Understanding Stars: Brightness, Temperature, and Distance
Explore the fascinating world of stars by learning about their brightness, surface temperature, and distance. Discover how these factors are interconnected and affect our understanding of the cosmos.
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Stars Part One: Brightness and Distance
Concept -1 Temperature max (metres) = 2.90 x 10-3 m k T (Kelvin) max = Peak black body wavelength T = The star s surface temperature in Kelvins So HOT = BLUE, COOL = RED
max = 2.90 x 10-3 m K T max From Jay Pasachoff s Contemporary Astronomy
Put this in your notes: A star has a surface temperature of 5787 K, what is its max? max = (2.90 x 10-3 m K)/T = (2.90 x 10-3 m K)/5787 = 501 nm 501 nm
A star has a max of 940 nm, what is its surface temperature? max = (2.90 x 10-3 m K)/T, T = (2.90 x 10-3 m K)/ max = (2.90 x 10-3 m K)/ (940E-9) = 3100 K 3100 K
Concept 0 Total power output Luminosity L = AT4 Luminosity L = The star s power output in Watts = Stefan Boltzmann constant = 5.67 x 10-8W/m2K4 A = The star s surface area = 4 r2 T = The star s surface temperature in Kelvins
Put this in your notes: Our Sun has a surface temp of about 5787 K, and a radius of 6.96 x 108 m. What is its Luminosity? L = AT4 = 5.67x10-8(4 (7x108 ) 2 )(5787)4 = 3.87x1026 Watts 3.87x1026 Watts
A star has a radius of 5 x 108 m, and Luminosity of 4.2 x 1026 Watts, What is its surface temperature? Luminosity L = AT4 , T =(L/( 4 (5x108)2)).25 =6968 K = 7.0x103 K 7.0x103 K
Concept 1 Apparent Brightness Apparent Brightness b = L 4 d2 b = The apparent brightness in W/m2 L = The star s Luminosity (in Watts) d = The distance to the star L is spread out over a sphere..
Apparent Brightness b = L/4d2 The inverse square relationship From Jay Pasachoff s Contemporary Astronomy
Put this in your notes: Our Sun puts out about 3.87 x 1026 Watts of power, and we are 1.50 x 1011 m from it. What is the Apparent brightness of the Sun from the Earth? (The Solar Constant ) b = L/4 d2 = 3.87E26/ 4 1.50E112 = 1370 W/m2 1370 W/m2
Another star has a luminosity of 3.2 x 1026 Watts. We measure an apparent brightness of 1.4 x 10-9 W/m2. How far are we from it? b = L/4 d2 , d = (L/4 b).5 = 1.3x1017 m 1.3x1017 m
Concept 2 Apparent Magnitude Apparent Magnitude: m = 2.5log10 (2.52 x 10-8W/m2/b) b = The apparent brightness in W/m2 m = The star s Apparent Magnitude Note that the smaller b is, the bigger m is. Logarithmic scale: x100 in b = -5 in m Put this in your notes: What is the apparent magnitude of a star with an apparent brightness of 7.2x10-10 Wm-2? What is that of a star with an apparent brightness of 7.2x10-12 Wm-2?
Apparent Magnitude: m = 2.5log10 (2.52 x 10-8W/m2/b) b = The apparent brightness in W/m2 m = The star s Apparent Magnitude Note that the smaller b is, the bigger m is. Logarithmic scale: x100 in b = -5 in m Example: What is the apparent magnitude of a star with an apparent brightness of 7.2x10-10 Wm-2? What is that of a star with an apparent brightness of 7.2x10-12 Wm-2? For the first: For the second: m = 2.5log(2.52E-8/7.2E-10) = 3.9 (no units) m = 2.5log(2.52E-8/7.2E-12) = 8.9 Notice that when it got dimmer by 100x, the magnitude went up 5. yeah it s weird.
So apparent magnitude is a counter-intuitive scale -27 is burn your eyes out, 1 is a normal bright star, and 6 is barely visible to a naked, or unclothed eye. (You can t see anything if you clothe your eyes!!) A magnitude 1 star delivers 100 times more W/m2 than a magnitude 6 star.
