arXiv:0803.1795v1  [astro-ph]  12 Mar 2008
Astrophysics and Space Science
DOI 10.1007/s•••••-•••-••••-•
The search for Primordial Quark Nuggets among Near
Earth Asteroids
J. E. Horvath
c⃝Springer-Verlag ••••
Abstract Primordial Quark Nuggets,remnants of the
quark-hadron phase transition, may be hiding most of
the baryon number in superdense chunks have been dis-
cussed for years always from the theoretical point of
view. While they seemed originally fragile at interme-
diate cosmological temperatures, it became increasingly
clear that they may survive due to a variety of eﬀects
aﬀecting their evaporation (surface and volume) rates.
A search of these objects have never been attempted to
elucidate their existence. We discuss in this note how
to search directly for cosmological fossil nuggets among
the small asteroids approaching the Earth.
“Aster-
oids” with a high visible-to-infrared ﬂux ratio, constant
lightcurves and devoid of spectral features are signals
of an actual possible nugget nature. A viable search
of very deﬁnite primordial quark nugget features can
be conducted as a spinoﬀof the ongoing/forthcoming
NEAs observation programmes.
Keywords Quark Nuggets, Dark matter, Near Earth
Asteroids
1 Introduction
Primordial quark nuggets (PQNs) have been postulated
to contain most of the baryonic number of the uni-
verse many years ago (Witten, 1984), being a physical
realization of the so-called strange matter hypothesis.
The strange matter hypothesis states that a cold, cat-
alyzed form of the quark gluon plasma could be the true
ground state of the hadronic matter and, if formed at
the QCD scale when color become conﬁned, remnants of
J. E. Horvath
Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Uni-
versidade de S˜ao Paulo, Rua do Mat˜ao 1226 , 05508-090 S˜ao
Paulo, SP, Brazil
substellar mass could help to ”hide” the baryon number
content and achieve a large value of Ωmatter ∼0.25 now
favoured by observations. The initial excitement about
this possibility gave place to several analysis addressing
whether the PQN could survive from the initial high-
temperature environment until the lower temperature
universe, where the contribution −T S to their free en-
ergy make them stable against evaporation-boiling. In
fact both processes (evaporation of ordinary hadrons
from the surface and bulk conversion -boiling-) have
been examined with varying results (Madsen and Ole-
sen, 1991; Alcock and Olinto, 1989; Olesen and Mad-
sen, 1993; Sumiyoshi and Kajino, 1991).
Generally
speaking, it can be stated that the slower the pro-
cess, the larger the mass that can survive; thus it is
of great interest to pinpoint the realistic models to es-
timate reliably a surviving mass. It is generally agreed
that the latter can not be larger than the mass in-
side the horizon, corresponding to a baryon number of
Ahor = 1049( 100 MeV
Tqcd
) (where Tqcd is the temperature
for the conﬁnement phase transition, assumed to be
ﬁrst order); and while no consensus has been achieved
on the exact value of this surviving nugget mass, val-
ues as low as A = 1040 have been estimated in the
literature (Sumiyoshi and Kajino, 1991; Bhattacharyya
et al., 2000). Recently we have shown that the inclu-
sion of pairing eﬀects in strange matter would increase
the binding energy of the nugget and hence push down
the survival mass substantially (Lugones and Horvath,
2004). There is a strong belief that dense quark mat-
ter should undergo pairing of some of all quark ﬂavors,
although the precise form of the phase diagram is still
under debate (Alford, 2006).
Given this attractive possibility we address here a
novel and feasible search for PQN in the asteroidal-mass
range; in several senses complementary to the searches
of smaller masses (nuclearities) already performed or
underway (Finch, 2006). We present a discussion of the

2
general features of the nuggets in Section 2. Section 3
addresses the detectability of this population by photo-
metric and spectroscopic techniques. A discussion and
some conclusions are summarized in last Section.
