deducing temperatures and luminosities of stars (and other objects…)
DESCRIPTION
Deducing Temperatures and Luminosities of Stars (and other objects…). Ultraviolet (UV). Radio waves. Infrared (IR). Microwaves. Visible Light. Gamma Rays. X Rays. Review: Electromagnetic Radiation. Increasing energy. 10 -15 m. 10 3 m. 10 -9 m. 10 -6 m. 10 -4 m. 10 -2 m. - PowerPoint PPT PresentationTRANSCRIPT
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Deducing Temperatures and Luminosities of Stars(and other objects…)
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Review: Electromagnetic Radiation
• EM radiation is the combination of time- and space- varying electric + magnetic fields that convey energy.
• Physicists often speak of the “particle-wave duality” of EM radiation.– Light can be considered as either particles (photons) or as waves, depending
on how it is measured
• Includes all of the above varieties -- the only distinction between (for example) X-rays and radio waves is the wavelength.
Gamm
a Ray
s
Ultrav
iolet
(UV)
X Ray
s
Visib
le Lig
ht
Infra
red (I
R)
Microwav
es
Radio
wav
es
10-15 m 10-6 m 103 m10-2 m10-9 m 10-4 mIncreasing wavelength
Increasing energy
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Electromagnetic Fields
Directionof “Travel”
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Sinusoidal Fields
• BOTH the electric field E and the magnetic field B have “sinusoidal” shape
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Wavelength of Sinusoidal Function
Wavelength is the distance between any two identical points on a sinusoidal wave.
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Frequency of Sinusoidal Wave
Frequency: the number of wave cycles per unit of time that are registered at a given point in space. (referred to by Greek letter nu])
is inversely proportional to wavelength
time
1 unit of time(e.g., 1 second)
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“Units” of Frequency
meterscyclessecondsecondmeters
cycle
cycle1 1 "Hertz" (Hz)
second
c
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Wavelength is proportional to the wave velocity v.Wavelength is inversely proportional to frequency. e.g., AM radio wave has long wavelength (~200 m), therefore it
has “low” frequency (~1000 KHz range). If EM wave is not in vacuum, the equation becomes
Wavelength and Frequency Relation
v
cwhere v and is the "refractive index"n
n
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Light as a Particle: Photons Photons are little “packets” of energy. Each photon’s energy is proportional to its
frequency. Specifically, energy of each photon energy is
E = hEnergy = (Planck’s constant) × (frequency of photon)h 6.625 × 10-34 Joule-seconds = 6.625 × 10-27 Erg-seconds
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Planck’s Radiation Law• Every opaque object at temperature T > 0-K (a human, a
planet, a star) radiates a characteristic spectrum of EM radiation – spectrum = intensity of radiation as a function of wavelength
– spectrum depends only on temperature of the object
• This type of spectrum is called blackbody radiation
http://scienceworld.wolfram.com/physics/PlanckLaw.html
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Planck’s Radiation Law• Wavelength of MAXIMUM emission max
is characteristic of temperature T
• Wavelength max as T
http://scienceworld.wolfram.com/physics/PlanckLaw.htmlmax
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Sidebar: The Actual Equation
• Complicated!!!!– h = Planck’s constant = 6.63 ×10-34 Joule - seconds– k = Boltzmann’s constant = 1.38 ×10-23 Joules -K-1
– c = velocity of light = 3 ×10+8 meter - seconds-1
2
5
2 1
1hc
kT
hcB T
e
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Temperature dependence of blackbody radiation
• As temperature T of an object increases:– Peak of blackbody spectrum (Planck function) moves
to shorter wavelengths (higher energies)
– Each unit area of object emits more energy (more photons) at all wavelengths
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Sidebar: The Actual Equation
• Complicated!!!!– h = Planck’s constant = 6.63 ×10-34 Joule - seconds– k = Boltzmann’s constant = 1.38 ×10-23 Joules -K-1
– c = velocity of light = 3 ×10+8 meter - seconds-1
– T = temperature [K] = wavelength [meters]
2
5
2 1
1hc
kT
hcB T
e
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Shape of Planck Curve
• “Normalized” Planck curve for T = 5700-K– Maximum value set to 1
• Note that maximum intensity occurs in visible region of spectrum
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
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Planck Curve for T = 7000-K
• This graph also “normalized” to 1 at maximum
• Maximum intensity occurs at shorter wavelength – boundary of ultraviolet (UV) and visible
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
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Planck Functions Displayed on Logarithmic Scale
• Graphs for T = 5700-K and 7000-K displayed on same logarithmic scale without normalizing– Note that curve for T = 7000-K is “higher” and peaks “to the left”
