IB Physics Power Pointswww.pedagogics.ca Option E Astrophysics E2. Stellar Radiation & Stellar Types
E.2.1 State that fusion is the main energy sourceof starsThe source of all energy in stars is hydrogen “burning”.TWO fusion reaction pathways for hydrogen (whichpathway occurs depends on core temperature of thestar)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
Energy release in fusion comes from mass defect in thefusion reaction (products have less mass than reactants)The proton-proton chain consists of three steps (eachstep liberates energy)1. 1 1 H 1 1 H 2 1 H 0 1 e ν (1.19MeV) 1 2 32. 1 H 1 H 2 He (5.49MeV) 3 3 4 1 13. 2 He 2 He 2 He 1 H 1 H (12.85MeV)Overall 1 4 0 4H 1 2 He 2 e 2 1
Practice ProblemDetermine the energy (in Joules) released in thefollowing reaction: 2 2 3 1 1 H H 1 2 He 0nGiven the following nuclide massesDeuteron = 2.015 uHelium-3 = 3.017 u click for solutionNeutron = 1.009 u m (1.009 3.017) 2(2.015) 0.004 E 0.004 931.5 E 3.73 MeV
As a result of fusion, stars lose mass! The rate ofmass loss by our Sun to fusion reactions is about4.33 × 109 kg s-1.Estimate the power output of our Sun. click for solution 2 E mc (for 1 second) 9 2 E (4.33 10 )c 26 E 3.90 10 W
Star StabilityE.2.2 Explain that in a stable star (for example, our Sun) thereis an equilibrium between radiation pressure andgravitational 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 thecore.In a stable star these two forces are a balanced equilibrium
Observing Stars – Key CharacteristicsThere are six principle characteristics used to describestars. They are: 1. Luminosity 2. Temperature 3. Radius 4. Mass 5. Chemical composition 6. AgeSTUDY 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.
Luminosity and BrightnessE.2.3 Define the luminosity of a starLuminosity (L) is an absolute value that measures thetotal 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 informationabout star structure and age.
Luminosity and BrightnessE.2.4 Define apparent brightness and state how it ismeasured.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.
L b 2 4 dApparent brightness b depends on two variables: 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.
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.
What you can conclude . . . .For two stars the same distance from Earth, the starwith the greatest luminosity will appear brighter. Note: both the surface temperature and size of a star affect luminosity.
E.2.5 Apply the Stefan-Boltzmann law to comparethe luminosities of different stars.The Stefan-Boltzmann law states: 4 Total Power Radiated A T surface surface 8 2 4 where 5.67 10 Wm KNOTE:Total Power Radiated = LUMINOSITY 2Surface area of a sphere A 4 r
Sample problem: F1 (c) M02 examAntares A has a surface temperature of 3000 K and is part ofa binary star system. The companion star Antares B has asurface temperature of 15 000 K and a luminosity that is1/40 of that of Antares A. Calculate the ratio of the radiusof Antares A to Antares B. Click for solutionSTUDY 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.
LALB use Stefan-Boltzmann Law 40 2 4 2 4 (4 rA )TA (4 rB )TB 4040rB2 (15000) 4 rA (3000) 4 2 18 2 13 22.025 10 r B 8.1 10 r ArA 160 (2 SF)rB
E.2.6 State Wien’s (displacement) law and apply it to explainthe connection between the color and temperature of stars.The color of a star is determined by the intensity of thewavelengths of visible light emitted by the star.Recall – in the visible spectrumRED light (longer wavelength, lower frequency)VIOLET light (shorter wavelength, higher frequency)
A star’s emission spectra is similar to atheoretical blackbody spectraPeak wavelength emissiongives an idea of surfacetemperature.The shorter the peakwavelength, the hotterthe blackbody.
Wein’s displacement law relates the peak wavelength(in metres) of an emission spectrum to surfacetemperature (in Kelvin). 3 T max surface a constant (2.9 10 m K ) shorter peak wavelength = higher surface temperature.Determine the surface temperature of our Sun if thepeak wavelength is 500 nm. Click for solution 3 2.9 10 T 9 5800 K 500 10
E.2.7 Explain how atomic spectra may be used todeduce chemical and physical data for starsStellar Spectra – Star DataRecall: what important characteristic of stars can beestimated from stellar spectra? Click for answer Surface temperature can be determined from peak wavelength 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.
