To a first approximation, planets and stars are round. Think of the
Earth we live on. Think of the Sun, the nearest star, and how it looks
in the sky.

But if you think more about it, you realize that this is not
completely true. Due to its daily rotation, the solid Earth is
slightly flattened (“oblate”) – its equatorial radius is some 21 km
(0.3%) larger than the polar one. Stars are enormous gaseous spheres
and some of them are known to rotate quite fast, much faster than the
Earth. This would obviously cause such stars to become flattened. But
how flat?

Recent observations with the VLT Interferometer (VLTI) at the ESO
Paranal Observatory have allowed a group of astronomers [1] to obtain
by far the most detailed view of the general shape of a fast-spinning
hot star, Achernar (Alpha Eridani), the brightest in the southern
constellation Eridanus (The River).

They find that Achernar is much flatter than expected – its equatorial
radius is more than 50% larger than the polar one! In other words,
this star is shaped very much like the well-known spinning-top toy, so
popular among young children.

The high degree of flattening measured for Achernar – a first in
observational astrophysics – now poses an unprecedented challenge for
theoretical astrophysics. The effect cannot be reproduced by common
models of stellar interiors unless certain phenomena are incorporated,
e.g. meridional circulation on the surface (“north-south streams”)
and non-uniform rotation at different depths inside the star.

As this example shows, interferometric techniques will ultimately
provide very detailed information about the shapes, surface conditions
and interior structure of stars.

The full text of this Press Release, with three photos (ESO PR Photos
15a-c/03) and all related links, is available at:

http://www.eso.org/outreach/press-rel/pr-2003/pr-14-03.html

VLTI observations of Achernar

Test observations with the VLT Interferometer (VLTI) at the Paranal
Observatory proceed well [2], and the astronomers have now begun to
exploit many of these first measurements for scientific purposes.

One spectacular result, just announced, is based on a series of
observations of the bright, southern star Achernar (Alpha Eridani; the
name is derived from “Al Ahir al Nahr” — “The End of the River”),
carried out between September 11 and November 12, 2002. The two 40-cm
siderostat test telescopes that served to obtain “First Light” with
the VLT Interferometer in March 2001 were also used for these
observations. They were placed at selected positions on the VLT
Observing Platform at the top of Paranal to provide a “cross-shaped”
configuration with two “baselines” of 66 m and 140 m, respectively, at
90=B0 angle, cf. PR Photo 15a/03.

At regular time intervals, the two small telescopes were pointed
towards Achernar and the two light beams were directed to a common
focus in the VINCI test instrument in the centrally located VLT
Interferometric Laboratory. Due to the Earth’s rotation during the
observations, it was possible to measure the angular size of the star
(as seen in the sky) in different directions.

Achernar’s profile

A first attempt to measure the geometrical deformation of a rapidly
rotating star was carried out in 1974 with the Narrabri Intensity
Interferometer (Australia) on the bright star Altair by British
astronomer Hanbury Brown. However, because of technical limitations,
those observations were unable to decide between different models for
this star. More recently, Gerard T. Van Belle and collaborators
observed Altair with the Palomar Testbed Interferometer (PTI),
measuring its apparent axial ratio as 1.140 =B1 0.029 and placing some
constraints upon the relationship between rotation velocity and
stellar inclination.

Achernar is a star of the hot B-type, with a mass of 6 times that of
the Sun. The surface temperature is about 20,000 =B0C and it is located
at a distance of 145 light-years.

The apparent profile of Achernar (PR Photo 15b/03), based on about
20,000 VLTI interferograms (in the K-band at wavelength 2.2 =B5m) with a
total integration time of over 20 hours, indicates a surprisingly high
axial ratio of 1.56 =B1 0.05 [3]. This is obviously a result of
Achernar’s rapid rotation.

