Lightcurve Survey of V-Type Asteroids in the Inner Asteroid Belt

Home , 1906 Naef, 477 Italia, Flora family

arXiv:1311.4653v1 [astro-ph.EP] 19 Nov 2013 leoadsz fatrist edtrie (M¨uller et determined be 2007; to asteroids al. obser- of the lightcurve enables size Kaasalainen data multi-epoch and occultation 1989; Combining albedo vec- or spin mid-infrared 2001). with and vations al. shapes et al. the (Magnusson et derive asteroids obser- to of lightcurve used tors be Multi-epoch this can although vations time. diameter, small considerable of takes aster- obser- telescopes photometric an an relative with of of by vations obtained lightcurve rate be The rotational readily the can lightcurve. oid determine its vec- to from spin possible and asteroid is shape, It size, albedo, tor. with along asteroids, of Introduction 1. aedsrbto fatriswoedaeesaelarger are diameters rotation whose the asteroids than that of known is distribution It rate evolution. asteroidal strain

PASJ: 12 1 Sunao c nttt fSaeadAtoatclSine aa Aerosp Japan Science, Astronautical and Space of Institute Setsuko srnm rga,Dprmn fPyia n srnm,S Astronomy, and Physical of Department Program, Astronomy oainlrt soeo h ai hsclparameters physical basic the of one is rate Rotational h oainrt fatrisi sflmast con- to means useful a is asteroids of rate rotation The 03 srnmclSceyo Japan. of Society Astronomical 2013. 3 Nagayama 6 ioOsraoy nttt fAtooy h nvriyo University The Astronomy, of Institute Observatory, Kiso eateto at n lntr cec,TeUiest o University The Science, Planetary and Earth of Department 5 ∼ ihcreSre fVtp seod nteInrAsteroid Inner the in Asteroids V-type of Survey Lightcurve seod ssbblint eea ilo er nage. of in years effect billion the several the to to that sub-billion due (4 implies is asteroid be asteroids and the may inner torques, from the inconsistency (YORP) ejecta in This O’Keefe–Radzievskii–Paddack as asteroids regarded distribution. V-type are Maxwellian that 59 family exc of Vesta the rates with the asteroids, rotational the of of rates distribution rotational the determined we lpa 35)Emlv,(90 nzvc 40)Daie,(438 Dyagilev, FZ (4005) 1992 Knezevic, (6331) (3900) Ermolova, (3657) Alupka, kym srpyia bevtr,Ntoa Astronomica National Observatory, Astrophysical Okayama 7 ul srn o.Jpn,1– , Japan Soc. Astron. Publ. Hasegawa 0k scoet awlindsrbto (Pravec distribution Maxwellian a to close is km 40 iohm srpyia cec etr iohm Univer Hiroshima Center, Science Astrophysical Hiroshima 11 10 9 e words: Key ehv bevdtelgtuvso 3Vtp seod ((1933) asteroids V-type 13 of lightcurves the observed have We shkw aps okioUiest fEuain Hoku 9 Education, of University Hokkaido Campus, Asahikawa eateto hsc,TkoIsiueo ehooy 2-12 Technology, of Institute Tokyo Physics, of Department Nishihara uehe l 2011). al. et Durech rdaeSho fSine aa oe’ nvriy 2-8- University, Women’s Japan Science, of School Graduate ˘ 8 , 8 ainlAtooia bevtr fJpn -11Osawa, 2-21-1 Japan, of Observatory Astronomical National 2 oy erpltnGvrmn,281Nsihnyk,Shi Nishishinjyuku, 2-8-1 Government, Metropolitan Tokyo Hiroyuki , 1 Seidai 1 , 84)19 N 125 eeihle,ad(02)Riad.U Reiland). (10320) and Renemichelsen, (10285) TN, 1998 (8645) , 1,6 4 oa ytm—mnrpaes asteroids planets, minor — system solar iaoOsraoy 8 asgmn,Mst,Wkym 640 Wakayama Misato, Matsugamine, 180 Observatory, Misato Akari Toda Miyasaka Masateru Harada ?? , 5 , Kouji , 2 Ishiguro , Hiroyuki 6 Okita Michitoshi kym 1-22 Japan 719-0232, Okayama Rcie cetd) accepted ; (Received , [email protected] eu 5-4,Korea 151-742, Seoul 5 , 12 Mito 5-20 Japan 252-5210, Nobuyuki Takumi Abstract Yoshida c xlrto gny -- ohndi aaiaa Kan Sagamihara, Yoshinodai, 3-1-1 Agency, Exploration ace , 3 Yuki rlsae aeegh n et otebnsfudin found bands the and to visible depth spec- and the wavelength, in in similar shape, are bands tral that absorption regions spec- wavelength has surface near-infrared Vesta The surface, core. of basaltic metal trum a a asteroid and with differentiated mantle, structure ultramafic only an internal the intact is an it with as planet terrestrial re- collisions, effects. (YORP) secondary Yarkovsky–O’Keefe–Radzievskii–Paddack as and the well from accretion, results that as rates suggests rotation impact, in This catastrophic change the for distribution. forces driving Maxwellian of a distribution low rate than rotation smaller the asteroids collisional contrast, by In produced remnants This disruption. main their the and/or of 1987). region planetesimals belt are that asteroids (Salo such shown that distribution asteroids have suggests of Maxwellian simulations history a collisional Numerical the generates by 2002). generated rates spin al. et oy,1723 iae io aao3700,Japan 397-0101, Nagano Kiso, Mitake, 10762-30 Tokyo, f olNtoa nvriy a 61 ilmdn,Gwanak-g Sillim-dong, 56-1, San University, National eoul bevtr,33- oj,Kmgt-h,Asakuchi, Kamogata-cho, Honjo, 3037-5 Observatory, l Abe Kawai iy iah-iohm,Hrsia7982,Japan 739-8526, Hiroshima Higashi-Hiroshima, sity, h seod()Vsai osdrdt etesmallest the be to considered is Vesta (4) asteroid The oy,731Hno uko oy 1-03 Japan 113-0033, Tokyo Bunkyo, Hongo, 7-3-1 Tokyo, f , Sarugaku 7 1Okym,Mgr,Tko1285,Japan 152-8551, Tokyo Meguro, Ookayama, -1 , Kenshi 1 eioa,Bny,Tko1288,Japan 112-8681, Tokyo Bunkyo, Mejirodai, 1 n Masanao and o,Aaiaa okio0082,Japan 070-8621, Hokkaido Asahikawa, mon, , 9 pino iui n eeihle.The Renemichelsen. and Nikulin of eption Machiko )Srg,(44 iui,(76 Lewis, (4796) Nikulin, (4434) Suruga, 3) et,i nossetwt h best-fit the with inconsistent is Vesta, ) juu oy 6-01 Japan 163-8001, Tokyo njyuku, iaa oy 8-58 Japan 181-8588, Tokyo Mitaka, Yanagisawa anbl,icuig2 ebr of members 29 including belt, main , 1 ice,(01 eeaia (2508) Veteraniya, (2011) Tinchen, olso vn htfre V-type formed that event collision Tomohiko Mori hra aito Yarkovsky– radiation thermal Abe 16,Japan -1366, ∼ 0k ndaee osntfol- not does diameter in km 40 , 10 1 , 5 Ozawa igteeobservations these sing Yasuhiro Tomohiko , 4 Daisuke Shimizu Sekiguchi Belt Kuroda , 5 Shogo , agawa 11 u, , 5 2 S. Hasegawa et al. [Vol. , spectra of howardite, eucrite, and diogenite (HED) mete- 2. Observations and data reduction procedures orites (McCord et al. 1970; Larson & Fink 1975). A vast crater 460 km in diameter and 13 km deep with a central Our observational survey of lightcurves for V-type as- peak and raised rim is present at Vesta’s south pole, which teroids was carried out using six different telescopes be- is a triaxial ellipsoid with dimensions of 578, 580, and 458 tween Fall 2004 and Spring 2005. Fifty-nine lightcurves km (Thomas et al. 1997). Zappalàet al. (1990b) in- were recorded at the Kiso Observatory using two dif- ferred that Vesta has an asteroid family and Mothé-Diniz ferent telescopes in Nagano, Japan (MPC code 381), et al. (2005) reported that the Vesta family contains ca. the Miyasaka Observatory in Yamanashi, Japan (MPC 4500 members. Numerous asteroids with Vesta-like visi- code 366), the Okayama Astrophysical Observatory ble spectra are typically referred to as ‘V-type asteroids’. in Okayama, Japan (MPC code 371), the Misato These asteroids have a near-Earth orbit (Cruikshank et Observatory in Wakayama, Japan (no MPC code), and al. 1991) in the inner main belt, which is influenced by a the UH88 telescope in Hawaii, USA (MPC code 568). 3:1 mean motion resonance and the ν6 secure resonance Details of the nightly observational conditions are listed of Jupiter (Binzel & Xu 1993). Approximately 3000 V- in Table 1. type asteroids have been identified by spectroscopic and Thirty-three lightcurve observations from the 1.05 m spectrophotometric methods (Cruikshank et al. 1991; Schmidt telescope at the Kiso Observatory were made us- Xu et al. 1995; Spahr et al. 1997; Binzel et al. 2001; ing an SITe TK2048E CCD detector (2048 x 2048 pix- Bus & Binzel 2002; Binzel et al. 2004a; Binzel et al. els), giving an image scale of 1.5′′/pixel located in the 2004b; Duffard et al. 2004; Lazzaro et al. 2004; Marchi Schmidt focus. The field of view of the CCD was 51′ × et al. 2005; Alvarez-Candal et al. 2006; de León et 51′. Integration times for the observations were 120 to al. 2006; Duffard et al. 2006; Roig & Gil-Hutton 2006; 300 s. The full-width half maximum of star images at this Davies et al. 2007; Carvano et al. 2010; Solontoi et site was typically 5–8′′. al. 2012; Sanchez et al., 2013). Gladman et al. (1997) Three lightcurves were recorded using the 0.30 m Dall– used numerical simulations to propose that most impact Kirkham telescope at the Kiso Observatory (K.3T). K.3T objects to Earth belong to the Vesta family and Binzel et consisted of a MUTOH CV16II CCD camera with a al. (2004b) noted that the most likely source of V-type Kodak KAF-1600 chip format, which captures 1536 × near-Earth asteroids is the Vesta family, given the lack of 1024 pixels with an image scale of 1.35′′/pixel under 2 × V-type Mars crossers. Carruba et al. (2007) showed that 2 binning, giving a 17.3′ × 11.5′ sky field. The integration V-type asteroids outside the Vesta family were scattered times for these observations were 300 s. by close encounters with Vesta, and that they formerly be- Eighteen of the lightcurves were obtained using the longed to the Vesta family. Roig et al. (2012) constrained 0.36 m Ritchey–Chrétien telescope at the Miyasaka the mechanisms of a large fraction of V-type asteroids that Observatory. The telescope was equipped with an SBIG are observed to be outside the Vesta family. These studies STL-1001E CCD camera with Kodak KAF-1001E detec- all suggest that most V-type asteroids in the inner main tor whose format is 1024 × 1024 pixels. This system pro- belt are ejecta from Vesta, and that HED meteorites are duced image dimensions of 1.7′′/pixel, yielding a field of sourced from Vesta and V-type asteroids through the 3:1 view of 29.4′ × 29.4′. The observational integration time and ν6 resonances. was 300 s. The full-width half maximum of stellar images The rotational rates of V-type asteroids are poorly con- at this site was typically 5–8′′. strained, due to the limited number of such asteroids Two lightcurves were made with the 0.50 m Classical– that have currently been studied. As such, in order to Cassegrain telescope (MITSuME) at the Okayama better constrain the rotational rate distribution of aster- Astrophysical Observatory (Yanagisawa et al. 2010). An oids sourced from Vesta, we have begun (since Fall 2003) Apogee U6 camera with a Kodak KAF-1001E detector lightcurve observations of V-type asteroids in the inner yielded a format of 1024 × 1024 pixels with an image scale < < main belt (semi major axis 2.1 ∼ a ∼ 2.5) and deter- of 1.5′′/pixel and a sky field of 25.6′ × 25.6′. Integration mined rotational rates, along with amplitude variations times for these two lightcurves were 120 s. The full-width (Hasegawa et al. 2004; Hasegawa et al. in press). Our half maximum of stellar images at this site was typically study contributes to determination of an increased num- 3–5′′. ber of reliable rotation rates that allows statistically mean- Two lightcurve observations were carried out with the ingful interpretations of this data for V-type asteroids to 1.05 m Cassegrain telescope at the Misato Observatory. be carried out. The lightcurves were recorded with a SBIG ST-9E CCD Herein, we present lightcurve observations for a number camera and Kodak KAF-0261E detector (512 × 512 pix- of V-type asteroids. Subsequent sections of this paper els; angular resolution of 1.0′′/pixel); sky field of 9′ × 9′). describe the observations and data reduction procedures Integration times for these observations were 30 to 180 s. (Section 2), results of the lightcurve analyses (section 3), The full-width half maximum of stellar images at this site and implications of our results for the origin(s) of V-type was typically 3–5′′. asteroids (Section 4). One lightcurve was recorded using the 2.24 m telescope at Mauna Kea (UH88), equipped with a wide-field imager

