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A&A
Volume 643, November 2020
Article Number A117
Number of page(s) 26
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/202038062
Published online 10 November 2020

© ESO 2020

1 Introduction

Basaltic V-type asteroids and their fragments, howardite-eucrite-diogenite (HED) meteorites, have been studied for about half a century. They provide important clues to the differentiation process, constrain the spatial mineralogical distribution and temperature gradient of the early Solar nebula, and even reveal some of the dynamical processes in the Solar System.

Asteroid (4) Vesta was the first object to be identified as basaltic (McCord et al. 1970; Consolmagno & Drake 1977). A number of spectroscopically similar asteroids in the vicinity of (4) Vesta, some of which were not Vesta family members, were later identified (Binzel & Xu 1993; Florczak et al. 2002; Lazzaro et al. 2004; Alvarez-Candal et al. 2006; Burbine et al. 2001). Numerical studies showed that those outside the Vesta family borders might have escaped through a combination of the Yarkovsky effect and dynamical resonances (Carruba et al. 2005; Nesvorný et al. 2008). Furthermore, two large collisional events are believed to have produced Vestoids (Milani et al. 2014; Spoto et al. 2015); two large craters found on the surface of Vesta are thought to be evidence of this (Thomas et al. 1997; Schenk et al. 2012).The surface of these craters was mapped by the Dawn mission (Roatsch et al. 2012) and provided further mineralogical evidence of the Vesta–V-type asteroid–HED meteorite link (De Sanctis et al. 2013, 2012; Russell et al. 2012; McSween et al. 2013).

Some V-type asteroids are well separated from Vesta and are thus considered non-Vestoids (Lazzaro et al. 2000; Roig et al. 2008; Moskovitz et al. 2008a; Duffard & Roig 2009; Ieva et al. 2015, 2018; Migliorini et al. 2017). These asteroids show spectral properties distinct from Vestoids (Hardersen et al. 2004a; Hammergren et al. 2006; Leith et al. 2017; Ieva et al. 2015, 2018; Medeiros et al. 2019) and have a low probability (~1%) of having evolved from Vesta (Roig et al. 2008; Carruba et al. 2007; Michtchenko et al. 2002). Carruba et al. (2014) indicated two possiblesource regions for V-types in the middle main belt, and Huaman et al. (2014) three of these in the outer main belt.

There issome debate about the presence of non-Vestoids in the inner main belt (Bottke et al. 2006a; Nesvorný et al. 2008; Scott et al. 2009; Roig et al. 2008; Moskovitz et al. 2010; Wasson 2013). Particularly, the low inclination (i ≤ 6°) V-types in the inner main belt were not sufficiently reproduced in numerical simulations by Nesvorný et al. (2008) and may originate in either a distinct parent body or from an older impact on Vesta. Furthermore, some V-types in the inner main belt have rotational properties inconsistent with migration from Vesta (Oszkiewicz et al. 2015, 2017).

This complex population is spread over the entire main belt. The V-type population is predominantly composed of small objects (< 10 km in diameter), well within the range in which the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect is expected to be significant. Distribution of rotational frequencies of the V-type asteroids has been so far poorly understood due to the limited number of objects studied (i.e., Hasegawa et al. 2014 examined the frequency distribution of 59 V-type asteroids). However, due to large surveys such as the SDSS and HST-VISTA, a large number of putative V-types can now be added to the spectrally known V-types and Vesta family members resulting in a large enough sample (>500 objects) for a statistical YORP analysis.

The YORP effect (Bottke et al. 2006b) modifies the Maxwellian rotational-frequency distribution expected from a purely collisionally evolved population (Salo 1987). This effect spins up or down irregularly shaped asteroids (Rubincam 2000) creating an excess of slow and fast rotators, thereby diluting the rotation spin distributions from Maxwellian. Large asteroids (> 40 km in diameter)could retain primordial spins, whereas smaller objects are more affected by the YORP effect (Pravec et al. 2002). An excess of fast to slow rotators has been previously observed for the Flora, Hungaria, and Koronis families (Warner et al. 2009a; Kryszczyńska et al. 2012; Slivan et al. 2003, 2009) and generally for the population of small main belt (MBA) and Mars-crossing asteroids (Pravec et al. 2008). Direct detections of the YORP effect spinning up objects have been made for few asteroids so far (Lowry et al. 2007; Ďurech et al. 2008; Kaasalainen & Durech 2007; Taylor et al. 2007).