1.1 Primordial Quark Nuggets
According to the Bodmer-Witten-Terazawa hypothe-
sis (Witten, 1984; see previous work by Bodmer, 1971
and Terazawa, 1979), a stable form of the QGP with
high strangeness content could be self-bound and there-
fore form objects from a minimum (nuclear) size until
∼M⊙at the onset of the general relativistic instability.
While the former (“strangelets”) are amenable to parti-
cle search techniques (Klingenberg, 1999) and the latter
may constitute compact stars (Witten, 1984; Alcock,
Farhi and Olinto, 1986; Haensel, Zdunik and Schaeﬀer
1986; Benvenuto and Horvath 1989), in the interme-
diate range PQNs would resemble extremely compact
asteroids.
For constant density ρ = 5 × 1014g cm−3
(which is an excellent approximation for this range; see
Alcock, Farhi and Olinto, 1986) the size of the nuggets
is
RN = 2 × 102 ×

MN
10−12M⊙
 1
3
cm
(1)
and we have scaled to the mass corresponding to a
baryon number A = 1045 above the evaporating mass
(Lugones and Horvath, 2004).
Because of the large size of the galactic halo, the
isotropic nugget ﬂux of this mass-scale is always very
small, of the order of 3 × 10−37cm−2s−1sr onto the
Earth neighborhood. For a minimum approach of one
PQN at a distance D ≤2× the Earth-Moon distance,
or 2 × RMoon (see below) a passage would happen at
a rate 10−6 yr−1.
This small rate gives no hope for
detecting PQNs freely roaming the halo passing by in
open orbits.
A captured nugget population in orbit provides much
better prospects. To be captured by the gravitational
ﬁeld of the Sun the nuggets coming from an isotropic
ﬂux must loose energy and angular momentum. A ﬁrst
viable mechanism would be a number of ﬂyby encoun-
ters with stars in the galactic disk.
Then a fraction
of these slower nuggets, having now E ≳0 respect
to the solar potential would be captured in ﬂy-by en-
counters with Jupiter. Let us stress that even if the
distribution of PQNs will not slow down statistically,
individual objects from that distribution may be eﬀec-
tively captured by this mechanism.
The PQNs with
this mass-scale do not slow down appreciably even by
passing through stars, since the basic energy loss rate
dE/dt = −πR2
Nρmatterv3
N (with ρmatter the density of
the traversed stellar material and vN the nugget veloc-
ity ∼250 km s−1) is many orders of magnitude smaller
than the incoming kinetic energy of the nugget.
The estimated number of PQNs eﬀectively captured
is always tiny, but perhaps enough to yield 10-100 of
them bound to the solar system out of the ∼1023
existing in the whole galactic population.
Note that
this capture rate, if extrapolated to all the stars in the
disk, would still mean a total capture nugget fraction
of ≤10−10. A variety of orbital elements is expected
because of the random incidence, however, since the
nuggets would have Apollo-like, planet-crossing orbits,
their residence in the solar system would be limited to a
dynamical time of ≤10 Myr. Finally, there should be a
huge number (≥107) of PQN at a given time inside the
bounds of the solar system, adding up to a mass com-
parable to several times the Earth’s mass. They may be
perturbed and directed to the inner solar system much
in the same way that ordinary cometary nuclei do, only
that they would remain unseen most of the time. The
identiﬁcation of the tiny dense nuggets among the sub-
population of NEAs would be the subject of the next
section.
2 How to detect nuggets among NEAs
A great deal of attention has been paid recently to the
issue of NEAs and the possible hazards for the Earth in
the case of direct collisions. Actually, a few observing
programs to look for close-by encounters are already op-
erating (for example, Spacewatch, see Mc Millan, 2006)
or being implanted.
A huge number of small NEAs,
those not very hazardous to the Earth in the ballpark
of ∼tens of meters are being currently detected. The
observations indicate that at a given time > 100 aster-
oids pass closer than the Moon, while at least one of
∼30 m and ≃10 of about 10 m collide with the Earth
each year. At a distance comparable to the Moon these
would have magnitudes mv = 13 and 15.5 respectively
(assuming, as usual, a zero phase angle; see Paczy´nski,
2006). These fast-moving boulders would be visible for
a ∼days at most because of their high velocities rela-
tive to the Earth, of the order of 20 km s−1.
