Spring Term Astrophysics Stellar Physics

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Spring Term Astrophysics Stellar Physics

• Dr P.A. Hatherly
• Modules PH2006, PH3811

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Topics to be Covered

• Properties of Stars
• Distances, velocities, dimensions, masses,
  temperatures, luminosities.
• Stellar Interiors
• Pressures and temperatures, compositions, power
  sources.
• Life-cycles of Stars
• Star formation, evolution and death.

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Resources Available

• 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 WebsiteNavigate via physicsnet at
  http//www.rdg.ac.uk/physicsnet/

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Unit Structure

• 14 Lectures/presentations
• Weeks 4 and 8 for private study
• 6 Workshops/discussion sessions
• Week 1 - no workshop
• 2 assessed problem worksheets and 1 formal
  examination

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Lecture Calendar
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Assessment

• Continuous Assessment
• Selected problems set in weeks 3 and 7
• Posted on website on 26th January and 23rd
  February
• Answers returned in weeks 5 and 9
• To the School Office by 1pm, 11th February and
  10th March
• Results/feedback in weeks 6 and 10
• Results posted on website and problems discussed
  in the following workshop
• Contribution 40

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Assessment

• Formal Examination
• 2 hour paper in Summer
• Contribution 60

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Assumed Knowledge

• Classical Mechanics and Optics
• Part 1
• Thermodynamics and Statistical Mechanics
• In progress
• Atomic and Molecular Physics
• Simple quantum ideas, in progress
• Ideas from Observational Astronomy
• (useful, but not essential)

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Distances of Stars
Stellar Parallax
d
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Distances of Stars

• The angle subtended, p, is simply given byp
  1/d (with d in AU and p in radians)
• Definition
• If a star gives a parallax of 1 (1 second of
  arc, arcsec 1/3600) then the distance to the
  star is 1 parsec (pc)
• Hence, d (pc) 1/p (arcsec)

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Distances of Stars

• Examples
• The first star to have its parallax measured was
  61 Cygni. Its parallax was 0.33. How far away is
  it?
• d 1/p 1/0.33 3 pc
• The nearest star, Proxima Centauri is at a
  distance of 1.3 pc. What is its parallax?
• p 1/d 1/1.3 0.77

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Distances of Stars

• Relationship to Other Units
• 1 pc 2.06x105 AU
• 1AU 1.5x108 km\1 pc 3.086x1013 km
• Distance light travels in 1 year 1 light year
  (ly) 9.46x1012 km \1 pc 3.26 ly

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Distances of Stars

• Limitations of Parallax
• Maximum distance from ground based observations,
  50 pc
• Maximum from space-based observations, 500 pc
• Other methods required for greater distances
• Standard candles

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Velocities of Stars

• Define
• Proper Motion The angular velocity of a star
  tangential to the line of sight
• Symbol, m Units, arcsec/year
• Tangential Velocity vt Units km/s
• related to the proper motion by vt 4.74md
  km/s (with d in pc)

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Velocities of Stars

• Define
• Radial Velocity The velocity of the star along
  the line of sight.
• Symbol, vr Units, km/s
• Note a negative radial velocity means a star is
  approaching us

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Velocities of Stars
vs
vt
q

• Example
• Barnards Star (distance, 1.82 pc)
• Proper motion 10.32 arcsec/year
• Tangential velocity 89.1 km/s
• Radial velocity -111 km/s
• Speed vs (vr2 vt2)1/2 142.3 km/s
• Angle to line of sight q tan-1(vt /vr )
  -38.75

vr
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Velocities of Stars

• Measurement of Velocities
• Proper motion - straightforward observation,
  maybe over many years, of the position of a star
• Radial velocity - Use Doppler Effect

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Velocities of Stars

• Example
• Barnards Star - 10.32 arcsec/year is easy to
  measure ( 0.6 angular diameter of full moon)
• Doppler shift due to vr Dn/n vr /c -0.04

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Stellar Magnitude Scale

• A logarithmic scale, defined such that a
  difference of magnitude of 5 corresponds to a
  change in intensity of 100
• Smaller magnitudes mean brighter stars
• e.g., a magnitude 0 star is 100x brighter than
  magnitude 5

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Stellar Magnitude Scale

• Relative Intensities (mag. 0 1)

Magnitude Relative Intensity -2 6.3 -1 2.152
(1001/5) 0 1 1 0.46 2 0.16 3 0.06 4 0.025 5
0.01
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Stellar Magnitude Scale