The YORP effect may also spin up objects over the spin barrier causing their disintegration and/or the formation of binary asteroids (Walsh et al. 2008). The spin barrier has been estimated at P about 2.2 h (or equivalently rotational frequency ω of around 10 d−1) for the general population of small (10 km > D > 150 m) asteroids (Harris 1996). Rubble-pile asteroids with a lower bulk density are expected to have a lower spin rate limit (Pravec & Harris 2000), thus the overall spin rate of C-type asteroids should be lower than that of the V- and S-type objects. Chang et al. (2015) estimated the critical density for S- and V-type asteroids independently as ρ = 2.0 g cm−3, and for C-type objects as ρ = 1.5 g cm−3. In that workit was also suggested that there is a need to confirm the results after supplementing the sample of objects. We are now dealing with a statistically larger sample because we supported the calculations with a significant number of new observations and putative V-types, described in the next section.

In Sect. 2, we describe the spectroscopic and photometric observations and the data reduction process. In Sect. 3, we taxonomically classify the observed asteroids and verify the high confirmation rate of putative V-types. New rotational periods are determined in Sect. 3. In Sect. 4, we perform statistical spin rate analysis for various V-type populations. The summary of our results is presented in Sect. 5.

2 Observations

2.1 Spectroscopic observations and data reduction

We obtained visible (VIS) spectra of 17 V-type and V-type candidate asteroids at three telescopes. The V-type candidates were selected out of putative V-types listed in the literature (Roig & Gil-Hutton 2006; Carvano et al. 2010; Hasselmann et al. 2012; Licandro et al. 2017; Moskovitz et al. 2008b). Most of the data were taken at the 2.5 m Nordic Optical Telescope (NOT), spectra of two asteroids were obtained at the 10 m South African Large Telescope (SALT) and the 4.3 m Lowell Discovery Telescope (LDT). The observing circumstances and optical elements used are summarized in Table A.1.

At the NOT we used the Alhambra Faint Object Spectrograph and Camera (ALFOSC) combined with grism NOT-11 or grism NOT-12 depending on the night. Both grisms are low resolution. Grism 11 covers wavelengths 3900–10 000 Å; however, fringes are noticeable starting from around 7500 Å. Grism 12 covers wavelengths 5100–11 000 Å, with fringes starting also around 7500 Å. It should be noted that grism 12 has deteriorated, and thus higher order Legendre polynomials had to be used to extract the spectra, and lamp identification was challenging. For this reason we repeated observations of some of the targeted asteroids with grism 11. For most objects we found that grism 12 is still usable; however, the reduction process was cumbersome and problematic, and the results questionable for some objects. Thus, we would recommend the decommissioning of grism 12. In Table A.1 we list the observed targets, telescope, and setup used. Slit widths are adjusted to seeing. We used non-sidereal tracking together with a five-point dither to obtain several spectra. The spectra were corrected for flat and bias. Wavelength calibration was done using He, Ne, and ThAr lamps. The collected spectra were averaged and divided by solar analog and normalized at 0.55 microns.

At the SALT we used the Robert Stobie Spectrograph (RSS) together with the low resolution grism PG0300 covering wavelengths 3700–9000 Å. Our reduction procedure followed that described in Oszkiewicz et al. (2014).

