Taking advantage of the very high spatial resolution provided by the
Very Large Telescope Interferometer, a team of French and Swiss
astronomers [1] has measured directly the change in angular diameter
of four southern Cepheid variable stars over their pulsation cycle.

When combined with spectroscopic radial velocity measurements, this
allowed the astronomers to measure very accurately the distances of
these stars in a quasi-geometrical way, and to calibrate the
zero-point of the Cepheid Period-Luminosity empirical law.

These observations constitute a fundamental step towards an
independent verification of the extragalactic distance scale by
interferometry.

The full text of this press release, with all photos and weblinks, is
available at:
http://www.eso.org/outreach/press-rel/pr-2004/pr-25-04.html

Cepheids and the cosmic distance ladder

It is very difficult to measure the distance to an astronomical
object. In fact, this is one of the greatest challenges facing
astronomers. There is indeed no accurate, direct way to determine the
distance to galaxies beyond the Milky Way: astronomers first determine
the distance to nearby stars in our galaxy as accurately as possible
and then use a series of other techniques that reach progressively
further into space to estimate distances to more distant systems.

This process is often referred as the “cosmic distance ladder”.

Over the years, a number of different distance estimators have been
found. One of these is a particular class of stars known as Cepheid
variables. They are used as one of the first “steps” on this cosmic
distance ladder.

Cepheids are rare and very luminous stars whose luminosity varies in a
very regular way. They are named after the star Delta Cephei in the
constellation of Cepheus, the first known variable star of this
particular type and bright enough to be easily seen with the unaided
eye.

In 1912, American astronomer Henrietta Leavitt observed 20 variable
stars of the Cepheid-type in the Small Magellanic Cloud (SMC), one of
the closest galaxies to the Milky Way. For all purposes, these stars
are all at the same distance (the size of the SMC is negligible
compared to its much larger distance from us). Apparently brighter
stars in this group are thus also intrinsically brighter (more
luminous). Henrietta Leavitt discovered a basic relation between the
intrinsic brightness and the pulsation period of Cepheid variable
stars in the SMC and showed that intrinsically brighter Cepheids have
longer periods.

This relation is now known as the “Period-Luminosity relation” and is
an important way to derive the distance to stars of this type. By
measuring the period of a Cepheid star, its intrinsic brightness can
be deduced and from the observed apparent brightness, the distance may
then be calculated. In this way, Cepheid stars are used by astronomers
as one of the “standard candles” in the Universe. They act either as
distance indicators themselves or are used to calibrate other distance
indicators.

The Cepheid stars have taken on an even more important role since the
Hubble Space Telescope Key Project on the extragalactic distance scale
relies completely on them for the calibration of distance indicators
to reach cosmologically large distances. In other words, if the
calibration of the Cepheid Period-Luminosity relation were wrong, the
entire extragalactic distance scale and with it, the rate of cosmic
expansion and the related acceleration, as well as the estimated age
of the Universe, would also be off.

A main problem is thus to calibrate as accurately as possible the
Period-Luminosity relation for nearby Cepheids. This requires
measuring their distances with the utmost precision, a truly daunting
task. And this is where interferometry now enters the picture.

The Baade-Wesselink method

Independent determinations of the distance of variable stars make use
of the so-called Baade-Wesselink method, named after astronomers
Walter Baade (1893 – 1960) and Adriaan Wesselink (1909 – 1995). With
this classical method, the variation of the angular diameter of a
Cepheid variable star is inferred from the measured changes in
brightness (by means of model atmosphere calculations) as it
pulsates. Spectroscopy is then used to measure the corresponding
radial velocity variations, hence providing the linear distance over
which the star’s outer layers have moved. By dividing the angular and
linear measures, the distance to the star is obtained.

This sounds straightforward. However, it would obviously be much
better to measure the variation of the radius directly and not to rely
on model atmosphere calculations. But here the main problem is that,
despite their apparent brightness, all Cepheids are situated at large
distances. Indeed, the closest Cepheid star (excluding the peculiar
star Polaris), Delta Cephei, is more than 800 light-years away. Even
the largest Cepheids in the sky subtend an angle of only 0.003
arcsec. To observe this is similar to view a two-storey house on the
Moon. And what astronomers want to do is to measure the change of the
stars’ sizes, amounting to only a fraction of this!

