emission, as well as the heat conduction (1 − AB)([1 − S(t)]ψ(t)Fsun + Fscat) + (1 − Ath)Frad into the subsurface. By comparing the theoretical flux dT 4 + κ = εσTx=0, and observational flux, we can constrain thermal param- dx x=0 (3) eters such as thermal inertia, geometric albedo, effective diameter, as well as roughness fraction. Thermal inertia ∂T plays a vital role in dominating the thermal conduction = 0, (4) ∂x x→∞ procedure on the surface of asteroid, which can be writ- where A is the bond albedo, S(t) indicates whether the ten as B facet is shadowed at time t, ε is the thermal emissivity, p Γ = κρC (1) ψ is the cosine value of the solar altitude, Ath is the albedo at specific thermal infrared wavelength. Fsun, where κ, ρ and C represent the thermal conductivity, Fscat and Frad represents the incident sunlight, multi- bulk density, and specific heat capacity of the aster- scattered and re-emitted thermal flux from other facets, oid, respectively. The thermal inertia is an intrinsic respectively. Eq.4 indicates that when it is deep enough parameter that depends on the characteristics of sur- below the asteroid’s surface, the temperature variation face component. Since κ is a function of temperature, tends to be zero. In addition, we adopt the method given thermal inertia is associated with the asteroid’s surface in Jiang et al.(2019) to remove the portion of reflected temperature. The presence of thermal inertia leads to sunlight in short wavelengths (such as W1 band of WISE surface temperature peaks at afternoon, as well as non- observations). zero temperature at the nightside (Delbo et al. 2015). In Furthermore, we download thermal-infrared addition, thermal inertia plays a significant part in the data from 3 source tables of the WISE archive Yarkovsky and Yarkovsky-O’Keefe-Radzievskii-Paddack (http://irsa.ipac.caltech.edu/applications/wise/), (YORP) effects, which can make the semi-major axis of WISE All-Sky Single Exposure (L1b), WISE 3- asteroids drift and alter their spin rate (Delbo’ et al. Band Cryo Single Exposure (L1b) Source Table and 2007). NEOWISE-R Single Exposure (L1b) Source Table. As Here we adopt the Advanced Thermophysical Model well-known, WISE surveyed the sky with 4 wavebands (ATPM) (Rozitis & Green 2011; Yu et al. 2017) to eval- centered at 3.4, 4.6, 12.0 and 22.0 µm, noted as W1, uate the temperature distribution and thermal emission W2, W3 and W4, respectively, while NEOWISE only from the asteroids. In ATPM, an asteroid is treated observes at W1 and W2 bands when the solid hydro- as a polyhedron composed of a number of triangular gen cryosat run out. We employ the Moving Object facets, and a hemispherical crater is also adopted to Catalog Search with a search cone radius of 100. We represent the rough surface. All shape models that we adopt similar criteria described in Grav et al.(2012) to employ can be retrieved from the Database of Aster- screen the dataset that the artifact identification flag oid Models from Inversion Techniques (DAMIT)1 and cc flag other than 0 and p (which indicates the source is are determined by the light curve inversion method unaffected by known artifacts), the photometric quality developed by Kaasalainen et al.(2002). Moreover, flag ph qual other than A, B, and C (which indicates the thermal observations we utilize can be acquired that the source is likely to have been a valid detection from the Wide-Field Infrared Survey Explorer (WISE) that have signal-to-noise ratio > 2), solar system object database (Wright et al. 2010). association flag sso flg other than 1 (which means the In order to obtain the distribution of temperature T source is associated with the predicted position of a on the asteroid’s surface, we need to solve the 1D heat known solar system object) are rejected. Moreover, as conduction equation on each shape facet (Delbo et al. mentioned in Jiang et al.(2020), for main-belt asteroids, 2015): the surface temperature is low enough that the observed data in W1 band contains a significant part (∼ 90%) ∂T κ ∂2T of reflected sunlight, indicating that the thermal part = 2 , (2) ∂t ρC ∂x only covers ∼ 10% of the total observed flux. Thus, we do not use W1 data in our fitting process. Although 1 https://astro.troja.mff.cuni.cz/projects/asteroids3D/web.php the W2 observation also contains a significant part of 4 Jiang & Ji reflected sunlight, the contribution is less than 50%. and can be treated as a single free parameter. Thus, Therefore, to cover a wider range of solar phase angles we totally have three free parameters Γ, pv (Deff ) and and wavelengths to improve the reliability of fitting fr in Eq.7. In the following section, we report the fit- results, here we adopt W2 data, as described in Jiang ting results of thermal parameters of 20 Themis family et al.(2019) and Jiang et al.(2020), to account for the asteroids. reflected sunlight during fitting procedure. 3.1. (62) Erato 3. RESULTS OF THEMIS FAMILY’S THERMAL Asteroid (62) Erato is a relatively large member PARAMETERS in the Themis family with an absolute magnitude of For convenience, we transform Eq.2 and the boundary 8.78. Masiero et al.(2017) presented the diameter and condition Eq.3 into a dimensionless form (see Lebof- albedo of this asteroid to be 92.197 ± 27.20 km and sky & Spencer(1989) for details), which can be ex- 0.1016 ± 0.1021, while Nugent et al.(2016) obtained the pressed as a function of Γ. As MBAs usually have diameter of 80.09 ± 24.95 km, and geometric albedo of small thermal inertia, we set the search range of Γ to 0.07 ± 0.11. Here we adopt 136 W2 observations from be 0 ∼ 200 Jm−2s−1/2K−1 at equally spaced steps of 5 NEOWISE to evaluate the thermal parameters of (62) Jm−2s−1/2K−1 during our fitting process. When Eq.2 is Erato in our fitting. As illustrated in Figure1(a), we solved, the radiance at observational wavelength λ can can obtain the best-fitting value of thermal inertia to +12 −2 −1/2 −1 +0.0 be calculated by the Planck function, be 55−12 Jm s K and roughness fraction 0.5−0.2 (3 σ error bars) with a minimum χ2 of 1.865, and give 2hc2 1 a visible geometric albedo of 0.0890+0.0070 and an effec- B(λ, T ) = 5 hc , (5) −0.0110 λ λkbT +5.528 e − 1 tive diameter of 81.064−3.011 km. The results of pv and where h is the Planck constat, c is the speed of light and Deff are close to those of Nugent et al.(2016). To verify the best-fitting parameters for (62) Er- kb is the Boltzmann constant. Thus the total theoretical thermal flux observed by the telescope can be written as: ato, here we employ the method of Yu et al.(2017) and Jiang et al.(2019) to exhibit the theoretical thermal light curves of (62) Erato as compared with N N M X X X WISE/NEOWISE observations. Since there are no W3 Fλ,th = (1−fr) πεfiSiB(λ, Ti)+fr πεB(λ, Tij)Sijfij,and W4 observations for this asteroid, only W2 ther- i=1 i=1 j=1 mal light curves of three years are shown in Figure2. (6) The shape of these curves are different because we use where f (f ), S (S ) and T (T ) are the view fac- i ij i ij i j various reference epoch of the zero rotation phase. tor, surface area and temperature of facet i (subfacet ij of the roughness facet) in the shape model, fr is the 3.2. (171) Ophelia roughness fraction that denotes the fractional coverage of hemispherical craters. We adopt the reduced χ2 in- Using 181 WISE/NEOWISE observations (157 in W2, troduced in Press et al.(2007) to evaluate the fitting 12 in W3 and 12 in W4), we compute the geometric albedo and effective diameter of Ophelia to be degree, +0.0060 +6.667 0.0595−0.0060 and 103.816−4.869 km, respectively, which n 2 2 1 X FCF ∗ Fmodel(λi) − Fobs(λi) agrees with those of 0.0773 ± 0.0198 and 104.103 ± χr = , (7) n − 3 σλ,i 1.389 km from Mainzer et al.(2011). In addition, we i=1 +15 −2 −1/2 −1 find that thermal inertia of Γ = 30−11 Jm s K +0.1 where n is the number of observed data points, FCF is and a roughness fraction of 0.5−0.0 (Figure1(b)), which the flux correction factor that is related to roughness perform a good fitting with the observed data. As shown fraction fr and bond albedo AB (AB = pv × qph, qph is in Figure3, we plot the theoretical thermal light curves the phase integral), which is introduced in Wolters et al. with respect to the observations at W2, W3 and W4 (2011). It should be emphasized that Fmodel in Eq.7 in 2010, here we use different colors (hereafter, blue for includes the thermal part Fth in Eq.6 and the reflected W2, red for W3 and black for W4, respectively) to rep- sunlight contribution (see Jiang et al.(2019) and Jiang resent different wavelengths, where we can observe that et al.(2020) for details). Besides, the effective diameter the ATPM results can reasonably fit most mid-infrared Deff and geometric albedo pv are correlated by (Fowler data points, but seem to underestimate the observations 2 & Chillemi 1992) at low rotation phases, and the χmin is 3.522.