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
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Features of Graph of Planck Law T1 < T2 (e.g., T1 = 5700-K, T2 = 7000-K)
• Maximum of curve for higher temperature occurs at SHORTER wavelength : max(T = T1) > max(T = T2) if T1 < T2
• Curve for higher temperature is higher at ALL WAVELENGTHS More light emitted at all if T is larger– Not apparent from normalized curves, must examine
“unnormalized” curves, usually on logarithmic scale
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Wavelength of Maximum EmissionWien’s Displacement Law
• Obtained by evaluating derivative of Planck Law over T
(recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns)
3
max
2.898 10meters
KT
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Wien’s Displacement Law
• Can calculate where the peak of the blackbody spectrum will lie for a given temperature from Wien’s Law:
(recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns)
3
max
2.898 10meters
KT
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• Wavelength of Maximum Emission is:
(in the visible region of the spectrum)
3
max
2.898 100.508 508
5700m m nm
max for T = 5700-K
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• Wavelength of Maximum Emission is:
(very short blue wavelength, almost ultraviolet)
max for T = 7000-K
3
max
2.898 100.414 414
7000m m nm
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Wavelength of Maximum Emission for Low Temperatures
• If T << 5000-K (say, 2000-K), the wavelength of the maximum of the spectrum is:
(in the “near infrared” region of the spectrum)
• The visible light from this star appears “reddish”
3
max
2.898 101.45 1450
2000m m nm
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Why are Cool Stars “Red”?
(m)
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
max
Visible Region
Less light in blueStar appears “reddish”
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• T >> 5000-K (say, 15,000-K), wavelength of maximum “brightness” is:
“Ultraviolet” region of the spectrum
Star emits more blue light than red appears “bluish”
3
max
2.898 100.193 193
15000m m nm
Wavelength of Maximum Emission for High Temperatures
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Why are Hotter Stars “Blue”?
(m)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
max
Visible Region
More light in blueStar appears “bluish”
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Betelguese and Rigel in Orion
Betelgeuse: 3,000 K(a red supergiant)
Rigel: 30,000 K(a blue supergiant)
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Blackbody curves for stars at temperatures of Betelgeuse and Rigel
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Stellar Luminosity• Sum of all light emitted over all wavelengths is the
luminosity– brightness per unit surface area– luminosity is proportional to T4: L = T4
– L can be measured in watts• often expressed in units of Sun’s luminosity LSun
– L measures star’s “intrinsic” brightness, rather than “apparent” brightness seen from Earth
82 4
Joules5.67 10 , Stefan-Boltzmann constant
m -sec-K
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Stellar Luminosity – Hotter Stars• Hotter stars emit more light per unit area of its
surface at all wavelengths– T4 -law means that small increase in temperature T
produces BIG increase in luminosity L– Slightly hotter stars are much brighter (per unit
surface area)
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Two stars with Same Diameter but Different T
• Hotter Star emits MUCH more light per unit area much brighter
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Stars with Same Temperature and Different Diameters
• Area of star increases with radius ( R2, where R is star’s radius)
• Measured brightness increases with surface area
• If two stars have same T but different luminosities (per unit surface area), then the MORE luminous star must be LARGER.
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How do we know that Betelgeuse is much, much bigger than Rigel?• Rigel is about 10 times hotter than Betelgeuse
– Measured from its color
– Rigel gives off 104 (=10,000) times more energy per unit surface area than Betelgeuse
• But the two stars have equal total luminosities Betelguese must be about 102 (=100) times
larger in radius than Rigel– to ensure that emits same amount of light over entire
surface
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So far we haven’t considered stellar distances...
• Two otherwise identical stars (same radius, same temperature same luminosity) will still appear vastly different in brightness if their distances from Earth are different
• Reason: intensity of light inversely proportional to the square of the distance the light has to travel– Light waves from point sources are surfaces of
expanding spheres
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Sidebar: “Absolute Magnitude”
• Recall definition of stellar brightness as “magnitude” m
• F, F0 are the photon numbers received per second from object and reference, respectively.