E.2.7 Explain how atomic spectra may be used todeduce chemical and physical data for starsStellar Spectra – Star DataRecall: what important characteristic of stars can beestimated 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.
5 minute physics concept – the Doppler Effect Surface temperature can be determined from peak wavelength 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.
Applied to stellar spectraRed shifts in the position of absorption lines indicatemotion away from usBlue shifts indicate motion towards us
E.2.8Describe the overall classification system of spectral classes 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 Oh be a fine girl/guy, kiss me!
E.2.9 Describe the different types of starsStellar Spectra – Star Data Ursa Major : The Big Dipper
Types of Stars – Binary Stars- two stars in orbit about their mutual centre of massVisual binary stars can be distinguished as separate starsusing a telescope.
Spectroscopic Binary Stars - identified by spectral analysis – look at absorption lines - spectral frequency of each star will shift depending on orbit position. BA B B A A A B A+B B A Blue Red
Interpreting Spectrum Shifts – The Doppler EffectA higher frequency than the source is observed if the sourceis approaching the observer i.e. a BLUE SHIFT.If the light source is receding from the observer, a RED SHIFTis observed. The “shift” in wavelength can be used to determine the speed the source is travelling. v c ref
Sample problem: F2 M02 exam 20 days B B A A B+A B A Day 1 Day 6 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)
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.
0.26 5 -1v c c 1.74 10 ms ref 448.3 Mass of star / system
Eclipsing BinariesIn an eclipsing binary system, the binary brightness showsregular variation. This occurs because one star gets betweenthe other and the observer blocking some of the emittedradiation.
Eclipsing binary information gives astronomers informationabout orbital period and the separation of the stars.
The Hertzsprung-Russell Diagram A Hertzsprung-Russell diagram is a plot of luminosity against surface temperature.
When plotted this way, a diagonal band appears thatcontains the majority of stars. These are called mainsequence stars.main sequence stars• are stable• derive their energy from hydrogen fusion.• comprise 90% of stars visible in the night skyThe two fundamental factors that determine a starsposition in the main sequence its mass andevolutionary state.
high luminosity, High mass 20 days low temperature short life giant starsLow luminosity, low masshigh temperature long lifedwarf stars
Practice Problem 1 A parsec (pc) is a unit of distance (see Data Booklet)
Practice Problem 1 A parsec (pc) is a unit of distance (see Data Booklet)
Practice Problem 2Suppose that the distances to two nearby stars can bereasonably estimated and this data, together withmeasured apparent brightness suggests that the twostars have a similar luminosity. The peak wavelength forone star is 700 nm (reddish) while for the other it is 350nm (bluish). Determine a) the surface temperature ofeach star and b) how much larger one star is than theother.
SummaryLuminosity is the total power output of a star. Luminositycan measured as a absolute value (in Watts) or relative tothe Sun (in L where L = 3.90 x 1026 W)Apparent brightness (or intensity) is a relative value andrepresents the portion (measured in W m-2) of a star’sluminosity that is observed on Earth. Apparent brightness,stellar distance and luminosity are related by: L b 2 4 d
Stars emit a radiation spectrum similar to that of atheoretical black-body. This allows the surface temperatureof a star to be estimated from the peak wavelength in aspectrum using Wien’s Law maxTsurface 2.9 10 3 m KThe temperature can be related to the luminosityand size of a star using the Stefan-Boltzmann Law 4 L A T surface surface 8 2 4 where 5.67 10 Wm K 2Recalling that Asurface 4 r
Stellar spectra are very important for a number of reasons1. Most peak wavelength indicates surface temperature(and color of star)2. The area under a stellar spectrum is an indication of totalpower emitted i.e. luminosity.3. Absorption lines in stellar spectra give an indication ofwhat elements are present in the atmosphere of the starand therefore an idea of what fusion reactions are takingplace (helps with star age etc)4. Stellar spectra give us important information aboutbinaries