1 hhttp://ssd.jpl.nasa.gov/horizons.cgi#topi. No. ] Lightcurve Survey of V-type Asteroids 3 comprising eight 2048 × 4096 pixel CCDs. The projected

′ × ′ ]

area was 33 33 , which corresponds to an angular res- g

′′ a 1933 Tinchen (P=3.671 hour) olution of 0.45 /pixel. The integration times were 30 s. -0.2 [m

The full-width half maximum of stellar images at this site ) was ca. 1′′. º =0 0 All observations were carried out through an R band ﬁl- ! (

ter. The dark images for correction were constructed from e a median combination of 5–20 dark frames. Dome ﬂat d tu

i 0.2 ﬁelding images were obtained from the 1.05 m Schmidt, gn

0.36 m Miyasaka, 1.05 m Misato, and UH88 telescopes. a m Flat ﬁelding images by K.3T and MITSuME were taken 0.4 during the evening and/or morning twilight. Stacked ﬂat ve 03/07-1.05m Schmidt

ti 03/08-1.05m Schmidt 03/12-0.36m Miyasaka a

fielding images for correction were created by a median l 03/13-0.36m Miyasaka e 0.6 combination of 10–20 flat fielding frames. Light image r 0 0.5 1 1.5 2 2.5 3 3.5 reduction involved dark subtraction and flat-field correc- rotational period [hour] tion, and was performed by Image Reduction and Analysis Facility (IRAF) software. The asteroids and stellar stars for comparison were measured through a circular aper- ture with a diameter three times that of the full-width Fig. 1. Composite rotational lightcurve of the asteroid half maximum size used for the APPOT task of IRAF. (1933) Tinchen. All lightcurves were constructed using relative magni- tudes. The fluxes of 5–20 stars in the same frame as each ] asteroid were measured for comparison. The flux differ- g

a 2011 Veteraniya (P=8.2096 hour) ence between the asteroid and sum of the comparison stars -0.4 [m were then computed. Variable stars were not used as com- ) º -0.2 parison stars. =0 !

