Determining Stellar Distances
Distance Determinations
in ‘Real Life’
We use various ways. (Think of some!)
Here’s an important one:
binocular vision  depth perception
Parallax
Two different points
of view.
The Trick
Each eye sees a slightly different image.
The brain merges these and interprets the
three-dimensional nature of the situation.
As Here
[compare the lampstand to the building]
Simulated - and Exaggerated!
Accomplishing
the Trick
- two images, one per eye
Need a Background
Frame of Reference
Fundamental Limitation
More remote objects display less parallax!
(Our ‘depth perception’ fails us beyond a
few tens of metres, and we have to use
other methods.)
To Improve Binocular Vision:
Spread the eyes apart!
Our Objective
Remember that some stars are nearby,
others much farther away (in the
‘background’).
If we can ‘spread’ our eyes far enough
apart, we will see the nearby stars slightly
displaced against the background pattern.
‘Geocentric’ Parallax
Imagine two ‘eyes’ separated by hundreds of
kilometers, looking at something relatively close.
Limitations of Geocentric Parallax
If the target is too far away, the parallax effect
becomes immeasurably noticeable, even from
widely-separated locations on Earth.
How About the Stars?
Even the very nearest stars are so far away that
we don’t notice any geocentric parallax.
These two people are looking in essentially parallel
directions, because the star is so remote!
The Solution
Remember that the Earth moves around the
sun once a year!
We can take one picture now, then a second
one six months later from a much
different location (300,000,000 km away).
This ‘spreads our eyes’to yield the effect
known as heliocentric parallax.
That Sounds Easy
Note: It’s Not Exactly Equivalent to
Human‘Depth Perception’
Our ‘binocular’ vision works because we compare
two different views (one with each eye) at the
same time.
In heliocentric parallax, we are comparing two
images taken at different times.
But the principle is fundamentally the same.
The Expected Result
We should see any nearby star shift
back-and-forth once a year relative
to more remote stars in the
background.
Indeed, This MUST Happen!
If the sun is truly at the centre of the Solar
System, nearby stars should show this
kind of parallax (because the Earth
moves!)
If they don’t, we have problems!
It Seems Trivially Easy!
If the red star is nearby, then:
in Jan, we see this
in July, we see this
- a conspicuous change in its position!
Note: You Don’t Have to Wait
The change is of course the largest after 6 months (since
we are then on opposite sides of the Sun in our orbit), but
you can observe at intermediate times and watch the star
appear to move back and forth across the background.
Try the Animations/Other Animations on this site:
http://www.astronexus.com/node/28
This shows the parallax effects we would see if we orbited
the Sun in a really huge orbit (1.5 light years across!).
So What’s the Problem?
Why did it take ~240 years, following
Galileo’s first use of the telescope, to detect
this behaviour?
First, Let’s Choose
Convenient Units
Stellar distances are vast: many tens of trillions of
kilometers at least.
So, we can use light years.
One light year = the distance that light travels in
a year ( ~ 10 trillion km). The nearest star is
about 4 l.y. away.
Sobering Reality
As we will learn, the nearest star is ~ 300,000x as
far away as the Sun.
Try drawing our ‘geocentric parallax’ sketch again,
correctly scaled.
The ‘parallax angle’ is very small. The position of
the nearby star changes almost imperceptibly
against the background even after 6 months!
In the Original Drawing:
The red star is shown to be less than 1.5 times as
far away from the Sun as we are -- that’s closer
than Mars!!
Let’s Define Some Angles
Degrees, Minutes, Seconds ‘of arc’
Successive Subdivisions
Look horizontally, then straight up. That shift of
viewpoint is through 90 degrees (a ‘right angle’)
Take just one of those degrees and split it into 60
smaller angles: ‘minutes of arc’
Take one of those minutes and split it into 60 yet
smaller angles: ‘seconds of arc’
So a second of arc is a truly tiny angle.
How Big Does a Dime Look?
[obviously it depends on the distance!]
(A dime is 18 mm in diameter)
Its ‘Angular Size’ is
One degree if it’s about 1 metre away
One minute of arc if it’s 62 metres away
One second of arc if it’s 3.7 km away
In Other Words:
Stand on the grounds of
St Lawrence College
Have a friend hold up a
dime in downtown Kingston
Now shift your gaze from the
top edge of the dime to the
bottom. That’s 1 arcsec -a truly tiny angle!
A New Unit of Distance
If the parallax angle,
p, is one second of arc
then the star is, by
definition, exactly one
parsec away.
(if there are any stars even closer
than that, they will show greater
parallax. Remote stars show less.)
1 parsec = 3.26 light years
Relating These Units
Astronomers quote distances in




