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) 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 Cepheid Instability Strip RR Lyrae

B. Cataclysmic (Eruptive) Variables 1)T Tauri; proto-star stage for mid-sized stars

Mira Instability Strip Semiregular Cepheid Instability 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 – mags

Novae: Nova Aquilae GK Persei

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 – 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  Cepheids The 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 M v = -19.5

Basic Equations and Relationships The Distance Modulus: M = m - 5log 10 (r) 10 Kepler’s 3 rd Law: (M A + M B ) = a 3 p 2 v = d ; a = v ; 2π a = vP ; F c = ma c ; a c = v 2 = rω 2 t t r 1 pc = 206,265 au = 3.26 ly = 3.08 x m 1° = 60 arcmin = 60´ ; 1´ = 60 arcsec = 60˝ Inverse Square Law: L = 1/r 2 Circumference, Area, Surface Area, and Volume of a Sphere REARRANGE ALL EQUATIONS FOR EACH VARIABLE

JD

JD W Cyg

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 Epoch Correct 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 Unchanged Epoch has Changed NOT Perfectly Periodic Different Period Each Day O – C Diagrams (Observed minus Calculated)

Stellar Evolution – A Journey with Chandra