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E2. Stellar Radiation & Stellar Types IB Physics Power Points Option E Astrophysics ww.pedagogics.ca

2012 astrophysics ppt e2

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Page 1: 2012 astrophysics ppt e2

E2. Stellar Radiation

& Stellar Types

IB Physics Power Points

Option E

Astrophysics

www.pedagogics.ca

Page 2: 2012 astrophysics ppt e2

E.2.1 State that fusion is the main energy source of starsThe source of all energy in stars is hydrogen “burning”.TWO fusion reaction pathways for hydrogen (which pathway occurs depends on core temperature of the star)

1. proton-proton chain – in stars like our Sun (core temperature < 16 x 106 K)

2. carbon-nitrogen-oxygen (CNO) cycle (hotter core temperatures) - not in the syllabus

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Energy release in fusion comes from mass defect in the fusion reaction (products have less mass than reactants)

The proton-proton chain consists of three steps (each step liberates energy)

Overall

MeV) (12.85 H H He He He .3

MeV) (5.49 He H H .2

MeV) (1.19 ν e H H H .1

11

11

42

32

32

32

21

11

01

21

11

11

1 4 01 2 14 2 2 H He e

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Practice ProblemDetermine the energy (in Joules) released in the following reaction:

n He H H 10

32

21

21

Given the following nuclide massesDeuteron = 2.015 uHelium-3 = 3.017 u click for solutionNeutron = 1.009 u

(1.009 3.017) 2(2.015)

0.004

0.004 931.5

3.73 MeV

m

E

E

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As a result of fusion, stars lose mass! The rate of mass loss by our Sun to fusion reactions is about 4.33 × 109 kg s-1.

Estimate the power output of our Sun.

click for solution2

9 2

26

(for 1 second)

(4.33 10 )

3.90 10 W

E mc

E c

E

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Star Stability

E.2.2 Explain that in a stable star (for example, our Sun) there is an equilibrium between radiation pressure and gravitational pressure.

In stars . . .

An outward force exists due to emitted radiation “pressure” (the energy emitted by fusion reactions)

Gravity pulls the outer part of the star inward towards the core.

In a stable star these two forces are a balanced equilibrium

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Nature of core changes as star ages

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Observing Stars – Key Characteristics

There are six principle characteristics used to describe stars. They are:

1. Luminosity2. Temperature3. Radius4. Mass5. Chemical composition6. Age

STUDY TIP: Stellar characteristics are often measured indirectly (like using brightness to determine luminosity, or peak wavelength to find surface temperature) AND these characteristics are often mathematically interrelated.

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Luminosity and Brightness

Luminosity (L) is an absolute value that measures the total power radiated by a star (in all directions).

• Luminosity is measured in watts• our Sun has a luminosity of about 3.90 x 1026 W.

Luminosity is very important in providing information about star structure and age.

E.2.3 Define the luminosity of a star

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Luminosity and Brightness

E.2.4 Define apparent brightness and state how it is measured.Apparent brightness (l) is a relative value.

• we measure apparent star brightness as the fraction of the luminosity received by us.

• brightness is measured in watts per square meter.

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Apparent brightness is proportional to the luminosity L of the star.

Apparent brightness is inversely proportional to the square of the distance d between the star and the observer.

24L

bd

Apparent brightness b depends on two variables:

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This can be misleading . . . .

This means that a brighter star is not necessarily closer to Earth, or larger, or hotter.

A high luminosity star that is farther from Earth can appear brighter.

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What you can conclude . . . .

For two stars the same distance from Earth, the star with the greatest luminosity will appear brighter.

Note: both the surface temperature and size of a star affect luminosity.

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E.2.5 Apply the Stefan-Boltzmann law to compare the luminosities of different stars.

The Stefan-Boltzmann law states:

4

8 2 4

Total Power Radiated

5.67 10

surface surfaceA T

where Wm K

NOTE:Total Power Radiated = LUMINOSITY

Surface area of a sphere 24A r

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Sample problem: F1 (c) M02 exam

Antares A has a surface temperature of 3000 K and is part of a binary star system. The companion star Antares B has a surface temperature of 15 000 K and a luminosity that is 1/40 of that of Antares A. Calculate the ratio of the radius of Antares A to Antares B.

Click for solution

STUDY TIP: Many problems are encountered like the one above where the answer is a ratio of two variables. Get used to working with variables and not always looking for a “plug and chug” type of solution strategy.

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2 42 4

2 4 2 4

18 2 13 2

use Stefan-Boltzmann Law40

(4 )(4 )

40

40 (15000) (3000)

2.025 10 8.1 10

160 (2 SF)

AB

A AB B

B A

B A

A

B

LL

r Tr T

r r

r r

r

r

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E.2.6 State Wien’s (displacement) law and apply it to explain the connection between the color and temperature of stars.

The color of a star is determined by the intensity of the wavelengths of visible light emitted by the star.

Recall – in the visible spectrum

RED light (longer wavelength, lower frequency)

VIOLET light (shorter wavelength, higher frequency)

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Peak wavelength emission gives an idea of surface temperature.

The shorter the peak wavelength, the hotter the blackbody.

A star’s emission spectra is similar to a theoretical blackbody spectra

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Wein’s displacement law relates the peak wavelength (in metres) of an emission spectrum to surface temperature (in Kelvin).

shorter peak wavelength = higher surface temperature.