Light travel time was corrected to obtain an accurate (

0 lightcurve epoch. A G parameter value for V-type as- e d

teroids is necessary for phase function correction, and we tu 0.2 i used values of 0.32 (G parameter value of Vesta) and 0.15 gn

(G parameter value of typical asteroids). Zappalàet al. a 0.4 m (1990a) and Ohba et al. (2003) reported that the amplitude of asteroid lightcurves is affected by the phase angle. ve 0.6 11/12-1.05m Schmidt ti 01/08-0.36m Miyasaka a As such, a coefficient value (m = 0.02) equal to the me- l 01/09-0.36m Miyasaka e 0.8 dian value for surface roughness of asteroids (Ohba et al. r 0 1 2 3 4 5 6 7 8 2003) was adopted to correct lightcurve amplitude for the rotational period [hour] phase angle = 0◦. Fourier analysis (FFT) and phase dispersion minimiza- tion methods (PDM) described by Stellingwerf (1978) were utilized for determination of the asteroidal rotational Fig. 2. Composite rotational lightcurve of the asteroid (2011) Veteraniya. periods. Rotational periods were finally determined by considering the best result obtained by the two methods. oid is valued as U = 3−. 3. Results 3.1.2. (2011) Veteraniya 3.1. V-type asteroids The asteroid (2011) Veteraniya has a Vesta-like spec- 3.1.1. (1933) Tinchen trum (Xu et al. 1995) and is a member of the Vesta The asteroid (1933) Tinchen is a V-type asteroid (Xu family (Mothé-Diniz et al. 2005). The diameter of the et al. 1995) that belongs to the Vesta family (Mothé- asteroid has been estimated to be 5.19 km (Masiero et Diniz et al. 2005). Masiero et al. (2011) reported that al. 2011), but the period of this asteroid was not known the diameter of (1933) Tinchen is 6.45 km. Tinchen was prior to our study. Veteraniya was observed during its observed during its apparition in March 2005 (Fig. 1), apparition in November 2004 and January 2005 (Fig. 2), ± and yielded a rotational period of 8.2096 ± 0.0003 h. The and a rotational period of 3.671 0.002 h was obtained. − On the Observatoire de Geneve website of Behrend asteroid is estimated as U = 3 . (http://obswww.unige.ch/∼behrend/page cou.html), the rotational period of (1933) Tinchen was reported to be 3.1.3. (2508) Alupka 3.67 h, which is in excellent agreement with our re- The asteroid (2508) Alupka is a Vestoid (Bus & Binzel sult. The quality code (U) scale as used for the Asteroid 2002) and a member of the Vesta family (Mothé-Diniz et Lightcurve Database by Warner et al. (2009). The aster- al. 2005). The size of the asteroid is 5.17 km in diameter 4 S. Hasegawa et al. [Vol. ,

] -0.2 ] -0.2 g g

a 2508 Alupka (P=17.70 hour) a 3657 Ermolova (P=2.582 hour) -0.1 [m [m

) 0 ) º º 0 =0 =0 ! ! ( ( 0.1 e 0.2 e d d tu tu

i i 0.2

gn 0.4 gn a a 0.3 m m

ve ve 0.4 11/12-1.05m Schmidt ti 0.6 ti 5/05-1.05m Schmidt 11/13-1.05m Schmidt

a a 5/09-1.05m Schmidt l 11/15-1.05m Schmidt l 5/14-1.05m Schmidt

e e 0.5 r 0 2 4 6 8 10 12 14 16 r 0 0.5 1 1.5 2 2.5 rotational period [hour] rotational period [hour]

Fig. 3. Composite rotational lightcurve of the asteroid Fig. 4. Composite rotational lightcurve of the asteroid (2508) Alupka. (3657) Ermolova.

(Masiero et al. 2011). The period of this asteroid was not

] -0.4 known prior to this study. Alupka was observed during its g

a 3900 Knezevic (P=5.324 hour) apparition in November 2004 (Fig. 3) and yielded a rota- -0.2 ± [m tional period of 17.70 0.05 h. The asteroid is evaluated ) º with U = 2−. 0 =0 ! (

3.1.4. (3657) Ermolova e 0.2 d

The asteroid (3657) Ermolova is a Vestoid (Xu et tu al. 1995) and part of the Vesta family (Mothé-Diniz i 0.4 gn et al. 2005). Thermal observations of the aster- a 0.6 m oid have indicated it has an effective diameter of 5.79 01/16-1.05m Schmidt km (Usui et al. 2011). Ermolova was observed dur- ve 0.8 01/17-1.05m Schmidt ti 01/18-1.05m Schmidt a ing its apparition in May 2005 (Fig. 4), and a rota- l 02/04-0.36m Miyasaka e 1 ± r tional period of 2.582 0.004 h was determined for 0 1 2 3 4 5 this asteroid. On the websites of Behrend and Pravec rotational period [hour] et al. (http://www.asu.cas.cz/∼ppravec/neo.htm) rotational periods of 2.6066 and 2.6071 h were reported for (3657) Ermolova, respectively. Even taking into account uncertainties, our rotational period result is slightly differ- Fig. 5. Composite rotational lightcurve of the asteroid ent to these web-published results. The asteroid is valued (3900) Knezevic. asU=2−. is 8.36 km. The period of this asteroid was not known 3.1.5. (3900) Knezevic before this study. Dyagilev was observed during its ap- The asteroid (3900) Knezevic is a V-type asteroid (Bus parition in March 2005 (Fig. 6) and yielded a rotational period of 6.400 ± 0.006 h. The asteroid is assessed at U & Binzel 2002) of the Vesta family (Mothé-Diniz et al. − 2005). The asteroid is 4.96 km in diameter (Masiero et al. = 3 . 2011). The period of this asteroid was not known prior to 3.1.7. (4383) Suruga our study. Knezevic was observed during its apparition in The asteroid (4383) Suruga has a Vesta-like spectrum January and February 2005 (Fig. 5) and gave a rotational (Roig & Gil-Hutton 2006), but is not a member of the period of 5.324 ± 0.001 h. The asteroid is rated as U = − Vesta family (Mothé-Diniz et al. 2005), although it is 3 . positioned in the inner main belt region. The diameter of this asteroid has been estimated to be 7.92 km (Masiero 3.1.6. (4005) Dyagilev et al. 2011). The period of this asteroid was not known The asteroid (4005) Dyagilev is a V-type asteroid (Xu before this study. Suruga was observed during its appari- et al. 1995), but is not a member of Vesta family (Mothé- tion in December 2004 (Fig. 7) and a rotational period Diniz et al. 2005). However, the asteroid is positioned of 3.811 ± 0.003 h was obtained for this asteroid. The in the inner main belt region. Masiero et al. (2011) esti- asteroid is estimated as U = 2−. mated that the diameter of the asteroid (4005) Dyagilev No. ] Lightcurve Survey of V-type Asteroids 5

] ] 0.2 g g

a -0.1 4005 Dyagilev (P=6.400 hour) a 4434 Nikulin [m [m

) ) 0.1 º º 0 =0 =0 ! ! ( (

0 e 0.1 e d d tu tu i i -0.1

gn 0.2 gn a a m m

0.3 -0.2 ve ve

ti 03/07-1.05m Schmidt ti 10/15-0.36m Miyasaka

a 03/08-1.05m Schmidt a 10/16-0.36m Miyasaka l 03/13-0.36m Miyasaka l 10/17-0.36m Miyasaka e 0.4 e -0.3 r 0 1 2 3 4 5 6 r 10 12 14 16 18 20 rotational period [hour] obs time (corrected light time) [hour]

Fig. 6. Composite rotational lightcurve of the asteroid Fig. 8. Composite rotational lightcurve of the asteroid (4005) Dyagilev. (4434) Nikulin.

