Download Stellar Distances - Red Hook Central School District

Measuring Stellar Distances
• Stellar Parallax few hundred pc
• Absolute & Apparent Magnitudes
• Spectroscopic Parallax
• Cepheid variables
distance
Stellar Distances
• Light Years – distance light travels 1 yr.
• Astronomical Units AU – distance Earth - Sun.
• Parsec – based on parallax.
• Meters.
Stellar Parallax
• Hold up pencil
• Blink eyes
• Pencil moves against backdrop.
• Look at post.
• Blink eyes.
Parallax Method Clip 11 min
• https://www.youtube.com/watch?v=XUQAI
ldqPww
Earth’s motion in orbit causes parallax.
1 AU
Sun
Near vs. Distant Star Parallax
Measure Parallax Angle
Angles are very small – measured in arc seconds.
Angular Measurements
Angular measure of object is expressed in degrees,
arc-minutes or arc-seconds.
360o in circle
1° = 1/360 of a circle or 60 minutes of arc.
1 arcminute = 1' = 1/60 of a degree or 60 sec of arc.
1 arcsecond = 1" = 1/60 of an arcminute = 1/3600 of
a degree.
Distance - Parcsec (pc)
(pc): distance at which an object would have a
parallax angle (p) of one arc second.
Equals approximately 3.26 light years (ly) or
about 206,265 astronomical units – AU.
AU – distance Earth to Sun. (1.5 x 1011m)
1 pc. =
distance
when p is
1 arc sec.
Stellar distance
d = 1/p
p = 1/d
d (dist) – #parsecs
p (parallax angle) – #arc-seconds.
Ex 1: The nearest star to Earth is Alpha Centauri,
which is at a distance of 4.37 ly. Calculate the
parallax angle that was measured to obtain
that distance.
• 4.37 LY / 3.26 = 1.34 pc.
• p = 1/d
• 0.746 arc-sec
1/1.34 pc
Ex 2: The nearest star has a parallax of
0.760 arc sec. What is this in parsecs?
• d = 1/p
• d = 1/ 0.76 = 1.3 pc.
Why can’t stellar parallax be used to
measure very distant stars?
• Angle gets too small. Few hundred pc
upper limit.
Starlight beginning thru parallax
• http://www.youtube.com/watch?v=jjmjEDY
qbCk
Absolute & Apparent Magnitudes
• Greeks classified stars - Apparent mag (m) –
bright = 1
dim = 6.
Greater than 6 need telescope to see.
• Now we can see further stars so stars can have neg
magnitudes.
Apparent and Absolute Mag’s
~ first 4 min
• http://www.youtube.com/watch?v=9
P8Veb_AlJ0
• m = 1 defined as 100x brighter than m = 6
• magnitude increase of 5 = increase brightness of factor
100x.
• Each step of 1 mag = changes brightness of Star by 2.511
5
100  2.511
• Apparent mag depends on luminosity & distance.
• Negative values appear brighter. Sun = -26.8.
To find brightness b using apparent magnitude; raise
2.51 to power Dm (mag).
Ex 3: A 2 magnitude difference is an apparent
brightness difference of 2.51 x 2.51 =
(2.511)2 = 6.25.
What difference in brightness is 3 magnitudes?
4 magnitudes?
• ~16
• ~40
If 2 stars have magnitudes of m1 and m2,
and apparent brightness of b1 & b2This relationship holds true:
b1
m1  m2
 2.511
b2
Ex 4: If the apparent magnitude of A & B are
m= 9.5 and -1.5 respectively, find the ratio of their
apparent brightness.
bA
9.5  ( 1.5 )
11
 2.511
 2.51
bB
= 2.49 x 104 .
Absolute Magnitude – M
If all stars were moved to 10 pc from us –
what would the apparent magnitude be?
Will the apparent magnitude of most stars
increase or decrease if we bring them to 10 pc?
Most would decrease – they will be brighter
& become more negative.
A few will increase it they are being moved
further away.
Using M and m to determine
distance
Relate apparent to absolute magnitude
and distance.
d 
m  M  5 log  
10 
M = absolute magnitude
m = apparent magnitude
d = distance in pc.
Ex 4: Alpha Centauri has an apparent magnitude of
0.10 & is 1.34 pc away. Calculate its absolute
magnitude, M.
d 
m  M  5 log  
10 
d 
M  m  5 log  
10 
1.34 
M  0.1  5 log 

10


= 4.5
Arcturus prb
Hwk.
• Read Hamper 337- 340
• Do 10,12 starting on pg 340.
• Do handout IB Stellar Distance 1 ques 1.
Spectroscopic Parallax
• Uses apparent brightness b, and
luminosity or apparent/absolute
magnitude to determine distance.
• Need to know spectral class (MS, WD, )
of star, & surface temp. & use HR
diagram.
Spectroscopic Parallax
Uses Luminosity & Apparent Brightness
• Use Wein’s Displacement to find surface T.
2.9 x10

T
3
Use spectral dark lines to find
composition which gives
spectral class. Usually main
sequence.
• Use H-R temp. to find luminosity (main
sequence) or absolute magnitude.
Use apparent brightness (W/m2) to calculate
distance (m). L in Watts.
L
b
2
4d
Or use apparent & absolute magnitude to
calculate distance (pc).
d 
m  M  5 log  
10 
Assumes star is on main sequence.
Ex 5: A study of a star suggests it is a main
sequence star. Its apparent brightness is 1 x 10-12
W/m2. The peak  is 600 nm.
a. Find the surface temperature.
b. If the temperature implies a luminosity of
1 x 10 26 W, what is the star’s distance in LY?
2.9 x10

T
3
L
b
2
4d
4.8 x 103 K
use Wein’s displacement.
L
d 
4b
2
d = 2.8 x 1018 m
= 300 LY
Beyond 10 Mpc, it’s hard to distinguish a
bright far star from a dimmer closer star.
A “standard candle” is a star of known L in a
cluster. We can then compare it with other
stars in the same galaxy or cluster to
determine the luminosity of other stars.
Cepheid Variables – luminosity varies
over time. Star expands & contracts.
The outer layers undergo variations in
Temp and surface area.
L  AT
4
Apparent brightness vs. time
(days)
Use to find period. Period relates to
luminosity/absolute mag M.
The luminosity or Absolute Magnitude
changes with the period in days.
• Can use the period to find L, then use
Cepheid as standard candle to find L for
other stars in galaxy.
Cepheid Variables
If Cepheid Variables close enough to measure d using stellar
parallax, then can use apparent brightness to find absolute
magnitude.
d 
m  M  5 log  
10 
Cepheid Variables Method
• Find the period.
• This gives the luminosity
• (use graph).
• Measure the apparent brightness (done with telescope).
• Determine d from the L &
brightness.
L
b
2
4d
• Where did this period-luminosity relation come
from?
When Cepheid’s are close enough to use stellar
parallax to measure distance, then the absolute
magnitude can be found from:
d 
m  M  5 log  
10 
IB Set Cepheid Variables.