properties of stars

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QuickTime™ and a decompressor

are needed to see this picture.

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 brightness (see text), apparent magnitude, absolute magnitude.

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

Learning goals:Learning goals:

2

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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PARSEC: Parallax ARc SECond

A star having a parallax of 1 arc second is 1 parsec away

1 parsec (pc) = 3.26 light years

1 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:

4

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

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

€

parallax = 0.75 arcseconds

distance = 1

0.75=1.3 pc = 4.3 ly

€


distance = 1

0.15= __?__ pc = __?__ ly

€


distance = 1

0.0015= __?__ pc = __?__ ly

6.7 22

667 2170 ly

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

5

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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Every 5 magnitudes difference means 100 x difference in brightness

One magnitude difference is 2.512 times in brightness.

(2.5125 = 100)QuickTime™ and a

decompressorare needed to see this picture.

• Define brightness, apparent magnitude, absolute magnitude

7

Using SIMBAD to find necessary measured (observed) quantities



41 Cygni data (partial)

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


are needed to see this picture.UV IR

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

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Work on star table -- Work on star table -- SIMBAD SearchSIMBAD Search

Star ID Spectral

Type Surface

Temp. (K) App. Mag

Parallax (mas)

Dist. (pc)

Abs. Mag Lstar/Lsun Rstar/Rsun

41 Cygni

52 Cygni

69 Cygni

xi Cygni

F5 Iab 4.02 4.246,900

G9.5 III 4.23 16.224,800

B0 Ib 5.94 0.3626,000

K4.5 Ib-II 3.72 3.873,900

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

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10

Solar dataSolar data



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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.

€

m − M = 5log10(dpc ) − 5

M = m − 5log10(dpc ) + 5

• Define apparent magnitude, absolute magnitude

41 Cygni dpc = 236 parsecs

mv = 4.016

€

Mv = mv − 5log10(dpc ) + 5

Mv = 4.016 − 5log10(236) + 5

Mv = 4.016 − 5(2.37) + 5 = −2.8

What does the answer tell you?

12

€

m − M = 5log10(dpc ) − 5

M = m − 5log10(dpc ) + 5

52 Cygni52 Cygni

€

parallax = _____ arcseconds

distance = 1

parallax= ______

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Relationship between absolute magnitude and luminosity Relationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculations- bring in the Sun! 41 Cygni’s calculations

€

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

€

Lstar =1070LSun

14

52 Cygni52 Cygni

€

Lstar

LSun

=10M Sun −M star( )

2.5 = ________

15

Depends on•Size (radius, R)•Temperature

€

L = 4πR2( ) σT 4

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

L = 4πR2( ) σT 4

Lstar = 4πRstar2

( ) σTstar4

LSun = 4πRSun2

( ) σTSun4

Lstar

LSun

=4πRstar

2

4πRSun2

σTstar4

σTSun4 =

Rstar

RSun

⎛

⎝ ⎜

⎞

⎠ ⎟

2Tstar

TSun

⎛

⎝ ⎜

⎞

⎠ ⎟

4

Lstar

LSun

⎛

⎝ ⎜

⎞

⎠ ⎟TSun

Tstar

⎛

⎝ ⎜

⎞

⎠ ⎟

4

=Rstar

RSun

⎛

⎝ ⎜

⎞

⎠ ⎟

2

Rstar

RSun

⎛

⎝ ⎜

⎞

⎠ ⎟=

Lstar

LSun

⎛

⎝ ⎜

⎞

⎠ ⎟TSun

Tstar

⎛

⎝ ⎜

⎞

⎠ ⎟

4

=TSun

Tstar

⎛

⎝ ⎜

⎞

⎠ ⎟

2Lstar

LSun

⎛

⎝ ⎜

⎞

⎠ ⎟

LuminosityLuminosity

€

Rstar

RSun

=TSun

Tstar

⎛

⎝ ⎜

⎞

⎠ ⎟

2Lstar

LSun

⎛

⎝ ⎜

⎞

⎠ ⎟ =

5770

6440

⎛

⎝ ⎜

⎞

⎠ ⎟2

1070

1

⎛

⎝ ⎜

⎞

⎠ ⎟

Rstar

RSun

= 26 or Rstar = 26RSun

41 Cygni

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52 Cygni52 Cygni

€

Rstar

RSun

=TSun

Tstar

⎛

⎝ ⎜

⎞

⎠ ⎟

2Lstar

LSun

⎛

⎝ ⎜

⎞

⎠ ⎟ =

Rstar

RSun

= _______

17

Work on star table -- Work on star table -- SIMBAD SearchSIMBAD Search

Star ID Spectral

Type Surface

Temp. (K) App. Mag

Parallax (mas)

Dist. (pc)

Abs. Mag Lstar/Lsun Rstar/Rsun

41 Cygni

52 Cygni

69 Cygni

xi Cygni

F5 Iab 4.02 4.246,900

G9.5 III 4.23 16.224,800

B0 Ib 5.94 0.3626,000

K4.5 Ib-II 3.72 3.873,900

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

properties of stars

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