Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/hoffmeister.ps Äàòà èçìåíåíèÿ: Mon Nov 4 13:15:13 1996 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 23:31:28 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 63

A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
10 (07.13.2; 07.19.2; 07.16.2: 1726 Hoffmeister)
ASTRONOMY
AND
ASTROPHYSICS
14.10.1996
The Hoffmeister asteroid family: Inferences from physical
data
F. Migliorini 1 , A. Manara 2 , M. Di Martino 3 , and P. Farinella 4
1 Dipartimento di Astronomia, Universit`a di Padova, vicolo dell'Osservatorio 5, I--35122 Padova, Italy
2 Osservatorio Astronomico di Brera, via Brera 28, I--20121 Milano, Italy
3 Osservatorio Astronomico di Torino, I--10025 Pino Torinese, Italy
4 Dipartimento di Matematica, Universit`a di Pisa, via Buonarroti 2, I--56127 Pisa, Italy
Received ...; accepted ...
Abstract. Asteroid (1726) Hoffmeister is the lowest--
numbered and probably the largest member of a small,
very compact dynamical family. Up to now, the only phys­
ical information available on this family consisted of the
comparatively low IRAS albedos of Hoffmeister and two
other family members. After discussing the properties of
the family, we report on our own observations of the opti­
cal reflectance spectrum of Hoffmeister, carried out with
the 1.54 m telescope of the Bologna Observatory and a
CCD spectrograph. The spectrum has been found to be
flat and featureless over the whole wavelength range be­
tween about 5200 and 9000 š A, resembling those of as­
teroids belonging to the C and F taxonomic types. This
result supports the hypothesis that the family was gen­
erated in the break--up of a carbon--rich parent asteroid
¸ 50 to 100 km in diameter, and that it is compositionally
distinct from (and genetically unrelated to) some neigh­
bouring groupings in proper element space.
Key words: asteroids -- spectroscopy -- (1726) Hoffmeis­
ter
1. Introduction
Asteroid families represent the outcomes of large--scale
collisions occurred in the main asteroid belt, which can be
recognized by looking for clusterings in the space of the so--
called proper orbital elements (Chapman et al. 1989, Mi­
lani et al. 1992, Zappal`a & Cellino 1994a). Although the
most populous families were discovered almost 80 years
ago by K. Hirayama, only in recent times a number of
small families --- where ``small'' refers both to the number
of member asteroids and to the size of the parent body ---
have been identified in a reliable way (Zappal`a et al. 1994,
Send offprint requests to: M. Di Martino
1995; Bendjoya 1993). Such small families are interesting
both because they can provide information on the prop­
erties and internal structure of their parent bodies, and
because their abundance and ages may set constraints on
the intensity of the collisional evolution process which has
shaped the asteroid population during the past 4:5 Byr.
In this paper, we discuss the properties of one such
small family, named after (1726) Hoffmeister. In particu­
lar, we show that the available physical data --- including
an optical spectrum of (1726) Hoffmeister obtained by us
--- are consistent with the conclusion that this family is
the outcome of the catastrophic break--up of a carbon--
rich parent asteroid, probably 50 to 100 km in diameter.
Also, the Hoffmeister family appears to be composition­
ally distinct from (hence genetically unrelated to) some
neighbouring groupings in proper orbital element space.
2. The Hoffmeister family
Asteroid (1726) Hoffmeister is the lowest--numbered and
(probably) largest member of a small, very compact fam­
ily. According to the most recent classification (Zappal`a et
al. 1995), the family includes 22 member asteroids, among
which only 8 have already been numbered. As shown in
Table I, the Hoffmeister family asteroids range in size be­
tween about 5 and 26 km. Given the average semimajor
axis and albedo of the family, the completeness diameter
(beyond which all the existing bodies are likely to have
already been discovered) has been estimated by Zappal`a
& Cellino (1994b) at 23:5 km, so that a significant number
of small family members are probably still to be found.
Table I also shows that the family has a comparatively
small spread in the three proper orbital elements, namely
ffi a 0 =a 0 ú ffi e 0 ú ffi (sin i 0 ) ú 10 \Gamma3 , corresponding to relative
speeds of only a few tens of m/s following the break--up of
the family's parent body. Since this is of the same order
as the escape velocity of the largest family members, it is
likely that self--gravitational reaccumulation processes oc­

2 F. Migliorini et al.: The Hoffmeister family
Table 1. Proper orbital elements and physical parameters of the Hoffmeister family members, taken from the data bases by
Milani et al. (1994) and Tedesco (1994)
Asteroid a 0 (AU) e 0 sin i 0 H p v D (km)
1726 2.78737 0.0469 0.0760 12.1 0.037 26.3
2930 2.78022 0.0463 0.0757 12.4 0.049 20.
