stellar radii - university of st andrewsstar-kdh1/sea/sea09.pdf · 2003. 10. 31. · stars &...
TRANSCRIPT
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 95
• To calculate R:• Observe:
. parallax p --> distance d=1/p.
. spectral type or colour index --> T
. apparent magnitude, e.g. V.
• Not highly accurate (10-50%)
424 TRL σπ=
)pc10/(log5 dMV V =− ..CBMM Vbol +=
( ))sun(/log5.2)sun( LLMM bolbol −=−
Stellar Radii
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 96
• Solar radius: Rsun=7x10^5 kmmain-sequence stars:
R ~ 0.1 - 10 Rsungiants: R ~ up to 100 Rsunsupergiants: red: R ~up to 1000 Rsun
blue: R ~20-50white dwarfs: R ~ 0.01 Rsun
Typical Radii
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 97
• Most accurate radii (
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 98
-- two stars in mutual gravitational attraction,orbiting their common centre of mass
-- only source of empirical masses for stars
-- accurate sizes, shapes, temperatures,luminosities (hence distances)
Binary Stars
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 99
Centre of Massa
m1 m2 a1 a2
mmm
aa
21
21 +
=
mama 2211 =
mmm
aa
21
12 +
=
primary star secondary star
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 100
Orbit Velocitiesa
V1
V 2
a1 a2
Pa
VVπ2
21 =+
P = orbit period
mm
aa
VV
1
2
2
1
2
1 ==
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 101
Elliptical Orbits
Model binary
binary1
Elliptical Orbits
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 102
Visual binary
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 103
Types of Binaries• visual binary
• spectroscopic binary. SB1 SB2 lines from 1 or 2 stars
• eclipsing binary
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 104
Spectroscopic binary
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 105
Eclipsing binaryStar sizes from timing
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 106
Proximity Effects
ellipsoidal variations
heating effects
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Types of Binaries
detached
semi-detached
contact
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 108
Binary Star with Accretion Disc
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 109
Light curves for close binary starsComputer Models ofEclipsing Binary Stars
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 110
Light curve of Contact Binary
Orbital Phase
Light curve of Contact Binary
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 111
redder
bluer
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 112
Velocity curves for binary starsVelocity curve
K1
K 2
Orbital Phase
Rad
ial V
eloc
ity
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 113
Orbit inclination
i = 0 for face-on orbit
i = 90 degrees for edge-on orbit
Doppler shifts measure. K = V sin i
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 114
To measure masses:- visual
– radial velocity and light variations - spectroscopic- eclipsing
velocity
+
-
11
4
2
2
34
orbitalphase(time)
C of M×
4
1
1
2
2
3
3
4
radial velocity curves
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 115
Masses
=
+AUyr
32
sun
21 aP
Mmm
Observe:
Kepler’s Law:
iVK sin11 =iVK sin22 =
P
PKKia )(sin2 21 +=π
Calculate masses:
KK
mm
1
2
2
1 =
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 116
• Analysis of RV curves gives"minimum masses"
and projected sizes of orbits
( ) ( )M i M i1 3 2 3sin , sin
( ) ( )a i a i1 2sin , sin
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 117
• Analysis of light curvesof eclipsing binaries gives– orbital inclination i– radii of both stars,
relative to the size of the orbit
ra
ra
1 2
,
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 118
• Hence, for eclipsing, spectroscopicbinaries, we obtain:
– masses M1 and M2– radii R1 and R2– luminosities L1 and L2
• (if T1 or T2 known)
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 119
– used as tests of theoretical models ofstars
L
T
HR Diagram
high mass
low mass
main sequence
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 120
• Empirical MASS-LUMINOSITYrelationship for main-sequence stars:. i.e.
(handout) plots log.log see LvsM
sunsunsunsun
MMMMM
LL
ML
104.0for
4
4
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 121
Mass-luminosity and HR diagram (T-L) for detached eclipsing binaries
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 122
Mass-radius plot for detached eclipsing binaries
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 123
Mass-Luminosity for Main Sequence
≅
sunsun
4
MM
LL
ML 4∝
Slope = +4
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Stars & Elementary Astrophysics: Introduction Press F1 for Help 124
Star Lifetimes• Energy supply:• Rate of burning:• Lifetime:
• Stars burn for a long time.• Big stars burn out faster.
(Joules) 2cME ∆=Joule/s)(W 4 =∝ ML
∆
∆=∆=
−
M
MMM
LcM
MM
LcM
LE
t
sun
3
10
22
0015.0
/yr 10~
~