``But I am constant as the Northern Star

Of whose true-fixed and resting quality

There is no fellow in the firmament.''

William Shakespeare,

Julius Caesar, 3, 1

Astronomy C -

Variable Stars -

2008

A. Pulsating Variables:1) Long Period Variables

a) Mira typeb) Semiregular

2) Cepheids3) RR Lyrae

B. Cataclysmic (Eruptive) Variables:1) R Coronae Borealis2) Flare Stars3) Dwarf Novae4) X-Ray Binaries5) Supernovae

a) Type IIb) Type Ia

C. Strangers in the Night

Astronomy C -

Variable Stars -

2008

A. Pulsating Variables:1) Long Period Variables

a) Mira type R Cygnib) Semiregular

V725 SGR

2) Cepheids

W Virginis

3) RR Lyrae

AH Leo

B. Cataclysmic (Eruptive) Variables:1) R Coronae Borealis RY Sagittarii2) Flare Stars UV Ceti3) Dwarf Novae SU Ursae

Majoris

4) X-Ray Binaries J1655-40, RX J0806.3+15275) Supernovae

a) Type II G11.2-0.3, SN2006gy b) Type Ia

DEM L71, Kepler’s

SNR

C. Strangers in the Night: V838 Mon

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

R Cygni

b) Semiregular

Variables

80 –

1000 days, 2.5 –

5.0 mag

30 –

1000 days, 1.0 –

2.0 mag

V725 Sgr

Mira Instability Strip

Semiregular

2) Cepheid Variable StarsW Virginis

(Type 2) [Periods of .8 –

35 days, .3 –

1.2 mag]

Type I (Classical) Cepheids: Young high-metallicity

stars

about 4 times more luminous than Type II Cepheids

Type II Cepheids: Older low-

metallicity

stars about 4 times

less luminous than classical Cepheids.

Type I and Type II Cepheid Variable Stars

3) RR Lyrae

Variable StarsAH Leo

[Periods of .2 –

1 day, .3 –

2.0 mag]

Cepheid and RR Lyrae

Variable Stars

[Mv

= 0.75]

Period-Luminosity Relationship and The Distance Modulus:

M = m -

5log10 (r)

10

Mira Instability Strip

Semiregular

CepheidInstability Strip

RR Lyrae

B. Cataclysmic (Eruptive) Variables1)

R Coronae Borealis

RY Sagittarii

[Irregular Period, up to 3 mag]

2) Flare Stars –

faint cool red dwarfs[irregular and unpredictable] UV Ceti

3) Dwarf NovaeDwarf Novae: Close Binary Systems

Sun-like main sequence star, white dwarf , accretion disk

SU Ursae

Majoris [Period 30-500 days, 2-5 mag]

4) X-Ray Binaries –

Close Binary Systems

GRO J1655-40

RX J0806.3+1527

White Dwarf, Neutron Star, orBlack Hole accreting material from a Companion Star

a)

b)

5) Supernovae a) Type II –

Core Collapse of a Massive Star

G11.2-0.3 SN 2006gy

b) Type Ia

–

Thermonuclear Destruction of aWhite Dwarf in a Binary System

DEM L71 Kepler’s

SNR

Supernovae Light Curves

C. Strangers in the Night

V838 Mon

R Cygni

V725 SGRType II G11.2-0.3, SN 2006gy Type Ia

DEM L71, Kepler

SU Ursae

Majoris

RY Sagittarii

W Virginis

AH Leo

Flare Stars UV Ceti

X-Ray Binaries GRO J1655, RXJ0806.3+1527

V838 Mon???

?

?

Cosmological DistancesCepheids

The Distance Modulus: M = m -

5log10 (r)

10

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

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 Shorterthen Lenthens

Perfectly Periodic

Correct PeriodWrong Epoch

Periodic

Period UnchangedEpoch has Changed

NOT Perfectly Periodic

Different PeriodEach Day

O –

C Diagrams(Observed minus Calculated)

Stellar Evolution –

A Journey with Chandra

Stellar Evolution –

A Journey with Chandra

Stellar Cycles Sets and Cosmic Connections Request URL:http://chandra.harvard.edu/edu/epo/request_special.htmldonna.young@tufts.edu

Stellar Cycles Card Set:

Additional Resources:

The American Association of Variable Star Observers

http://www.soinc.org/store/TG-DVD-06v10.htm

UPDATED COACHES MANUAL COMING SOON!!!(AVAILABLE ONLINE AT THE NSO WEBSITE)