astro 113 week2 - GMU College of Science

Astronomy 113Dr. Joseph E. Pesce, Ph.D.

© Dr. Joseph E. Pesce, Ph.D.

The Nature of Stars


8-2

ParallaxFor �nearby� stars - measure distances with parallax

d

1 AU

p

³ d = 1/p (arcsec) [pc]³ 1pc when p=1arcsec; 1pc=206,265AU=3 x 1013 km³ P = VERY small!! (<<1�)³ Using satellites, can measure start to d~1,000pc

away

A

July

JanuaryA

A


8-3

BrightnessApparent Magnitude (log scale - the eye’s response)

+1 +6 (naked-eye limit)Bright Faint1 magnitude = 2.5 times real brightness (so 1 to 6 is 100 times

difference: 2.55 = 100)

Magnitudes can be negative too. So,Sun = -25Moon = -12Sirius = 0

Faintest objects = +30 (with HST, for example)© Dr. Joseph E. Pesce, Ph.D.

8-4

Magnitudes³ Apparent magnitude (m) is not �real� brightness³ Apparent brightness decreases inversely with square of

distance - the �inverse square law�:Double distance apparent brightness decreases (1/2)2 =1/4Triple distance … … … … (1/3)2 =1/9

Need to be able to compare real brightness, so correct for distance

Absolute magnitude (M) = apparent magnitude an object would have if it were at 10 pc

Sun = +4.8 (range for stars: -10 to +17)Measure m and d, then: M = m - 5log(d/10)


8-5

Inverse-square Law


8-6

Luminosity³ Absolute magnitude is related to Luminosity (the physical

brightness of an object)

L =sAT4 = s 4p r2 T4 (r = Radius; s is a constant)

³ Solar luminosity = 3.9 x 1026 Watts³ Call this 1 L

Stars with:M = -10 have 106 LM = +17 have 10-5 L


8-7

Stellar Temperatures³ Remember Wien’s law? (lmax = 1/T; color related to surface tempature)

U B V

Inte

nsity

Wavelength

Use a photometer to measure light intensity and filters to measure intensity at different �bands�:

U (UV), B (blue), V (visual)

That is, 3 apparent magnitudes which tell us where most energy in spectrum is (B-V = color index; if small, object is blue, if large, it is red)

From blackbody curves, get T vs. B-V, and thus a surface temperature

At different temperatures, different elements produce different emission lines - can measure temperature this way too


8-8

Spectral Types³ A star’s surface temperature determined from color index or spectral

line strengths³ In the 1920s, Cecilia Payne classified stars based on spectral features

visible (and ordered them by surface temperature)³ Spectral types:

O B A F G K MHottest

T~35,000 K

HeII (singly ionized)

SiIV (triply ionized)

Coolest

T~3,000 K

Molecules (TiO)

Further subdivided: B0 - B9Hottest Coolest

Sun = G2


8-9

Spectral Types


Types of Stars


9-2

The Hertzsprung-Russell DiagramSupergiants

Giants

Sun

Main Sequence

White DwarfsO0 B0 A0 F0 G0 K0 M0

-10

-5

0

+5

+10

+15

Faint

Bright

Lum

inos

ity

Abso

lute

Mag

nitu

de

Hot 40,000K

Cool 2,500K

Surface Temperature

1000100

10

1

0.01

0.001


9-3

The Hertzsprung-Russell Diagram³ Pattern when color-index is plotted against absolute magnitude

² Also called �Color-Magnitude� diagram

Surface Temperature and Absolute Magnitude are Related!

³ Main Sequence: 90% of stars in Solar neighborhood are on Main Sequence (called �dwarf� stars)² M-type stars most common² O-type stars rarest² Most M.S. stars are like the Sun


9-4

The Hertzsprung-Russell Diagram


9-5

Giants

³ From Stefan-Boltzmann Law:

E = T4

³ Cool objects radiate less E than hot (per unit surface area)

³ So, for Giants to be so bright, they must be huge!

T ~ 3,000 - 6,000K

R ~ 10 - 100x Solar Radius

Red

Example: Arcturus


9-6

Supergiants³Even bigger and brighter than Giants³Example: Betelgeuse³1% of all stars in Solar neighborhood

9% of stars in Solar neighborhood are �white

dwarfs� - more later


9-7

Binary Stars³ Two stars gravitationally bound³ Orbital motion of binaries shifts spectral lines (Doppler Shift)

Approaching

Receding

Rad

ial

Velo

city

0Time

Radial Velocity Curve


9-8

Eclipsing Binaries³ We see stars along their orbital plane³ Causes effects in light curve:

Intensity

TimeTime to cross disk

³ Total eclipses allow us to measure radii of stars


9-9

Stellar Masses³ How do you measure mass?³ Newton’s adaption of Kepler’s Law:

M1 + M2 = a3 / p2 (both measured in binaries)

Mass-Luminosity Relationship:

On the Main Sequence, the more massive a star, the more luminous

0.150 Mass

L/L

10-410-21102104106


9-10

Contact Binaries³ Roche Lobe - Sphere of gravitational influence

�Detached�Binaries

�Semi-detached� Binaries

�Contact� Binaries


Stellar Motion³ Proper Motion: True motion on the plane of the sky

³ Radial Motion: “3-D” motion along the line-of-sight


Thank You!


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astro 113 week2 - GMU College of Science