Download Celestial Distances

Celestial Distances
22 March 2005
AST 2010: Chapter 18
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Stellar Distances
To infer the luminosity, mass, and size of a star from
observations (as in a celestial census), we need to
know the distance to the star
How can we measure the great distances to stars?
We use various techniques, useful at different scales,
with each scale connecting to the next, like a ladder
On the Earth, lengths are specified in precise units such
as the meter
Distances within the solar system are determined by
timing how long it takes radar signals to travel from the
Earth to a planet or other body and then return
Beyond the solar system, …
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Parallax (1)
To observers at
points A and B,
the tree at C
appears in
different
directions
This apparent
displacement,
or change in direction, of a remote object due to a
change in vantage point is called parallax
The angle that lines AC and BC makes is also called
parallax
The distance between A and B (length of line AB)
is called the baseline
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Parallax (2)
How far away is the tree from each observer?
One can use triangulation, a method for
finding the distance
to an inaccessible
object
If the baseline (B in
this figure) and the
parallax angle p are
measured, then
the observers’
distances to the tree
can be calculated
using trigonometry
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Parallax for Stars (1)
The triangulation
method can be
applied to relatively
nearby stars
As the Earth orbits
the Sun, a nearby
star appears to us
to move back and
forth against the
background of
distant stars
This parallax can be
used to find the
distance d to the
star
if the baseline and the parallax angle are known
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Parallax for Stars (2)
Since stellar distances are very large, the for has to
be very large as well
For a relatively
nearby star, a
sufficiently large
baseline is the
Earth-Sun
distance, which
is 1 AU
The farther the star, the smaller the angle p
For relatively far stars, extremely sensitive
measurements of p are required
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The Parsec
Since the parallax shifts of stars are very small, the
arcsecond is used as the unit of the parallax angle
One arcsec (second of arc) is an angle of 1/3600 of a
degree
The parallax of the ball on the tip of a ballpoint pen
viewed from across the length of a football field is about
1 arc second
With a baseline of 1 AU, how far way would a star
have to be to have a parallax (p) of 1 arcsec?
The answer is 206,265 AU, or 3.26 LY
Astronomers take this number as another unit
(besides the light year) for astronomical distances,
called the parsec (abbreviated pc)
In other words, 1 parsec is the distance to a star that
has a parallax of 1 second of arc
Thus, 1 pc = 206,265 AU = 3.26 LY
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More on the Parsec
Which unit to use to specify distances: the light
year or the parsec?
Both are fine and are used by astronomers
For example, Proxima Centauri, the nearest star
beyond the Sun, is about 4.3 LY, or 1.3 pc,
away from us
If the distance (D) of a star is in parsecs and its
parallax (p) in arcseconds, then D and p are
related by a simple formula: D = 1/p
Thus, a star with a parallax of 0.1 arcsec would be
found at a distance of 10 pc, and another star
with a parallax of 0.05 arcsec would be 20 pc
away
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What about More Distant Stars?
The triangulation method fails for stars farther than
1000 LY away
The baseline of 1 AU would be too small for sufficiently precise
measurements of the parallax
Thus, completely new techniques are needed for more
distant stars
The breakthrough in measuring the enormous
distances came from the study of variable stars, or
variables
These are stars that vary in luminosity
Thus, their brightness changes with time
In contrast, most stars are constant in their luminosity (at
least within a percent or two)
Many variables change in luminosity on a regular cycle
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Cepheid Variable Stars
One of the two special types of variable stars used for
measuring distances are the cepheids
They are are large, yellow, pulsating stars named for
the first-known one of the group, Delta Cephei
Its variability was discovered by English astronomer
John Goodricke in 1784
It has a magnitude varying with a period of 5.4 days
time
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Cepheid light curve
AST 2010: Chapter 18
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Cepheid Variables
Several hundred
cepheids have been
found in our Galaxy
Most have periods in
the range of 3 to 50
days and luminosities
in the range of 1,000
to 10,000 times
greater than that of
Animation
the Sun
Polaris, the North Star, is a cepheid variable
It used to vary by 0.1 magnitude every 4 days
More recent measurements indicate that its
pulsation is decreasing, which suggests that in the
future it will no longer be a pulsating variable
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Cepheid Variables in NGC 3370 and M100 Galaxies
The observations was taken by the Hubble
Space Telescope
The cepheid in NGC 3370
is in the center of a
crowded region of stars
and has a period of about
50 days
A cepheid in a very distant
galaxy called M100
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RR Lyrae Stars
Another special special types of variable stars used for
measuring distances are called the RR Lyrae variables
They are named for the star RR Lyrae, the best-known
member of the group
They are more common than the cepheids, but less
luminous
Their periods are always less than one day, and their
changes in brightness are typically less than about a
factor of 2
From observations, astronomers have concluded that
RR Lyrae variables all have nearly the same intrinsic
luminosity, of about 50 times that of the Sun
Thus, they are like standard light bulbs
The RR Lyrae stars can be detected out to a distance
of about 2 million LY
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Why A Cepheid Variable Varies
Its changes in color
indicates a change
in temperature
The Doppler shift of
its spectrum
indicates a change
in its size
Its luminosity
changes when its
temperature and
size change
pressure
from hot
gas
 In a normal star, the pressure and gravity balance
cloud
 In a variable star, the pressure and gravity are out of
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weight
from
gravity
synch
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Period –Luminosity Relation (1)
Studying photographs of
the Magellanic Clouds, two
small galaxies near ours,
Henrietta Levitt in 1908
found 20 cepheids that
were expected to be at
roughly the same distance
and discovered a relation
between their luminosities
and variation periods
The longer the period, the
greater the luminosity
To define the period-luminosity relation with actual
numbers (to calibrate it), astronomers first had to measure
the actual distances to a few nearby cepheids (in other
clusters of stars) in another way
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Period –Luminosity Relation (2)
Cepheids and their period-luminosity relation
can be used to estimate distances out to over
60 million LY
under the assumption that all the cepheids obey
the same period-luminosity relation
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Distances from H-R Diagram
Variables are rare and, therefore, cannot always be found
near the a star of interest
If variables are not available,
the H-R diagram may come
to the rescue
A detailed examination of a
star’s spectrum can tell us its
spectral class/type (O, B, A, etc.)
pressure and hence size (bigger
stars have lower pressures)
Knowing the spectral class
and size of a star can help us make an educated guess
whether it is a main-sequence, giant, or supergiant star
This then allows us to pinpoint where the star is on the H-R
diagram and establish its luminosity
The luminosity, with the apparent brightness of the star,
finally leads to its distance
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Summary
Distances to nearest stars can be measured
using the parallax (triangulation) method
For farther stars in our own and nearby
galaxies, the distances can be determined
using the RR Lyrae variables and the H-R
diagram
The cepheids and their period-luminosity
relation are useful for finding larger distances
up to 60 million LY
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