Determine the surface temperature of our Sun if the peak wavelength is 500 nm. Click for solution

3max a constant (2.9 10 ) surfaceT m K

3

9

2.9 105800 K

500 10T

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E.2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars

Stellar Spectra – Star DataRecall: what important characteristic of stars can be estimated from stellar spectra? Click for answer

In addition, wavelengths missing from stellar spectra indicate chemical nature of the outer layers of a star. Think resonance, and relate this idea to greenhouse gases.

Surface temperature can be determined from peak wavelength

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E.2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars

Stellar Spectra – Star DataRecall: what important characteristic of stars can be estimated from stellar spectra? Click for answer

In addition, wavelengths missing from stellar spectra indicate chemical nature of the outer layers of a star. Think resonance, and relate this idea to greenhouse gases.

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5 minute physics concept – the Doppler Effect

If a wave source is moving towards or away from an observer, what the observer detects depends on their position relative to the wave source.

Surface temperature can be determined from peak wavelength

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Applied to stellar spectra

Red shifts in the position of absorption lines indicate motion away from us

Blue shifts indicate motion towards us

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Class Surface Temp. K Colour

O 28000 - 50000 Blue

B 9900 - 28000 Blue-white

A 7400 - 9900 White

F 6000 - 7400 Yellow-white

G 4900 - 6000 Yellow

K 3500 - 4900 Orange

M 2000 - 3500 Orange-red

E.2.8 Describe the overall classification system of spectral classes

Oh be a fine girl/guy, kiss me!

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•E.2.9 Describe the different types of stars

Stellar Spectra – Star Data

Ursa Major : The Big Dipper

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Mizar

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Types of Stars – Binary Stars- two stars in orbit about their mutual centre of mass

Visual binary stars can be distinguished as separate stars using a telescope.

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Spectroscopic Binary Stars

- identified by spectral analysis – look at absorption lines

- spectral frequency of each star will shift depending on orbit position.

A B

A B

A

B

A + B

B A

B A

Blue Red

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Interpreting Spectrum Shifts – The Doppler EffectA higher frequency than the source is observed if the source is approaching the observer i.e. a BLUE SHIFT.

If the light source is receding from the observer, a RED SHIFT is observed.

The “shift” in wavelength can be used to determine the speed the source is travelling.

ref

v c

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observer

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observer

AB

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A

B

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observer

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Sample problem: F2 M02 exam

20 days

Day 6 and 26 are at the same phase of the cycle.

On Day 6, the lines in the spectra from Star A are red shifted (right) and those for Star B are blue shifted (left)

B A

B A Day 6

A

B

B + ADay 1

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Sample problem: F2 M02 exam

Circular or elliptical orbits drawn around the centre of mass.

Star spectra shifts towards blue when moving towards Earth and towards red when moving away. As one star is moving towards Earth while the other moves away, a red shift in a binary system is always accompanied by a blue shift.

No shift occurs when stars are moving perpendicular to Earth.

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Mass of star / system

5 -10.261.74 10 ms

448.3ref

v c c

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In an eclipsing binary system, the binary brightness shows regular variation. This occurs because one star gets between the other and the observer blocking some of the emitted radiation.

Eclipsing Binaries

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Eclipsing binary information gives astronomers information about orbital period and the separation of the stars.

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Background information - apparent brightness

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A Hertzsprung-Russell diagram is a plot of luminosity against surface temperature.

The Hertzsprung-Russell Diagram

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When plotted this way, a diagonal band appears that contains the majority of stars. These are called main sequence stars.

main sequence stars • are stable• derive their energy from hydrogen fusion. • comprise 90% of stars visible in the night sky

The two fundamental factors that determine a star's position in the main sequence its mass and evolutionary state.

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20 days

Low luminosity, high temperature dwarf stars

high luminosity, low temperature giant stars

High massshort life

low masslong life

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L

Apparent brightness if 10 pc away

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L

Apparent brightness if 10 pc away

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L

Apparent brightness if 10 pc away

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L

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Practice Problem 1

A parsec (pc) is a unit of distance (see Data Booklet)

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Practice Problem 1

A parsec (pc) is a unit of distance (see Data Booklet)

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Practice Problem 2

Suppose that the distances to two nearby stars can be reasonably estimated and this data, together with measured apparent brightness suggests that the two stars have a similar luminosity. The peak wavelength for one star is 700 nm (reddish) while for the other it is 350 nm (bluish). Determine a) the surface temperature of each star and b) how much larger one star is than the other.

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Summary

Luminosity is the total power output of a star. Luminosity can measured as a absolute value (in Watts) or relative to the Sun (in L where L = 3.90 x 1026 W)

Apparent brightness (or intensity) is a relative value and represents the portion (measured in W m-2) of a star’s luminosity that is observed on Earth. Apparent brightness, stellar distance and luminosity are related by:

24L

bd

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Stars emit a radiation spectrum similar to that of a theoretical black-body. This allows the surface temperature of a star to be estimated from the peak wavelength in a spectrum using Wien’s Law

The temperature can be related to the luminosity and size of a star using the Stefan-Boltzmann Law

Recalling that

4

8 2 4

L

5.67 10

surface surfaceA T

where Wm K

3max 2.9 10 surfaceT m K

24surfaceA r

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Stellar spectra are very important for a number of reasons

1. Most peak wavelength indicates surface temperature (and color of star)

2. The area under a stellar spectrum is an indication of total power emitted i.e. luminosity.

3. Absorption lines in stellar spectra give an indication of what elements are present in the atmosphere of the star and therefore an idea of what fusion reactions are taking place (helps with star age etc)

4. Stellar spectra give us important information about binaries