Such an observing feat is only possible with long-baseline
interferometry. Also on this front, the VLT Interferometer is now
opening a new field of observational astrophysics.

Three VLTI baselines

Some time ago, an undaunted team of French and Swiss astronomers [1]
started a major research programme aimed at measuring the distance to
several Cepheids by means of the above outlined Baade-Wesselink
interferometric method. For these observations they combined sets of
two beams – one set from the two VLTI Test Siderostats with 0.35m
aperture and the other set from two Unit Telescopes (Antu and Melipal;
8.2m mirrors) – with the VINCI (VLT Interferometer Commissioning
Instrument) facility. Three VLTI baselines were used for this
programme with, respectively, 66, 140 and 102.5m ground length. ESO PR
Photo 30b/04 shows the respective positions on the VLTI platform.

The observations were made in the near-infrared K-band.

A total of 69 individual angular diameter measurements were obtained
with the VLTI, over more than 100 hours of total telescope time,
distributed over 68 nights; the largest angular diameter measured was
0.0032 arcsec (L Car at maximum).

Seven Cepheids observable from Paranal Observatory were selected for
this programme: X and W Sagittarii, Eta Aquilae, Beta Doradus, Zeta
Gemini, Y Ophiocus and L Carinae. Their periods range from 7 to 35.5
days, a fairly wide interval and an important advantage to properly
calibrate the Period-Luminosity relation.

The distances to four of the stars (Eta Aql, W Sgr, Beta Dor and L
Car) were derived using the interferometric Baade-Wesselink method, as
their pulsation is detected by the VLTI. ESO PR Photo 30c/04 shows the
angular diameter measurements and the fitted radius curve of L Car
(P = 35.5 days); this measures its distance with a relative precision
better than 5%.

For the remaining three objects of the sample (X Sgr, Zeta Gem and Y
Oph), a hybrid method was applied to derive their distances, based on
their average angular diameter and pre-existing estimations of their
linear diameters.

The new calibration

Combining the distances measured by this programme with the apparent
magnitudes of the stars, the astronomers determined the absolute
magnitude (intrinsic brightness) of these stars and arrived at a very
precise calibration of the zero-point of the Period-Luminosity
relation (assuming the slope from previous work).

It turned out that this new and independently derived value of the
zero-point is exactly the same as the one obtained during previous
work based on a large number of relatively low-precision Cepheid
distance measurements by the ESA Hipparcos astrometric satellite.

The agreement between these two independent, geometrical calibrations is
remarkable and greatly increases the confidence in the cosmic distance
scale now in use.

Prospects with AMBER

With 1.8m Auxiliary Telescopes soon to be ready on the VLTI platform,
the astronomers will be able to observe many more Cepheids with a
precision at least as good as the present high-precision VINCI
observations of L Car. In addition, the future AMBER instrument will
extend the VLTI capabilities toward shorter wavelengths (J and H
bands), providing even higher spatial resolution than what is now
possible with VINCI (K band).

The combined effect of these two improvements will be to extend
significantly the accessible sample of Cepheids. It is expected that
the distances to more than 30 Cepheids will then be measurable with a
precision better than 5%. This will provide a high precision
calibration of both the reference point (down to ±0.01 mag) and the
slope of the Galactic Cepheid Period-Luminosity.

More information

The information contained in this press release is based on a series
of three research articles which are being published by the European
research journal “Astronomy & Astrophysics” by P. Kervella and
collaborators (Paper I : 2004, A&A, 416, 941, Paper II : 2004, A&A,
423, 327 and Paper III : in press). The present press release is
published exactly three years after the first observations with two
8.2-m VLT Unit Telescopes and the VLTI with VINCI were achieved,
cf. ESO PR 23/01.

Note

[1]: The team consists of Pierre Kervella and Vincent Coude du Foresto
at the Paris Observatory in France, David Bersier of the Space
Telescope Science Institute (USA), Nicolas Nardetto and Denis Mourard
(Observatoire de la Cote d’Azur, France), and Pascal Fouque
(Observatoire Midi-Pyrenees, France).

Contacts

Pierre Kervella
Observatoire de Paris-Meudon
France
Phone : +33 1 45 07 79 66
Email : Pierre.Kervella@obspm.fr

Denis Mourard
Observatoire de la Cote d’Azur
France
Phone : +33 4 93 40 54 92
Email : Denis.Mourard@obs-azur.fr