2.2 Photometric observations and data reduction

Photometric observations were conducted using several telescopes listed in Table 1. Most of the data were taken with a Cousins RC filter, but some with Johnson V, wide-band VR, or a clear filter. The VR filter used at the Hall telescope at Lowell Observatory has a passband similar to Sloan r′. The half maximum wavelengths are close to 5200 and 7000 Å, compared to the Sloan r′ limits of about 5600 and 6950 Å. Thus, it is only slightly wider on the blue side of the nominal r′ passband. The L filter used at the RBT telescope at Winer Observatory is an interferometric luminosity filter with a transmission window from 3700 to 7000 Å. Altogether we obtained data on 213 nights, mostly at Modra Observatory and Lowell Observatory. We performed standard photometric reduction with bias and flat-field correction followed by ordinary aperture photometry. We used the commercial software Canopus (version 10.7.12.7) for data from the Lowell Observatory, Mauna Kea Observatories, and Odessa-Mayaki Observatory, making use of its built-in photometric catalog and Gaia DR2 catalog to obtain approximate RC or Sloan r′ nightly zero points. At Modra Observatory a clear filter was used, and for the data processing MaxIm DL and their own software. Linkages to nearly the same magnitude level (within 0.05 mag) were done using the Carlsberg Meridian Catalogue stars with the help of Astrometrica (method described in Dymock & Miles 2009). This resulted in magnitudes close to the Cousins R filter. We also used the Starlink package (version NAMAKA) for data from the Roque de los Muchachos Observatory, Kitt Peak Observatory, and Winer Observatory. We generally used three (in Starlink) to five (in Canopus) comparison stars in each field, usually of much higher signal-to-noise ratio than the target, and selected to have near-asteroidal colors if possible (i.e., roughly 0.5 <B − V < 0.95 or 0.35 < g − r < 0.85). For asteroids near their stationary points, we could use the same comparison star sets on multiple nights. The measuring apertures were generally 8–12 arcsec in diameter, depending on the image quality. Thetypical mean nightly root mean square scatter of the ensemble of comparison stars was 0.006–0.01 mag.

Table 1

Telescopes and instruments used for the photometric observations.

3 Results

3.1 Spectral classification

We report spectra of 17 asteroids, for 11 of which optical spectra were obtained for the first time. Out of these 7 asteroids had not been observed at either near-infrared (NIR) or visible and infrared (VIR) wavelengths previously, thus those constitute new classifications. Asteroids (1914) Hartbeespoortdam, (2704) Julian Loewe, (4434) Nikulin, (5037) Habing, 5525 (1991 TS4), and (7558) Yurlov were observed for comparison with the literature (Alvarez-Candal et al. 2006; Spahr et al. 1997; Burbine & Binzel 2002; Bus & Binzel 2002; Solontoi et al. 2012; Wisniewski 1991; Moskovitz et al. 2008b). In Fig. 1, we present all the obtained optical spectra, and in Fig. 2, the spectra concatenated with available NIR spectra from the literature. The obtained spectra closely match those reported in the literature.

We classified the observed spectra using the M4AST online tool and the standard error method of Popescu et al. (2012). In Table 2 we report two closest classes for each spectrum, along with the distance to the class templates and reliability asdefined by Popescu et al. (2012, 2011). Reliability is a function of wavelength range covered and number of discrete data points used in the classification. The mathematical formulation of this parameter can be found in Popescu et al. (2012, 2011). Most of our targets (with the exception of 3302 Schliemann and 9652 1996 AF2) are consistent with the V- or R-type templates (DeMeo et al. 2009). The computed distance between the data and the V- and R- templates is very similar. This is due to the fact that the two classes are very similar in VIS wavelengths and differ more in the NIR wavelengths. Since R-types are very rare we consider the 15 observed objects V-types. This results in an 88% rate of success for confirmation on V-types.

High confirmation rates were also found by other authors i.e., 90% in Moskovitz et al. (2008b) or 78% in Solontoi et al. (2012). This very high confirmation rate leads us to assume that most of the asteroids that have their SDSS colors consistent with the V-type template are indeed V-types, and thus may be used in further analysis.

In Table3 we derived the reflectivity gradient in the 5000–7500 Å and 8000–9200 Å range (slope A and slope B, respectively) and 1.0 μm band depth (as in Ieva et al. 2015) for the observed asteroids. As noted by Ieva et al. (2015) a steeper slope A could be indicative ofweathered surfaces (Fulvio et al. 2012, 2016), while a deeper apparent depth could be indicative of bigger grain size or fresh unweathered pyroxene (Hiroi et al. 1995; Cloutis et al. 2013). The derived parameters are consistent with typical Vestoidal values. We do not list parameters for objects observed with grism 12 because the mechanical damage of the grism the wavelength calibration required fitting a high order polynomial and may be imprecise. Some spectra covered the 1.0 μm band well, which allowed us to determine band minima (BI) by fitting a third-degree polynomial. The resulting values are listed in Table 3.

