The orbit of S2
Dance of Stars
Results - The orbit of S2
Nature's 17 Oct 2002 issue (get article)
we report on having observed 2/3 of a complete orbit of the star currently
closest to the enigmatic radio source Sagittarius A*, which is thought to
mark the location of our Milky Way's massive central black hole. As explained
below, this orbit provides overwhelming evidence that SgrA* is indeed a supermassive
black hole of more than 2 million solar masses. Figures 1,2, and 4 on this
page are taken from the article in Nature. See the star S2 swing around the
black hole in this movie.
Observations by our group and by the
UCLA group of the velocities and accelerations of stars in the Galactic
Center over the course of the last decade have already provided strong evidence
that SgrA* is in fact a black hole of about 2.6 million solar masses. However,
these measurements could not rule out some alternatives to the black hole
model. Two such alternatives are a ball of massive, degenerate fermions,
like neutrinos, or a cluster of dark astrophysical objects, such as stellar
mass black holes or neutron stars. These two alternative explanations
can now be excluded by analyzing the orbit of S2:
In spring 2002 S2 was passing with the extraordinary velocity of more
than 5000 km/s at a mere 17 light hours distance -- about three times the
size of our solar system -- through the perinigricon, the point of
closest approach to the black hole. By combining all measurements of the
position of S2 made between spring 1992 and summer 2002, we have obtained
enough data in order to determine a unique keplerian orbit for this star,
presented in Figure 1. It is highly elliptical (eccentricity 0.87), has a
semimajor axis of 5.5 light days, a period of 15.2 years and an inclination
of 46 degrees with respect to the plane of the sky. From Kepler's 3rd law
we can determine the enclosed mass in a straightforward manner to be 3.7±1.5
million solar masses. Therefore at least 2.2 million solar masses have to
be enclosed in a region with a radius of 17 light hours. It is not possible
to explain this result with a neutrino ball model because the required neutrino
masses would be too large, or with a dense cluster of dark astrophysical
objects because such a cluster would have the extremely short lifetime of
at most a few hundred thousand years. Compared to the lifetime of our Galaxy
of the order of 10 billion years this configuration is highly improbable.
The only remaining alternative to the black hole model is a ball of bosons,
which would be hard to distinguish from a black hole because of its small
size. However, eventually, after some time such a ball would eventually collapse
to a black hole after having accreted enough matter from its surroundings.
Hence, the observed keplerian orbit of S2 around SgrA* provides compelling
evidence for the existence of a massive black hole at the center of our Galaxy.
On the figure below one can see the enclosed mass derived from different
studies of gas dynamics and stellar dynamics at various distances from the
Galacic Center. The point at the shortest distance is the mass measurement
added with the aid of the newly determined orbit. The fascinating feature
of this plot is that the best fit curve for the enclosed mass is flat inside
of about 0.2 parsecs. From this we draw the compelling conclusion that a
massive black hole must be present at the center of the Milky Way.. From
the best fit model to all the data we derive a black hole mass of 2.6±0.2
million solar masses. The long dash-short dash curve is the power-law model
for just the stellar cluster without the black hole. The dashed curve is
for a hypothetical cluster of dark astrophysical objects, such as neutron
stars or black holes, with a power-law exponent of 5 (Plummer model). Such
a cluster would have a mass density higher than 1x1017Mopc-3.
It's lifetime would be shorter than about 100,000 years.
Why is this finding important to astronomers?
Over the last decades, it has become a standard paradigm that massive
black holes are located at the centers of most, if not all, galaxies. They
are believed to be the central engines powering the enormous energy ouput
and luminosity of active galactic nuclei and of quasars, the most distant
and most luminous objects observed in our universe. Observations of other
galactic nuclei have already provided strong evidence that these massive
black holes exist. However, this evidence has always been indirect and did
not exclude alternative explanations (such as the neutrino ball model).
By showing in a direct and straightforward way that such a massive black
hole does indeed exist in the heart of our own galaxy, the Milky Way, we
provide a firm and compelling fundament for this key hypothesis of modern
How were these observations done?
From 1992 to 2002 we have been observing the center of our Milky Way with
the near-infrared speckle imaging camera SHARP
(developed at MPE) at the European Southern Observatory's
(ESO) NTT telescope in La Silla Chile. Speckle imaging is a special technique
in order to compensate the atmospheric turbulence and to obtain sharp images
at the theoretical diffraction limit of a telescope despite of the degrading
influence of the Earth's atmosphere. Speckle imaging
involves taking hundreds or thousands of short exposure images of an astronomical
object and the later reconstruction of a sharp image with the aid of a computer.
Another way of compensating atmospheric turbulence is the technique of
adaptive optics. It is more costly and elaborate than speckle imaging, but
provides usually significantly better results. At the end of 2001/beginning
of 2002 the near-infrared adpative optics system/infrared camera
NAOS/CONICA was installed on one of ESO's four 8.2 m VLT telescopes.
The combination of these two new powerful instruments porovided us with the
deepest images that were taken of the Galactic Center with an 8m-class telescope
up to date (see image).
How do we know where the black hole is?
We cannot see the massive black hole at the center of our Milky Way on
our infrared images. However, in order to examine the dynamics of the stars
in its environment it is essential to know its location on our infrared images
with a very high precision. There exists a certain kind of stars that give
off strong radiation in radio wavelengths as well as in the near-infrared
light. On the images of the Galactic Center taken with NAOS/CONICA we can
find seven of these so-called maser stars. These stars are marked
by circles in the image below. With the knowledge of the exact position of
the maser stars relative to the black hole we can determine the pixel scale,
orientation and possible distortions of our infrared image. In this way we
obtain the accurate position for hundreds of stars relative to the black
hole for a given time.
© Infrared and Submillimeter Astronomy Group at MPE
24/11/2008, editor of this page: Thomas Ott