1329 × 10−H/5 3.3. (222) Lucia Deﬀ = √ , (8) pv Thermophysical modeling of Themis Family 5

10 15 14 15 (a) (62) Erato (b) (171) Ophelia (c) (222) Lucia (d) (468) Lina 8 10 10 10 2 6 2 2 2 χ χ χ χ 5 6 5 4 2 0 2 0 0 50 100 150 200 0 50 100 150 0 50 100 150 200 0 20406080100 Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) 25 20 16 (e) (526) Jena (f) (767) Bondia (g) (936) Kunigunde (h) (996) Hilaritas 20 15 15 14

2 15 2 2 2

χ χ χ χ 12 10 10 10 10 5 5 5 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) 15 20 (j) (1576) Fabiola (k) (1633) Chimay (l) (1687) Galrona (i) (1082) Pirola 15 14 15 2 10 2 10 2 2 χ χ χ χ 10 10 5 5 5 6 0 50 100 150 0 50 100 150 200 0 50 100 150 0 20406080100120 Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) 25 25 16 20 (m) (1691) Oort (n) (2528) Mohler (o) (2592) Hunan (p) (2659) Millis 20 20 14 12 15 2 2 2 2

χ 15 χ 15 χ χ 10 10 10 10 8

0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) 20 20 30 30 (q) (2673) Lossignol (r) (2708) Burns (s) (2718) Handley (t) (2803) Vilho 15 15 20 2 2 2 20 2 χ χ χ χ 10 10 10 10 5 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1) Γ (Jm -2s-1/2K-1)

fr=0 fr=0.1 fr=0.2 fr=0.3 fr=0.4 fr=0.5 χ2 3-sigma min

Figure 1. The Γ − χ2 proﬁles of the 20 Themis family members. The solid lines in diﬀerent colors represents the roughness fraction, and the 3-σ range of Γ is constrained by the horizontal dashed line. The minimum value of χ2 are marked with ’+’ , which has the same color as the corresponding fr.

(62) Erato 7.0 3.0 W2 fmodel W2 fobs (2014) 4.75 W2 fmodel W2 fobs (2016) W2 fmodel W2 fobs (2017) 6.5 2.8 4.50 2.6 6.0 4.25 2.4 5.5 4.00 2.2 3.75 5.0 flux(mjy) flux(mjy) 3.50 flux(mjy) 2.0 4.5 3.25 1.8

4.0 3.00 1.6

3.5 2.75 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 2. W2 thermal light curves of (62) Erato. 6 Jiang & Ji

Table 1. Orbital and physical parameters of the investigated Themis members (epoch JD=2459000.5, MPC)

◦ ◦ Asteroid a (au) e i ( ) Porb (yr) Prot (hr) Pole ( ) H Spec.type (62) Erato 3.1286 0.1677 2.2366 5.53 9.2182 (87,22) 8.78 Bt/Cb (171) Ophelia 3.1301 0.1320 2.5468 5.54 6.6645 (144,29) 8.60 Ct/Cb (222) Lucia 3.1430 0.1312 2.1490 5.57 7.8367 (293,49) 9.63 Bt (468) Lina 3.1332 0.1974 0.4369 5.55 15.4784 (74,68) 9.76 Ct (526) Jena 3.1208 0.1335 2.1737 5.51 11.8765 (194,54) 10.17 Bt/Cs (767) Bondia 3.1220 0.1822 2.4118 5.52 8.3376 (106,15) 10.20 Cb (936) Kunigunde 3.1323 0.1762 2.3660 5.54 8.8265 (234,50) 10.45 Bst/Bsb (996) Hilaritas 3.0901 0.1398 0.6589 5.43 10.0515 (281,-57) 11.19 Bt (1082) Pirola 3.1241 0.1813 1.8525 5.52 15.8540 (123,-42) 10.48 Ct (1576) Fabiola 3.1429 0.1671 0.9542 5.57 6.8891 (229,75) 11.15 Bt (1633) Chimay 3.1929 0.1238 2.6764 5.71 6.5906 (116,81) 10.75 S∗ (1687) Glarona 3.1688 0.1722 2.6358 5.64 6.4960 (132,76) 10.70 S∗ (1691) Oort 3.1636 0.1757 1.0860 5.63 10.2684 (223,58) 10.98 Ct (2528) Mohler 3.1472 0.1708 0.5119 5.58 6.4918 (56,-64) 12.28 C∗ (2592) Hunan 3.1205 0.1232 1.3369 5.51 49.9871 (184,-73) 12.22 C∗ (2659) Millis 3.1317 0.1029 1.3214 5.54 6.1246 (109,-49) 11.77 Bb/Cs (2673) Lossignol 3.2055 0.1511 2.2773 5.74 4.9379 (274,44) 12.55 C∗ (2708) Burns 3.0821 0.1777 2.7828 5.41 5.3236 (183,-59) 12.17 Bb (2718) Handley 3.1201 0.1553 1.4921 5.51 13.0980 (261,-53) 11.89 Cs (2803) Vilho 3.1410 0.1790 1.3300 5.57 10.3728 (285,-67) 12.01 C∗