] -0.05 ] g g

a 4383 Suruga (P=3.811 hour) a 4796 Lewis (P = 3.5080 hr) -0.2 [m [m ) ) º 0 º

=0 =0 0 ! ! ( (

e e

d 0.05 d tu tu

i i 0.2 gn gn a a

m 0.1 m 0.4

ve ve 9/15-1.05m Misato

ti ti 10/1-0.36m Miyasaka 12/17-1.05m Misato a a 10/14-0.30m K.3T l 12/20-2.24m UH88 l 10/15-0.30m K.3T e 0.15 e 0.6 r 0 0.5 1 1.5 2 2.5 3 3.5 r 0 0.5 1 1.5 2 2.5 3 3.5 rotational period [hour] rotational period [hour]

Fig. 7. Composite rotational lightcurve of the asteroid Fig. 9. Composite rotational lightcurve of the asteroid (4383) Suruga. (4796) Lewis.

3.1.8. (4434) Nikulin (4796) Lewis has been estimated to be ∼ 5.2 km, using The asteroid (4434) Nikulin has a Vesta-like spectrum the assumption that its albedo is the same as the median (Xu et al. 1995), but does not belong to the Vesta family value of other V-type asteroids (pv = 0.343; Mainzer et (Mothé-Diniz et al. 2005). However, this asteroid is al. 2012). The period of this asteroid was not known be- positioned in the inner main belt region. The asteroid is fore this study. Lewis was observed during its apparition 5.11 km in diameter (Masiero et al. 2011). The period of in September and October 2004 (Fig. 9) and determined (4434) Nikulin was not known before this study. Nikulin to have a rotational period of 3.5080 ± 0.0002 h. The was observed during its apparition in October 2004 (Fig. asteroid is evaluated with U = 2+. 8). Despite three nights of observations, the rotational period of (4434) Nikulin was not able to be determined 3.1.10. (6331) 1992 FZ1 due to its small amplitude. The asteroid (6331) 1992 FZ1 is a Vestoid (Duffard et al. 2004) that belongs to the Vesta family (Mothé-Diniz 3.1.9. (4796) Lewis et al. 2005). The asteroid has an effective diameter of The asteroid (4796) Lewis is a V-type asteroid (Bus & 5.32 km (Masiero et al. 2011). The period of this asteroid Binzel 2002), but is not a member of the Vesta family was not known before this study. 1992 FZ1 was observed (Mothé-Diniz et al. 2005). However, the asteroid is po- during its apparition in October and November 2004 (Fig. sitioned in the inner main belt region. The diameter of 10) and yielded a rotational period of 9.3333 ± 0.0005 h. 6 S. Hasegawa et al. [Vol. , ] ]

g -0.2 g a 6331 1992 FZ1 (P=9.3333 hour) a -0.4 10285 Renemichelsen [m [m ) )

º 0 º -0.2 =0 =0 ! ! ( (

0.2 e e

d d 0 tu tu

i 0.4 i gn gn

a a 0.2

m 0.6 m

10/15-0.30m K.3T ve ve 10/16-0.50m Okayama 11/12-1.05m Schmidt ti ti 0.4 0.8 10/17-0.50m Okayama 11/13-1.05m Schmidt a a

l 11/6-0.36m Miyasaka l 11/15-1.05m Schmidt e e r 0 2 4 6 8 r 8 10 12 14 16 18 rotational period [hour] obs time (corrected light time) [hour]

Fig. 10. Composite rotational lightcurve of the asteroid Fig. 12. Composite rotational lightcurve of the asteroid (6331) 1992 FZ1. (10285) Renemichelsen.

Vesta family (Moth´e-Diniz et al. 2005). Thermal ob-

] -0.2

g servations of this asteroid have indicated that it has an

a 8645 1988 TN (P=7.616 hour) -0.1 eﬀective diameter of 3.91 km (Masiero et al. 2011). [m

) The period of this asteroid was not known before this º 0 study. Renemichelsen was observed during its appari- =0

! tion in November 2004 (Fig. 12). Although (10285) ( 0.1

e Renemichelsen was observed for three nights, determina- d 0.2 tion of its rotational period was not possible due to its tu i 0.3 small amplitude. gn a

m 0.4 3.1.13. (10320) Reiland

ve 0.5 The asteroid (10320) Reiland is a Vestoid (Duﬀard et ti 02/04-1.05m Schmidt

a 02/05-0.36m Miyasaka l 02/11-0.36m Miyasaka al. 2004) and a member of the Vesta family (Mothé- e 0.6 r 0 1 2 3 4 5 6 7 Diniz et al. 2005). The diameter of this asteroid is 2.86 km (Masiero et al. 2011), but the period of this asteroid rotational period [hour] was not known prior to this study. Reiland was observed during its apparition in November 2004 (Fig. 11), and a rotational period of 5.92 ± 0.01 h was determined. The Fig. 11. Composite rotational lightcurve of the asteroid asteroid is valued as U = 2−. (8645) 1988 TN. 3.2. non-V-type asteroids The asteroid is assessed at U = 2+. Lightcurves of some non-V-type asteroids were obtained whilst making observations of V-type asteroids. 3.1.11. (8645) 1988 TN The asteroid (8645) 1988 TN is a V-type asteroid (Roig 3.2.1. (477) Italia & Gil-Hutton 2006), but is not a member of the Vesta The asteroid (477) Italia is a S-type asteroid (Tholen family (Mothé-Diniz et al. 2005). However, the asteroid 1994, Bus & Binzel 2002) with a diameter of 25.02 km is positioned in the inner main belt region. Masiero et al. (Usui et al. 2011). This asteroid was observedin the same (2011) determined the diameter of this asteroid to be 5.08 frame as (1933) Tinchen for four nights. The period of this km. The period of this asteroid was not known before asteroid was known prior to this study. Italia was observed this study. 1988 TN was observed during its apparition in during its apparition in 2004 (Fig. 14) and a rotational February 2005 (Fig. 11) and a rotational period of 7.616 period of 19.32 ± 0.01 h obtained. On the website of ± 0.002 h determined for this asteroid. The asteroid is Behrend, the rotational period for this asteroid is reported rated as U = 3−. to be 19.42 h, which is consistent with our results. The asteroid is estimated as U = 2−. 3.1.12. (10285) Renemichelsen The asteroid (10285) Renemichelsen has a Vesta-like spectrum (Duffard et al. 2004) and is a member of the No. ] Lightcurve Survey of V-type Asteroids 7

] -0.2 ] -0.05 g g

a 10320 Reiland (P=5.920 hour) a 10389 Robmanning (P=2.75 hour)

[m -0.1 [m ) ) º º 0

=0 0 =0 ! ! ( (

e e

d 0.1 d 0.05 tu tu i i

gn 0.2 gn a a

m m 0.1

0.3 ve ve 11/12-1.05m Schmidt ti 11/13-1.05m Schmidt ti a a

l 11/15-1.05m Schmidt l 11/15-1.05m Schmidt

e 0.4 e 0.15 r 0 1 2 3 4 5 6 r 0 0.5 1 1.5 2 2.5 3 rotational period [hour] rotational period [hour]

Fig. 13. Composite rotational lightcurve of the asteroid Fig. 15. Composite rotational lightcurve of the asteroid (10320) Reiland. (10389) Robmanning.

] 0 ] -0.1 g g

a 477 Italia (P=19.32 hour) a 10443 van der Pol (P=3.32 hour) -0.05

[m 0.05 [m ) ) º º 0

=0 0.1 =0 ! !

( ( 0.05

e e

d 0.15 d 0.1 tu tu i i 0.15 gn 0.2 gn a a

m m 0.2

0.25 ve 03/07-1.05m Schmidt ve 0.25

ti 03/08-1.05m Schmidt ti

a 03/12-0.36m Miyasaka a l 03/13-0.36m Miyasaka l 11/15-1.05m Schmidt e 0.3 e 0.3 r 0 5 10 15 20 r 0 0.5 1 1.5 2 2.5 3 3.5 rotational period [hour] rotational period [hour]

Fig. 14. Composite rotational lightcurve of the asteroid Fig. 16. Composite rotational lightcurve of the asteroid (477) Italia. (10443) van de Pol.

