Unformatted text preview: Photometry Hipparchus [160  127 BC]
Hipparchus compiled a catalog of about a
thousand stars in the second century, BC.
He classified them into six categories of
brightness, now called magnitudes.
bi h
ll d Magnitudes
Recognizing that (a) the response of the human eye is basically logarithmic
and (b) the average flux difference between first and sixth magnitudes stars
is about 100, Norman Robert Pogson (1856) proposed that:
5 magnitudes exactly corresponds to a ratio of 100 : 1, or
1 magnitude corresponds to a flux ratio of 2.512 : 1.
( 2.512 )5 = 100.0
Note that numerically smaller numbers correspond to brighter stars. Apparent Magnitudes
F2 / F1 = 100(m1 – m2)/5
log (xn) = n log (x)
log (F2 / F1) = (m1 – m2) / 5 log (100) = 2 (m1 – m2) / 5 Δm = m1 – m2 = 2.5 log ( F2 / F1 ) Apparent Magnitudes
Δm = m1 – m2 = 2.5 log ( F2 / F1 )
25
Δm
0.0
00
0.5
1.0
2.0
2.5
3.0
4.0
5.0
10.0
10 0 Flux Ratio
1.0
10 :1
1.6 : 1
2.5 : 1
6.3 : 1
10 : 1
16 : 1
40 : 1
100 : 1
10,000
10 000 : 1 Example
m1 – m2 = 2.5 log ( F2 / F1 )
Let m1 = 4.2m and F2 / F1 = 27 4.2 – m2 = 2.5 log ( 27 )
4.2 – m2 = 3.6
m2 = 4.2 – 3.6
m2 = 0.6m PRS Question
1. If Star A has a magnitude of 15, and Star B is 10,000X brighter, then
the magnitude of Star B is
a. 25
d. 10
b. 20
e. 5
c. 15 The Pleiades Magnitude Scale
Object
Sun
Full Moon
Venus
Jupiter
Sirius
Nakedeye limit
Binoculars
4m telescope
Hubble m
26.7
12.6
4.4
2.0
1.4
6.5
10
26
30 Full Range
Δm = m1 – m2 = 2.5 log ( F2 / F1 )
Δm = 30 – (26.7) = 56.7
(
)
56.7 = 2.5 log ( F2 / F1 )
log ( F2 / F1 ) = 56.7 / 2.5 = 22.7 ≅ 23
F2 / F1 = 1023
100,000,000,000,000,000,000,000 : 1 Luminosity and Flux
Luminosity (power) is the rate at which electromagnetic energy is
radiated into space by an astronomical object.
Lsun = 3.826 x 1026 J/s
“Brightness” of a star is radiant flux F – The total amount of light energy
of all wavelengths that crosses a unit area perpendicular to the direction of
the light’s travel in unit time. The flux is the number of joules per second
at 1 cm2 of a detector aimed at the star.
F = L / (4 π d2) Propagation of Light
Apparent Brightness
Flux
Fl = Luminosity / 4 π d2
L i it Inverse Square L
I
S
Law
Flux1
4 π d22
d22
 =  = Flux2
4 π d12
d12 FluxDistanceLuminosity
Brightness = Flux = Luminosity / 4 π d2
b = F = L / d2
F1 d12
F2 d22 L1
= L2 The Pleiades How to Compare Magnitudes
The way to compare the intrinsic brightness is to compare the magnitudes
for a given distance, which is 10 pc.
Example:
E ample:
m = 7.5 mag d = 100 pc Change d to 10 pc
Distance has been reduced by 10X,
so the Brightness has increased by (10)2 = 100X or
100X,
the Magnitude must decrease by 5.0 mag
Therefore, M = 7.5 – 5.0 = 2.5 mag
,
g Absolute Magnitudes
m1 – m2 = 2.5 log ( F2 / F1 )
F = L / 4 π d2
F(10) / F(d) = ( d / 10 )2
m – M = 5 l ( d / 10 )
log Example
m – M = 5 log ( d / 10 )
Let m = 6.3m and d = 38 pc 6.3 – M = 5 log ( 38 / 10 )
6.3 – M = 2.9
M = 6.3 – 2.9
M = 3 m
3.4 PRS Question
2. What is the distance to Star C if its m = +20 mag and its M = 5 mag?
a. 106 pc
d. 103 pc
b.
b 105 pc
e.
e 102 pc
c. 104 pc The Sun’s Absolute Magnitude
m – M = 5 log ( d / 10 )
Let m = 26.7m and d = 1/206265 pc 26.7 – M = 5 log (1/206265 / 10 )
26.7 – M = 31.5
M = 26.7 + 31.5
M = 4.8m
8 Color and Temperature UBV Filter Bandpasses Color Indices
Filters U
B
V Ultraviolet
Blue
Visual ( U – B ) and ( B – V ) are color indices
B – V = MB – MV
Ultraviolet, blue, and visual magnitude scales are adjusted to be equal to
,
,
g
j
q
one another, so that they give a color index of 0 to a star with a
temperature of about 10,000 K. The (B – V) index ranges from about 0.4
(bluest, hottest stars) to more than +2.0 (redder, coolest stars). Color and Temperature Bolometric Magnitudes
Occasionally, astronomers do discuss the magnitudes of stars based on
their entire luminosity. In other words, no filter is used. The Bolometric
Magnitude covers the entire electromagnetic spectrum.
Instead of using Flux, one uses the Luminosity of the Sun:
Lsun = 3.826 x 1026 J/s
The corresponding magnitude is Mbol = 4.75 mag . Table of Colors ...
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 Spring '12
 Jarrio

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