Notes: a: semi-major axis, e: eccentricity, i: orbital inclination, Porb: orbital period, H: absolute magnitude are from the Minor Planet Center (MPC)). Prot: rotation period, Pole: orientation are obtained Hanuˇset al.(2011, 2013, 2016), Marciniak et al.(2019), and Durechˇ et al.(2016, 2018, 2019). Spectral types with superscript t: Tholen taxonomic classification (Tholen 1989), b: Bus-Demeo and Bus-Binzel taxonomic classification (Bus & Binzel 2002; DeMeo et al. 2009), s: SDSS taxonomic classification (Carvano et al. 2010), st and sb: Tholen-like and Bus-like in S3OS2 taxonomic classification (Lazzaro et al. 2004) and *: spectral types in Asteroid Lightcurve Database (LCDB). Thermophysical modeling of Themis Family 7

Table 2. Derived thermal parameters of Themis family asteroids based on ATPM and WISE/NEOWISE observations

−2 −1/2 −1 ∗ ∗ 2 Asteroid Γ (Jm s K ) pv pv Deff (km) Deff (km) fr χmin +12 +0.0070 +5.528 +0.0 (62) Erato 55−12 0.0890−0.0110 0.0910 ± 0.0020 81.064−3.011 78.620 ± 0.900 0.5−0.2 1.865 +15 +0.0060 +5.667 +0.0 (171) Ophelia 30−11 0.0595−0.0060 0.0773 ± 0.0198 103.816−4.869 104.103 ± 1.389 0.5−0.1 3.522 +22 +0.0110 +4.332 +0.1 (222) Lucia 70−20 0.0670−0.0085 0.1233 ± 0.0177 61.729−4.518 56.520 ± 0.832 0.4−0.1 2.385 +23 +0.0025 +2.372 +0.2 (468) Lina 5−5 0.0520−0.0035 0.0488 ± 0.0342 66.915−1.552 59.673 ± 18.220 0.1−0.1 2.211 +16 +0.0065 +4.046 +0.1 (526) Jena 10−10 0.0530−0.0070 0.0580 ± 0.0177 55.120−3.098 51.032 ± 0.742 0.0−0.0 7.395 +30 +0.0095 +4.776 +0.1 (767) bondia 65−17 0.0575−0.0095 0.0900 ± 0.0200 50.546−3.720 45.300 ± 4.500 0.2−0.1 2.854 +20 +0.0500 +8.462 +0.0 (936) Kunigunde 65−25 0.0749−0.0237 0.0650 ± 0.1400 40.391−9.113 42.230 ± 1.040 0.5−0.0 3.871 +16 +0.0120 +1.767 +0.0 (996) Hilaritas 50−26 0.0770−0.0090 0.0824 ± 0.0180 27.560−1.925 30.902 ± 0.417 0.5−0.3 8.555 +14 +0.0075 +1.651 +0.0 (1082) Pirola 45−12 0.0725−0.0055 0.0867 ± 0.0105 41.054−1.972 37.363 ± 1.036 0.5−0.1 5.621 +27 +0.0135 +2.471 +0.3 (1576) Fabiola 10−10 0.0830−0.0130 0.0746 ± 0.0139 27.796−2.018 30.150 ± 0.400 0.0−0.0 3.172 +18 +0.0065 +3.993 +0.2 (1633) Chimay 30−13 0.0405−0.0060 0.0785 ± 0.0135 47.849−3.431 37.732 ± 0.426 0.1−0.1 5.479 +23 +0.0065 +1.442 +0.5 (1687) Glarona 15−10 0.1155−0.0090 0.0795 ± 0.0130 34.852−0.941 42.007 ± 0.515 0.0−0.0 6.475 +19 +0.0085 +2.595 +0.2 (1691) Oort 10−10 0.0635−0.0085 0.0672 ± 0.0150 34.844−2.121 33.163 ± 0.534 0.3−0.1 7.921 +15 +0.0063 +1.088 +0.0 (2528) Mohler 35−28 0.0764−0.0090 0.0567 ± 0.0045 16.826−0.654 19.443 ± 0.121 0.5−0.5 10.084 +46 +0.0087 +0.963 +0.2 (2592) Hunan 40−40 0.0636−0.0060 0.0724 ± 0.0035 18.958−1.177 18.533 ± 0.107 0.3−0.3 6.823 +19 +0.0125 +1.674 +0.0 (2659) Millis 35−16 0.0645−0.0072 0.0498 ± 0.0028 27.463−2.328 27.878 ± 0.337 0.5−0.3 6.231 +29 +0.0117 +1.376 +0.3 (2673) Lossignol 15−15 0.0860−0.0147 0.0773 ± 0.0140 14.005−0.865 15.119 ± 0.160 0.2−0.2 5.967 +25 +0.0110 +2.003 +0.0 (2708) Burns 65−48 0.0570−0.0097 0.0836 ± 0.0151 20.492−1.731 20.085 ± 0.110 0.5−0.5 8.218 +16 +0.0038 +1.924 +0.0 (2718) Handley 30−30 0.0519−0.0073 0.0550 ± 0.0054 24.431−0.849 25.929 ± 0.234 0.5−0.4 8.069 +12 +0.0071 +0.394 +0.0 (2803) Vilho 110−29 0.0360−0.0010 0.0732 ± 0.0104 27.757−2.389 21.441 ± 0.301 0.5−0.2 5.218 ∗ ∗ Notes: pv and Deff are the previous results of geometric albedo and effective diameters from Mainzer et al.(2011); Masiero et al.(2012); Nugent et al.(2016); Al´ı-Lagoaet al.(2016); Masiero et al.(2017).

Lucia was well observed by WISE/NEOWISE, servation to obtain the pv and Deff to be 0.0488 ± Mainzer et al.(2011) derived the pv and Deff to be 0.0342 and 59.676 ± 18.22 km. Here we adopt 206 0.1233 ± 0.0177 and 56.52 ± 0.832 km, here we en- WISE/NEOWISE observations (164 in W2, 21 in W3 tirely use 193 data points (159 in W2, 17 in W3 and and 21 in W4) in our fitting, and we obtain a low ther- +23 −2 −1/2 −1 17 in W4) combined with the ATPM model to de- mal inertia of 5−5 Jm s K , and a small rough- +0.2 rive its thermal parameters. As can be seen from Fig- ness of 0.1−0.1 (Figure1(d)). Our derived geometric +0.0025 ure1(c), the best-fitting thermal inertia and roughness albedo pv = 0.0520−0.0035 is slightly larger than that of +22 −2 −1/2 −1 +0.1 are 70−20 Jm s K and 0.4−0.1, while pv and Deff Masiero et al.(2017), thereby giving rise to a diameter of +0.0110 +4.332 +2.372 are constrained to be 0.0670−0.0085 and 61.729−4.518 km, 66.915−1.552 km. The 3-bands thermal light curves are respectively. Our results of pv and Deff are different from plotted in Figure5. Our ATPM fluxes can reasonably 2 those of Mainzer et al.(2011), which may be caused match the observations in W3 and W4, and the χmin is by the usage of different thermal model. Thermal light constrained to be 2.211. curves of W2, W3 and W4 are exhibited in Figure4, in which the modeled fluxes are slightly smaller than the 3.5. (526) Jena observations, and the minimum value of χ2 is 2.385. Mainzer et al.(2011) predicted the albedo and diameter of 0.0580 ± 0.0177 and 51.032 ± 0.742 km by using 3.4. (468) Lina the NEATM model, which are very close to those of Li- Marciniak et al.(2019) provided the thermal inertia candro et al.(2012). In this study, we fit the ATPM of (468) Lina Γ = 20 Jm−2s−1/2K−1 with the data from fluxes with 190 WISE/NEOWISE observations (150 in WISE (W4 band), IRAS and AKARI, while Masiero W2, 20 in W3 and 20 in W4). The best-fitting values +0.0065 +4.046 et al.(2017) used the NEATM model and WISE ob- are pv = 0.0530−0.0070, Deff = 55.120−3.098 km, a low 8 Jiang & Ji

(171) Ophelia 14 13000

W2 fmodel W2 fobs (2010) 4000 W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 13 12000

12 3500 11000 11 3000 10000 10 9000

flux(mjy) 9 flux(mjy) 2500 flux(mjy) 8000 8 2000 7 7000

6 1500 6000 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 3. W2, W3 and W4 thermal light curves of (171) Ophelia.

