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Astronomy C - Variable Stars
A. Pulsating Variables:
1) Long Period Variables
a) Mira type
b) Semiregular
2) Cepheids
3) RR Lyrae
4) RV Tarui
B. Cataclysmic (Eruptive) Variables:
1) T Tauri
2) Novae
3) Dwarf Novae
4) Recurrent Novae
5) Supernovae
a) Type II
b) Type Ia
Astronomy C - Variable Stars
A. Pulsating Variables:
1) Long Period Variables
a) Mira type Mira
b) Semiregular Betelgeuse
2) Cepheids Delta Cephei
3) RR Lyrae [Globular Clusters]
4) RV Tarui R Scuti
B. Cataclysmic (Eruptive) Variables:
1) T Tauri [Protostars]
2) Novae GK Persei, Nova Aquilae
3) Dwarf Novae Z Cam, SS Cygni
4) Recurrent Novae [between Dwarf and Nova]
5) Supernovae
a) Type II Cas A, SN 1987A, DEM L316
b) Type Ia Tycho’s SNR, DEM L316
Light Curves – Variation over Time
Maximum (Maxima)
Minimum (Minima)
Apparent Magnitude vs Julian Day
Period
A. Pulsating Variable Stars;
1) Long Period Variables (LPVs)
a) Miras
Omicron Ceti (Mira)
80 – 1000 days, 2.5 – 5.0 mag
b) Semiregular Variables
Betelgeuse
(Alpha Orionis)
30 – 1000 days, 1.0 – 2.0 mag
Semiregular
Mira
Instability Strip
2) Cepheid Variable Stars
Delta Cephei
2) Cepheids [Periods of 1 – 70 days, 1.0 – 2.0 mag]
Delta Cephei
A Cepheid Variable Star in M100
3) RR Lyrae Variable Stars
47 Tuc
Periods of a few hours to one day, .3– 2.0 mag
Cepheid and RR Lyrae Variable Stars
Period-Luminosity Relationship and The Distance Modulus:
M = m - 5log10 (r)
10
[Mv = 0.75]
4) RV Tauri – a Stellar Missing Link?
R Scuti
Cepheid
Instability Strip
RR Lyrae
Semiregular
Mira
Instability Strip
B. Cataclysmic (Eruptive) Variables
1) T Tauri; proto-star stage for
mid-sized stars
Cepheid
Instability Strip
RV Tauri
RR Lyrae
T-Tauri
Semiregular
Mira
Instability Strip
Stellar Nurseries
- sites of protostar
& T-Tauri formation
M 42 – The Orion Nebula
2) Novae
Close binary systems – main sequence star & a white dwarf
1 to 300 days, 7.0 – 16.00 mags
Novae:
GK Persei
Nova Aquilae
3) Dwarf Novae
Dwarf Novae:
Close binary systems – main sequence star, white dwarf
and an accretion disk
Two of three subclasses; U Gem – SS Cygni
Z Cam – Z Cam
SS Cygni
Dwarf Novae:
SS Cygni
Z Cam
4) Recurrent Novae
Close binary systems – main sequence star & a white dwarf
1 to 300 days, 7.0 – 16.00 mags
*** Similar to novae but often resemble dwarf novae
5) Supernovae
a) Type II
SN 1987A
Cas A
b) Type Ia
Tycho’s SNR
Mira
DEM L316
Type II Supernova
Type Ia Supernova
MZ 3 – The Ant Nebula (planetary nebula)
Algol Beta Persei
Eclipsing Binary
Cosmological Distances
Variables
Spectroscopic
Parallax
Cepheids
RR Lyrae
Cosmological Distances
Spectroscopic Parallax
Cepheids
The Distance Modulus: M = m - 5log10 (r)
10
The Distance Modulus: M = m - 5log10 (r)
10
Cosmological Distances & Candles
Type Ia Supernovae – Standard Candle
Mv = -19.5
Basic Equations and Relationships
The Distance Modulus: M = m - 5log10 (r)
10
Kepler’s 3rd Law: (MA + MB) = a3
p2
v = d ; a = v ; 2π a = vP ; Fc = mac ; ac = v2 = rω2
t
t
r
1 pc = 206,265 au = 3.26 ly = 3.08 x 1016m
1° = 60 arcmin = 60´ ; 1´ = 60 arcsec = 60˝
Inverse Square Law: L = 1/r2
Circumference, Area, Surface Area, and Volume of a Sphere
REARRANGE ALL EQUATIONS FOR EACH VARIABLE
JD 2449050
JD 2449835
43
74
55
59
W Cyg
64
53
61
40
68
67
55
67
69
69
75
70
Phase Diagrams
1) Cepheid Light Curve
2) Superposition of Periods
3) Same Data Plotted Twice
4) Same data starting at
Maxima
O – C Diagrams
(Observed minus Calculated)
Theory Matches Observation
Perfectly Periodic
Correct Epoch
Correct Period
Perfectly Periodic
Correct Period
Wrong Epoch
Perfectly Periodic
Correct Epoch
Wrong Period
**True Period longer
Periodic
Period Unchanged
Epoch has Changed
** The slope of each line is the difference between its period and the estimated period.
Perfectly Periodic
Change in Period
**True Period Shorter
then Lenthens
NOT Perfectly Periodic
Different Period
Each Day
Stellar Evolution – A Journey with Chandra