As is well-known, one of the simplest forms for de-
termining the albedo A (and hence gather information
on their composition) of an asteroid is to perform at
least simultaneous V and I images to infer A from the
quotient of ﬂuxes.
The exotic nature of the nuggets
allows one relatively easy form of distinguishing them
from conventional asteroids: since the strange quark
matter is expected to have a plasma frequency as high

Quark nuggets among NEAs
3
as 20 MeV (well in the hard γ-ray frequencies), the bare
quark surface would act as a perfect mirror to the in-
cident solar light. Hence, contrary to the case of even
metallic asteroids for which A ∼0.1, we expect albe-
dos ≈1 and therefore a quotient FV /FI much larger
than any reasonable normal surface. Therefore a PQN
would appear to have a magnitude mV ≃20 at a dis-
tance ∼RMoon, looking like a larger “normal” asteroid
but showing the abnormal ﬂux quotient. Speciﬁc pro-
grammes like the Spacewatch (Mc Millan, 2006) already
mentioned and several other programs (see for example
the compilation of the NASA, 2007) currently monitor
objects fainter than mV ∼20, and should be able to
detect ∼1 m nuggets out to ∼RMoon (hence the dis-
tance estimate given in the former Section). A recent
discussion by Paczy´nski (2006) has shown the conve-
nience of a satellite at the L1 Lagrangian point for the
NEAs study and early alert. The main diﬃculties for
such identiﬁcations are the high proper motion of the
candidates, which render them observable for a short
time ∼1 day, and also the large number of candidates
in a given night, provided that there is no simple way
of selecting a subsample, for instance, based on orbits.
A second prediction for these objects is that their
spectra would be essentially solar and devoid of any
characteristic line that distinguish asteroidal composi-
tions. This seems promising, although spectroscopy of
dim fast-moving objects is certainly diﬃcult.
In any
case the slower candidates (say, with µ ≤1”/s) could be
scanned by suitably setup devices. Thus both the pho-
tometric and spectroscopic measurements would show
signatures of the exotic nugget features diﬃcult to miss
for good observational data. This feature (and the for-
mer ﬂux quotient as also) implicitly assumes that the
surface of the nugget is not covered with normal mat-
ter, which would restore the ability of radiating con-
ventionally the reﬂecting light. The situation is quite
like the discussion of strange stars (Alcock, Farhi and
Olinto, 1986; Haensel, Zdunik and Schaeﬀer 1986; Ben-
venuto and Horvath 1989), but now referring to much
smaller objects, 12 orders of magnitude less massive
than a strange star, with a correspondingly small sur-
face gravity. This consideration supports, but does not
prove, the expectation of a bare surface.
A third complementary signature could be obtained
by precise stellar occultation observations, given that
the tiny nugget with high albedo would mimic a larger
radius asteroid (at least 10 times bigger) but would
show a very short occultation time corresponding to
a small and sharp edge ball. Even the lack of occulta-
tion where it should be one (if the asteroid was normal)
could be helpful for characterizing the PQN candidates.
Finally we note that a very uniform light curve, (in con-
trast with most of the asteroids of irregular size which
tumble and rotate) is expected from the spherical super-
dense nugget, quite independently of the wavelength.
This completes a short list of testable predictions for
these objects.
Several contemporary sources (as opposite to the dis-
cussed primordial population) that could supply a ﬂux
of small nuggets have been advanced, like the disrup-
tion of binary strange stars (Madsen, 2005; however see
Klu´zniak and Lee, 2002 for a calculation of a strange
star-black hole encounter not leaving any ejected de-
bris).
It is amusing to note that long ago Friedman
and Caldwell (1991) predicted the stripping of nuggets
of precisely A = 1045 from the simple balance of tidal
and surface forces in a binary merging. However, the
small number of events of this type ∼10−5yr−1 argues
against stripped nuggets of this origin being a signif-
icant source when compared to the hypothetical pri-
mordial population, and in any case there is no way for
distinguishing both.