(222) Lucia 3.5 1000 3200

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 3000 900 3.0 2800 800 2600 2.5

700 2400

2.0 flux(mjy) flux(mjy) flux(mjy) 2200 600 2000 1.5 500 1800

1.0 400 1600 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 4. W2, W3 and W4 thermal light curves of (222) Lucia.

+16 −2 −1/2 −1 thermal inertia Γ = 10−10 Jm s K with rough- thermal light curves supply intuitively acceptable fits +0.1 ness fraction fr = 0.0−0.0 (see Figure1(e)). Our results with the observed data at W3 and W4 bands, but is of geometric albedo and effective diameter of (526) Jena underestimated at W2 (see Figure7), and the value of are consistent with those of Mainzer et al.(2011). Fig- minimum χ2 is 2.854. ure6 shows that the thermal light curves can agree well with the observations at W3, but in W2 and W4 bands, 3.7. (936) Kunigunde the observations are not well fitted at several rotation Based on the measurements of space-based infrared 2 phases, providing χmin = 7.395, which indicates a rela- telescopes, AKARI, IRAS (The Infrared Astronomical tively poor fit. Satellite) and WISE, the geometric albedo of the asteroid were derived to be 0.124 ± 0.007, 0.1129 ± 0.007, 3.6. (767) Bondia 0.065 ± 0.014, respectively, with respect to each diam- The early studies individually reported pv of 0.0956 ± eter of 38.08 ± 0.94, 39.56 ± 1.2, 43.227 ± 1.035 km 0.0179 and 0.09 ± 0.02, along with a diameter of (Tedesco et al. 2004; Usui et al. 2011; Masiero et al. 43.100 ± 0.730 km and 45.3 ± 4.5 km (Mainzer et al. 2012). In this work, 136 WISE/NEOWISE data (125 in 2011; Al´ı-Lagoa et al. 2016). Here we utilize 163 W2 and 11 in W3) were used to calculate its thermal +20 −2 −1/2 −1 WISE/NEOWISE observations (135 in W2, 14 in W3 parameters, and we present Γ = 65−25 Jm s K +0.0 +0.0500 and 14 in W4). We derive the geometric albedo with fr = 0.5−0.0 (Figure1(g)), pv = 0.0749−0.0237 and +0.0095 +4.776 +8.462 0.0575−0.0095, the diameter 50.546−3.720 km, the ther- Deff = 40.391−9.113 km, respectively. Our derived best- +0.1 mal roughness fraction 0.2−0.1 ,and thermal inertia fitting albedo and diameter are very close to those of +30 −2 −1/2 −1 65−17 Jm s K (from Figure1(f)). The ATPM Masiero et al.(2012). The thermal light curves versus Thermophysical modeling of Themis Family 9

(468) Lina 7500 W2 f W2 f (2010) 3500 W3 f W3 f (2010) W4 f W4 f (2010) 25 model obs model obs model obs 7000

3000 6500 20 6000

2500 5500

flux(mjy) 15 flux(mjy) flux(mjy) 5000 2000 4500 10

4000 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 5. W2, W3 and W4 thermal light curves of (468) Lina.

2 the data at W2, W3 are shown in Figure8, and the χmin 3.10. (1576) Fabiola value is calculated to be 3.871. On the basis of IRAS, AKARI and WISE/NEOWISE 3.8. (996) Hilaritas measurements, the geometric albedo of (1576) Fabi- ola were given to be 0.0746 ∼ 0.123, and the effec- Using AKARI and WISE observations, Usui et al. tive diameter 21.33 ∼ 30.150 km (Tedesco et al. 2004; (2011) and Mainzer et al.(2011) reported its geomet- Usui et al. 2011; Mainzer et al. 2011; Al´ı-Lagoaet al. ric albedo to be 0.069 ± 0.008 and 0.0824 ± 0.0180, 2016). Here we use the ATPM model in combination respectively, producing an effective diameter of ∼ with WISE/NEOWISE observations (92 in W2, 9 in 33.67 ± 1.8 km and 30.902 ± 0.417 km. Using 138 W3 and 9 in W4) to derive its thermal parameters, and WISE/NEOWISE observations (112 in W2, 13 in W3 we present the best-fitting Γ = 10+27 Jm−2s−1/2K−1, and 13 in W4), we present a smaller effective diameter −10 f = 0.0+0.3 (Figure1(j)), p = 0.0830+0.0135, D = of (996) Hilaritas to be 27.560+1.767 km as compared r −0.0 v −0.0130 eff −1.925 27.796+2.471 km, and a low roughness can better fit the with those of the former studies, thus with a geometric −2.018 observations. Our results of albedo and diameter for albedo 0.0770+0.0120. From Figure1(h), we further show −0.0090 this asteroid are slightly different from those in litera- a best-fitting value of Γ = 50+16 Jm−2s−1/2K−1 and −26 ture. As seen from Figure 11, the thermal light curves f = 0.5+0.0. Figure9 displays the calculated thermal r −0.3 can reasonably fit the data at W2-W4 bands, and the light curves versus observations at W2, W3 and W4 for χ2 value is 3.172. (996) Hilaritas, revealing that the model are in good ac- min cordance with the data at W3 and W4, but is somewhat underestimated at W2. Here we obtain χ2 = 8.555. min 3.11. (1633) Chimay 3.9. (1082) Pirola With AKARI and WISE/NEOWISE observations, The previous exploration showed that the geomet- (1633) Chimay measures 36.26 ± 0.86 km and 37.732 ± ric albedo of (1082) Pirola varies from 0.052 to 0.867, 0.426 km in diameter, 0.088 ± 0.005 and 0.0785 ± 0.0135 with an effective diameter in the range 37.363 ∼ in geometric albedo (Usui et al. 2011; Mainzer et al. 48.378 km (Mainzer et al. 2011; Usui et al. 2011; Mainzer 2011). During our fitting, 164 WISE/NEOWISE ob- et al. 2016; Nugent et al. 2015). In this work, 189 servations (134 in W2, 15 in W3 and 15 in W4) are WISE/NEOWISE observations (157 in W2, 16 in W3 utilized to derive its thermal parameters. As shown and 16 in W4) are adopted to calculate its thermal pa- in Figure1(k), the minimum value of χ2 is correlated +18 −2 −1/2 −1 rameters. As shown in Figure1(i), the best-fitting value to thermal inertia of 30−13 Jm s K and rough- +14 −2 −1/2 −1 +0.2 of Γ and fr is given to be 45−12 Jm s K and ness fraction of 0.1−0.01, with respect to the geomet- +0.0 +0.0075 +0.0065 fr = 0.5−0.1. The pv is evaluated to be 0.0725−0.0055, ric albedo pv = 0.0405−0.0060 and effective diameter +1.651 +3.993 corresponding to Deff = 41.054−1.972. Figure 10 dis- Deff = 47.849−3.431 km. Such low value of the derived plays thermal light curves of Pirola at W2, W3 and W4 geometric albedo is indicative of that (1633) Chimay bands, and the modeled fluxes slightly overestimate the may be a C-type or B-type asteroid. Here we present W2 and W3 bands data, leading to a minimum χ2 of the thermal light curves with the data at W2, W3 and 5.621. W4 bands (Figure 12), and the minimum χ2 is 5.479. 10 Jiang & Ji

