spring term astrophysics stellar physics dr p.a. hatherly modules: ph2006, ph3811

Spring Term Astrophysics Spring Term Astrophysics Stellar PhysicsStellar Physics

Dr P.A. Hatherly Dr P.A. Hatherly

Modules: PH2006, PH3811Modules: PH2006, PH3811

Topics to be Covered:Topics to be Covered:

Properties of StarsProperties of Stars– Distances, velocities, dimensions, Distances, velocities, dimensions,

masses, temperatures, luminosities.masses, temperatures, luminosities. Stellar InteriorsStellar Interiors

– Pressures and temperatures, Pressures and temperatures, compositions, power sources.compositions, power sources.

Life-cycles of StarsLife-cycles of Stars– Star formation, evolution and death.Star formation, evolution and death.

Resources AvailableResources Available

Recommended Texts:Recommended Texts:– “Universe”

(4th or 5th edition, W.J. Kaufmann) – "The Physics of Stars"

(2nd edition, A.C. Phillips) IT

– CD-ROMS on Departmental PCs – Unit Website

Navigate via physicsnet at Navigate via physicsnet at http://www.rdg.ac.uk/physicsnet/http://www.rdg.ac.uk/physicsnet/

Unit StructureUnit Structure

14 Lectures/presentations14 Lectures/presentations– Weeks 4 and 8 for private studyWeeks 4 and 8 for private study

6 Workshops/discussion sessions6 Workshops/discussion sessions– Week 1 - no workshopWeek 1 - no workshop

2 assessed problem worksheets 2 assessed problem worksheets and 1 formal examinationand 1 formal examination

Lecture CalendarLecture CalendarSun Mon Tue Wed Thu Fri Sat Week Key:

Jan 11 12 13 14 15 16 17 118 19 20 21 22 23 24 2 Lecture 9-1125 26 27 28 29 30 31 3 Lecture 9-11, Workshop 11-12

Feb 1 2 3 4 5 6 7 4 Open discussion and revision 9-128 9 10 11 12 13 14 5 Private Study

15 16 17 18 19 20 21 622 23 24 25 26 27 28 7 Release Assessment 1 on 26th January29 8 Return Assessment 1 on 11th February

March 1 2 3 4 5 6 87 8 9 10 11 12 13 9 Release Assessment 2 on 23rd February

14 15 16 17 18 19 20 10 Return Assessment 2 on 10th March

All Lectures in the Gordon Theatre, EngineeringAll Workshops in 131, PhysicsAll Assessments to be returned to the School Office (Room 217, Physics) by 13:00 on the due date

AssessmentAssessment

Continuous AssessmentContinuous Assessment– Selected problems set in weeks 3 and 7Selected problems set in weeks 3 and 7

Posted on website on 26Posted on website on 26thth January and 23 January and 23rdrd February February

– Answers returned in weeks 5 and 9Answers returned in weeks 5 and 9 To the School Office by 1pm, 11To the School Office by 1pm, 11thth February and 10 February and 10thth

MarchMarch

– Results/feedback in weeks 6 and 10Results/feedback in weeks 6 and 10 Results posted on website and problems discussed in Results posted on website and problems discussed in

the following workshopthe following workshop

– Contribution: 40%Contribution: 40%

AssessmentAssessment

Formal ExaminationFormal Examination– 2 hour paper in Summer2 hour paper in Summer– Contribution: 60%Contribution: 60%

Assumed Knowledge:Assumed Knowledge:

Classical Mechanics and OpticsClassical Mechanics and Optics– Part 1Part 1

Thermodynamics and Statistical Thermodynamics and Statistical MechanicsMechanics– In progressIn progress

Atomic and Molecular PhysicsAtomic and Molecular Physics– Simple quantum ideas, in progressSimple quantum ideas, in progress

Ideas from Observational AstronomyIdeas from Observational Astronomy– (useful, but not essential)(useful, but not essential)

Distances of StarsDistances of Stars

p

1 AU

d

Stellar Stellar ParallaxParallax


The angle subtended, The angle subtended, p,p, is simply is simply given by:given by:pp = 1/ = 1/dd (with (with dd in AU and in AU and pp in in radians)radians)

Definition:Definition:– If a star gives a parallax of 1” (1 second If a star gives a parallax of 1” (1 second

of arc, arcsec = 1/3600°) then the of arc, arcsec = 1/3600°) then the distance to the star is 1 parsec (pc)distance to the star is 1 parsec (pc)

– Hence, Hence, dd (pc) = 1/ (pc) = 1/p p (arcsec)(arcsec)


Examples:Examples:– The first star to have its parallax The first star to have its parallax

measured was 61 Cygni. Its parallax measured was 61 Cygni. Its parallax was 0.33”. How far away is it?was 0.33”. How far away is it?