For asteroid 8645 we obtained both VIS and NIR spectra for the first time. For asteroids (5235) Jean-Loup and (5560) Amytis the obtained spectra are complementary to the NIR data in the literature. The minima of the 1.0 μm band that we obtained are consistent, within the uncertainties, with those derived by Hardersen et al. (2014b) based on NIR spectra. We note that the variability of methods used for band characterization between different authors does not allow a direct comparison of the spectral parameters. For example, Moskovitz et al. (2010) used polynomial fits and continuum removal for the 1.0 μm band, but not for the 2.0 μm band; Leith et al. (2017) used a modified Gaussian model (Sunshine et al. 1990); and Birlan et al. (2016) followed the method of Cloutis et al. (1986), which uses polynomial fitting in selected regions for finding band minima and removing of double sloped linear continuum for the band centers.

thumbnail Fig. 1

Visible spectra obtained in this project. Spectral templates are denoted as follows: V (orange stars), R (green diamonds), Sr (red pentagons), Sv (blue triangles).
thumbnail Fig. 1

continued.

3.2 Rotational periods outside the Vesta family asteroids

We determined new rotational periods for 18 V-type asteroids outside the dynamical Vesta family. We list them in Table 4 along with diameters, geometric albedos, and the observed light curve amplitudes. For asteroids with unknown albedo we list the average value for the Vesta family of pv = 0.361 ± 0.111 (Masiero et al. 2013). A similar value is given by Thomas et al. (2011) for main belt V-types. Usui et al. (2012) gives lower average value of pv= 0.297 ± 0.131, but this estimate is based on only four objects.

Composite light curves for these objects are shown in Fig. A.1. The combined distribution of rotational properties of V-types in the inner main belt is derived in Sect. 4. All composite light curves were obtained using Fourier analysis, as in Kwiatkowski et al. (2010). For most of the observed asteroids the rotation periods were computed based on data spanning long time intervals, resulting in a synodic period averaged over that interval. Corresponding uncertainties are thus small and do not fully reflect the changes in synodic period. Therefore, we round the computed uncertainties to the first significant digit and provide the determined synodic periods to the same accuracy.

Asteroids (2247) Hiroshima, (2823) van der Laan, (5235) Jean-Loup, 7558 Yurlov, (8761) Crane, (9481) Menchu, and (9531) Jean-Luc are spectroscopically confirmed V-types (Wisniewski 1991; Moskovitz et al. 2008b, 2010; Sanctis et al. 2011; Solontoi et al. 2012; Hicks et al. 2014; Hardersen et al. 2014b, 2018). For (3331) Kvistaberg and (6819) McGarvey, we confirmed their V-type classification. Objects (7798) 1996 CL, (22113) 2000 RH9, and (27192) Senegali are putative V-types (Roig & Gil-Hutton 2006; Carvano et al. 2010; Hasselmann et al. 2012; Licandro et al. 2017). Asteroid (5037) Habing was indicated by Carvano et al. (2010) and Hasselmann et al. (2012) as a QVp type. In our work and that of Solontoi et al. (2012), its spectrum shows a deep 0.9 μm absorption band, typical of V-types.

thumbnail Fig. 2

Spectra obtained in this project for asteroids having both VIS and NIR spectra (NIR data obtained by us or from the literature). The orange line with stars represents the V-type template from DeMeo et al. (2009).
Table 2

Taxonomic classification using the standard error method.

Table 3

Spectral parameters: Slope A, Slope B, and apparent depth, as in Ieva et al. (2015), and without phase correction, center of the 1.0 μm (BI) band.

4 Statistical analysis of rotational periods of V-type and V-type candidate asteroids

We supplement the rotational periods estimated in Sect. 3 with those known from the literature for spectroscopically confirmed V-types (V), V-type candidates (Vc), and dynamical Vesta family members (assumed to be V-types) to perform statistical analysis. Since the V-type candidates have high confirmation rates, as shown in Sect. 3, we consider this to be a reasonable approach that does not skew our statistics substantially.