• Definitions
• Apparent Magnitude, m The magnitude a star
  appears to be
• Absolute Magnitude, M The apparent magnitude a
  star would have if it were viewed from a distance
  of 10 pc

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Stellar Magnitude Scale

• Relationship between M and m
• (m - M ) 5log10d - 5d is the distance to the
  star in pc
• The quantity (m - M ) is known as the Distance
  Modulus
• Example Sirius has an apparent magnitude of
  -1.46. It is 2.7 pc away, what is its absolute
  magnitude?
• m -1.46, d 2.7 pc
• M -1.46 - 5log102.7 5 1.38

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Relative Luminosities

• Often convenient to refer to the relative
  luminosities of stars.
• From the definition of magnitudes, if two stars
  have absolute magnitudes M1 and M2 , and
  luminosities L1 and L2 ,

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Relative Luminosities

• Example
• The absolute magnitude of the Sun is 4.8 and
  that of Sirius is 1.38. What is the ratio of
  their luminosities?
• Lsirius /L 100(4.8-1.38)/5 23.3

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Colour Correction

• Careful observation of stars reveals they have a
  range of colours
• Black-body or thermal radiation
• Stefans Law - power per unit areaP sT 4 (T in
  K)
• Wiens Lawlmax(nm) 2.9x106/T

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Colour Corrections

• Examples of spectra

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Colour Corrections

• Clearly, many stars produce a large amount of
  light outside the visible
• Observe stars through a variety of filters.
• U - 300 - 400 nm
• B - 380 - 550 nm
• V - 500 - 650 nm

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Colour Corrections

• From the filters, we obtain
• bu, bb and bv
• Ratios bv /bb and bb /bu
• Examples
• Sun, bv /bb 1.77, bb /bu 1.10,T 5800 K
• Sirius, bv /bb 1.00, bb /bu 0.95,T 10000 K
• Betelgeuse, bv /bb 5.50, bb /bu 6.67, T
  2400 K

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Colour Corrections

• Note that
• bv /bb and bb /bu lt1 with bb /bu lt bv /bb Þ hot,
  blue star, T gt20000 K.
• bv /bb and bb /bu roughly equal and 1 Þ cooler,
  white star, T 9000 K.
• bv /bb and bb /bu gt1 with bb /bu gt bv /bb Þ
  cool, orange/red star T lt4000 K.

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Stellar Spectra

• Examination of stellar spectra reveal absorption
  lines on the black body background
• Due to neutral or ionised atoms or molecules in
  the stellar atmosphere
• Gives composition of star, another handle on
  temperature and a means of classification.

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Stellar Spectra

• The spectra of stars are classified according to
  the schemeO B A F G K M

• Each class is further divided from 0-9, with 0
  being the hottest and 9 the coolest
• Note This scheme can be remembered by the
  traditional mnemonic Oh Be A Fine Girl (Guy,
  Gorrilla...) Kiss Me

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Stellar Spectra

• Historical Note
• Originally (19th C), classification was based on
  the strength of the hydrogen Balmer absorption
  spectrum, and ran from A to P in order of
  decreasing absorption
• The current scheme arose as a more logical
  classification in terms of temperature

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Stellar Spectra
Ha
Hb
Hg
O
B
A
F
G
K
M
Na
Mg I
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Stellar Spectra
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Stellar Classification

• We now have two vital pieces of information
• Luminosity, via distance and magnitude
• Temperature from spectroscopy
• Is there any correlation between these
  parameters?
• Very important result - a plot of luminosity
  versus temperature (spectral class)
• The Hertzprung-Russel (H-R) Diagram

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

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The H-R Diagram

• Points to note
• The narrow band of stars scattered close to the
  solid line.
• Most stars occur along this band an indication
  that this is where stars spend most of their
  lives. For this reason, it is known as the Main
  Sequence.

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The H-R Diagram

• Other regions to note are stars of high
  luminosity but low temperature (indicating they
  are large hence the term red giant) and stars
  of high temperature but low luminosity
  (indicating small diameters, hence white dwarf )
• As we shall see, the H-R diagram is extremely
  useful in many aspects of stellar physics

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Next Lecture

• Dimensions of Stars
• Luminosity and Spectral Class
• Spectroscopic Parallax
• Masses of Stars
• Mass-Luminosity Relationship
• Stellar Interiors
• Hydrostatic Equilibrium