3.2.2. (10389) Robmanning November 2004 (Fig. 16) and gave a rotational period of The spectral type of asteroid (10389) Robmanning is 3.32 h. The website of Pravec et al. reports a rotational unknown. The diameter of the asteroid has been esti- period of 3.34501 h for this asteroid, which is consistent mated to be 4.12 km (Masiero et al. 2011). This asteroid with our result. The asteroid is rated as U = 2−. was monitored in the same frame as (11320) Reiland for one night. The period of this asteroid was not known 3.2.4. (11321) Tosimatsumoto before this study. Robmanning was observed during its The spectrum of asteroid (11321) Tosimatsumoto clas- apparition in March 2004 (Fig. 15) and yielded a rota- siﬁes it as XL-type (Carvano et al. 2010), which has a tional period of 2.75 h. The asteroid is evaluated with U diameter of 9.19 km (Masiero et al. 2011). This asteroid = 2−. was monitored in the same frame as (8645) 1988 TN for two nights. The period of this asteroid was not known 3.2.3. (10443) van de Pol before this study. Tosimatsumoto was observed during its The asteroid (10443) van de Pol is an S-type asteroid apparition in February 2005 (Fig. 17) and a rotational (Ivezi´cet al. 2002). Masiero et al. (2011) reported that period of 7.80 ± 0.09 h was obtained. The asteroid is the diameter of this asteroid is 3.44 km. The asteroid was assessed at U = 1+. observed in the same frame as (11320) Reiland for one night. van de Pol was observed during its apparition in 8 S. Hasegawa et al. [Vol. ,

] ] -0.2 g g 168 a 11321 Tosimatumoto (P~7.80 hour) a 22034 1999 XL (P~3.35 hour) -0.2 -0.1 [m [m ) ) º º 0

=0 0 =0 ! ! ( ( 0.1 e e

d 0.2 d tu tu

i i 0.2 gn gn

a 0.4 a 0.3 m m

ve ve 0.4 ti 0.6 02/04-1.05m Schmidt ti a a

l 02/05-0.36m Miyasaka l 11/12-1.05m Schmidt

e e 0.5 r 0 1 2 3 4 5 6 7 r 0 0.5 1 1.5 2 2.5 3 rotational period [hour] rotational period [hour]

Fig. 17. Composite rotational lightcurve of the asteroid Fig. 19. Composite rotational lightcurve of the asteroid (11321) Tosimatsumoto. (22034) 1999 XL168 ] ] -0.2 g g 9 a 29976 1999 NE a 18590 1997 YO10 (P~2.95 hour) -0.4 [m [m -0.1 ) ) º

º -0.2 =0 =0 ! ! 0 ( ( 0

e e d d 0.2 tu

tu 0.1 i i gn gn a

a 0.4 0.2 m m

ve 0.6 ve ti ti 0.3 01/16-1.05m Schmidt a a l l 11/12-1.05m Schmidt 01/17-1.05m Schmidt e e 0.8 r r 0 0.5 1 1.5 2 2.5 16 16.5 17 17.5 18 18.5 19 19.5 20 rotational period [hour] obs time (corrected light time) [hour]

Fig. 18. Composite rotational lightcurve of the asteroid Fig. 20. Composite rotational lightcurve of the asteroid (18590) 1997 YO10 (22034) 1999 XL168

3.2.5. (18590) 1997 YO10 The period of this asteroid was not known prior to this The asteroid (18590) 1997 YO10 is an S-type asteroid study. 1999 XL168 was observed during its apparition in (Ivezićet al. 2002; Carvano et al. 2010). Thermal obser- November 2004 (Fig. 19), and resulted in a calculated ro- vations of this asteroid have shown that it has an effective tational period of ∼3.35 h. The asteroid is estimated as diameter of 5.02 km (Masiero et al. 2011). The aster- U = 1. oid was monitored in the same frame as (2011) Veteraniya for one night. The period of this asteroid was not known 3.2.7. (29976) 1999 NE6 The asteroid (29976) 1999 NE6 is a D-type asteroid prior to this study. 1997 YO10 was observed during its apparition in November 2004 (Fig. 18), yielding a rota- (Carvano et al. 2010). The diameter of this asteroid tional period of ∼2.95 h. The asteroid is evaluated with has been estimated to be 9.56 km (Masiero et al. 2011). U = 1. This asteroid was observed in the same frame as (3900) Knezevic for two nights. The period of this asteroid was not known before this study. 1999 NE6 was observed dur- 3.2.6. (22034) 1999 XL168 ing its apparition in January 2005 (Fig. 20). Despite two The spectral type of asteroid (22034) 1999 XL168 is unknown. This asteroid has an effective diameter of 5.15 nights of observations, a solution for the rotational period of this asteroid was not possible due to its small ampli- km (Masiero et al. 2011). (22034) 1999 XL168 was monitored in the same frame as (2011) Veteraniya for one night. tude. No. ] Lightcurve Survey of V-type Asteroids 9

] -0.2 ] -0.4 g g

a 41051 1999 VR10 (P=4.04 hour) a 46121 2001 FB36 (P~4.2 hour)

[m [m -0.2

) 0 ) º º =0 =0

! ! 0 ( (

0.2 e e d d

tu tu 0.2 i 0.4 i gn gn a a 0.4 m m 0.6 ve ve

ti ti 0.6 01/16-1.05m Schmidt a a

l 11/15-1.05m Schmidt l 01/17-1.05m Schmidt

e 0.8 e r 0 0.5 1 1.5 2 2.5 3 3.5 4 r 0 0.5 1 1.5 2 2.5 3 3.5 4 rotational period [hour] rotational period [hour]

Fig. 21. Composite rotational lightcurve of the asteroid Fig. 22. Composite rotational lightcurve of the asteroid (41051) 1999 VR10 (46121) 2001 FB36

3.2.8. (41051) 1999 VR10

] -0.4

The spectral type of asteroid (41051) VR10 is unknown. g The diameter of the asteroid has been estimated to be a 89481 2001 XH27 [m

11.12 km (Masiero et al. 2011). The asteroid was moni- )

º -0.2 tored in the same frame as (11320) Reiland for one night. =0

The period of this asteroid was not known prior to this ! (

study. 1999 VR10 was observed during its apparition in e 0 November 2004 (Fig. 21), yielding a rotational period of d tu 4.04 h. The asteroid is evaluated with U = 2−. i gn 0.2 a m 3.2.9. (46121) 2001 FB36

The asteroid (46121) 2001 FB36 is a C-type asteroid ve ti 0.4 10/16-0.36m Miyasaka a

(Ivezi´cet al. 2002; Carvano et al. 2010). Masiero et l 10/17-0.36m Miyasaka e al. (2011) reported that the diameter of this asteroid is r 10 12 14 16 18 20 6.26 km. This asteroid was observed in the same frame obs time (minus light time) [hour] as (3900) Knezevic for two nights. The period of this asteroid was not known prior to this study. 2001 FB36 was observed during its apparition in January 2005 (Fig. 22) and a rotational period of ∼4.2 h was determined. Fig. 23. Composite rotational lightcurve of the asteroid The asteroid is assessed at U = 1. (89481) 2001 XH27

