Belgrade-MACHO
Project: first two years' results
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Vesna
Milosevic-Zdjelar
Dept. of Physics
& Astronomy, University of Manitoba, Winnipeg, Mb,
R3T 2N2, CANADA
e-mail: bmilose@escape.ca
Srdjan
Samurovic
Dipartimento
di Astronomia, Universita degli Studi di Trieste,
Via Tiepolo
11, I-34131,
Trieste, ITALY
e-mail: srdjan@ts.astro.it
Milan
M. Cirkovic
Astronomska
Opservatorija, Volgina 7, 11000 Belgrade, SERBIA
Dept. of Physics
& Astronomy, SUNY at Stony Brook,
Stony Brook,
NY 11794-3800, USA
e-mail: mcirkovic@aob.aob.bg.ac.yu
Abstract
The activities of
the Belgrade-MACHO project during its first two years of work are reviewed.
The theoretical work on the microlensing optical depths and their connection
with the problem of the baryonic dark matter, the shape of the disk and
halo of the Milky Way, already yielded significant results. The emphasis
is put on the intense use of today's common software and Internet resources.
International collaborations and future plans are also briefly considered.
Microlensing and Galactic
Dynamics
Microlensing (ML) search
has proved to be one of the most important tools for investigating the
properties of the halo and disk of our galaxy (e.g. Paczynski 1986; Sackett
& Gould 1993; Gould 1996; Alcock et al. 1996, 1997a; Ansari et al.
1996). Comparison of theoretical models and ML data led to intriguing results
(e.g. Gates, Gyuk & Turner 1995). Under the Copernican assumption that
the Milky Way is a typical zero-redshift L* galaxy, one can ask what consequences
recently discovered Massive Compact Halo Objects (MACHOs) have for the
global picture of baryonic structure evolution in the universe. Exact shape
of the Galactic gravitational potential, orbits of celestial bodies in
this potential, and the interaction of Galactic subcomponents (thin and
thick disk, bulge, bar, halo, etc.) can be discussed with more observational
constraints than ever before.
Vigorous astrophysical
research addresses these problems. As an illustration, we point out that
the bibliography of Samurovic, Cirkovic & Milosevic-Zdjelar (1999,
SCMZ) amounts to 119 refereed research papers and 16 review articles. Entire
NASA ADS microlensing bibliography (http://adswww.harvard.edu),
represented in the Fig. 1 for the last quarter of a century, searched by
key words, has 794 units. Almost exponential growth with time (with best
fit time constant $\tau \sim 5$ years) is faster than in almost any other
field of contemporary research, not only within astronomical disciplines.
ML events caused
by MACHOs serve various astrophysical purposes: constraining mass distribution
in the Galaxy and present-day stellar mass function (see Gould 1996). With
this in mind, the investigation of global consequences of statistics of
ML events along various lines of sight on the Galactic structure and dynamics,
other galaxies and universe as a whole, had started at the beginning of
1998, within the framework of the Belgrade-MACHO Project. Hereby we would
like to summarize some of the most significant results. Finally, we point
out further directions of Belgrade-MACHO project and our collaborations
within the world network of gravitational lensing research.
Figure 1. The
temporal distribution of the scientific publications on microlensing and
related topics in the last quarter of a century.
Figure 2. Predicted
ML optical depth towards sources located at D=50 kpc in a model with moderate
halo flattening q=0.6
MACHOs and Baryonic
Dark Matter
Baryonic dark matter
(BDM) properties are one of the most important problems of today's astrophysics.
MACHOs have been included into the total cosmological baryonic budget (Fields,
Freese & Graff 1998). Existing ML searches are still insufficient to
accurately determine the total MACHO abundance for two basic reasons:
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All significant ML
results are still within $\simeq 50$ kpc: Galactic bulge (surveys by MACHO
http://wwwmacho.mcmaster.ca
and ML Alerts http://darkstar.astro.washington.edu,
DUO and OGLE http://www.astro.princeton.edu/~ogle
(Optical Gravitational Lensing Experiment) collaborations) or Magellanic
Clouds (MACHO and EROS http://www.lal.in2p3.fr/recherche/eros
(Experience pour la Recherche d'Objets Sombres) collaborations). This is
a fundamental constraint, until results towards more distant sources, like
M31, are obtained. It may be expected soon, since MEGA and AGAPE http://cdfinfo.in2p3.fr/Experiences/AGAPE
(Andromeda
Galaxy and Amplified Pixels Exp.) coll. already started a survey (Gyuk
1999
private communication).
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Statistics are still
insufficient to determine optical depths in given directions with uncertainties
smaller than $\delta \tau /\tau =0.5$.
Theoretical example
for a source at a distance of 50 kpc, like the LMC, assuming moderate
halo flattening,
is shown in the Fig. 2 (SCMZ).
One of the major
conclusions of ScMZ is that nearly spherical haloes contain too much baryonic
matter in the form of MACHOs. Although not in direct conflict with the
BBNS constraints, it is uncomfortable, since other components of baryonic
matter (intergalactic medium manifested through the Ly$\alpha$ forest),
also pretend to be dominant in the total budget. This situation, and related
value of Hubble constant, are shown in the Fig. 3. Proposal of Milosevic-Zdjelar,
Samurovic & Cirkovic (1999), removes the inconsistency by taking into
account moderate flattening of Milky Way's halo, see Fig. 4, and agrees
with recent CMBR studies (Lineweaver et al. 1997), BBNS and light element
abundances constraints (Burles et al. 1999), and IGM studies (Burles &
Tytler 1998).
Figure 3. Various
components of the cosmological baryon density as functions of the Hubble
parameter h (from SCMZ) for q=0.2.

