IB Astrophysics option part 3. See also http://nothingnerdy.wikispaces.com

1. presents
a production
STELLAR DISTANCES
based on the IB Astrophysics option
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2. STELLAR DISTANCES
How far away are stars and galaxies?
Parsec
Stellar Parallax
Spectroscopic parallax
Cepheid variables
Apparent magnitude
Absolute magnitude
Image: Carina Nebula by ESO

3. Measuring distances
By observation, we can measure how
bright an object appears. In order to
calculate the actual magnitudes or
luminosities of stars, we must know how
far away they are. There are several
ways of doing this depending on how
great the distance is.

4. Astronomical units
Reminders
1 Astronomical unit = 150 million km
(average Sun-Earth distance)
1 light year = 10 000 billion km
(distance light travels in 1 year)

5. Angle facts
360 degrees in a circle
60 arc-minutes in a
degree
60 arc-seconds in an
arcminute
There are approx. 1.3
million arc-seconds in
a full circle

6. The parsec
One parsec = 3.26 light years = 30 000 billion km
“Parsec” is short for
The parsec (pc) – this is parallax arc-second
the distance at which 1
AU subtends an angle of
1 arc-second.
Nearest
star is
approx
1.3 pc
away

7. Stellar Parallax
The method of measuring distance using the
apparent change in position of nearby stars
Every six months, the
Earth is at the opposite
side of its orbit and nearby
stars shift position relative
to faraway stars. We can
measure the angle, p.
For very small angles, p = angle in arcsec
tan p ≈ p (angles in R = base in AU
rads) d = distance in pc

8. Measurement of parallax
For parallax measurements
from the Earth, R is 1 AU, so
Proxima Centauri subtends a parallax
angle of 0.769 arc sec, so its distance is
1/0.77 = 1.30 pc

9. The limit of parallax
The farther away
an object gets, the
smaller its shift.
A parallax angle of 0.005 arc-sec is
Eventually, the shift is near the limit of measurability from
too small to see. the Earth, which corresponds to a
distance of 200 pc.
Space telescopes are increasing the range of parallax, but
there will always be limits due to the tiny angles involved.

10. Spectroscopic parallax
The method of measuring distance using the HR diagram.
Absorption spectrum of the star
This may tell us the type of star, eg main sequence, dwarf or giant
Wien’s law
Calculate the temperature from
the most intense wavelength
Finally, use L
H-R diagram and b to find d
Identify the luminosity
of the star using the
temperature

11. The limit of spectroscopic parallax
Beyond 10 mega-parsecs
(30 million light years),
stars are too distant to give
enough light to determine
the temperature.
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12. Cepheid variables
The method of measuring distances using
stars whose brightness changes predictably
Their temperature and
luminosity place them here
on the HR diagram.
A Cepheid variable is a
very bright, unstable star
which pulsates brighter
and dimmer.
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13. Cepheid calculation
Cepheids in another galaxy can be used to measure its distance.
The period of the Cepheid variable is related to its
luminosity: the brighter it is, the slower it pulses.
The graph of log L vs log T is linear.
From observing the period, use the graph to find the
luminosity (L). From L and apparent brightness (b), find
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the distance, d.

14. Different distances
require different methods of measurement
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15. Apparent magnitude
Apparent magnitude
(m) assigns a number
to an object to describe
how bright it appears
from Earth
Faintest objects are
Betelgeuse and Rigel, larger positive numbers
stars in Orion with
apparent magnitudes
0.3 and 0.9 Brightest objects are smaller
positive and even negative numbers

16. Magnitude scale
Each magnitude corresponds to a factor
of 2.5 change in brightness (a log scale)
Every 5 magnitudes is
a factor of 100
change in brightness
5
b +1
= 2.5 ≈ 100
b +6 1
where b+m is brightness
of star magnitude m

17. Absolute Magnitude (M)
The magnitude an object would have if
we put it 10 parsecs away from Earth
Apparent magnitude, m depends on the position of the
object. Absolute Magnitude, M puts them all on the
same scale.
For the Sun,
m = -26.7
M = +4.8
Not forgetting that a bright star has a low magnitude number

18. Relation of M and m
Knowing the apparent magnitude (m) and the
distance in pc (d) of a star, its absolute magnitude
(M) can be found using the equation:
What is the absolute magnitude of the Sun (m=-26.7)?
The distance of Sun from Earth is 1 AU = 4.9x10-6 pc
M = -26.7 – 5*log (4.9x10-7)= +4.8

19. a production
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