– dd = 1/ = 1/pp = 1/0.33 = 3 pc = 1/0.33 = 3 pc– The nearest star, Proxima Centauri is The nearest star, Proxima Centauri is

at a distance of 1.3 pc. What is its at a distance of 1.3 pc. What is its parallax?parallax?

– p p = 1/= 1/dd = 1/1.3 = 0.77” = 1/1.3 = 0.77”


Relationship to Other UnitsRelationship to Other Units– 1 pc = 2.06x101 pc = 2.06x1055 AU AU– 1AU = 1.5x101AU = 1.5x1088 km km

1 pc = 3.086x101 pc = 3.086x101313 km km– Distance light travels in 1 year = 1 Distance light travels in 1 year = 1

light year (ly) = 9.46x10light year (ly) = 9.46x101212 km km 1 pc = 3.26 ly1 pc = 3.26 ly


Limitations of ParallaxLimitations of Parallax– Maximum distance from ground Maximum distance from ground

based observations, 50 pcbased observations, 50 pc– Maximum from space-based Maximum from space-based

observations, 500 pcobservations, 500 pc– Other methods required for greater Other methods required for greater

distancesdistances ““Standard candles”Standard candles”

Velocities of StarsVelocities of Stars

Define:Define:– Proper Motion: The angular velocity of Proper Motion: The angular velocity of

a star tangential to the line of sighta star tangential to the line of sight– Symbol, Symbol, ; Units, arcsec/year; Units, arcsec/year

– Tangential Velocity: Tangential Velocity: vvt t ; Units km/s; Units km/s

– related to the proper motion by:related to the proper motion by: vvt t = 4.74= 4.74d d km/s (with km/s (with dd in pc) in pc)


Define:Define:– Radial Velocity: The velocity of the Radial Velocity: The velocity of the

star along the line of sight.star along the line of sight.

– Symbol, Symbol, vvrr ; ; Units, km/sUnits, km/s

– Note a negative radial velocity means Note a negative radial velocity means a star is approaching usa star is approaching us

Example:Example:– Barnard’s Star (distance, 1.82 pc)Barnard’s Star (distance, 1.82 pc)– Proper motion = 10.32 arcsec/yearProper motion = 10.32 arcsec/year– Tangential velocity = 89.1 km/sTangential velocity = 89.1 km/s– Radial velocity = -111 km/sRadial velocity = -111 km/s

– Speed Speed vvss = (= (vvrr22 + + vvtt

22))1/21/2 = 142.3 km/s = 142.3 km/s

– Angle to line of sight Angle to line of sight = tan = tan-1-1((vvt t //vvr r ) = -38.75°) = -38.75°

vr

vt

Velocities of StarsVelocities of Starsvs


Measurement of VelocitiesMeasurement of Velocities– Proper motion - straightforward Proper motion - straightforward

observation, maybe over many years, observation, maybe over many years, of the position of a starof the position of a star

– Radial velocity - Use Doppler EffectRadial velocity - Use Doppler Effect

Red shift - Red shift - vvrr positive positive

No shift - No shift - vvrr zero zero

Blue shift - Blue shift - vvrr negative negative


Example:Example:– Barnard’s Star - 10.32 arcsec/year is Barnard’s Star - 10.32 arcsec/year is

easy to measure (= 0.6% angular easy to measure (= 0.6% angular diameter of full moon)diameter of full moon)

– Doppler shift due to Doppler shift due to vvrr //= = vvrr /c = -0.04% /c = -0.04%

Stellar Magnitude ScaleStellar Magnitude Scale

A logarithmic scale, defined such A logarithmic scale, defined such that a difference of magnitude of 5 that a difference of magnitude of 5 corresponds to a change in corresponds to a change in intensity of 100intensity of 100

Smaller magnitudes mean brighter Smaller magnitudes mean brighter starsstars– e.g., a magnitude 0 star is 100x e.g., a magnitude 0 star is 100x

brighter than magnitude 5brighter than magnitude 5


Relative Intensities (mag. 0 = 1)Relative Intensities (mag. 0 = 1)