parsecs (for the nearby stars)
kiloparsecs (for distances within the Milky Way)
megaparsecs (for distances to other galaxies)
gigaparsecs (for the most remote observable parts of the
universe)
Remember the ‘look-back times.’
about 3 million light years.
One megaparsec is
Is She Fast?
http://www.astro.queensu.ca/~hanes/ASTR102-Winter2016/ANIMS/Cantina.mp4
Now a Sobering Dose of Reality
Other than the Sun, no star is as close as
one parsec.
In other words, as we orbit the Sun, no star
will seem to shift back and forth against
the background by even as much as as
one second of arc.
Meet Proxima
Centauri
(lower right) --the
very closest star
Ask yourself how this
picture will look six
months from now.
Proxima will seem to
have moved, but by less
than the size of the little
dot of light! -- and this
is the closest star of all.
And We Have it Comparatively Easy!
We can take pictures of the sky, months apart,
and intercompare them later, at leisure.
In the early 1800’s, no such technology existed.
Astronomers had to measure the angles between
stars to map out the detailed pattern. Repeat
the exercise six months later to see if things had
changed perceptibly. Repeat, year after year!
An Additional Complication
Individual stars move through space!
Consequently, the annual parallactic shift (a tiny
back-and-forth motion) is superimposed on a
general accumulating change in position of any
individual star.
Example:
Barnard’s Star
It travels across the sky
(because of its own
motion), and also
appears to shift back
and forth (thanks to our
changing vantage point
as the Earth orbits the
Sun).
That’s Why, Historically…
…parallax was devilishly hard to discover!
Astronomers simply couldn’t look at ALL stars, to try and
detect this tiny effect among a few of them that happen
to be nearby. That’s impractical!
Narrow the Field
They needed to focus their efforts on stars that
are probably nearby.
But there are literally millions of stars visible
through telescopes.
Which ones do you suspect are the closest ones to
us? On what grounds?
To Make Progress:
Find some independent indication that a
particular star may be nearby.
Then study its position over years and
years, with the hope of detecting its
parallax.
Any Suggestions?
Which of These Stars is Likely to be Closest to Us?
The Obvious Thought
If all stars were similar, the nearest ones
would be the brightest ones.
So: pick the stars that look brightest to the
eye! (Betelgeuse, Antares, Sirius, Rigel, Vega…)
Perhaps they are ‘on our doorstep’…
This Doesn’t Work
Most of the apparently bright stars actually lie at
very large distances and display very little
parallax.
So why do they look so bright? It’s because they
are so ultra-luminous that they show up
conspicuously despite their large distances!
(Sirius is an exception: it actually is moderately
close, only 9 light years away.)
Look Again
at Proxima
Centauri
It is quite
undistinguished –
very faint. Who
would have
guessed that it’s
so close to us!
Stymied! (late 1700s)
The brightest stars are not the optimal
targets.
Studying stars chosen at random seems to
be likewise hopeless!
How will we make progress?
One Clever Idea
(from Herschel)
Two Stars Apparently Side-by-Side
Maybe one is close to us, the other one a lot farther away
As Time
Passes, We
Expect…
Because the Earth
goes back and
forth in its orbit,
the nearer star
seems to shift back
and forth relative
to the more remote
one.
Analogy
`
Hold up two fingers as shown, and blink
your eyes alternately. Note how one
finger seems to move relative to the
other.
What
Herschel
Discovered
Instead
- the stars are
in mutual orbit!
That is, Binary Stars Exist!!
[A critical discovery. They are very important]


Binary stars allow us to
determine stellar
masses!
They are the homes of
exotic physics (such as
when one member is a
neutron star or black
hole).


