Transcript Lecture 1 - University of Reading

Spring Term Astrophysics
Stellar Physics
Dr P.A. Hatherly
Modules: PH2006, PH3811
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.
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 Website
Navigate via physicsnet at http://www.rdg.ac.uk/physicsnet/
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
Lecture Calendar
Sun Mon Tue Wed Thu Fri Sat Week
1
17
15 16
14
13
12
11
Jan
2
24
22 23
21
20
19
18
3
31
29 30
28
27
26
25
4
7
6
5
4
3
2
1
Feb
5
14
12 13
11
10
9
8
6
21
19 20
18
17
16
15
7
28
26 27
25
24
23
22
8
29
8
6
5
4
3
2
1
March
9
13
11 12
10
9
8
7
10
20
18 19
17
16
15
14
Key:
Lecture 9-11
Lecture 9-11, Workshop 11-12
Open discussion and revision 9-12
Private Study
Release Assessment 1 on 26th January
Return Assessment 1 on 11th February
Release Assessment 2 on 23rd February
Return Assessment 2 on 10th March
All Lectures in the Gordon Theatre, Engineering
All Workshops in 131, Physics
All Assessments to be returned to the School Office
(Room 217, Physics) by 13:00 on the due date
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%
Assessment

Formal Examination
– 2 hour paper in Summer
– Contribution: 60%
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)
Distances of Stars
Stellar Parallax
d
p
1 AU
Distances of Stars
The angle subtended, p, is simply given
by:
p = 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)
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”
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
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”
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)
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
Velocities of Stars
vt

Example:
vs
q
vr
– Barnard’s 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°
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
Red shift - vr positive
No shift - vr zero
Blue shift - vr negative
Velocities of Stars

Example:
– Barnard’s 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%
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
Stellar Magnitude Scale

Relative Intensities (mag. 0 = 1)
Magnitude
-2
-1
0
1
2
3
4
5
Relative Intensity
6.3
2.152 (=1001/5)
1
0.46
0.16
0.06
0.025
0.01
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
Stellar Magnitude Scale

Relationship between M and m :
– (m - M ) = 5log10d - 5
d 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
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 ,

L1
( M2 M1 )/ 5
 100
L2
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
Colour Correction

Careful observation of stars reveals they
have a range of colours
– Black-body or thermal radiation
– Stefan’s Law - power per unit area
P = sT 4 (T in K)
– Wien’s Law
lmax(nm) = 2.9x106/T
Colour Corrections

Examples of spectra
UV
Visible
IR
Sun
Betelgeuse
Sirius
0
200
400
600
800
Wavelength (nm)
1000
1200
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
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
Colour Corrections

Note that:
– bv /bb and bb /bu <1 with bb /bu < bv /bb
 hot, blue star, T >20000 K.
– bv /bb and bb /bu roughly equal and ~1
 cooler, white star, T ~9000 K.
– bv /bb and bb /bu >1 with bb /bu > bv /bb
 cool, orange/red star T <4000 K.
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.
Stellar Spectra

The spectra of stars are classified
according to the scheme:
OBAFGKM


Increasing Temperature
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
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
Stellar Spectra
Hg
Ha
Hb
O
B
A
F
G
K
M
Mg I TiO
Na
TiO
Stellar Spectra
Class
Colour
Temp.
(x103 K)
Spectral lines
Examples
O
Blue-violet
28 – 50
Ionised atoms
 Pup1,  Ori2
B
Blue-white
10 – 28
He, some H
a Vir3, b Ori4
A
White
7.5 – 10
Strong H, some
ionised metals
a Cma5, a Lyr6
F
Yellow-white
6 – 7.5
H and Can+, Fen+.
a Car7, a Cmi8
G
Yellow
5–6
Can+, other ionised
and neutral metals
Sun, a Aur9
K
Orange
3.5 – 5
Neutral metals
a Boo10, a Tau11
M
Red-orange
2.5 – 3.5
TiO and Ca
a Sco12, a Ori13
Common names: 1Naos, 2Mintaka, 3Spica, 4Rigel, 5Sirius, 6Vega, 7Canopus,
8
Procyon, 9Capella, 10Arcturus, 11Aldebaran, 12Antares, 13Betelgeuse
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

H-R Diagram
for a number of
the brightest
and nearest
stars
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.
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
Next Lecture:
Dimensions of Stars
 Luminosity and Spectral Class

– Spectroscopic Parallax

Masses of Stars
– Mass-Luminosity Relationship

Stellar Interiors
– Hydrostatic Equilibrium