Figure 4. Dependence
of ${\Omega_B}$ on h for moderate halo flattening
q=0.6 (from
Milosevic-Zdjelar, Samurovic & Cirkovic 1999).
Further investigations
are necessary, especially of MACHO formation epoch, probed by early damped
Ly$\alpha$ and similar gas-rich systems. This, coupled with ML advances,
should be
able to solve the
problem of baryonic component of DM and unify several branches of astrophysical
research into a coherent picture of the evolution of baryonic matter in
the universe (Cirkovic, Samurovic & Milosevic-Zdjelar 1999).
MACHOs and the Shape
of the Milky Way
ML studies enable us
to determine, in principle, the shape of Milky Way's components:
Spiral arms. First
results are obtained by EROS search (Ansari 1999 private comm.)
Disk. Besides other
methods that confirmed that Galaxy has a weak bar inclined $10^o - 30^o$
to the Sun-Galactic Centre line (surface photometry, star counts, gas and
stellar kinematics), Samurovic et al. (1998) proposed that it could be
detected by changes in ML optical depth along the bulge (ML events show
excess compared to theoretical estimates).
Halo. The most
important parameter is q -- the degree of flattening. It was shown in SCMZ
that extreme values (like $q \sim 0.2$) for the dynamically dominant halo
component, required by some models, like the Pfenniger, Combes & Martinet
(1994) molecular DM model, are incompatible with the ML data, see Figure
5. Recent analysis of the local stellar velocity distribution based upon
HIPPARCOS data agrees with that (Bienayme 1999). Different arguments point
to an oblate gravitating dark halo, which, in turn, causes flattening of
stellar and gaseous (Ly$\alpha$-absorbing) haloes.

Figure 5: Dependence
of the MACHO halo mass (in units of $10^{11}\; M_\odot$) for three choices
of flattening parameter q as a function of halo core radius (ScMZ). Square
points represent spherical (q=1), circles extremely flattened (q=0.2),
and crosses the intermediate case (q=0.6). Moderate halo flattening agrees
with the most recent estimate of the total mass of the halo within 50 kpc,
by Wilkinson & Evans (1999) on $\sim 5.4^{+0.2}_{-3.6}\times 10^{11}
M{}_\odot$.}
Various software
packages were used in order to obtain results. Most of the work was done
using a free version of Unix operating system, Linux. Software ranges from
free GNU codes (compilers, editors, utilities) to commercial large mathematical
packages (Mathematica and Maple).
Unfortunately,
no application can perform all: complete calculation, production of plots
and detailed analysis.
Plans for the Future
There are several lines
of research we would like to pursue in the near future.
(1) Construction
of models incorporating both gaseous and MACHO haloes, strongly constrained
by ML observational data. In order to built a total set of constraints
in which the realistic model of the composition of the baryonic matter
in the universe should be built, we should consider BBNS which entered
the epoch of very high precision, Gunn-Peterson optical depths for both
HI and HeII (e.g. Jakobsen 1998), vast statistics of the Ly$\alpha$ forest
lines, observations of low-redshift absorption in well-defined galactic
haloes (e.g. Chen et al. 1998) and improved X-ray data on the
hot gas distribution
in both clusters and small groups of galaxies. Models should also be able
to account for known large-scale phenomena, particularly the Magellanic
Stream, which shows presence of Galactic gaseous halo up to of $\sim 50$
kpc (Weiner & Williams 1996) . Within reach of current knowledge, the
development of such models is clearly defined task of near future.
(2) Inclusion of
MACHO formation in cooling flows would present a powerful theoretical basis
for analysis of universality and evolution of the BDM (e.g. Nulsen &
Fabian 1997). Detailed understanding of these processes is still lacking.
(3) The detailed
probing of the Galactic potential remains the main effort of Belgrade-MACHO
project. Apart from lines of sight towards M31 (for which we are insured
from AGAPE and MEGA coll. to have data in less than two years) and several
globular clusters, lines of sight towards
distant pulsars
may also be of interest in this respect, due to Shapiro Phase Shift (changes
in their stable beat by any object crossing along the line-of-sight), e.g.
Fargion & Conversano (1998). Monitoring pulsars could, therefore, presents
a tool for discovering dark objects, even planets as close as within Solar
System.
(4) Lensing of stars
by spherical gas clouds (Henriksen & Widrow 1995, Draine 1998) could
explain the extreme scattering effects (ESEs) (Fiedler et al. 1985) manifested
as a class of variations at GHz frequences. Extragalactic point radio sources
can be amplified and deamplified when the lens crosses the line of sight.
Walker & Wardle (1998) suggested that this can be due to a halo
population of $\sim
10^{14}$ molecular gas clouds that have mass $\approx 10^{-3}M_\odot$ and
radius $R\approx 3$ AU (Shchekinov 1998).
Belgrade-MACHO project
relies on the data of large observational ML network maintaining constant
contact with EROS, AGAPE, MEGA and PLANET teams.
In order to provide
the information concerning the latest research we created the home page:
http://www.geocities.com/CapeCanaveral/7102/Belgrade-MACHO.html.
Acknowledgements
The authors express
gratitude to all those people and organizations who in any way helped their
work. Special thanks go to Drs. Penny Sackett, Geza Gyuk, Reza Ansari and
Slobodan Ninkovic, who frequently offered inspiration, encouragement and
advice. SS acknowledges the financial support of the University of Trieste
and the hospitality of the people at the Trieste Department of Astronomy
and the Observatory.
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Figure 6. Vesna
Milosevic-Zdjelar with Penny Sackett at the conference
"Gravitational
Lensing: Recent Progress and Future Goals",
George Sherman
Union Building, Boston University, July 1999.
Figure 7. Vesna
Milosevic-Zdjelar with Paul Schechter at the same Conference.
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