astro 113 week2 - gmu college of science
TRANSCRIPT
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
© Dr. Joseph E. Pesce, Ph.D.
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)
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
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
© Dr. Joseph E. Pesce, Ph.D.
9-10
Contact Binaries³ Roche Lobe - Sphere of gravitational influence
�Detached�Binaries
�Semi-detached� Binaries
�Contact� Binaries
© Dr. Joseph E. Pesce, Ph.D.
Stellar Motion³ Proper Motion: True motion on the plane of the sky
³ Radial Motion: “3-D” motion along the line-of-sight
© Dr. Joseph E. Pesce, Ph.D.