2996 2.78237 0.0476 0.0757 11.8 0.069 22.1
4124 2.78659 0.0471 0.0760 12.6 0.041 19.7
4516 2.77771 0.0451 0.0804 12.4 0.049 20.
5091 2.78333 0.0472 0.0758 12.0 0.049 24.
5591 2.77997 0.0488 0.0759 12.1 0.049 23.
5866 2.78997 0.0471 0.0762 13.8 0.049 10.
1979 MA 7 2.78035 0.0440 0.0757 15.5 0.049 5.
1981 EZ 10 2.78449 0.0474 0.0758 13.8 0.049 10.
1984 SG 1 2.78164 0.0470 0.0762 12.7 0.049 17.
1988 RX 3 2.78769 0.0476 0.0765 15.2 0.049 5.
1989 BH 2.79243 0.0442 0.0740 14.0 0.049 9.
1990 RO 1 2.79055 0.0471 0.0749 13.0 0.049 15.
1990 SU 10 2.79006 0.0459 0.0767 12.5 0.049 19.
1992 HH 1 2.79105 0.0472 0.0765 14.0 0.049 9.
2281 T 1 2.78548 0.0527 0.0760 13.0 0.049 15.
2088 PL 2.78985 0.0464 0.0758 14.8 0.049 7.
2589 PL 2.78881 0.0467 0.0755 15.0 0.049 6.
2598 PL 2.79295 0.0451 0.0750 14.4 0.049 8.
6059 PL 2.78778 0.0435 0.0762 13.6 0.049 11.
9519 PL 2.76612 0.0513 0.0753 15.0 0.049 6.
curred after the initial ejection of the fragments (Zappal`a
et al. 1984). Also, it is easy to show that relative velocities
``at infinity'' much lower than the escape velocity of the
parent body are unlikely, and therefore the small spread of
the family in proper element space entails that the diame­
ter of the parent body was not much larger than the lower
bound of about 50 km, obtained by summing up the vol­
umes of all the known family members (assuming spherical
shapes). Thus, a reasonable guess is that the Hoffmeister
parent body was an asteroid in the 50 to 100 km diam­
eter range. Another consequence of the small volume of
the family in proper element space and of the very sparse
background of ``field asteroids'' in the neighbouring re­
gions (Migliorini et al. 1995) is that it is unlikely that the
family contains any chance interloper, and therefore all its
members should be genetically related to each other.
The only physical data available so far on this fam­
ily are the albedo values derived by IRAS for three num­
bered members, including (1726) Hoffmeister (Tedesco et
al. 1992). From albedos and H magnitudes, asteroid di­
ameters can be easily estimated. In Table 1, we give di­
ameter estimates for all the Hoffmeister family members;
for the non--IRAS--observed bodies, we have just assumed
an albedo value of 0:049, that is the average for the IRAS--
observed asteroids (in the Table the corresponding albe­
dos and diameters are rounded off to one fewer decimal
than for the IRAS--observed bodies). In columns 2 to 7 of
the Table we have listed, respectively, the proper orbital
elements (semimajor axis, eccentricity, sine of the inclina­
tion), the absolute magnitude (H), the measured/assumed
albedo (p V ), and the estimated diameter (D) of the 22
family asteroids.
In general, low albedo values (say, less than ¸ 0:07)
are typical for taxonomic types C, F, P and D, com­
monly interpreted as carbon--rich mineralogic assemblages
and most abundant in the outer region of the main belt,
whereas they are not consistent with types S, K, V, M, A
and E, corresponding to silicate and/or metal--rich com­
positions and common in the inner and middle parts of
the main belt (Tedesco et al. 1989, Gaffey et al. 1993). As
for the Hoffmeister family asteroids observed by IRAS, it
should be taken into account that all of them had a sta­
tistical flux overestimation correction applied, with two
[(2996) and (4124)] observed only once (but in two bands)
and none detected more than 50% of the time the IRAS fo­
cal plane crossed over them; as a consequence, IRAS albe­
dos are probably uncertain by ¸ 50% (E.F. Tedesco, per­
sonal communication, 1995). Thus, a carbon rich compo­
sition appears very likely for asteroids (1726) and (4124),
whereas for (2996) Bowman the situation is more uncer­
tain. Its higher IRAS albedo does not allow one to rule out
the moderate--albedo C--related types G and T, nor other
types for which a very different mineralogy has been in­
ferred, such as M and K (Gaffey et al. 1993). Clearly, more

F. Migliorini et al.: The Hoffmeister family 3
spectroscopy or multi--color photometry data are needed
to obtain unambiguous taxonomic classifications and min­
eralogic interpretations for this intriguiging family.
