Download 4Stars_Part_One

Stars Part One:
Brightness and Distance
Concept -1 – Temperature
λmax = 2.90 x 10-3 m/K/T
λmax = Peak black body wavelength
T = The star’s surface temperature in Kelvins
λmax = 2.90 x 10-3 m/K/T
λmax
From Jay Pasachoff’s Contemporary Astronomy
A star has a surface temperature
of 5200 K, what is its λmax?
λmax = 2.90 x 10-3 m/K/T = 2.90 x 10-3 m/K/5200
= 558 nm
558 nm
A star has a λmax of 940 nm, what
is its surface temperature?
λmax = 2.90 x 10-3 m/K/T, T = 2.90 x 10-3 m/K/
λmax = 2.90 x 10-3 m/K/ 940E-9 = 3100 K
3100 K
Concept 0 – Total power output
Luminosity L = σAT4
Luminosity L = The star’s power output in Watts
σ = Stefan Boltzmann constant = 5.67 x 10-8W/m2K4
A = The star’s surface area = 4πr2
T = The star’s surface temperature in Kelvins
Our Sun has a surface temp
Of about 5000 K, and a radius of
7 x 108 m. What is its Luminosity?
L = σAT4 = 5.67x10-8(4π(7x108 ) 2 )(5000)4 =
2.2x1026 Watts
2.2x1026 Watts
A star has a radius of 5 x 108 m,
26
and Luminosity of 4.2 x 10 Watts,
What is its surface temperature?
Luminosity L = σAT4 ,
T =(L/(σ4(5x108)2)).25 =6968 K = 7.0x103 K
7.0x103 K
Concept 1 – Apparent Brightness
Apparent Brightness b = L/4πd2
b = The apparent brightness in W/m2
L = The star’s Luminosity (in Watts)
d = The distance to the star
The idea here is that the total power is spread out
over the area of an sphere whose surface is where you
are, with the center on the star.
Apparent Brightness b = L/4πd2
The inverse square relationship
From Jay Pasachoff’s Contemporary Astronomy
26
10
Our Sun puts out about 2.2 x
Watts
of power, and we are 1.5 x 1011 m from
it. What is the Apparent brightness of
the Sun from the Earth?
2
L/4πd =
b=
2.2E26/
2
= 778 W/m
778 W/m2
2
4π1.5E11
Another star has a luminosity of 3.2 x
1026 Watts. We measure an apparent
brightness of 1.4 x 10-9 W/m2. How far
are we from it?
b = L/4πd2 , d = (L/4πb).5 = 1.3x1017 m
1.3x1017 m
Concept 2 – Apparent Magnitude
Apparent Magnitude m = 2.5log10 (2.52 x 10-8W/m2/b)
b = The apparent brightness in W/m2
m = The star’s Apparent Magnitude
The idea here is that a ratio of apparent brightness
of 100, would lead to a difference in apparent
magnitude of 5.
2.52E-8/b = 100(m/5) = 102(m/5) = 10(m/2.5)
Log10(2.52E-8/b) = m/2.5…
Note that the smaller b is, the bigger m is.
From Jay Pasachoff’s Contemporary Astronomy
So apparent magnitude is a counter-intuitive scale
-27 is burn your eyes out,
1 is a normal bright star, and
6 is barely visible to a naked, or unclothed eye.
(You can’t see anything if you clothe your eyes!!)
Remember if you go down by a factor of 5, you go
up in brightness by a factor of 100. A magnitude 1
star delivers 100 times more W/m2 than a
magnitude 6 star.
What is the Apparent Magnitude
of a star that has an apparent
brightness of 1.4 x 10-9 W/m2 ?
m = 2.5log10 (2.52 x 10-8W/m2/b) =
2.5log10 (2.52 x 10-8W/m2/ 1.4 x 10-9
W/m2) = 3.1
3.1
The Hubble can see a object with
an apparent magnitude of 28. What
is the apparent brightness of such
a star or galaxy?
m = 2.5log10 (2.52 x 10-8W/m2/b) ,
b = 2.52 x 10-8W/m2 /10(m/2.5)
= 1.6 x10-19 W/m2
1.6 x10-19 W/m2
Concept 3 – Absolute Magnitude
Absolute Magnitude M = m - 5 log10(d/10)
M = The Absolute Magnitude
d = The distance to the star in parsecs
m = The star’s Apparent Magnitude
The absolute magnitude of a star is defined as what
its apparent magnitude would be if you were 10
parsecs from it.
Absolute Magnitude M = m - 5 log10(d/10)
M = The Absolute Magnitude
d = The distance to the star in parsecs
m = The star’s Apparent Magnitude
Suppose you were 100 pc from a star with an apparent
magnitude of 6. If you were 10 pc away, you would
be 10 times closer and receive 100 times the light.