MagnitudeMagnitude Relative IntensityRelative Intensity-2-2 6.36.3-1-1 2.152 (=1002.152 (=1001/51/5))00 1111 0.460.4622 0.160.1633 0.060.0644 0.0250.02555 0.010.01


Definitions:Definitions:– Apparent Magnitude, Apparent Magnitude, m m : :

The magnitude a star appears to beThe magnitude a star appears to be– Absolute Magnitude, Absolute Magnitude, M M : :

The apparent magnitude a star would The apparent magnitude a star would have if it were viewed from a distance have if it were viewed from a distance of 10 pcof 10 pc


Relationship between Relationship between MM and and m m ::– ((mm - - MM ) = 5log ) = 5log1010dd - 5 - 5

dd is the distance to the star in pc is the distance to the star in pc– The quantity (The quantity (mm - - MM ) is known as the ) is known as the

Distance ModulusDistance Modulus– Example: Sirius has an apparent magnitude Example: Sirius has an apparent magnitude

of -1.46. It is 2.7 pc away, what is its of -1.46. It is 2.7 pc away, what is its absolute magnitude?absolute magnitude?

– mm = -1.46, = -1.46, dd = 2.7 pc = 2.7 pc– MM = -1.46 - 5log = -1.46 - 5log10102.7 + 5 = 1.382.7 + 5 = 1.38

Relative LuminositiesRelative Luminosities

Often convenient to refer to the Often convenient to refer to the relative luminosities of stars.relative luminosities of stars.

From the definition of magnitudes, From the definition of magnitudes, if two stars have absolute if two stars have absolute magnitudes magnitudes MM11 and and MM22 , and , and luminosities luminosities LL11 and and LL22 , ,L

LM M1

2

5100 2 1 ( )/

Relative LuminositiesRelative Luminosities

Example:Example:– The absolute magnitude of the Sun is The absolute magnitude of the Sun is

+4.8 and that of Sirius is +1.38. What +4.8 and that of Sirius is +1.38. What is the ratio of their luminosities?is the ratio of their luminosities?

– LLsirius sirius //LL =100=100(4.8-1.38)/5(4.8-1.38)/5 = 23.3 = 23.3

Colour CorrectionColour Correction

Careful observation of stars Careful observation of stars reveals they have a range of reveals they have a range of colourscolours– Black-body or thermal radiationBlack-body or thermal radiation– Stefan’s Law - power per unit areaStefan’s Law - power per unit area

PP = = TT 4 4 ((T T in K)in K)

– Wien’s LawWien’s Lawmaxmax(nm) = 2.9x10(nm) = 2.9x1066//TT

Colour CorrectionsColour Corrections

Examples of spectraExamples of spectra

0 200 400 600 800 1000 1200

Wavelength (nm)

SunBetelgeuseSirius

UVUV IRIRVisiblVisiblee


Clearly, many stars produce a Clearly, many stars produce a large amount of light outside the large amount of light outside the visiblevisible– Observe stars through a variety of Observe stars through a variety of

filters.filters.– U - 300 - 400 nmU - 300 - 400 nm– B - 380 - 550 nmB - 380 - 550 nm– V - 500 - 650 nmV - 500 - 650 nm


From the filters, we obtain:From the filters, we obtain:– bbuu, , bbbb and and bbvv

– Ratios Ratios bbv v //bbbb and and bbb b //bbuu

Examples:Examples:– Sun, Sun, bbv v //bbbb = 1.77, = 1.77, bbb b //bbuu =1.10, =1.10,TT = 5800 K = 5800 K

– Sirius, Sirius, bbv v //bbbb = 1.00, = 1.00, bbb b //bbuu =0.95, =0.95,TT = 10000 K = 10000 K

– Betelgeuse, Betelgeuse, bbv v //bbbb = 5.50, = 5.50, bbb b //bbuu =6.67, =6.67, TT = 2400 K = 2400 K


Note that:Note that:– bbv v //bbbb and and bbb b //bbuu <1 with <1 with bbb b //bbuu < < bbv v //bbbb

hot, blue star, hot, blue star, T T >20000 K.>20000 K.

– bbv v //bbbb and and bbb b //bbuu roughly equal and ~1 roughly equal and ~1 cooler, white star, cooler, white star, T T ~9000 K.~9000 K.

– bbv v //bbbb and and bbb b //bbuu >1 with >1 with bbb b //bbuu > > bbv v //bbbb cool, orange/red star cool, orange/red star T T <4000 K.<4000 K.