Other motivations to obtain such physical data are the
following. First, in the same region of the asteroid belt
where Hoffmeister is found several other small families are
also located, branching off a complex clan (see Farinella
et al. 1992 for this terminology), whose lowest--numbered
object is (110) Lydia. As noted by Zappal`a et al. (1995),
in the Hierarchical Clustering Method (HCM) for family
classification the Hoffmeister grouping splits from the clan
at the relatively high cut--off ``distance'' of 190 m/s [but
still including (272) Antonia, found in the family also by
the alternative Wavelet Analysis Method (WAM) proce­
dure], and this suggests that it may be unrelated to the
other groupings. However, taking into account the com­
plex secular dynamics of this zone (Milani & KneŸzevi'c
1992), which may have affected the time stability of the
proper elements of some bodies, physical data are required
to assess whether the clan consists of relatively close but
genetically unrelated groupings, or some complex, hierar­
chical collisional process might explain the overall mor­
phology of the Lydia clan.
Another problem is related to the age of the family. As
shown by Milani & Farinella (1994) in the case of the Ver­
itas family, a ``chaotic chronology'' method can lead one
to estimate an upper limit for the age of a family when the
proper elements of (some of) its members undergo a slow
process of chaotic diffusion. For (1726) Hoffmeister, a nu­
merical integration of its orbit over a 70 Myr time span has
shown very long periodic and/or secular trends in proper
eccentricity and inclination, of amplitude comparable to
the observed spread of the family (A. Milani, personal
communication, 1994). Therefore, whereas no bound on
the age can be derived for the moment, it is possible that
some upper limit could be derived by more extensive nu­
merical experiments in the near future. Relatively young
families are of particular interest, because they should ex­
pose to our view relatively ``fresh'' fracture surfaces from
the former interior of their parent body, and because their
existence constrains the intensity of the ongoing collisional
evolution process (Farinella 1994, Marzari et al. 1995).
3. Hoffmeister's optical spectrum
With the motivations explained above, we have carried
out spectroscopic observations of (1726) Hoffmeister. The
observations were performed on 29 October 1994, using
the 1.54--m G.D. Cassini telescope of the Bologna Obser­
vatory (Loiano observing station, Italy), equipped with a
BFOSC (Bologna Faint Objects Spectrograph & Camera)
instrumentation and a 1024 \Theta 1024 Thomson coated CCD
as a detector. The grism we used has a dispersion of 220
š A/mm in the first order. The CCD has a 19 ¯m square
pixel, yielding a dispersion of 4.2 š A/pixel in the wave­
length direction. The useful spectral range is from about
5200 š A to 9000 š A, with an instrumental FWHM of 8.4 š A.
A single exposure of 45 minutes was obtained at a mean
airmass of 1.4. The slit was set at 5 arcsec, in order to
avoid loss of light due to bad telescope tracking. The as­
teroid was very faint (V ¸ 16:2), but well distinguishable
from the stellar background owing to its relatively high
proper motion. The data reduction was made by using
an ULTRIX workstation and the well--known IRAF pack­
age with the standard procedure, as described in Di Mar­
tino et al. (1995). This procedure includes subtraction of
bias level, flattening of data, removal of cosmic rays, sub­
traction of the sky, wavelength calibration, collapsing the
two--dimensional spectra, extinction correction, division of
the asteroid spectrum and solar analog spectra (Hardorp
1978, 1980a, 1980b, 1981, 1982).
In addition to (1726) Hoffmeister, the solar analog star
64 Hyades, flat fields, bias images and lamp spectra (He,
Ar) were all observed as simultaneously as possible us­
ing an identical instrument configuration. The aspect data
(right ascension, declination, ecliptic longitude and lati­
tude, heliocentric and geocentric distances, V magnitude)
of the asteroid at the observation time are listed in Table
2, whereas Table 3 reports the S/N ratios and the slope of
the spectrum of (1726) Hoffmeister shown in Fig. 1. The
spectrum has been normalized at 7000 š A.
Hoffmeister's spectrum is clearly flat and neutral, that
is no significant slope or absorption feature is appar­
ent. This is not surprising, since in the middle region of
the main belt, where the Hoffmeister family is located,
over two thirds of the (bias--corrected) asteroid population
are spectrally neutral. Among the low--albedo taxonomic
types discussed in Sec. 2, Hoffmeister's spectrum clearly
favours a C-- or F--type classification, while it rules out the
P and D types, which are characterized by reddish slopes
(and are anyway rare at semimajor axes ! 3 AU).