Our sample contains 536 asteroids (Tables A.2–A.7), including 428 Vesta family members (Nesvornỳ 2015), and 108 outside the Vesta family. In total, there are 155 spectroscopically confirmed V-types and 131 V-type candidates. The remaining objects are dynamical Vesta family members assumed to be V-types (Moskovitz et al. 2008b estimate that ~20% of the Vesta familyare interlopers). We list them in Tables A.2–A.7 together with their synodic period, diameter, proper (or osculating for near-Earth asteroids, hereafter NEAs) orbital elements, and classification. Around 15% of NEAs are considered binary (Pravec et al. 1999; Pravec & Harris 2007; Bottke & Melosh 1996). A similar fraction is expected among small MBAs (d < 10 km). Since most V-types are smaller than 10 km in diameter, we expect around 15% binaries in our sample. However only 12 objects (3703, 3782, 5474, 5481, 18527 (Vesta family) 809, 2486, 5037, 32008 (Vesta fugitives) 854, 4383 (inner other group) 164121 (near-Earth)) are confirmed binaries. Thus, our sample may contain a larger number of undiscovered binaries.

Asteroids of known spectral type other than V-type were excluded from our analysis (e.g., those in the Vesta family were assumed to be interlopers). Spectral candidates are taken from Carvano et al. (2010), Hasselmann et al. (2012), Solontoi et al. (2012), Moskovitz et al. (2008b), and Licandro et al. (2017).

We subdivide our sample into several dynamically important groups, similarly to Ieva et al. (2018):

  • Vesta family: Vesta family members, as defined by Nesvornỳ (2015) using the hierarchical clustering method (having orbital elements within ranges 2.26 au < a < 2.48 au, 0.03 < e < 0.16, 5° < i < 8.3°). This sample contains 27 spectrally confirmed, 89 candidate, and 312 assumed V-types.

  • Vesta fugitives: asteroids that escaped the Vesta family borders and are no longer identifiable as Vesta family members using the traditional clustering methods. Following the definition of Nesvorný et al. (2008), a Vesta family fugitive is a V-type asteroid with a < 2.3 au and a comparable e and i to the Vesta family. This sample contains 19 confirmed and 16 putative V-types.

  • Low-i: Low inclination V-types with a comparable semi-major axis to the Vesta family and smaller inclinations (i < 6° and 2.3 au < a < 2.5 au, as defined by Nesvorný et al. 2008). There are 15 confirmed and 12 putative V-types in this group.

  • Inner Other (IO): the remaining V-type asteroids in the inner main belt were identified as IOs (a < 2.5 au). There are 10 confirmed and 12 putative V-types.

  • V-type NEAs: a V-type asteroid in the near-Earth region (with a perihelion q < 1.3 au). This sample contains 20 confirmed and 1 putative V-type.

  • Middle outer V-type (MOV): an asteroid located in the middle and outer main belt (2.5 au < a < 5.0 au). There is only one spectrally confirmed MOV.

This division reflects interesting regions that may show various YORP signatures.

Table 4

Asteroid synodic periods and amplitudes found within this project.

4.1 Signatures of the YORP effect

In Fig. A.1, we present the frequency distributions for the different subgroups. It should be noted that there are known observational biases working against small-amplitude and long-period asteroids (Marciniak et al. 2015, 2018) that are challenging to take into account. However, longer periods contribute to the low frequency bins amplifying the conclusions on YORP affecting the distribution. Small-amplitude objects may contribute to all bins. Rotations of the primaries of the binary systems were added into the frequency distributions. They mostly contribute to the fast-rotating bins and to the area near the spin barrier limit in Fig. 4, thus helping to constrain it.

The rotational frequency distribution for the Vesta family varies from that of the general inner main belt population (Lupishko et al. 2019). A significantly smaller excess of slow rotators and almost no fast rotators are observed for the Vesta family. The number of slowest rotating asteroids (ω ~ 0−1 d−1) in the general inner main belt population (Lupishko et al. 2019) is about the same as in the peak bin (ω ~ 4−5 d−1, which coincides with the rotation of (4) Vesta), whereas for the Vesta family we observe around ~50% fewer asteroids among the slowest rotators than in the peak bin. Fast rotators from the last three bins constitute around 30% of the peak bin in the general population and around 20% of the peak bin in the Vesta family. However, we note that the size distribution varies between objects in this study (0.7–10 km) and that of Lupishko et al. (2019) (3–15 km), and therefore differences are expected.

Similarly the frequency distribution for V-types outside the Vesta family varies from that of the general inner main belt population (Lupishko et al. 2019). Slow rotators constitute around 50% of the peak bin and fast rotators around 50% of the peak bin. Therefore, there is a smaller excess of slow rotators among V-types outside the Vesta family than in the general inner main belt population and larger excess of fast rotators.