100
2.5 logF
mF
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Sidebar: “Absolute Magnitude”
• “Absolute Magnitude” M is the magnitude measured at a “Standard Distance”– Standard Distance is 10 pc 33 light years
• Allows luminosities to be directly compared– Absolute magnitude of sun +5 (pretty faint)
10
102.5 log
F pcM m
F earth
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Sidebar: “Absolute Magnitude” Apply “Inverse Square Law”
• Measured brightness decreases as square of distance
2
2
2
110 10 distance
10pc1distance
F pc pc
F earth
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Simpler Equation for Absolute Magnitude
2
10
10
distance2.5 log
10pc
distance5 log
10pc
M m
m
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Stellar Brightness Differences are “Tools”, not “Problems”
• If we can determine that 2 stars are identical, then their relative brightness translates to relative distances
• Example: Sun vs. Cen– spectra are very similar temperatures, radii almost
identical (T follows from Planck function, radius R can be deduced by other means)
luminosities about equal– difference in apparent magnitudes translates to relative
distances– Can check using the parallax distance to Cen
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Plot Brightness and Temperature on “Hertzsprung-Russell Diagram”
http://zebu.uoregon.edu/~soper/Stars/hrdiagram.html
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H-R Diagram
• 1911: E. Hertzsprung (Denmark) compared star luminosity with color for several clusters
• 1913: Henry Norris Russell (U.S.) did same for stars in solar neighborhood
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Hertzsprung-Russell Diagram
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http://www.anzwers.org/free/universe/hr.html
90% of stars on Main Sequence10% are White Dwarfs<1% are Giants
“Clusters” on H-R Diagram
• n.b., NOT like “open clusters” or “globular clusters”
• Rather are “groupings” of stars with similar properties
• Similar to a “histogram”
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H-R Diagram
• Vertical Axis luminosity of star– could be measured as power, e.g., watts
– or in “absolute magnitude”
– or in units of Sun's luminosity:star
Sun
L
L
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Hertzsprung-Russell Diagram
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H-R Diagram• Horizontal Axis surface temperature
– Sometimes measured in Kelvins. – T traditionally increases to the LEFT– Normally T given as a ``ratio scale'‘– Sometimes use “Spectral Class”
• OBAFGKM– “Oh, Be A Fine Girl, Kiss Me”
– Could also use luminosities measured through color filters
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“Standard” Astronomical Filter Set
• 5 “Bessel” Filters with approximately equal “passbands”: 100 nm– U: “ultraviolet”, max 350 nm
– B: “blue”, max 450 nm
– V: “visible” (= “green”), max 550 nm
– R: “red”, max 650 nm
– I: “infrared, max 750 nm
– sometimes “II”, farther infrared, max 850 nm
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Filter Transmittances
200 300 400 500 600 700 800 900 1000 1100
0
10
20
30
40
50
60
70
80
90
100U
V
B
R
I
II
U,B,V,R,I,II Filters
Wavelength (nm)
Transmission (%)
Visible Light
UB V
R III
Wavelength (nm)
100
50
0
200 300 400 500 600 700 800 900 1000 1100
Tra
nsm
ittan
ce (
%)
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Measure of Color
• If image of a star is:– Bright when viewed through blue filter– “Fainter” through “visible”– “Fainter” yet in red
• Star is BLUISH
and hotter (m)
0.3 0.4 0.5 0.6 0.7 0.8
Visible Region
L(s
tar)
/ L
(Sun
)
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Measure of Color
• If image of a star is:– Faintest when viewed through blue filter– Somewhat brighter through “visible”– Brightest in red
• Star is REDDISH
and cooler
(m)
0.3 0.4 0.5 0.6 0.7 0.8
Visible Region
L(s
tar)
/ L
(Sun
)
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How to Measure Color of Star• Measure brightness of stellar images taken
through colored filters– used to be measured from photographic plates– now done “photoelectrically” or from CCD images
• Compute “Color Indices”– Blue – Visible (B – V)– Ultraviolet – Blue (U – B)– Plot (U – V) vs. (B – V)