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