2 3.12. (1687) Glarona estimated at W2 and W3 with a χmin of 10.084, which Mainzer et al.(2011) presented the albedo and di- indicates a relatively poor fitting degree. ameter of (1687) Glarona: p = 0.0795 ± 0.0130, v,WISE 3.15. (2592) Hunan Deff,WISE = 42.007 ± 0.515 km. Here, 151 WISE observations (121 in W2, 15 in W3 and 15 in W4) are The WISE/NEOWISE observations combined with employed in our fitting to understand its thermophys- the NEATM model give the albedo and diameter of Hu- ical characteristics. As shown in (Figure1(l)), a low nan ranges from 0.072 ∼ 0.08 and 15.260 ∼ 18.533 km +23 −2 −1/2 −1 (Mainzer et al. 2011; Nugent et al. 2016; Mainzer et al. thermal inertia of Γ = 15−10 Jm s K , as well as +0.5 2016). In our thermal modeling process, we adopt 57 a low roughness of 0.0−0.0 can be given, with respect 2 W2, W3 and W4 WISE/NEOWISE observations (33 to a χmin = 6.475. The geometric albedo is derived +0.0065 in W2, 12 in W3 and 12 in W4). The best-fitting to be pv = 0.1155−0.0090, with an effective diameter +1.442 values are Γ = 40+46 Jm−2s−1/2K−1, f = 0.3+0.2, Deff = 34.852−0.941 km. Our results of pv and Deff −40 r −0.3 +0.0087 +0.963 slightly vary from those of Mainzer et al.(2011) in that pv = 0.0636−0.0060 and Deff = 18.958−1.177 km. The it may be induced by the usage of ATPM. The W2, results of pv and Deff are similar to those of Mainzer W3 and W4 bands thermal light curves are exhibited in et al.(2016). We plot the W2, W3 and W4 thermal light 2 curves in Figure 16. As can be seen from Figure 16, the Figure 13, with the χmin of 6.475. calculated ATPM fluxes perform a reasonable fitting at W3 and W4 bands, but underestimate W2 observations, 3.13. (1691) Oort where the minimum χ2 is 6.823. The previous studies showed that Oort’s effective diameter was measured to be 33.6 ∼ 37.37 km, and geo- 3.16. (2659) Millis metric albedo ranges from 0.053 to 0.065 (Mainzer et al. The albedo and diameter of Millis from NEATM 2011; Usui et al. 2011; Masiero et al. 2014). In this work, spans from 0.0498 to 0.071 and 26.42 ∼ 29.53 km, re- we employ 157 WISE/NEOWISE observations (129 in spectively (Tedesco et al. 2004; Usui et al. 2011; Al´ı- W2, 14 in W3 and 14 in W4) to calculate the thermal Lagoa et al. 2016; Mainzer et al. 2011; Nugent et al. parameters of the asteroid, and find that a low ther- 2015). Here, we use 140 WISE/NEOWISE observa- mal inertia is confined to be 10+19 Jm−2s−1/2K−1 with −10 tions (114 in W2, 13 in W3 and 13 in W4) to inves- a medium roughness fraction of 0.3+0.2 (Figure1(m)). −0.1 tigate the thermal parameters for (2659) Millis. The The value of Γ is close to that of Hanuˇset al.(2018), Γ − χ2 profile is plotted in Figure1(p), where a χ2 = of 22 ± 22 Jm−2s−1/2K−1. Moreover, we further eval- min 6.2311 is relevant to a best-fitting thermal inertia Γ = uate the geometric albedo of 0.0635+0.0085 and the ef- −0.0085 35+19 Jm−2s−1/2K−1, a roughness fraction 0.5+0.0, a fective diameter of 34.884+2.595 km. The thermal light −16 −0.3 −2.121 geometric albedo p = 0.0645+0.0125, and an effective curves are shown in Figure 14. Our ATPM results pro- v −0.0072 diameter D = 27.463+1.674 km. Figure 17 exhibits vide acceptable fits at W4 band, but seem to slightly eff −2.328 that the thermal light curves versus the data at W2, deviate from the observations at W2 and W3, with W3 and W4, however, the ATPM fluxes at W2 deviate χ2 = 7.9214. min a lot from the observations, but are roughly consistent with those at W3 and W4 bands. 3.14. (2528) Mohler There are comparatively fewer WISE/NEOWISE data 3.17. (2673) Lossignol points that are available for this object (45 in W2, 12 With WISE/NEOWISE observations and NEATM in W3, 12 in W4). According to Figure1(n), the mini- model, the albedo and diameter of (2673) Lossignol mum χ2 of 10.0837 indicates a relatively poor fit, and the were determined to be 0.077 and 15.119 km (Mainzer +15 −2 −1/2 −1 corresponding thermal inertia is 35−28 Jm s K , et al. 2011, 2016). In our modeling, there are simply +0.0 with respect to a relatively high roughness of 0.5−0.5. 29 WISE/NEOWISE data points are adopted (11 in However, our results of albedo and diameter are con- W2, 9 in W3, 9 in W4). From Figure1(q), we ob- +0.0063 +29 −2 −1/2 −1 sistent with the typical values, pv = 0.0764−0.0090, tain a best-fitting solution of Γ = 15−15 Jm s K , +1.088 +0.3 Deff = 16.826−0.654 km, which are similar to those of and fr = 0.2−0.2. The geometric albedo and effec- +0.0117 Mainzer et al.(2011), who obtained pv = 0.0567±0.0045 tive diameter are estimated to be 0.0860−0.0147 and +1.376 and Deff = 19.443±0.121 km. Figure 15 shows the ther- 14.005−0.865 km, respectively. The outcomes of pv and mal light curves plotted against the observations at W2, Deff are in agreement with the literature results. Fig- W3 and W4, although the theoretical fluxes can conduct ure 18 shows 3-bands thermal light curves, and the value 2 good fitting with the data at W4 band, the fit is over- of χmin is 5.967. Thermophysical modeling of Themis Family 11