Fig. 1. Optical reflectance spectrum of (1726) Hoffmeister ob­
tained on 1994 October 29.809. The asteroid spectrum has been
divided by that of the solar analog star 16 Cygni B.

4 F. Migliorini et al.: The Hoffmeister family
Table 2. Aspect data of the observed asteroid
Date R.A. Decl. Long. Lat. r \Delta Phase V
[0 UT] [2000.0] [2000.0] [AU] [AU] [deg] [mag]
1994 10 29 00 35.4 +06 49.1 10.12 2.75 2.76 1.84 8.9 16.2
Table 3. Parameters of the spectrum of (1726) Hoffmeister shown in Fig. 1
SNR SNR Slope
5500 -- 6500 š A 7500 -- 8500 š A %/š A
29.8 18.0 2.41\Theta10 \Gamma3
4. Conclusions
The main conclusions from this work are the following:
(1) The flat and featureless spectrum of (1726) Hoff­
meister, as shown in Fig. 1, strongly suggests that it be­
longs to the C or F taxonomic classes, both interpreted
as being rich in carbonaceous minerals but possibly sub­
ject to different degrees of alteration and metamorphism
(Gaffey et al. 1993). This is consistent with its low IRAS
albedo (p v = 0:037). More detailed conclusions about the
mineralogy of this object require that spectroscopic obser­
vations are extended to the ultraviolet and near--IR spec­
tral domains.
(2) The fact that both the other Hoffmeister family mem­
bers observed by the IRAS satellite have also compara­
tively low albedo values supports the genetic relationship
among the family members, and suggests that the family
was generated in the break--up of a carbon--rich parent as­
teroid, approximately 50 to 100 km in diameter. Spectra
or multi--color photometry of other family members are
required to confirm or disproof this interpretation, and to
investigate to what extent the parent body was composi­
tionally homogeneous. Recently a few spectra of Hoffmeis­
ter family asteroids have been obtained by R.P. Binzel and
coworkers in the frame of their extensive Small Main--belt
Asteroid Spectroscopic Survey (R.P. Binzel, private com­
munication, 1995), although they were not included in the
first published paper on this survey (Xu et al. 1995). It will
be interesting to compare their results with those reported
here for (1726) Hoffmeister.
(3) The available physical data on objects not belonging to
the Hoffmeister family, as defined by the HCM method­
ology in Zappal`a et al. (1995), but close to it in proper
element space, suggest that several additional groupings
forming the ``Lydia clan'' (see Sec. 1) are not genetically
related to each other, in the sense of deriving from a com­
mon parent body. Asteroid (272) Antonia (diameter ¸ 25
km), associated to the family by the WAM procedure ---
which however is much less suited than the HCM method
to identify very tight and dense families (see discussion in
Zappal`a et al. 1995) --- has not been assigned a taxonomic
type yet, but its IRAS albedo (p v = 0:14) is not consistent
with a C--type or a related classification. Another ``neigh­
bour'' of the Hoffmeister family, (308) Polyxo (diameter
148 km), has a low albedo but a quite reddish spectrum;
while Tholen (1989) has classified it as a T-- or D--type
body, according to Tedesco et al. (1989) it probably has a
peculiar surface mineralogy. Other asteroids belonging to
different groupings in the clan, such as (110) Lydia, (125)
Liberatrix and (847) Agnia, have been assigned to the M
(the former two) and S (the third one) types, and this
is also at odds with the hypothesis of a common parent
body. Therefore, the ``Lydia clan'' is most probably the
outcome of several independent break--up events occurred
in the same region of the proper element space.
(4) As we mentioned in Sec. 1, future dynamical work
may lead to the conclusion that the Hoffmeister family
is younger than a few times 10 8 yr. If this will be the case,
it should not be seen as a surprising result. If the size of
the parent body was in the 50 to 100 km range, as argued
above, current estimates for the collisional lifetimes of such
asteroids are of ¸ 2 to 7 \Theta 10 9 yr (see e.g. Farinella 1994,
Table 2). Since about 500 of these bodies exist in the main
belt, one of them should be disrupted every ¸ 10 7 yr. If
the Hoffmeister family will prove to be rich in small mem­
bers, it would be possible to infer that it is the outcome of
one of the most recent such disruption events. The model
developed recently by Marzari et al. (1995) might be used
to test this hypothesis.
Acknowledgements. We are grateful to the reviewer E.F. Te­
desco for many very helpful suggestions and to R.P. Binzel,
Z. KneŸzevi'c and A. Milani for useful discussions and com­
ments. This work has been supported by grant ASI--94--RS--69
of the Italian Space Agency (ASI) and by the Italian Ministry
for University and Scientific Research (MURST).
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