properties of stars

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are needed to see this picture.

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http://stardate.org/radio/program/delta-lyrae

http://stardate.org/radio/program/delta-lyrae

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Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.

Define arc second, parsec.

Define brightness, apparent magnitude, absolute magnitude.

Describe the methods used to determine the temperature, luminosity, and radius of a star.

Learning goals:Learning goals:

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Questions:Questions:Which stars are the brightest?

Which stars are putting out the most watts? (luminosity = energy per second)

NEED TO KNOW:NEED TO KNOW:

Distances

The most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars.

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You already know about the parallax effect:

•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.

Demonstrating parallax

Parallax of Stars

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Define arc second

How many degrees in a circle? How many arc minutes in a degree? How many arc seconds in an arc minute?How many arc seconds in a degree?How many arc seconds in a circle?

__?__ radians = 360 degrees1 radian = 57.3 degrees

How many arc seconds in 1 radian? 360, 60, 60, 3600; 1,296,000; 2 pi; 206,265 arc sec/rad

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PARSEC: Parallax ARc SECond

A star having a parallax of 1 arc second is 1 parsec away1 parsec (pc) = 3.26 light years1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc

Baseline is 1 Astronomical Unit

Small angle formula for distance in AU’s:

• Define arc second, parsec

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Works accurately for stars within about 200 pc (Hipparchos satellite)

Biggest problem: measuring the miniscule shift of a star against more distant stars

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parallax = 0.75 arcseconds

distance = 1

0.75=1.3 pc = 4.3 ly

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distance = 1

0.15= __?__ pc = __?__ ly

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distance = 1

0.0015= __?__ pc = __?__ ly

6.7 22

667 2170 ly


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Using SIMBAD to find the parallaxes of the stars of Exercise 2



41 Cygni data (partial)

Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc seconds

Distance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly

http://simbad.u-strasbg.fr/simbad/

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Inverse square law for lightInverse square law for light



p. 494

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How the star looks to US HERE ON EARTH.

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10 times farther away

100 Watt 1000 Watt

1 Watts

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1000 times farther away

2 x farther away, 1/4 as bright 3 x farther away, 1/9 as bright

• Define brightness, apparent magnitude, absolute magnitude

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apparent brightness = L

4πD2

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Every 5 magnitudes difference means 100 x difference in brightness

One magnitude difference is 2.512 times in brightness.

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When you see only “magnitude,” that means APPARENT magnitude.

1. The magnitude (m) of star A is 1, the magnitude (m) of star B is 6. How many times brighter is A than B?

a) 5 b) 10 c) 100 d) 1000

2. m of star C is 12, m of star D is 2: How many times brighter is star D than star C? (Or, equally stated, how many times dimmer is star C than star D?)

a) 10 b) 24 c) 100 d) 10,000

• The Sun is the brightest star in the sky, with an apparent magnitude of about -26.5 Sirius is next in line, with an apparent magnitude of -1.5; how many times brighter is the Sun than Sirius?

a) 25 b) 28 c) 100,000 d) 10,000,000,000

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Using SIMBAD to find the apparent magnitudes of the stars of Exercise 2




V = apparent magnitude through “visual” filterThink of it as mv .


are needed to see this picture.UV IR


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Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs.

Relates luminosities by “placing” stars on common scale.Smaller the absolute magnitude number, the more luminous the star.

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m − M = 5log10(dpc ) − 5

M = m − 5log10(dpc ) + 5


41 Cygni dpc = 236 parsecsmv = 4.016

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Mv = mv − 5log10(dpc ) + 5

Mv = 4.016 − 5log10(236) + 5Mv = 4.016 − 5(2.37) + 5 = −2.8

What does the answer tell you?

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Define brightness, apparent and absolute magnitudeDefine brightness, apparent and absolute magnitude

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Supergiant IBright-Giant IIGiant IIISub-Giant IVMain Sequence Star (dwarf) V

We estimate the luminosity of a star by measuring how broad the absorption lines are in its spectrum.

At a given temperature, the less luminous stars have atoms colliding a lot more than in the giant stars.

• Describe the methods used to determine temperature, luminosity, radius

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Lum

inos

ityHigh

Low

TemperatureHigh Low

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Using SIMBAD to find the parallaxes of the stars of Exercise 2




F5 Iab


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The H-R The H-R DiagramDiagram

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L = 4πR2( ) σT 4

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Relationship between absolute magnitude and luminosity Relationship between absolute magnitude and luminosity - bring in the Sun!- bring in the Sun!

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MSun − Mstar = 2.5log10Lstar

LSun

⎛ ⎝ ⎜ ⎞

⎠ ⎟

MSun − Mstar( )2.5 = log10

LstarLSun

⎛ ⎝ ⎜ ⎞

⎠ ⎟

10M Sun −M star( )

2.5 =10log10

LstarLSun

⎛ ⎝ ⎜ ⎞

⎠ ⎟

10M Sun −M star( )

2.5 =Lstar

LSun

Lstar

LSun

=10M Sun −M star( )

2.5

Lstar

LSun

=104.74 −(−2.8)( )

2.5 =1070

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Lstar =1070LSun

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Depends on•Size (radius, R)•Temperature

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L = 4πR2( ) σT 4

• Describe the methods used to determine temperature, luminosity, radius€

L = 4πR2( ) σT 4

Lstar = 4πRstar2( ) σTstar

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LSun = 4πRSun2( ) σTSun

4

Lstar

LSun

=4πRstar

2

4πRSun2

σTstar4

σTSun4 =

Rstar

RSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Tstar

TSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟4

Lstar

LSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟TSun

Tstar

⎛ ⎝ ⎜

⎞ ⎠ ⎟4

=Rstar

RSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Rstar

RSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟=

Lstar

LSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟TSun

Tstar

⎛ ⎝ ⎜

⎞ ⎠ ⎟4

=TSun

Tstar

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Lstar

LSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟

LuminosityLuminosity

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Rstar

RSun

=TSun

Tstar

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Lstar

LSun

⎛ ⎝ ⎜

⎞ ⎠ ⎟ =

57706440 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2 1070

1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

Rstar

RSun

= 26 or Rstar = 26RSun

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The H-R The H-R DiagramDiagram

properties of stars

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