3.2.10. (89481) 2001 XH27 of these asteroids range from 3 to 10 km, respectively, on (89481) XH27 is an X-type asteroid (Carvano et al. the basis of an assumed albedo of the median value of 2010) with an albedo that is the same as the median value V-type asteroids. of X-type asteroids (Mainzer et al. 2012). The size of this Figure 24 is a histogram of the rotational rate for the asteroid is ∼ 2.8 km. The Jupiter Trojan asteroid was 59 V-type asteroids in the inner main belt and 29 V-type monitored in the same frame as (4434) Nikulin for two Vesta family asteroids, excluding 4 Vesta. Both V-type nights. The period of this asteroid was not known before Vesta family asteroids and V-type asteroids in the inner this study. 2001 XH27 was observed during its apparition main belt exhibit a non-Maxwellian distribution compared in October 2005 (Fig. 23). Although observed for two with the Maxwellian distribution expected for a collision- nights, its rotational period was not able to be determined ally evolved population. due to its small amplitude. There is certainly present an observational bias against slow rotators with spin rates slower than 1 rev/day and 4. Discussion probably also against asteroids with spin rates faster than 7 rev/day. Measurements of rotation periods for slow ro-

We have now determined the rotational rate of 59 V- 2 hhttp://obswww.unige.ch/∼behrend/page cou.htmli. type asteroids in the inner main belt, which includes our 3 hhttp://www.minorplanetobserver.com/PDO/PDOLightcurves.htmi. 11 new and 48 previous results (Table 2). The diameters 4 hhttp://www.asu.cas.cz/∼ppravec/neo.htmi. 10 S. Hasegawa et al. [Vol. ,

oid 243 Ida (Greenberg et al. 1996), and age–color re-

x x x x x x

x x x x x

6 x lationships from photometric observations (Nesvorn´yet

x x x x x x

x x x x x

x al. 2005). Kryszczyn´ska et al. (2012) showed that

x x x x x x

xxxxxxxxxxxx x x x x x x

xxxxxxxxxxxx x x x x x

5 x the rotational rates of the Flora family also have a non- xxxxxxxxxxxx x x x x x x

xxxxxxxxxxxx x x x x x x

xxxxxxxxxxxx x x x x x

x Maxwellian distribution. This result clearly demonstrates

xxxxxxxxxxxx x x x x x x

xxxxxxxxxxxx x x x x x xxxxxx

4 x

xxxxxxxxxxxx x x x x x xxxxxx

x the inﬂuence of YORP eﬀects on the Flora family. The

xxxxxxxxxxxx x x x x x xxxxxx x

xxxxxxxxxxxx x x x x x xxxxxx

x age of the Flora family (Nesvorn´yet al. 2005) is also

xxxxxxxxxxxx x x x x x xxxxxx x

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

3 x

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

x consistent with the timescale of YORP eﬀects. Pravec

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

x et al. (2008) showed that the distribution of main belt

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

number

xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

2 x

xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

x and Mars-crossing asteroids with diameters of 3–15 km

xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

x has a non-Maxwellian distribution due to YORP torques.

xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

1 x In light of these examples of other asteroid families, it

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx

x is probable that the rotational rate distribution of V-

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx x

xxxxxx xxxxxx xxxxxx xxxxxx xxxxxxxxxxxx xxxxxx xxxxxx xxxxxx x x x x x xxxxxx 0 x type asteroids can be explained by long-term modiﬁca- 0 2 4 6 8 10 tion by YORP torques. The YORP eﬀect is dependent rotation rate [rev/day] on asteroid size, shape, spin vector, and heliocentric distance (Rubincam 2000). As such, we speculate that

the timescale for generation of V-type asteroids with 3

x x x x x

x < <

x x x x x

12 x

x x x x x

x ∼ Diameter ∼ 10 km ranges from sub-billion to several

x x x x x x

x x x x x

x billion years.

x x x x x x

x x x x x

10 x

x x x x x

x The results of Marzari et al. (1996) indicate that the

x x x x x x

x x x x x

x cratering event that formed the Vesta family occurred ∼1

x x x x x x

x x x x x

8 x

x x x x x

x Gyr ago. Carruba et al. (2007) implied the Vesta fam-

x x x x x x

x x x x x

x ily age is (1.2 ± 0.7) Gyr in age. The Dawn spacecraft x x x x x x

x x x x x x

x x x x x

6 x

x x x x x

x scanned the surface of Vesta and the two largest impact

x x x x x x

x x x x x

x craters were estimated to have formed about 1 Gyr ago

number

x x x x x x

x x x x x

4 x

x x x x x

x (Marchi et al. 2012). Nesvorn´yet al. (2008) also sug-

x x x x x x

x x x x x

x ∼

x x x x x

x gested that the Vesta family has existed for at least 1

x x x x x x

x x x x x

2 x Gyr and, if members of the Vesta family were liberated

x x x x x x

x x x x x

x from the surface of Vesta, that the impact event occurred

x x x x x x

x x x x x 0 x at 3.8 Gyr. Using a collisional evolution model Bottke 0 2 4 6 8 10 et al. (2005), determined with a 19% probability that a rotation rate [rev/day] major impact has occurred on asteroid (4) Vesta and produced the Vesta family in the last 3.5 Gyr. Several large impact-heating events have also been shown to have oc- Fig. 24. Distribution of rotational rates for V-type asteroids curred on the asteroid 4 Vesta between 3.4 and 4.5 Gyr ago in the inner main belt. (a) only V-type Vesta family asteroids. (b) all V-type asteroids. Asteroid 4 Vesta has been excluded through Ar–Ar radiometric dating of eucrites (Bogard & from this figure. The dashed curve represents the best-fit Garrison 2003). In summary, the timescale for formation Maxwellian distribution. of the Vesta family and ejecta from Vesta, if YORP effects are invoked to explain their rotational rate distribution, is tators as well as for low amplitude ones are more difficult consistent with dating of HED meteorites, numerical sim- than for asteroids with more ordinary periods between 4 ulations of the Vesta family, and crater counting of Vesta and 24 hours. Fast rotators with more than 7 rev/day by the Dawn mission. close to the spin rate barrier that is at f about 10 rev/day tend to have spheroidal shapes and thus lower lightcurve 5. Conclusions amplitudes. Therefore, there become fewer data of these asteroids than real distribution. Taking into account ob- We have determined the rotational rate of a num- servational bias, the real distributions of V-type Vesta ber of V-type asteroids in the inner main belt: (1933) family asteroids and V-type asteroids in the inner main Tinchen, (2011) Veteraniya, (2508) Alupka, (3657) belt are more different from Maxwellian distribution. Ermolova, (3900) Knezevic, (4005) Dyagilev, (4383) Slivan et al. (2008) showed that the distribution of Suruga, (4434) Nikulin, (4796) Lewis, (6331) 1992 FZ1, rotation rates of the Koronis family is non-Maxwellian. (8645) 1998 TN, (10285) Renemichelsen, and (10320) Vokrouhlickýet al. (2003) suggested that the rotation Reiland. Lightcurves in the R-band of rotation periods rates and obliquities of the spin vector for the Koronis were found for Tinchen, Veteraniya, Alupka, Ermolova, family have been influenced by YORP effects for sev- Knezevic, Dyagilev, Suruga, Lewis, 1992 FZ1, 1998 TN, eral billion years. The timescale of YORP effects for the and Reiland. A compilation of rotational rates of 59 V- Koronis family is consistent with the age of the Koronis type asteroids in the inner main belt shows that the ro- family as estimated by numerical simulations (Marzari et tation rate distribution is non-Maxwellian, which may be al. 1999), crater counting of the Koronis family aster- explained by the long-term effect of YORP torques. No. ] Lightcurve Survey of V-type Asteroids 11

We would like to express our gratitude to staff mem- Han, X. L. 2013, Minor Planet Bul., 40, 99 bers of Kiso Observatory, Misato Observatory, and UH88 Hasegawa, S., Miyasaka S., & Mito, H. 2004, in Proc. for their support during lightcurve observations. We are 37th ISAS Lunar Planet. Symp., ed. H. Mizutani & M. grateful to Richard Binzel and Julian Oey for sharing Kato (Sagamihara: Institute of Space and Astronautical with us valuable information about V-type asteroids. This Science), 259 work was partially supported by the Japan Society for the Hasegawa, S., et al. in International Science Symposium on Sample Returns from Solar System Minor Bodies ∼ The Promotion of Science under a Grant-in-Aid for Scientific 1st HAYABUSA Symposium, ed. H. Yano, A. Fujiwara, Research (B) 17340133. This study was partially sup- D. Yeomans, & M. Zolensky, (ASP Conference series), in ported by the Space Plasma Laboratory, ISAS, and JAXA press5 as a collaborative research program. 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Table 1. Observational conditions.∗

