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Astronomy C - Variable Stars

A. Pulsating Variables:1) Long Period Variables

a) Mira type Mira

b) Semiregular Betelgeuse2) 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 Cygni4) Recurrent Novae [between Dwarf and Nova]

5) Supernovae

a) Type II Cas A, SN 1987A, DEM L316b) Type Ia Tychos SNR, DEM L316


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Light Curves Variation over Time

Maximum (Maxima)

Minimum (Minima) Period

Apparent Magnitude vs Julian Day


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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


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Mira

Instability Strip

Semiregular


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2) Cepheid Variable Stars

Delta Cephei


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2) Cepheids [ Periods of 1 70 days, 1.0 2.0 mag]

Delta Cephei


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A Cepheid Variable Star in M100


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3) RR Lyrae Variable Stars

Periods of a few hours to one day, .3 2.0mag

47 Tuc


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C h id d RR L V i bl St


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Cepheid and RR Lyrae Variable StarsPeriod-Luminosity Relationship and The Distance Modulus:

[Mv = 0.75]

M = m - 5log10 (r)10


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4) RV Tauri a Stellar Missing Link?

R Scuti


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Mira

Instability Strip

Semiregular

Cepheid

Instability Strip

RR Lyrae

B C t l i (E ti ) V i bl


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B. Cataclysmic (Eruptive) Variables

1) T Tauri; proto-star stage for

mid-sized stars


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Stellar Nurseries

- sites of protostar

& T-Tauri formation


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M 42 The Orion Nebula


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2) Novae

Close binary systems main sequence star & a whitedwarf

1 to 300 days, 7.0 16.00 mags

Novae:


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Novae:

Nova Aquilae

GK Persei

3) Dwarf Novae


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3) Dwarf Novae

Dwarf Novae:

Close binary systems main sequence star, white dwarfand an accretion disk

Two of three subclasses; U Gem SS Cygni

Z Cam Z Cam


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SS Cygni

Dwarf Novae:


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Dwarf Novae:

SS Cygni

Z Cam


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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


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5) Supernovae

a) Type II

Cas A

SN 1987A


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b) Type Ia

Tychos SNR Mira

T I SDEM L316


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Type Ia Supernova

Type II Supernova

DEM L316


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MZ 3 The Ant Nebula (planetary nebula)


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(p y )

Al l B t P i


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Algol Beta Persei

Eclipsing Binary


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Cosmological Distances


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Spectroscopic

Parallax

Variables

Cepheids

RR Lyrae



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g

CepheidsdThe Distance Modulus: M = m - 5log10 (r)

10

Spectroscopic ParallaxThe Distance Modulus: M = m - 5log10 (r)

10

Cosmological Distances &


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Type Ia Supernovae Standard CandleCandles

Mv= -19.5

Basic Equations and Relationships


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The Distance Modulus: M = m - 5log10(r)

10

Keplers 3rdLaw: (MA + MB) = a3

p2

v = d ; a = v ; 2 a = vP ; Fc= mac ; ac= v2= r2

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


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JD 2449050


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JD 2449110


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JD 2449150


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JD 2449180


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JD 2449240


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JD 2449300


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JD 2449350


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JD 2449375


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JD 2449435


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JD 2449500


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JD 2449540


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JD 2449635


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JD 2449700


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JD 2449740


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JD 2449760


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JD 2449800


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JD 2449870


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JD 2449950


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JD 2449835

43


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W Cyg

61 40

55

59

53

68

55

696967

67

64

75

74

70

JD 2449859


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W Cyg

40

53

68

55

69

55

59

43

61

64

6767

69

75

70

74

JD 2449917

43


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W Cyg

4061

53

68

55

6967

69

75

70

67

55

59

74

43

JD 2449951

43


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W Cyg

61 40

74

43

55

5953

68

55

69

67

67 69

75

70

64

JD 2449979

43


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W Cyg

61 40

74

43

55

5964

67

67

69

75

70

53

68

55

69

JD 2449991


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W Cyg

4061

64

74

43

55

5953

68

55

6967

69

75

67

70

JD 2450013

43


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W Cyg

4061

64

74

55

5953

68

55

69

67

69

75

67

70

Phase Diagrams


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1) Cepheid Light Curve

3) Same Data Plotted Twice

2) Superposition of Periods

4) Same data starting at

Maxima

Th M h Ob i

O C Diagrams(Observed minus Calculated)


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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 UnchangedEpoch has Changed

NOT Perfectly Periodic

Different Period

Each Day

Stellar Evolution A Journey with Chandra


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Stellar Evolution A Journey with Chandra


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Stellar Cycles Sets and Cosmic Connections Request URL:

http://chandra.harvard.edu/edu/epo/request_special.html


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Stellar Cycles Card Set:

http://www.chandra.harvard.edu/edu/epo/[email protected]

http://www.tufts.edu/as/wright_center/


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Additional Resources:


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The American Association of Variable Star Observers


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


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UPDATED COACHES MANUAL COMING SOON!!!

(AVAILABLE ONLINE AT THE NSO WEBSITE)

variable stars 2007

Documents