The possibility of a direct impact onto the Earth is
extremely small (about one event per Hubble time) for
halo PQNs, but grows considerably for a captured pop-
ulation. Speciﬁc signatures of such an hypothetic colli-
sion (likely giving rise to a huge epilinear earthquake)
have never been worked out in full detail.
However,
lighter PQNs from astrophysical origin may be candi-
dates to direct impacts with masses down to tens of
tons (see Herrin, Rosenbaum and Teplitz, 2006, for this
milder but related signal search).
3 Conclusions
We have discussed some observations which may pos-
sibly test the presence of a population of primordial
quark nuggets captured in solar orbits. We have been
led by the fact that the mass range predicted by the-
oretical calculations falls precisely in the ballpark of
small asteroids, and by the existence of advanced pro-
grammes of NEAs search. We suggested a few obser-
vational tests to reveal the nature of the nuggets as
they approach the Earth. If an eﬃcient setup for the
fast-moving candidates can be established it would be
possible to identify some deﬁnite signatures predicted
by the basic physics of the nugget surface reﬂecting sun-
light. Although the search for PQNs could be diﬃcult
and take several years, the payoﬀwould be uttermost
rewarding even if they are not ﬁnally found.
In any
case, valuable information about the normal asteroid
population would be gathered. Few other programmes
could be suitable for searching such an elusive primor-
dial relics.

4
Acknowledgements
CNPq (Brazil) is acknowledged
for ﬁnancing JEH through a fellowship. C. Beaug´e, F.
Roig and S. Ferraz-Mello have provided scientiﬁc ad-
vice to this work. Finally, the criticisms of an anony-
mous referee have added a few interesting points to the
present article.

Quark nuggets among NEAs
5
References
Alcock, C., Olinto, A.V.: Phys. Rev. D 39, 1233 (1989)
Alcock, C., Farhi, E., Olinto, A.V.: ApJ310, 261 (1986)
Alford, M.G.: hep-lat/0610046 (2006) and references therein
Benvenuto, O.G., Horvath, J.E.: MNRAS241, 43 (1989)
Bhattacharyya, A., Jan-e Alam, Sarkar, S., Roy, P., Sinha,
B., Raha, S., Bhattacharjee, P.: Phys. Rev. D61, 083509
(2000)
Bodmer A.: Phys. Rev. D4, 1601 (1971)
Caldwell, R.R., Friedman, J.L.:
Phys. Lett. B264, 143
(1991)
Finch, E.: nucl-ex/0605010 (2006)
Haensel, P.; Zdunik, J. L.; Schaefer, R.:
A&A160, 121
(1986)
Herrin, E. T.; Rosenbaum, D. C., Teplitz, V. L.: Phys. Rev.
D 73, 043511 (2006)
Klinbenerg, R.: Jour. Phys. G25, R273 (1999)
Klu´zniak, W., Lee, W.: MNRAS335, L29 (2002)
Lugones, G., Horvath, J.E.: Phys. Rev. D69, 063509 (2004)
Madsen, J., Olesen, M.: Phys. Rev. D 43, 1069 (1991)
Madsen, J.: J. Phys. G31, 833 (2005)
McMillan, R. S., in Near Earth Objects, Our Celestial
Neighbors: Opportunity and Risk, International Astro-
nomical Union. Symposium 236, (2006), unpublished
NASA info available at http://neo.jpl.nasa.gov/programs/
(2007)
Olesen, M., Madsen, J.: Phys. Rev. D47, 2313 (1993)
Paczy´nski, B.: astro-ph/0609161 (2006)
Sumiyoshi, K., Kajino, T.: Nucl. Phys. B. Proc. Supp. 24,
80 (1991)
Terazawa H.: INS-Report 336 (1979), unpublished
Witten E.: Phys. Rev. D 30, 272 (1984)
This manuscript was prepared with the AAS LATEX macros v5.2.