3.18. (2708) Burns 4. THERMAL PARAMETERS Asteroid (2708) Burns is a B-type Themistian with 4.1. Size Distribution literature geometric albedo that measures from 0.06 ∼ With the aid of NEOWISE data, Masiero et al.(2013) 0.12 and diameter in the range of 13.63 ∼ 22 km (Al´ı- measured the size-frequency distribution (SFD) for 76 Lagoa et al. 2013; Nugent et al. 2015; Al´ı-Lagoaet al. asteroid families. SFD can be expressed by N ∝ Dα, 2016; Mainzer et al. 2016, 2011). Here we totally use 93 where N is the number of family members that have di- WISE/NEOWISE observations (63 in W2, 15 in W3 and ameter larger than D, and α is the SFD slope. Masiero 15 in W4) to evaluate its thermal parameters. From the et al.(2015) gave the value α of −2.313 ± 0.017 for 2 χ −Γ profile in Figure1(r), we constrain the thermal in- Themis family and the SFD range of 7.3 ∼ 55.6 km. +25 −2 −1/2 −1 ertia of (2708) Burns to be 65−48 Jm s K , as well As illustrated in the right panel of Figure 22, we ob- as a relatively high roughness of 0.5+0.0. In addition, the −0.5 tain the range of Deff to be 14.005 ∼ 103.816 km, where geometric albedo and effective diameter are estimated asteroid (171) Ophelia have a maximum effective diam- +0.0110 +2.003 to be pv = 0.0570−0.0097, Deff = 20.492−1.731 km. The eter of 103.816 km. Delbo’ & Tanga(2009) provided thermal light curves are plotted in Figure 19, we obtain the power law relationship between thermal inertia and 2 a relatively large χ value of 8.2179, because the W2 −ξ min effective diameter to be Γ = d0D , and a best-fitting thermal light curve performs a poor fit. d0 and ξ of 300 ± 47 and 0.48 ± 0.04, respectively, indicating an inversely proportional relationship between 3.19. (2718) Handley Γ and diameter. In addition, Delbo’ & Tanga(2009) The AKARI and WISE/NEOWISE observations mea- derived ξ for MBAs (1.4 ± 0.2) and NEAs (0.32 ± 0.09), sure similar geometric albedo of Handley to be 0.055 ∼ respectively. However, when the asteroid population is 0.058, and the diameter ranges from 25.309 ∼ 25.929 km large enough, especially for the main-belt asteroids with (Usui et al. 2011; Mainzer et al. 2011, 2016). In our fit- a relatively low thermal inertia (< 100 Jm−2s−1/2K−1 ting, 114 WISE/NEOWISE measurements are adopted ), this inverse relationship becomes unclear (Figure 22) (86 in W2, 14 in W3, 14 in W4) to further investigate and requires deeper exploration based on diverse aster- its thermal nature. From Figure1(s), we can see that a oid families. minimum value of χ2 is correlated to thermal inertia of +16 −2 −1/2 −1 +0.0 4.2. Geometric Albedo 30−30 Jm s K and roughness of 0.5−0.4. The ge- +0.0038 ometric albedo is constrained to be 0.0519−0.0073, and an The collisional events that formed the asteroid families +1.924 effective diameter 24.431−0.849 km. Moreover, for this are expected to produce materials (i.e., the family mem- asteroid, Figure 20 indicates that our computed fluxes bers) from the parent body. For a heterogeneous parent perform a close matching with the infrared data, and we body, a wide range of color indexes, albedos and spec- have derived the minimum χ2 of 8.069. trals are expected, while for a homogeneous parent, the resultant family members usually have relatively narrow 3.20. (2803) Vilho range of these physical parameters (Masiero et al. 2015). For C-type Themistian (2803) Vilho, the literature re- Licandro et al.(2012) showed that 5 − 14 µm spectra of sults of albedo and diameter ranges from 0.068 ∼ 0.1 8 Themis family asteroids and obtained a mean albedo and 17.72 ∼ 22.96 km (Usui et al. 2011; Mainzer et al. of 0.07 ± 0.02 based on NEATM. Furthermore, Masiero 2011; Nugent et al. 2015; Mainzer et al. 2016). In this et al.(2013) gave a mean value of pv = 0.066 ± 0.021 work, we utilize 52 WISE/NEOWISE observations (26 for Themis family members. In this work, we obtain in W3 and 26 in W4) for fitting. The best-fitting so- an average geometric albedo of Themis family to be lution gives a comparatively high thermal inertia of 0.067 ± 0.018, which is in good agreement with that of +12 −2 −1/2 −1 +0.0 110−29 Jm s K and high roughness of 0.5−0.2 Masiero et al.(2013). Figure 23 exhibits the distribution 2 (see Figure1(t)) with a minimum χ value 5.217. The of pv and Deff , where red error bars indicate the results +0.0071 geometric albedo is derived to be 0.0360−0.0010, and of our work, which are similar to the pv of their parent +0.394 Deff = 27.757−2.389 km. The derived geometric albedo body (24) Themis. We further superimpose the MBAs’ and effective diameter of (2803) Vilho are quite differ- albedos from Masiero et al.(2013); Hanuˇset al.(2018); ent from those of previous works. We show that (2803) Jiang et al.(2019) (marked up by light gray dots), and Vilho is the only asteroid that bears thermal inertia we offer other Themis family asteroids in Masiero et al. larger than 100 Jm−2s−1/2K−1. Figure 21 displays the (2013) by green dots. Most of Themistians appear to thermal light curves at W3 and W4 bands, where the have relatively low geometric albedos, which agrees with ATPM fluxes coincide with the observations, and the the typical values of C-type asteroids. As a comparison, 2 χmin is calculated to be 5.218. we give the Vesta family’s albedo distribution with blue 12 Jiang & Ji

(526) Jena 1.2 400 W2 f W2 f (2010) W3 f W3 f (2010) W4 f W4 f (2010) model obs model obs 1400 model obs

1.0 350 1200 300 0.8 1000 250 flux(mjy) flux(mjy) flux(mjy) 0.6 800 200 0.4 600 150 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 6. W2, W3 and W4 thermal light curves of (526) Jena.

(767) Bondia 220 W2 f W2 f (2010) W3 f W3 f (2010) W4 f W4 f (2010) model obs model obs 850 model obs 0.5 200 800

180 750 0.4 700 160 650

flux(mjy) 0.3 flux(mjy) flux(mjy) 140 600

550 0.2 120 500

100 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 7. W2, W3 and W4 thermal light curves of (767) Bondia.

(936) Kunigunde 1.2

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) 350 1.0

300 0.8

250

flux(mjy) 0.6 flux(mjy)

0.4 200

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase

Figure 8. W2 ∼ W3 thermal light curves of (936) Kunigunde. Thermophysical modeling of Themis Family 13

(996) Hilaritas 1.8 450 1300

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 1200 1.6 400 1100 1.4 350 1000 1.2 300 900 1.0 250 800 flux(mjy) 0.8 flux(mjy) flux(mjy) 700 200 0.6 600 150 0.4 500

0.2 100 400 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 9. W2, W3 and W4 thermal light curves of (996) Hilaritas.