NUM NAME Type Date Duration Rh ∆ α Telescope Band [hr] [AU] [AU] [◦] 1933 Tinchen V 2005.3.7 6.3 2.611 1.632 4.7 1.05 m - Kiso R 1933 Tinchen V 2005.3.8 4.9 2.611 1.63 4.2 1.05 m - Kiso R 1933 Tinchen V 2005.3.12 4.2 2.613 1.623 2.4 0.36 m - Miyasaka R 1933 Tinchen V 2005.3.13 6.4 2.614 1.622 2.0 0.36 m - Miyasaka R 477 Italia S 2005.3.7 6.3 2.824 1.846 4.3 1.05 m - Kiso R 477 Italia S 2005.3.8 4.9 2.823 1.842 4.0 1.05 m - Kiso R 477 Italia S 2005.3.12 4.2 2.820 1.830 2.2 0.36 m - Miyasaka R 477 Italia S 2005.3.13 6.4 2.819 1.827 1.8 0.36 m - Miyasaka R 2011 Veteraniya V 2004.11.12 3.6 2.563 2.213 22.4 1.05 m - Kiso R 2011 Veteraniya V 2005.1.8 8.6 2.633 1.694 7.9 0.36 m - Miyasaka R 2011 Veteraniya V 2005.1.9 9.1 2.634 1.691 7.5 0.36 m - Miyasaka R 18590 1997 YO10 S 2004.11.12 3.6 2.566 2.213 22.4 1.05 m - Kiso R 22034 1999 XL168 2004.11.12 3.6 2.589 2.237 22.2 1.05 m - Kiso R 2508 Alupka V 2004.11.12 8.7 2.461 1.531 10.1 1.05 m - Kiso R 2508 Alupka V 2004.11.13 4.1 2.462 1.528 9.7 1.05 m - Kiso R 2508 Alupka V 2004.11.15 8.2 2.464 1.521 8.8 1.05 m - Kiso R 3657 Ermolova V 2005.5.5 0.5 2.538 1.716 16.1 1.05 m - Kiso R 3657 Ermolova V 2005.5.9 1.6 2.534 1.749 17.3 1.05 m - Kiso R 3657 Ermolova V 2005.5.14 2.0 2.529 1.794 18.7 1.05 m - Kiso R 3900 Knezevic V 2005.1.16 2.1 2.342 1.386 7.3 1.05 m - Kiso R 3900 Knezevic V 2005.1.17 2.5 2.344 1.384 6.8 1.05 m - Kiso R 3900 Knezevic V 2005.1.18 1.1 2.346 1.382 6.3 1.05 m - Kiso R 3900 Knezevic V 2005.2.4 7.5 2.372 1.393 3.8 0.36 m - Miyasaka R 29976 1999 NE6 D 2005.1.16 2.1 5.114 4.169 3.4 1.05 m - Kiso R 29976 1999 NE6 D 2005.1.17 2.5 5.114 4.164 3.2 1.05 m - Kiso R 46121 2001 FB36 C 2005.1.16 2.1 2.891 1.940 6.0 1.05 m - Kiso R 46121 2001 FB36 C 2005.1.17 2.5 2.891 1.935 5.6 1.05 m - Kiso R 4005 Dyagilev V 2005.3.7 6.7 2.801 1.832 5.5 1.05 m - Kiso R 4005 Dyagilev V 2005.3.8 3.3 2.800 1.829 5.2 1.05 m - Kiso R 4005 Dyagilev V 2005.3.13 3.3 2.798 1.817 4.0 0.36 m - Miyasaka R 4383 Suruga V 2004.12.17 3.2 2.281 1.382 13 1.05 m - Misato R 4383 Suruga V 2004.12.20 2.1 2.282 1.401 14.1 2.24 m - UH88 R 4434 Nikulin V 2004.10.15 6.2 2.119 1.127 4.0 0.36 m - Miyasaka R 4434 Nikulin V 2004.10.16 7.7 2.119 1.127 3.6 0.36 m - Miyasaka R 4434 Nikulin V 2004.10.17 7.7 2.119 1.127 3.4 0.36 m - Miyasaka R 89481 2001 XH27 X 2004.10.16 7.7 1.826 0.834 4.4 0.36 m - Miyasaka R 89481 2001 XH27 X 2004.10.17 7.7 1.826 0.833 4.0 0.36 m - Miyasaka R 4796 Lewis V 2004.9.15 1.9 1.983 1.033 13.3 1.05 m - Misato R 4796 Lewis V 2004.10.1 2.6 2.003 1.008 4.4 0.36 m - Miyasaka R 4796 Lewis V 2004.10.14 3.9 2.021 1.030 4.5 0.30 m - Kiso R 4796 Lewis V 2004.10.15 1.4 2.022 1.033 5.0 0.30 m - Kiso R 6331 1992 FZ1 V 2004.10.15 3.5 2.171 1.191 6.6 0.30 m - Kiso R 6331 1992 FZ1 V 2004.10.16 1.4 2.172 1.194 6.8 0.50 m - Okayama R 6331 1992 FZ1 V 2004.10.17 5.7 2.173 1.197 7.1 0.50 m - Okayama R 6331 1992 FZ1 V 2004.11.6 1.7 2.200 1.309 14.7 0.36 m - Miyasaka R 8645 1988 TN V 2005.2.4 3.4 2.471 1.491 3.5 1.05 m - Kiso R 8645 1988 TN V 2005.2.5 7.4 2.471 1.491 3.2 0.36 m - Miyasaka R 8645 1988 TN V 2005.2.11 7.0 2.475 1.493 3.1 0.36 m - Miyasaka R 11321 Tosimatsumoto XL 2005.2.4 2.0 3.255 2.277 2.6 1.05 m - Kiso R 11321 Tosimatsumoto XL 2005.2.5 7.4 3.255 2.276 2.4 0.36 m - Miyasaka R 10285 Renemichelsen V 2004.11.12 2.8 2.374 1.449 10.9 1.05 m - Kiso R 10285 Renemichelsen V 2004.11.13 5.9 2.376 1.455 11.2 1.05 m - Kiso R 10285 Renemichelsen V 2004.11.15 8.1 2.378 1.470 12.0 1.05 m - Kiso R 10320 Reiland V 2004.11.12 8.8 2.310 1.328 3.9 1.05 m - Kiso R 10320 Reiland V 2004.11.13 5.1 2.312 1.329 3.7 1.05 m - Kiso R 14 S. Hasegawa et al. [Vol. ,

Table 1. (Continued.)