Theoretical implications of the VLTI observations

The angular size of Achernar’s elliptical profile as indicated in PR
Photo 15b/03 is 0.00253 =B1 0.00006 arcsec (major axis) and 0.00162 =B1
0.00001 arcsec (minor axis) [4], respectively. At the indicated
distance, the corresponding stellar radii are equal to 12.0 =B1 0.4 and
7.7 =B1 0.2 solar radii, or 8.4 and 5.4 million km, respectively. The
first value is a measure of the star’s equatorial radius. The second
is an upper value for the polar radius – depending on the inclination
of the star’s polar axis to the line-of-sight, it may well be even
smaller.

The indicated ratio between the equatorial and polar radii of Achernar
constitutes an unprecedented challenge for theoretical astrophysics,
in particular concerning mass loss from the surface enhanced by the
rapid rotation (the centrifugal effect) and also the distribution of
internal angular momentum (the rotation velocity at different depths).

The astronomers conclude that Achernar must either rotate faster (and
hence, closer to the “critical” (break-up) velocity of about 300
km/sec) than what the spectral observations show (about 225 km/sec
from the widening of the spectral lines) or it must violate the
rigid-body rotation.

The observed flattening cannot be reproduced by the “Roche-model” that
implies solid-body rotation and mass concentration at the center of
the star. The failure of that model is even more evident if the
so-called “gravity darkening” effect is taken into account – this is a
non-uniform temperature distribution on the surface which is certainly
present on Achernar under such a strong geometrical deformation.

Outlook

This new measurement provides a fine example of what is possible with
the VLT Interferometer already at this stage of implementation. It
bodes well for the future research projects at this facility.

With the interferometric technique, new research fields are now
opening which will ultimately provide much more detailed information
about the shapes, surface conditions and interior structure of
stars. And in a not too distant future, it will become possible to
produce interferometric images of the disks of Achernar and other
stars.

More information
The research described in this press release is presented in a Letter
to the Editor, soon to appear in the European research journal
Astronomy & Astrophysics (“The spinning-top Be star Achernar from
VLTI-VINCI” by Armando Domiciano de Souza et al.).

Notes
[1] The team consists of Armando Domiciano de Souza, Lyu Abe and
Farrokh Vakili (Laboratoire Univ. d’Astrophysique de Nice – LUAN,
France), Pierre Kervella (ESO-Santiago), Slobodan Jankov (Observatoire
de la Cote d’Azur, Nice, France), Emmanuel DiFolco and Francesco
Paresce (ESO-Garching).

[2] More information about the VLTI and photos of many of the
components of the facility are available at the VLTI website, as well
as in ESO PR 06/01 (“First Light” in March 2001 and explanation of the
interferometric measurements), ESO PR 23/01 (observations with two
8.2-m telescopes in October 2001) and ESO PR 16/02 (observations with
four 8.2-m telescopes in September 2002), ESO PR 22/02 (measurements
of the diameters of small stars in November 2002) and ESO PR 11/03
(installation of the first MACAO adaptive optics unit in May 2003).

[3] Strictly speaking, the elliptical shape shown in PR Photo 15b/03
is the best fit to the interferometric data, assuming that Achernar is
a uniformly illuminated ellipsoidal body. In fact, the true shape of
the star’s photosphere (visible “surface”) may be slightly different
in the presence of a light-emitting circumstellar envelope. However,
the astronomers monitored the star’s emission for signs of such an
envelope (an “equatorial disk”) during the VLTI observations; there
were no signs and they were therefore able to establish narrow limits
on the possible influence of this effect on the apparent flatness of
the star.

[4] The mean angular diameter of Achernar is equivalent to the angle
subtended by a 1 Euro coin at a distance of about 2500 km, or by a car
(4 metres long) on the surface of the Moon.

Contacts

Armando Domiciano de Souza
Laboratoire Univ. d’Astrophysique de Nice (LUAN)
France
Phone: +33 4 9340 5372
Email: armando.domiciano@obs-azur.fr

Pierre Kervella
ESO
Santiago de Chile
Phone: +56 2 463 3000
Email: pkervella@eso.org