Introduction
Measuring the distances to other celestial
objects is difficult. For near objects, like the
moon and some planets, it can be done by
sending radio-signals and measure the time
it takes for them to be reflected back to the
Earth. Even for near stars it is possible to
get quite acurate distances by using the
parallax-method.
But for distant objects, determining their
distance becomes very difficult. From Earth,
we can only measure the apparant
magnitude and not how bright they really
are. A small, dim star that is close to the
Earth can appear to look the same as a
large, bright star that is far away from Earth.
As long as the early 20
th
century it was not
possible to resolve this major problem in
distance determination. At this time, one
was especially interested in determining the
distance to the so called „nebulas“. One
has found many of this diffuse looking
objects in the sky. Some astronomers
thought them to be clouds of gas inside our
milky way. Others believed, that there wer
islands full of stars, galaxies of their own
and at extremly large distances. If this
would be true, our universe would be much
more larger than previously thought.
But without a way to determine their
distance, it was not possible to resolve this
debate. The first hint on how the measure
their distance came from Henrietta Swan
Leavit. In 1912 she investigated a group of
variable stars called „Cepheids“. Those
stars change their brightness periodically
over some days. Leavitt found that the
period of the luminosity variations is
connected to the absolute magnitude of the
star! If one thus knows the period P of a
cepheid, one can use the following formula
to determine the absolute magnitude M:
M = -1.43 – 2.81 * log (P)
(P is measured in days)
One now knows how bright the star really is
an can compare that value with the
apparent magnitude m, which can be easily
measured. Knowing, how bright the star is
and how bright he appears, one can use
the so called distance modulus:
m – M = -5 + 5 log r
where r is the distance of the object
measured in parsec (1 parsec is 3.26
lightyears or 31 trillion kilometers).
With this method, in 1923 Edwin Hubble
was able to observe Cepheids in the
Andromeda nebula and thus determine its
distance: it was indeed an object far outside
the milky way and an own galaxy!
Measuring the distance to
Andrimeda with Aladin
To measure the distance to Andromeda
with Aladin, one first needs observational
data. To make use of the Period-
Brightness-Relation, we search the Virtual
Observatory (VO) for data on cepheids in
the Andromenda galaxy:
File -> Open, then choose „All ViZieR“ from
the „catalog server“ menu
In the form field, enter „Andromeda“ (or
„M31“) as the „target“. Since we do not lnow
in which catalog we can find our data, we
enter „cepheid“ in the field for „free text“.
Klicking on „Submit“ will start the search.
Image 1: Searching the VO for cepheid data.
We will obtain three catalogs as our result
(the field „description“ contains more
information about the data):
We chose the most recent catalog from
2003. In the main window of Aladin, we will
now see the position of the objects in the
catalog; in the stack on the right we can see
the symbol of the catalog „J.A+A 402.113):
In the next step, we want to examine the
catalog data in more detail. We select the
„select“-tool from the toolbar menu on the
right side of the Aladin window and mark all
the objects. In the measurement window
(below the main window) we can see the
data from the catalog:
„ID“ gives the Identifier of the star;
„RAJ2000“ and „DEJ2000“ are the right
ascension and declination of the star.
„Rcmag“ and „Icmag“ are the apparent
magnitudes of the stars in different filters.
„DeltaRc“ is the error bar of the
measurement and „IcFile“ and „RcFile“ link
to the detailed Lightcurves of the stars.
The column labeled „Per“ gives the Period
of the star and is the one we are interested
in. But looking at the complete list of
objects, we notice, that not all contain
values for the period. To display only the
stars for that peroids were measured, we
can define a special filter:
Catalog -> Create a new filter
There we change to the „Advanced mode“
and chose „Per“ from the „Columns“-menu.
In the filter-window, we will see the term „$
{Per}“. Since we only want the objects,
where a Period exists, we change this to „$
{Per} > 0“. To draw those entries in the
Aladin window, we add a last modification:
„${Per} > 0 {draw}“. Klicking „apply“, the
filter is activated and in the main Aladin
Image 2: 3 catalogs were found
Image 3: A catalog was loaded
Image 4: Displaying the catalog data
Image 5: Creating a filter
window we will now see just the stars with a
known period.
We now use the period-brigtness-relation to
calculate the distance to the stars.
First, we create a new column in the
catalog:
Catalog -> Add a new column
In the „Column calculator“-window, we first
enter a name for the new column, e.g. „M“,
the traditional label for the absolute
magnitude (we can ignore the fields for
UCD and unit).
We now have to specify how the new
column has to be calculated. In the field
expression, we enter the formula for the
period-brightness-relation:
1.43 - 2.81 * log(${Per})
Klicking on „Add new column“ performs the
calculation and displays the new column.
We now need an aditional new column
where we calculate the distance, using the
distance modulus.
Thus, we repeat the procedure and now
use the expression
(10^(${Icmag} - ${M}+5)/5)*3.26
The multiplication with 3.26 converts the
output from parsec directly to lightyears.
The measurement-window in Aladin now
shows the distance of all the cepheids.
Note that this method is a relatively crude
one. To obtain exact results, one has to
fine-tune the constants in the period-
brightness-relation to the filters used in the
luminosity-measurements.
But if one calculates a mean-value of all the
distances, we obtain a quite good result:
the Andromeda galaxy has a distance of
2.52 +/- 0.14 million lightyears!
Image 6: Calculating a new column in the
catalog