(1082) Pirola 8 2800 W2 f W2 f (2010) W3 f W3 f (2010) W4 f W4 f (2010) model obs 1400 model obs model obs 2600 7

1200 2400 6 2200 1000 5 2000

flux(mjy) flux(mjy) 800 flux(mjy) 1800 4 1600 3 600 1400

2 400 1200 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 10. W2, W3 and W4 thermal light curves of (1082) Pirola.

(1576) Fabiola 2.4 1200 W2 f W2 f (2010) W3 f W3 f (2010) W4 f W4 f (2010) model obs 400 model obs model obs 2.2 1100 2.0 350 1000 1.8

1.6 900 300

flux(mjy) 1.4 flux(mjy) flux(mjy) 800

1.2 250 700 1.0

0.8 200 600 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 11. W2, W3 and W4 thermal light curves of (1576) Fabiola. 14 Jiang & Ji

(1633) Chimay 0.6 800 W2 f W2 f (2010) W3 f W3 f (2010) W4 f W4 f (2010) model obs 180 model obs model obs

0.5 700 160

0.4 600 140

0.3 500 flux(mjy) flux(mjy) 120 flux(mjy)

0.2 100 400

0.1 80 300 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 12. W2, W3 and W4 thermal light curves of (1633) Chimay.

(1687) Galrona

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 900 2000 3.5

800 1800 3.0

700 1600 2.5 1400 600 flux(mjy) 2.0 flux(mjy) flux(mjy) 1200 500 1.5 1000 400 1.0 800 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 13. W2, W3 and W4 thermal light curves of (1687) Glarona.

(1691) Oort 0.6 700 200 W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 180 0.5 600

160 0.4 500 140

0.3 120 400 flux(mjy) flux(mjy) flux(mjy)

0.2 100 300 80 0.1 60 200 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 14. W2, W3 and W4 thermal light curves of (1691) Oort. Thermophysical modeling of Themis Family 15

(2528) Mohler 180 450

0.8 W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 160 400 0.7 140 0.6 350 120 0.5 300 100 0.4 flux(mjy) flux(mjy) flux(mjy) 250 0.3 80

200 0.2 60

0.1 40 150 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 15. W2, W3 and W4 thermal light curves of (2528) Mohler.

(2592) Hunan 0.6 400

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 120 0.5 350

100 300 0.4

250 80 0.3 flux(mjy) flux(mjy) flux(mjy)

200 0.2 60 150

0.1 40 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 16. W2, W3 and W4 thermal light curves of (2592) Hunan.

(2659) Millis 0.45 140 550

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 0.40 130 500

0.35 120 450

0.30 110 400

0.25 100 350

flux(mjy) 0.20 flux(mjy) 90 flux(mjy) 300 0.15 80 250 0.10 70 200 0.05 60 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 17. W2, W3 and W4 thermal light curves of (2659) Millis. 16 Jiang & Ji

(2673) Lossigol 70 220 0.24 W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 65 0.22 200 60 0.20 180 55 0.18 50 160 0.16 45 140

flux(mjy) 0.14 flux(mjy) flux(mjy) 40 120 0.12 35 100 0.10 30

0.08 25 80 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 18. W2, W3 and W4 thermal light curves of (2673) Lossignol.

(2708) Burns 0.7

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 450 0.6 140 400 0.5 120 350

0.4 100 300 flux(mjy) flux(mjy) flux(mjy) 0.3 80 250

0.2 200 60 0.1 150 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 19. W2, W3 and W4 thermal light curves of (2708) Burns.

(2718) Handley 180 600

W2 fmodel W2 fobs (2010) W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 550 0.5 160 500

0.4 140 450

400 120 0.3 350 flux(mjy) flux(mjy) flux(mjy)

100 300 0.2 250 80 0.1 200 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase rotation phase

Figure 20. W2, W3 and W4 thermal light curves of (2718) Handley. Thermophysical modeling of Themis Family 17

(2803) Vilho

80 300

W3 fmodel W3 fobs (2010) W4 fmodel W4 fobs (2010) 275 70 250

60 225

200 50 175 flux(mjy) flux(mjy) 40 150

30 125

100 20 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 rotation phase rotation phase

Figure 21. w3 and W4 thermal light curves of (2803) Vilho.

) Main-belt asteroids (24) Themis ) Main-belt asteroids (24) Themis

0 133P Themis Family 0 133P Themis Family

00 00

0 0

Thermal inertia ( inertia Thermal 0 ( inertia Thermal 0 00 0 0 0 00 0 0 Geometric albedo Effective diameter (km)

Figure 22. The Γ − pv and Γ − Deff relationships of Themis family members (Red dots with error bars) and the main-belt asteroids (Gray dots) in Hanuˇset al.(2018). We also plot the results of (24) Themis ( marked up by black pentagram) and 133P/Elst-Pizarro (marked up by green pentagram) from O’Rourke et al.(2020); Yu et al.(2020). 18 Jiang & Ji dots in Figure 23, which are retrieved from Masiero et al. bution of main-belt asteroids in Figure 22, the thermal (2013); Jiang et al.(2019). Unlike the Themis family, inertia is relatively evenly distributed between the max- the Vesta family’s albedo varies in a wide range, im- imum and minimum values. This phenomenon also oc- plying a heterogeneous parent body and differentiated curs in other asteroid families. As shown in Figure 25, surface layers through their long-term evolution. red error bars represent the derived thermal inertia Γ of As a comparison, in Figure 24, we show our results this work, whereas those of other families from Hanuˇs of geometric albedos against their semi-major axis (red et al.(2018) are plotted with diverse colors, where the error bars) as well as those of other prominent asteroid size of circles stands for the size of asteroids. However, families in Masiero et al.(2013). As shown in Figure 24, it is not easy to distinguish different asteroid families the families like Themis or Hygiea are mainly composed by thermal inertia. As described in Delbo et al.(2015), of B- or C-type members, which are located in the outer the asteroid’s thermal inertia is associated with the sur- asteroid belt, and simply cover a very small range of pv face temperature, relying on heliocentric distance, thus compared to other asteroid families (here we obtain a it can be expressed as (Delbo et al. 2015) minimum and maximum value of pv to be 0.0360 and √ 3/2 −3/4 0.1155 for the Themistians under study, respectively). Γ ∝ κ ∝ T ∝ r . (9) This is consistent with the inference that carbonaceous However, even we normalised the value of thermal iner- (C-type, B-type, etc, which have low albedos) asteroids tia into 1 AU from the Sun according to Eq.9, the dif- dominate the outer region of the asteroid belt (Wiegert ferences in Γ distribution between various families are et al. 2007). To our best knowledge, C-type asteroids are still unclear. This is probably because most main-belt believed to have primordial components, considering the objects have undergone long-term resurface processes. fact that asteroids usually have undergone considerable Therefore, although the asteroid families formed at var- evolution processes since their formation, such as space ious time, their surfaces may have evolved into similar weathering, surface morphology, etc. Here we may infer morphological characteristics (such as fine regolith lay- that the Themis family, which is mainly composed of C- ers), thereby leading to similar thermal inertia distribu- type or B-type asteroids, seems to be a relatively antique tion. Subsequently, finely powdered regolith covered on family that have not experienced significant migration asteroid’s surface is a poor heat conductor (as compared arising from gravitational perturbation of giant planets with bare rocks or a single particle) because of the ex- after they are separated from their parent body Themis istence of tiny intervals between regolith grains thereby due to collision events at early stage. inducing a very low thermal inertia. Therefore, according to the value of Γ, we can infer whether there exist 4.3. Thermal Inertia thermally insulating powdered surface materials (Delbo As mentioned above, the Themis family asteroids et al. 2015). Furthermore, by using specific thermal con- have roughly primitive materials. Like most of main- duction model described in Gundlach & Blum(2013) belt asteroids, a large number of Themistians in this and the value of thermal inertia, we can further esti- work have a very low thermal inertia that are lower mate the regolith grain sizes of these Themistians. Con- than 100 Jm−2s−1/2K−1, except (2803) Vilho. The sidering the volume filling factor of 0.0 to 0.6, and the average thermal inertia of 20 Themistians is 39.5 ± temperature of 200 K, we obtain the mean regolith grain 26.0Jm−2s−1/2K−1, which is very similar to that of sizes of these Themistians vary from 0.077 to 8.322 mm, Vesta family of 42 Jm−2s−1/2K−1 (Jiang et al. 2019), with an average value of 1.616 ± 0.494 mm. but is a bit larger than that of (24) Themis (marked As described above, Themis family is probably closely up by black pentagram in Figure 22) of O’Rourke et al. connected with the active MBAs as well as the main belt (2020). Note that (2803) Vilho is the only one that comets, e.g., 133P/Elst-Pizarro and 176P/LINEAR. has thermal inertia greater than 100 Jm−2s−1/2K−1, Thus we give the thermal parameters of 133P/Elst- which obviously differs from others in this study, im- Pizarro (Yu et al. 2020) in Figure 22 (marked up by plying the existence of interlopers in Themis family or green pentagrams). We find that both thermal inertia this object that may originate from a distinct composi- and geometric albedo of 133P/Elst-Pizarro are within tional layer of the parent body. However, the geomet- the range of Themistians we investigated. Using the ric albedo of (2803) Vilho is consistent with the typical data from MPC, Ferr´ın et al.(2017) reduced 192016 value of Themistians, thus we need to take additional magnitude observations of 165 Themis family aster- clues (such as spectral features) into consideration to oids, among which 25 (15.2%) of them exhibit bumps determine whether this object can be treated as an ’in- or enhancements in brightness that might suggest low- terloper’. According to the Γ − pv and Γ − Deff distri- level cometary activity. Besides, the activity of aster- Thermophysical modeling of Themis Family 19

