Lecture 6: Stellar Distances
and Brightness Sections 19.1-19.3 in book
Key Ideas about Distances
Distances are the most
important and most difficult quantity to measure in astronomy.
Method of Trigonometric
parallaxes
direct geometric
distance method
Units of distance
parsec (parallax arcsecond)
light year
Why Are Distances Important?
They are necessary for
measuring
Energy emitted by a
object (that is, converting brightness to luminosity)
Masses of objects
from their orbital motions
True motion of
objects through space
Physical sizes of
objects
But distances are hard to
measure. For the stars, we resort to using GEOMETRY.
Method of Trigonometric
Parallax
Relies on apparent shift in position of a nearby stars against the
background of distant stars and galaxies.
p=parallax angle.
Parallax decreases with
distance
Closer stars have larger
parallaxes
Distant stars have smaller
parallaxes
Stellar Parallaxes
All stellar parallaxes are
smaller than 1 arcsecond.
The nearest star: Proxima
Centauri
Parallax of p=0.772
arcsec
First parallax observed in
1837 by Bessel for the star 61 Cygni
Use photography or digital
imaging today.
1 arcsec=1/1,296,000 of a
circle and is the angular size of a dime at 2 miles or a hair width from 60
feet.
Parallax Formula
p=parallax angle in arcseconds
d=distance in parsecs
Parallax Second = Parsec (pc)
The parsec (pc) is a fundamental distance unit in Astronomy
ÒA star with a parallax of 1 arcsecond has a distance of 1
parsecÓ
1 pc is equivalent to:
206,265 AU
3.26 Light years
3.085x1013
km
Light Year (ly)
The light year (ly) is an alternative unit of distance
Ò1 light year is the distance
traveled by light in one yearÓ
1 ly is equivalent to
0.31 pc
63,270 AU
Examples:
a Centauri has a parallax of p=0.742 arcsec. Derive the
distance.
A more distant star has a
parallax of p=0.02 arcsec. Derive the distance.
Limitations:
If stars are too far away,
the parallax will be too small to measure accurately
The smallest parallax
measureable from the ground is about 0.01 arcsec
Measure distances
out to ~100 pc
Get 10% distances
only to a few parsecs
But
there are only a few hundred stars this close, so the errors are much bigger
for most stars.
Blurring
caused by the atmosphere is the main reason for the limit from the ground.
From space:
Hipparcos Satellite
Errors
in parallaxes of 0.001 arcseconds
Parallaxes
of 100,000 stars
Good
distances out to 1000 pc
GAIA Satellite
Positions
and motions for about 1 billion stars
Parallaxes
for > 200 million stars
Precision
of 10 microarcseconds
Reliable
distances out to 10,000 pc away (includes the Galactic Center at about 8000 pc
away).
When we know the distances to
the stars, we can see the constellations as the three dimensional objects they
actually are. Example: Orion.
Other Ways of Measuring
Distances
They exist! (which is good,
since we canÕt measure parallaxes for that many stars, and certainly not for
stars outside the Milky Way)
But they are indirect, and
rely on assumptions such as:
This star has the
same luminosity as the Sun
This star has the
luminosity given by a model
We will return to this in
much more detail when we start talking about galaxies.
Stellar Brightness
Key Ideas
Luminosity of a star:
Total energy output
Independent of
distance
Apparent Brightness of
a star depends on
Distance
Luminosity
Photometry
How ÒBrightÓ is a Star?
Intrinsic Luminosity
Measures the Total
Energy Output per second by the star in Watts
Distance
independent
Apparent Brightness:
Measures how bright
the star appears to be as seen
from a distance
Depends on the distance to the star
Inverse Square Law of
Brightness
Consequence of geometry as
the light rays spread out from the source at the center.
(See Figure 19-4)
The apparent brightness of a
source is inversely proportional to the square of its distance from you.
Implications
For a light source of a given
Luminosity
Closer=Brighter
2x closer=4x
brighter
Further=Fainter
2x further=4x
fainter
Apparent Brightness of Stars
The apparent brightness of stars is what we can measure
How bright any given star
will appear depends on 2 things:
How bright it is
physically (Luminosity)
How far away it is (Distance)
Related through the inverse
square law
At a particular luminosity,
the more distant an object is, the fainter its apparent brightness becomes as
the square of the distance.
Does a star look ÒbrightÓ
because
it is intrinsically
very luminous?
it is intrinsically
faint but very nearby?
To know for sure you must
know either
the distance to the
star, or
some
other, distance independent property of the star that clues you in about its
intrinsic brightness
Measuring Apparent Brightness
The measurement of apparent
brightness is called Photometry
Two ways to express apparent
brightness:
as Stellar
Magnitudes
as Absolute Fluxes
(energy/second/area)
Both are used
interchangeably.
Flux Photometry
Count the photons from a star
using a light-sensitive detector:
Photographic Plate
(1880s-1960s)
Photoelectric
Photometer (photomultiplier tube )(1930s-1990s)
Solid State
Detectors (photodiodes or CCD) (1990s-present)
Calibrate the detector by
observing Òstandard starsÓ of known brightness
Measuring Luminosity
To measure a starÕs
luminosity to need two measurements: the apparent brightness and the distance
The biggest source of
uncertainty is in measuring the distance to a star.
Practical Issues
We can measure the apparent
brightnesses of many millions of stars. But only have good distances
(parallaxes) for only about 100,000 stars. Therefore only that number have direct estimates of their luminosities. Since luminosity
depends on distance squared, small errors in distance are effectively doubled
(a 10% distance error gives a 20% luminosity error)
Example Problem
If the Sun quadrupled its
mass, what would the circular speed of the Earth need to be to stay in orbit at
its present radius (pick the closest answer)?
(a) It would need to be 2 x
slower
(b) It would need to be 2 x
faster
(c) It would need to be 4 x
slower
(d) It would need to be 4 x
faster