They explain some
interesting variability
(such as eclipsing
binaries)
There is general
astrophysical interest
(about 50% of all stars
are in binary or multiple
systems - but not the
Sun)
Determining Stellar Masses
Remember the see-saw
Newton Tells Us How
[see ASTR 101]
A Brief Digression:
Variable Stars
There are two kinds:

intrinsic variables (in which the star itself
changes in some way)

extrinsic variables (where a star appears to
change because of some independent effect, like
being eclipsed by another object)
1. Intrinsic Variables
Exploding stars:
novae, supernovae, cataclysmic variables, flare
stars, etc. (Some of these happen because the
star is in a close binary system.)
Pulsating variables:
(pumping in and out like a heart beating):
Cepheids, RR Lyrae stars,…
2. Extrinsic Variables
One example:
eclipsing binaries
Eclipses Simulated
Visit this site
http://astro.unl.edu/naap/ebs/animations/ebs.html
and try out the simulations shown there.
Notice how the precise behaviour of the eclipse
depends on the nature of the stars involved, and
the angle from which we see it.
Anyway, Herschel’s Clever Idea Failed
Let’s forget about binary stars for now.
How will we select stars that we think are
probably close, and then hunt for parallax
effects?
What’s another indicator of close proximity?
Hint: Compare These Motions
The Solution
Assume that all stars move through space with
comparable speeds (not unreasonable)
Then those that are closest to us will seem to shift
position across the sky more quickly than the
more remote ones.
So identify the stars that have high proper motions
and try to measure their parallaxes!
For Example
Visit
http://www.astronexus.com/node/28
and look at the 3D animations (based on real
astronomical data!).
Notice the stars with high ‘proper motions’ – in
particular, 61 Cygni.
Success!!
In 1837, parallaxes were measured for
three different stars (by three different
astronomers!):
61 Cygni
Vega
Proxima Centauri
The Important Implications
1.
The Earth really does orbit the Sun!
2.
The stars really are far away!
3.
We are now able to work out the physics
of the stars – their intrinsic luminosities,
their masses (using binaries), and so on.
The Critical
Point
If we can measure the parallax, we can determine the
distance of the star. It is just like surveying!
We only need to know the ‘baseline’ (the separation
between the two observing points) plus the measured
angle (the parallax).
Remember the
Fundamental Limitations
The method of parallaxes
only works for relatively
nearby stars (just as our
depth perception has a
limited range)
The reason is the same:
a limited ‘baseline’
Until Recent Decades
Reliable parallaxes had been measured for
only a few thousand stars
(There are an estimated hundred billion in
our own galaxy!)
Recent Improvements
Telescopes in satellites!
This does not increase the baseline (‘spread our
eyes apart’), but it allows sharper, crisper
images since we avoid the ‘blurring’ caused by
the Earth’s atmosphere.
Result: better precision, many more stars.
HIPPARCOS (1989-1993)
What it Did
HIPPARCOS = High Precision Parallax and
Coordinates for Stars. (a great acronym!)
(The name is in homage to Hipparchus, the great
astronomer of antiquity.)
This led to very precisely determined parallaxes for
100,000 stars; and less precise results for 1-2
million more.
Visit http://www.rssd.esa.int/Hipparcos/
But Even With HIPPARCOS…
…parallax measurements, though critical and
fundamental, have a definitely limited range.
(Fewer than 0.01% of the stars in the Milky Way
galaxy are within reach of our direct parallax
measurements.)
To derive distances to more remote stars, and to
other galaxies, different techniques are used.
Where We Stand Now
Now that we know the true distances to many of
the stars, we can work out lots of things:




Their true brightnesses
Their masses (thanks to binaries)
Their sizes
etc..
Given this information, we can do astrophysics!