Increasing your brightness by a factor of 100
decreases your apparent magnitude by 5, and so the
star would have an absolute magnitude of 1, or
M = 6 - 5 log10(100/10) = 1
The Sun has an apparent magnitude
of -26.8, we are 1.5 x 108 km or 4.9 x
10-6 pc from the sun. What is the sun’s
absolute magnitude?
M = m - 5 log10(d/10)
= -26.8 - 5 log10(4.86 x 10-6 /10) = 4.7
4.7
You are 320 pc from a star with
an absolute magnitude of 6.3.
What is its apparent magnitude?
M = m - 5 log10(d/10),
m = M + 5 log10(d/10) = 6.3 + 5
log10(320/10) = 14
14
SO…
T=
surface temperature in K
L=
b=
m=
M=
luminosity in W
2
brightness in W/m
apparent magnitude
absolute magnitude
SO…
T=
2.90 x 10-3 m/K/ λmax
4
σAT
L=
2
b = L/4πd
-8W
m = 2.5log10 (2.52 x 10 /m2/b)
M = m - 5 log10(d/10)
Concept 4 – H-R diagrams
In 1910, Enjar
Hertzsprung of
Denmark, and
Henry Norris Russell
at Princeton plotted M
vs T in independent
research.
Most stars fell on a diagonal band, called the main
sequence. Our sun falls on the main sequence. New
and old stars are off the main sequence.
From Douglas Giancoli’s Physics
Bright
Dim
Hot
Cooler
From Douglas Giancoli’s Physics
Bright
Dim
Hot
Cooler
From Jay Pasachoff’s Contemporary Astronomy
O
B
A
F
G
K
M
Oh (Hot)
be
a
fine
girl,
kiss
me! (Cooler)
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
BAFGKM-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A-
FGKM-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F-
GKM-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F - 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines
(Canopus (S.H.) and Polaris are type F)
G-
KM-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F - 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines
(Canopus (S.H.) and Polaris are type F)
G - 5,000 - 6,000K, yellow stars like the sun. Strongest H and K
lines of Ca appear in this star.
K-
M-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F - 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines
(Canopus (S.H.) and Polaris are type F)
G - 5,000 - 6,000K, yellow stars like the sun. Strongest H and K
lines of Ca appear in this star.
K - 3,500 - 5,000K, spectrum has many lines from neutral metals.
Reddish stars (Arcturus and Aldebaran are type K stars)
M-
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F - 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines
(Canopus (S.H.) and Polaris are type F)
G - 5,000 - 6,000K, yellow stars like the sun. Strongest H and K
lines of Ca appear in this star.
K - 3,500 - 5,000K, spectrum has many lines from neutral metals.
Reddish stars (Arcturus and Aldebaran are type K stars)
M - 3,500 or less, molecular spectra appear. Titanium oxide lines
appear. Red stars (Betelgeuse is a prominent type M)
Spectral types:
O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are
spread out. O types are rare and gigantic.
B - 10,000 - 30,000K, H lines are stronger, lines are less spread out
(Rigel, Spica are type B stars)
A - 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K)
(Sirius, Deneb and Vega are A type stars)
F - 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines
(Canopus (S.H.) and Polaris are type F)
G - 5,000 - 6,000K, yellow stars like the sun. Strongest H and K
lines of Ca appear in this star.
K - 3,500 - 5,000K, spectrum has many lines from neutral metals.
Reddish stars (Arcturus and Aldebaran are type K stars)
M - 3,500 or less, molecular spectra appear. Titanium oxide lines
appear. Red stars (Betelgeuse is a prominent type M)
Suffixes 0 (hottest) - 9 (coolest) so O0, O1…O9, then B0, B1…
The atmosphere
The Star
Light from star is
filtered by atmosphere
From Jay Pasachoff’s Contemporary Astronomy
SO…
Hot stars are:
Big, Bright, Brief and Blue
Cool stars are:
Diminuitive, Dim, and Durable and um… reD
More about brief and durable next time…
Spectroscopic “parallax”
Since astronomers can
tell by the spectrum of
a star if and where it
falls on the main
sequence, they can get
the absolute magnitude.
If you then measure the
apparent magnitude,
it is a relatively simple process to calculate the
distance to the star: M = m - 5 log10(d/10)
And you know M, and m…
From Douglas Giancoli’s Physics
M = m - 5 log10(d/10)
5 log10(d/10) = m - M
log10(d/10) = (m - M)/5
d/10 = 10((m - M)/5)
d = (10 pc)10((8 - -4.3)/5)
d = 2884 pc
How far is an B0 that has an m of 8?
2884 pc
d = (10 pc)10((14 - 5.8)/5)
d = 437 pc
How far is an K0 that has an m of 14?
437 pc
Ok, now…
Drool.