100 Themis family Vesta family other main-belt This work

10−1

(24) Themis Geometric albedo

10−2 100 101 102 Effective diameter (km)

Figure 23. The pv − Deﬀ relationship of main belt asteroids. The Vesta family and Themis family are plotted in blue and green dots, respectively, while other main-belt asteroids are shown by gray dots. Red dots with error bars are the results of this work, where (24) Themis is marked up by black pentagram. Note that each axis is logarithmic, thus the Themis family covers a much smaller range of geometric albedo.

1.0 Vesta family Flora family Hygiea family Eos family Eunomia family Themis family Koronis family Hungaria family This work 0.8

0.6

0.4 Geometric albedo 0.2

0.0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Semi-major Axis (AU)

Figure 24. Geometric albedo versus semi-major axis (in AU) for the Themis family members and several prominent families in Masiero et al.(2013); Jiang et al.(2020). The Vesta family and Hungaria family have a wide range of geometric albedo, while for Themis and Hygiea family, the ranges of geometric albedo are relatively smaller. 20 Jiang & Ji oid might be triggered by water-ice sublimation, but ilies, which is in line with the typical values of B-type only a small portion of the Themistians are discovered and C-type asteroids in main-belt. In addition, for var- to have cometary activities. This may be the reason ious asteroid families, the value of pv varies notably but that different family members originate from different may have similar distribution of thermal inertia. Finally, parts of the parent body. Although Campins et al. According to the given diameters of a large portion of (2010) predicted that water-ice is widely spread on (24) main-belt asteroids, the decreasing relationship of Γ−D Themis, several family members may be the fragments becomes unclear, thereby not following the power law that have no water-ice and thus detect no apparent ac- given by Delbo’ & Tanga(2009), this is probably due to tivities. An alternative explanation is that the lifetime the small sample population we adopted in this work. of water-ice is much less than the age of the family. As Therefore, the similarity in thermal inertia and geomet- mentioned in Schorghofer(2008), the existing time of ric albedo of Themis members may reveal their close water-ice is strongly affected by temperature of the body connection in origin and evolution. (which is mainly concerned with thermal inertia), and However, it should be noteworthy that Themis family the dust/gas production rate is in connection with the are ancient families, which may have been formed 1 Gyr effective diameter (Yu et al. 2020). Hence, our results ago, and they are located in the middle or outer region of Themis family members can help us explore their ac- of the main-belt. Thus, it is very important to have a tivities in the future work. full picture of thermal characteristics for other asteroid populations, e.g., Erigone family that may have much younger age with low geometric albedos and 60% hy- 5. CONCLUSIONS drated, or the Pallas family that is the birthplace of a In this work, we apply ATPM combined with great many of active asteroids. The forthcoming inves- WISE/NEOWISE mid-infrared measurements to inves- tigation will enable us to have a better understanding tigate the thermal inertia, geometric albedo, effective of formation and evolution of the asteroid belt and even diameter and roughness fraction of 20 Themis family as- the Solar system. teroids. Here we summarize the major results of the asteroids as follows: the average thermal inertia is derived −2 −1/2 −1 to be Γmean = 39.5 ± 26.0Jm s K . The geomet- ACKNOWLEDGMENTS ric albedo spans from 0.0360 to 0.1155, with an averaged We thank two referees for constructive comments and value of pv,mean = 0.067 ± 0.018, which agrees well with suggestions to improve the manuscript. This work is that of the former study (Masiero et al. 2013). The financially supported by the B-type Strategic Priority average effective diameter of the investigated Themis- Program of the Chinese Academy of Sciences (Grant tians are 41.173 ± 22.663 km. The family members bear No. XDB41000000),the National Natural Science Foun- a moderate roughness fraction on the surfaces, with a dation of China (Grant Nos. 12033010, 11661161013, mean value of 0.33 ± 0.19. 11633009), CAS Interdisciplinary Innovation Team and Moreover, we present the distribution of these param- Foundation of Minor Planets of the Purple Moun- eters and explore the relation among thermal parame- tain Observatory. This research has made use of the ters. The thermal inertia of the Themistians are derived NASA/IPAC Infrared Science Archive, which is oper- to be relatively small, implying that a fine and mature ated by the Jet Propulsion Laboratory, California In- regolith layer may exist on their surfaces due to long- stitute of Technology, under contract with the National term space weathering or other effects. In comparison Aeronautics and Space Administration. Research using to several prominent families, we find that the pv val- WISE Release data is eligible for proposals to the NASA ues of Themistians are rather smaller, and only cover ROSES Astrophysics Data Analysis Program. a very small range compared to other prominent fam-

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