Astronomy C - Variable Stars
A. Pulsating Variables: 1) Long Period Variables a) Mira type b) Semiregular 2) Cepheids 3) RR Lyrae 4) RV TaruiB. 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 ScutiB. 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 TimeMaximum (Maxima)
Minimum (Minima) Period
Apparent Magnitude vs Julian Day
A. Pulsating Variable Stars; 1) Long Period Variables (LPVs)a) Miras
Omicron Ceti (Mira)
b) Semiregular Variables
80 – 1000 days, 2.5 – 5.0 mag
Betelgeuse (Alpha Orionis)
30 – 1000 days, 1.0 – 2.0 mag
Mira Instability Strip
Semiregular
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
Periods of a few hours to one day, .3– 2.0 mag
47 Tuc
Cepheid and RR Lyrae Variable Stars
[Mv = 0.75]
Period-Luminosity Relationship and The Distance Modulus: M = m - 5log10 (r) 10
4) RV Tauri – a Stellar Missing Link?
R Scuti
Mira Instability Strip
Semiregular
CepheidInstability Strip
RR Lyrae
B. Cataclysmic (Eruptive) Variables1)T Tauri; proto-star stage
for mid-sized stars
Mira Instability Strip
Semiregular
CepheidInstability Strip
RR Lyrae
T-Tauri
RV Tauri
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:
Nova Aquilae
GK Persei
3) Dwarf NovaeDwarf 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 NovaeClose 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
Cas A
SN 1987A
b) Type Ia
Tycho’s SNR Mira
Type Ia Supernova
Type II Supernova
DEM L316
MZ 3 – The Ant Nebula (planetary nebula)
Algol Beta Persei
Eclipsing Binary
Cosmological Distances
Spectroscopic Parallax
Variables
Cepheids RR Lyrae
Cosmological Distances
CepheidsThe Distance Modulus: M = m - 5log10 (r) 10
Spectroscopic Parallax The Distance Modulus: M = m -
5log10 (r) 10
Type Ia Supernovae – Standard Candle
Cosmological Distances & Candles
Mv = -19.5
Basic Equations and Relationships
The Distance Modulus: M = m - 5log10 (r) 10Kepler’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 1016m1° = 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
W Cyg
61 40
43
5559
53
6855
696967
67
64
75
74
70
1) Cepheid Light Curve
3) Same Data Plotted Twice
2) Superposition of Periods
4) Same data starting at Maxima
Phase Diagrams
Theory Matches Observation
Perfectly Periodic
Correct EpochCorrect Period
** The slope of each line is the difference between its period and the estimated period.
Perfectly Periodic
Correct Epoch
Wrong Period
**True Period longer
Perfectly Periodic
Change in Period
**True Period Shorter then Lenthens
Perfectly Periodic
Correct Period Wrong Epoch
Periodic
Period UnchangedEpoch has Changed
NOT Perfectly Periodic
Different Period Each Day
O – C Diagrams(Observed minus Calculated)
Stellar Evolution – A Journey with Chandra