The population of V-types outside the Vesta family (and its sub-populations: fugitives and low-i) shows a surplus of slow and fast rotating objects compared to a Maxwellian distribution. The fraction of fast rotators is also larger than that in the Vesta family. However, the fugitives and low-i constitute a small sample, thus valid conclusions can only be made for the collective population of V-types outside the Vesta family.

Interestingly, fewer fast rotators are observed in the Vesta family than in the population outside the family. This is likely due to the YORP effect spinning up small irregular asteroids, which are also more likely to migrate (via the Yarkovsky drift and resonances) outside the Vesta family, leaving more YORP-modification resistant objects (i.e., larger or more regularly shaped) in the core of the family. Farinella et al. (1998) showed that the Yarkovsky drift for basaltic objects is optimized for objects with diameters of ~10 km. The diameters of the V-types outside the Vesta family vary from less than 1 km to around 10 km, which is reasonably close in the range to theoptimal diameter. We show the histograms for NEAs and IO in Fig. 3. Due to the low number of known periods in these populations no compelling conclusions can be made.

To verify the influence of adding candidates to the samples, we plotted the distributions exclusively for spectrally confirmed V-types. Due to the small number of spectrally confirmed V-types in the Vesta family we cannot judge the influence of the candidates on the final sample. For asteroids outside the Vesta family we still have a substantial excess of fast rotators and a small excess of slow rotators, thus the conclusions remain unchanged.

thumbnail Fig. 3

Number vs. rotation frequency (in cycles per day) for different V-type populations. Rotation periods from LCDB (Warner et al. 2009b) and this work.

4.2 Spin barrier

In Fig. 4, we present the location of the spectroscopically confirmed and candidate V-type asteroids in the size–frequency space. The spectroscopically confirmed V-types offset to the left of the plot (toward smaller sizes) are NEAs. The visible lack of spectroscopically confirmed objects with intermediate sizes is likely due their low apparent brightness, making them difficult targets for spectroscopy. Generally, the rotational properties of our sample resemble those of the general asteroid population. This means that most V-types and V-type candidates have rotation periods that are greater than about 2.2 h, with the majority being between 2.4 and 21 h.

We determined the spin barrier in frequency–light curve amplitude space. Light curve amplitudes for each asteroid (with quality code U-code ≥ 2) were taken from the online service by Warner et al. (2009b) and this work. The frequency plot is shown in Fig. 5. The theoretical lines expected for various bulk densities according to Pravec & Harris (2000) are indicated. The critical period corresponds to the period of a body with an ideal balance of the acceleration of gravity at the surface with the centrifugal acceleration at the equator (Pravec & Harris 2000). The critical period depends on object elongation (and thus light curve amplitude) and density (both of which correlate with tensile strength). The derivation of the critical period can be found in Pravec & Harris (2000).

The critical bulk density, estimated as Pcritical=3π/Gρ≈3.3/​​ρ$P_{\textrm{critical}} = \sqrt{3\pi/G\rho} \approx 3.3/\!\!\sqrt{\rho}$, exceeds the 2.0 g cm−3 estimated by Chang et al. (2015); one object is located at around 2.52 g cm−3. For comparison, the bulk density of the HED meteorites is around 3.17 g cm−3 (McSween et al. 2011).

thumbnail Fig. 4

Size–frequency distribution for dynamical Vesta family, V-types, and V-type candidates asteroids (top) and the same for thediameter range between 0.5 and 10 km (bottom).
thumbnail Fig. 5

Observed light curve amplitude vs. spin rate of V-type asteroids. The dashed curves are approximate upper limits of spin rates of bodies held together by self-gravitation only, with bulk densities plausible for asteroids.

5 Summary

We confirmed the taxonomic type of 17 objects (11 observed spectroscopically in the visible wavelengths for the first time) outside the Vesta family. We found that their spectral parameters are well within Vestoidal values.

We found synodic periods for 18 asteroids. We supplemented them with rotation periods from the literature and determined the distribution of rotational frequencies for V-types in the Vesta family and those outside the family. This sort of juxtaposition is presented for the first time for V-types in the literature.