Stellar SpectraStellar Spectra

Examination of stellar spectra reveal Examination of stellar spectra reveal absorption lines on the black body absorption lines on the black body backgroundbackground

– Due to neutral or ionised atoms or Due to neutral or ionised atoms or molecules in the stellar atmospheremolecules in the stellar atmosphere

– Gives composition of star, another handle Gives composition of star, another handle on temperature and a means of on temperature and a means of classification. classification.


The spectra of stars are classified The spectra of stars are classified according to the scheme:according to the scheme:

O B A F G K MO B A F G K MIncreasing Temperature Each class is further divided from 0-9, Each class is further divided from 0-9,

with 0 being the hottest and 9 the coolestwith 0 being the hottest and 9 the coolest Note: This scheme can be remembered Note: This scheme can be remembered

by the “traditional” mnemonic: by the “traditional” mnemonic: Oh Be A Oh Be A Fine Girl (Guy, Gorrilla...) Kiss MeFine Girl (Guy, Gorrilla...) Kiss Me


Historical Note:Historical Note:– Originally (19th C), classification was Originally (19th C), classification was

based on the strength of the based on the strength of the hydrogen Balmer absorption hydrogen Balmer absorption spectrum, and ran from A to P in spectrum, and ran from A to P in order of decreasing absorptionorder of decreasing absorption

– The current scheme arose as a more The current scheme arose as a more logical classification in terms of logical classification in terms of temperaturetemperature


OO

BB

AA

FF

GG

KK

MM

HHHHHH

NaNaTiOTiO TiOTiOMg IMg I

Stellar SpectraStellar SpectraClass Colour Temp.

(x103 K)Spectral lines Examples

O Blue-violet 28 – 50 Ionised atoms Pup1, Ori2

B Blue-white 10 – 28 He, some H Vir3, Ori4

A White 7.5 – 10 Strong H, someionised metals

Cma5, Lyr6

F Yellow-white 6 – 7.5 H and Can+, Fen+. Car7, Cmi8

G Yellow 5 – 6 Can+, other ionisedand neutral metals

Sun, Aur9

K Orange 3.5 – 5 Neutral metals Boo10, Tau11

M Red-orange 2.5 – 3.5 TiO and Ca Sco12, Ori13

Common names: 1Naos, 2Mintaka, 3Spica, 4Rigel, 5Sirius, 6Vega, 7Canopus,8Procyon, 9Capella, 10Arcturus, 11Aldebaran, 12Antares, 13Betelgeuse

Stellar ClassificationStellar Classification We now have two vital pieces of information:We now have two vital pieces of information:

– Luminosity, via distance and magnitudeLuminosity, via distance and magnitude– Temperature from spectroscopyTemperature from spectroscopy

Is there any correlation between these parameters?Is there any correlation between these parameters?– Very important result - a plot of luminosity versus temperature (spectral class)Very important result - a plot of luminosity versus temperature (spectral class)– The Hertzprung-Russel (H-R) DiagramThe Hertzprung-Russel (H-R) Diagram

H-R Diagram H-R Diagram for a number for a number of the of the brightest and brightest and nearest starsnearest stars

The H-R DiagramThe H-R Diagram

Points to note:Points to note:

– The narrow band of stars scattered The narrow band of stars scattered close to the solid line. close to the solid line.

– Most stars occur along this band – an Most stars occur along this band – an indication that this is where stars indication that this is where stars spend most of their lives. For this spend most of their lives. For this reason, it is known as the reason, it is known as the Main Main SequenceSequence..

The H-R DiagramThe H-R Diagram

– Other regions to note are stars of high Other regions to note are stars of high luminosity but low temperature luminosity but low temperature (indicating they are large – hence the (indicating they are large – hence the term term red giantred giant) and stars of high ) and stars of high temperature but low luminosity temperature but low luminosity (indicating small diameters, hence (indicating small diameters, hence white dwarf white dwarf ))

– As we shall see, the H-R diagram is As we shall see, the H-R diagram is extremely useful in many aspects of extremely useful in many aspects of stellar physicsstellar physics

Next Lecture:Next Lecture:

Dimensions of StarsDimensions of Stars Luminosity and Spectral ClassLuminosity and Spectral Class

– Spectroscopic ParallaxSpectroscopic Parallax Masses of StarsMasses of Stars

– Mass-Luminosity RelationshipMass-Luminosity Relationship Stellar InteriorsStellar Interiors

– Hydrostatic EquilibriumHydrostatic Equilibrium

spring term astrophysics stellar physics dr p.a. hatherly modules: ph2006, ph3811

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