What is the Apparent Magnitude of a star that has an apparent brightness of 1.4 x 10-9 W/m2 ? m = 2.5log10 (2.52 x 10-8W/m2/b) = 2.5log10 (2.52 x 10-8W/m2/ 1.4 x 10-9 W/m2) = 3.1 3.1
The Hubble can see an object with an apparent magnitude of 28. What is the apparent brightness of such a star or galaxy? m = 2.5log10 (2.52 x 10-8W/m2/b) , b = 2.52 x 10-8W/m2 /10(m/2.5) = 1.6 x10-19 W/m2 1.6 x10-19 W/m2
Concept 3 Absolute Magnitude Absolute Magnitude: m - M = 5 log10(d/10) M = The Absolute Magnitude d = The distance to the star in parsecs m = The star s Apparent Magnitude The absolute magnitude of a star is defined as what its apparent magnitude would be if you were 10 parsecs from it.
Absolute Magnitude: m - M = 5 log10(d/10) M = The Absolute Magnitude d = The distance to the star in parsecs m = The star s Apparent Magnitude Example: 100 pc from an m = 6 star, M = ? (10x closer = 100x the light = -5 for m) M = 6 - 5 log10(100/10) = 1
Put this in your notes: The Sun has an apparent magnitude of -26.8, we are 1.5x108 km or 4.9 x 10-6 pc from the sun. What is the sun s absolute magnitude? M = m - 5 log10(d/10) = -26.8 - 5 log10(4.86 x 10-6 /10) = 4.7 4.7
You are 320 pc from a star with an absolute magnitude of 6.3. What is its apparent magnitude? M = m - 5 log10(d/10), m = M + 5 log10(d/10) = 6.3 + 5 log10(320/10) = 14 14
Concept 4 H-R diagrams In 1910, Enjar Hertzsprung of Denmark, and Henry Norris Russell at Princeton plotted M vs T in independent research. Main Sequence From Douglas Giancoli s Physics
Bright Dim Hot Cooler From Douglas Giancoli s Physics
Bright Dim Hot Cooler From Jay Pasachoff s Contemporary Astronomy
O Oh B be A a F fine G girl, K kiss M me! (Cooler) (Hot)
The atmosphere Light from star is filtered by atmosphere The Star
Spectral types: O - 30,000 - 60,000 K, ionized H, weak H lines, spectral lines are spread out. O types are rare and gigantic. 10,000 - 30,000K, H lines are stronger, lines are less spread out (Rigel, Spica are type B stars) 7,500 - 10,000K, strong H lines, Mg, Ca lines appear (H and K) (Sirius, Deneb and Vega are A type stars) 6,000 - 7,500K, weaker H lines than in type A, strong Ca lines (Canopus (S.H.) and Polaris are type F) 5,000 - 6,000K, yellow stars like the sun. Strongest H and K lines of Ca appear in this star. 3,500 - 5,000K, spectrum has many lines from neutral metals. Reddish stars (Arcturus and Aldebaran are type K stars) 3,500 or less, molecular spectra appear. Titanium oxide lines appear. Red stars (Betelgeuse is a prominent type M) B - A - F - G - K - M - Suffixes 0 (hottest) - 9 (coolest) so O0, O1 O9, then B0, B1
SO Hot stars are: Big, Bright, Brief and Blue Cool stars are: Diminuitive, Dim, and Durable and um reD More about brief and durable next time
Spectroscopic parallax Bright Spectrum = M (from diagram) Measure m Find d Dim From Douglas Giancoli s Physics
M = m - 5 log10(d/10) 5 log10(d/10) = m - M log10(d/10) = (m - M)/5 d/10 = 10((m - M)/5) d = (10 pc)10((8 - -4.3)/5) d = 2884 pc Put in your notes: How far is an B0 that has an m of 8? 2884 pc
d = (10 pc)10((14 - 5.8)/5) d = 437 pc How far is an K0 that has an m of 14? 437 pc
Ok, now Drool.