NUM NAME Type Date Duration Rh ∆ α Telescope Band 10320 Reiland V 2004.11.15 8.3 2.315 1.331 3.6 1.05 m - Kiso R 10389 Robmanning 2004.11.15 8.3 1.950 0.966 4.1 1.05 m - Kiso R 10443 van de Pol S 2004.11.15 8.3 2.028 1.045 4.2 1.05 m - Kiso R 41051 1999 VR10 2004.11.15 8.3 2.665 1.684 3.2 1.05 m - Kiso R ∗ The heliocentric distance (Rh), geocentric distance (∆), and phase angle (α) for observing asteroids were obtained through the JPL HORIZON ephemeris generator system of NASA1. No. ] Lightcurve Survey of V-type Asteroids 15

Table 2. Rotational properties and orbital elements for V-type asteroids in the inner main belt. NUM NAME Spin rate Da∗ a e i Spectrum Vesta Lightcurve [rev/day] [km] [AU] [◦] refference† family literature 809 Lundia 1.56 10.26WS 2.2829 0.1925 7.14 S3,D4 Kryszczyńska et al. (2009) 854 Frostia 0.64 9.49AF 2.3682 0.1740 6.09 AC Behrend et al. (2004) 956 Elisa 6.17 10.47WS 2.2982 0.2038 5.96 S3,D4 Behrend, R. website2 1273 Helma 3.94 10.39WS 2.3935 0.1622 5.42 SM1 1 Higgins & Goncalves (2007) 1906 Naef 2.18 8.06WS 2.3732 0.1351 6.47 SM1 1 Durkee&Pravec (2007) 1929 Kollaa 8.03 7.77WS 2.3630 0.0746 7.78 SM1 1 Behrend, R. website2 1933 Tinchen 6.54 6.45WS 2.3527 0.1229 6.88 SM1 1 This work 1946 Walraven 2.35 9.21WS 2.2934 0.2352 8.17 AC VanGent (1993) 2011 Veteraniya 2.92 5.19WS 2.3863 0.1502 6.20 SM1 1 This work 2113 Ehrdni 1.82 5.20KA 2.4730 0.0970 6.44 SM1 Binzel (1987) 2442 Corbett 2.40 8.33W3 2.3874 0.1182 5.09 SM1 Behrend, R. website2 2486 Metsahovi 5.39 8.42WS 2.2687 0.0797 8.41 AC Pikler et al. (2007) 2508 Alupka 1.36 5.17WS 2.3682 0.1276 6.08 SM2 1 This work 2511 Patterson 5.79 7.85WS 2.2985 0.1039 8.05 SM2 1 Hasegawa et al. (in press) 2579 Spartacus 6.60 4.60WS 2.2104 0.0753 5.78 SM2 Warner, B.D. website3 2590 Mourao 1.54 7.88W4 2.3431 0.1173 6.12 SM1 1 Galád et al. (2005) 2640 Hallstrom 1.05 5.70KA 2.3981 0.0883 6.65 SM2,RG Hasegawa et al. (in press) 2653 Principia 4.35 9.88W3 2.4444 0.0800 4.74 SM2 Hasegawa et al. (in press) 2763 Jeans 3.08 7.52WS 2.4049 0.2174 3.54 SM2,D4 Stephens (2013) 2768 Gorky 5.33 10.79WS 2.2347 0.1713 6.28 AC Pray et al. (2008) 2795 Lepage 0.40 6.14W3 2.2955 0.0283 6.03 SM2 Hasegawa et al. (in press) 2851 Harbin 4.43 8.84W3 2.4791 0.1229 8.55 SM2,D4 Albers et al. (2010) 2912 Lapalma 4.20 6.52W3 2.2896 0.0707 7.28 SM2 Brinsfield (2008) 3155 Lee 2.89 6.85WS 2.3425 0.1011 7.20 SM1,SM2,D4 1 Warner (2003) 3268 De Sanctis 1.41 6.03WS 2.3472 0.1264 6.35 SM1,D4 1 Wisniewski (1991) 3307 Athabasca 4.90 3.63W3 2.2593 0.0955 6.37 SM2 1 Hasegawa et al. (in press) 3376 Armandhammer 3.03 8.17WS 2.3487 0.0661 6.35 SM2 1 Pravec, P. et al. website4 3536 Schleicher 4.15 3.64WS 2.3431 0.0492 6.56 SM2 Binzel et al. (1992) 3657 Ermolova 9.30 5.80AF 2.3124 0.1324 5.79 SM1 1 This work 3703 Volkonskaya 7.42 3.73WS 2.3319 0.1340 6.74 BP 1 Ryan et al. (2004a) 3782 Celle 6.25 5.92WS 2.4148 0.0943 5.25 SM2,RG 1 Ryan et al. (2004b) 3850 Peltier 9.88 3.77KA 2.2343 0.1621 5.27 SM2 Oey et al. (2007) 3900 Knezevic 4.51 4.96WS 2.3707 0.1376 6.73 SM2 1 This work 3968 Koptelov 1.15 5.97KA 2.3212 0.0923 6.21 SM1 1 Behrend, R. website2 4005 Dyagilev 3.75 8.36WS 2.4511 0.1497 6.84 SM1 This work 4147 Lennon 0.18 5.17WS 2.3617 0.0802 5.74 SM1 1 Hasegawa et al. (in press) 4215 Kamo 1.91 6.55W3 2.4175 0.0619 5.75 SM2 1 Wetterer et al. (1999) 4383 Suruga 6.30 6.47WS 2.4244 0.0630 7.15 RG This work 4796 Lewis 6.84 5.20KA 2.3553 0.1803 2.27 SM2,D4 This work 4977 Rauthgundis 0.39 3.86WS 2.2924 0.1113 5.88 SM2 Hasegawa et al. (in press) 5111 Jacliff 8.45 6.69WS 2.3542 0.1266 5.81 RG 1 Behrend, R. website2 5240 Kwasan 4.49 7.27WS 2.3831 0.1004 5.61 SM2 1 Ivanova et al. (2002) 5481 Kiuchi 6.63 5.70KA 2.3400 0.0625 5.96 S3,RG 1 Ku˘snirák et al. (2008) 5524 Lecacheux 2.85 19.9W3 2.3662 0.0284 7.49 CA Pravec, P. et al. website4 5560 Amytis 3.11 4.70WS 2.2856 0.1084 5.62 RG Hawkins & Ditteon (2008) WS 5599 1991 SG1 6.63 7.17 2.4195 0.1337 6.46 RG Willis (2004) WS 2 5754 1992 FR2 2.70 5.70 2.2676 0.1416 5.54 CA Behrend, R. website 5875 Kuga 4.32 7.47WS 2.3792 0.0492 6.47 CA Carbo et al. (2009) 6159 1991 YH 2.26 5.34WS 2.2916 0.0618 6.86 D4 1 Warner (2006) WS 6331 1992 FZ1 2.57 5.32 2.3585 0.1338 7.76 D4 1 This work 6406 1992 MJ 3.52 4.06W3 2.2758 0.1774 8.17 AC Higgins & Goncalves (2007) 6877 Giada 5.75 4.66WS 2.3231 0.1344 6.18 RG 1 Behrend, R. website2 6976 Kanatsu 5.96 5.50WS 2.3334 0.1694 8.25 CA Carbo et al. (2009) 16 S. Hasegawa et al. [Vol. ,

Table 2. (Continued.) NUM NAME rate Da a [AU] e i [◦] spectrum family literature 8645 1988 TN 3.15 5.08WS 2.4311 0.0608 5.28 RG This work 10320 Reiland 4.05 2.86WS 2.2881 0.1340 6.34 D4 1 This work 17035 Velichko 8.28 4.76WS 2.4440 0.1463 6.24 RG 1 Behrend, R. website2 19979 1989 VJ 3.17 6.85KA 2.4588 0.1023 5.17 RG 1 Han et al. (2013) 35062 Sakuranosyou 1.26 3.21WS 2.3695 0.2388 10.51 CA Pravec, P. et al. website4 45073 Doyanrose 7.59 2.73KA 2.3336 0.1479 6.91 CA 1 Ruthroff (2011) ∗ References for diameter. AFUsui et al. (2011); WSMasiero et al. (2011); W3Masiero et al. (2012); KAassuming albedo is the same as the median value of V-type asteroids (pv = 0.343; Mainzer et al. 2012). † References for spectral type. AC: Alvarez-Candal et al. (2006); BP: Binzel, R.P. private comm. CA: Carvano et al. (2010); D4: Duffard et al. (2004); D6: Duffard et al. (2006); RG: Roig & Gil-Hutton (2006); SM1: Xu et al. (1995); SM2: Bus & Binzel (2002); S3: Lazzaro et al. (2004).