The V-types outside the Vesta family show a significant surplus of fast rotators compared to the Vesta family. These might be objects evolved from the Vesta family that are more susceptible to both YORP and Yarkovsky effect. Thus, the YORP timescale must be comparable to the migration timescale for those objects.

We show for the first time that the spin barrier for the V-type asteroids exceeds the critical density of 2.0 g cm-3.

Acknowledgements

This work has been supported by grant No. 2017/26/D/ ST9/00240 from the National Science Centre, Poland. The work at Modra was supported by the Slovak Grant Agency for Science VEGA, Grant 1/0911/17. Based on observations made with 1.83 m Perkins and 1.07 m Hall and 0.79 m telescopes at Lowell Observatory, 2.24 m University of Hawaii telescope at Mauna Kea Observatory, 1.0 m Jacobus Kapteyn Telescope and 2.5 Nordic Optical Telescope at the Roque de los Muchachos Observatory on La Palma, 4.3 m Lowell Discovery Telescope, 0.7 m Roman Baranowski telescope at Winer Observatory, 0.6 m Zeiss telescope at Modra Observatory, 0.8 m Odessa Multifunctional Telescope and 0.48 m AZT-3 telescope at Odessa-Mayaki Observatory. Some of the observations reported in this paper were obtained with the Southern African Large Telescope (SALT). Polish participation in SALT is funded by grant No. MNiSW DIR/WK/2016/07.

Appendix A Additional tables and figures

Table A.1

Observing setup and circumstances for VIS spectra.

Table A.2

Spectral V-types and V-type candidates (Vc) in the Vesta family population, their physical and orbital parameters.

Table A.3

As in Table A.2, but for the fugitive population.

Table A.4

As in Table A.2, but for the low inclination population.

Table A.5

As in Table A.2, but for the inner other population.

Table A.6

As in Table A.2, but for the NEA population.

Table A.7

As in Table A.2, but for the Middle/Outer Main Belt population.

thumbnail Fig. A.1

Composite light curves of the observed V-type asteroids (as in Table 4).
thumbnail Fig. A.1

continued.
thumbnail Fig. A.1

continued.

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All Tables

Table 1

Telescopes and instruments used for the photometric observations.

In the text
Table 2

Taxonomic classification using the standard error method.

In the text
Table 3

Spectral parameters: Slope A, Slope B, and apparent depth, as in Ieva et al. (2015), and without phase correction, center of the 1.0 μm (BI) band.

In the text
Table 4

Asteroid synodic periods and amplitudes found within this project.

In the text
Table A.1

Observing setup and circumstances for VIS spectra.

In the text
Table A.2

Spectral V-types and V-type candidates (Vc) in the Vesta family population, their physical and orbital parameters.

In the text
Table A.3

As in Table A.2, but for the fugitive population.

In the text
Table A.4

As in Table A.2, but for the low inclination population.

In the text
Table A.5

As in Table A.2, but for the inner other population.

In the text
Table A.6

As in Table A.2, but for the NEA population.

In the text
Table A.7

As in Table A.2, but for the Middle/Outer Main Belt population.

In the text

All Figures

thumbnail Fig. 1

Visible spectra obtained in this project. Spectral templates are denoted as follows: V (orange stars), R (green diamonds), Sr (red pentagons), Sv (blue triangles).
In the text
thumbnail Fig. 1

continued.
In the text
thumbnail Fig. 2

Spectra obtained in this project for asteroids having both VIS and NIR spectra (NIR data obtained by us or from the literature). The orange line with stars represents the V-type template from DeMeo et al. (2009).
In the text
thumbnail Fig. 3

Number vs. rotation frequency (in cycles per day) for different V-type populations. Rotation periods from LCDB (Warner et al. 2009b) and this work.
In the text
thumbnail Fig. 4

Size–frequency distribution for dynamical Vesta family, V-types, and V-type candidates asteroids (top) and the same for thediameter range between 0.5 and 10 km (bottom).
In the text
thumbnail Fig. 5

Observed light curve amplitude vs. spin rate of V-type asteroids. The dashed curves are approximate upper limits of spin rates of bodies held together by self-gravitation only, with bulk densities plausible for asteroids.
In the text
thumbnail Fig. A.1

Composite light curves of the observed V-type asteroids (as in Table 4).
In the text
thumbnail Fig. A.1

continued.
In the text
thumbnail Fig. A.1

continued.
In the text

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