Continuous Spectrum of Light 31 Stellar Parallax dpc 1p where p is the parallax in arc seconds dpc is the distance in parsecs 1 pc 326 light years and is the distance at which a star would have a parallax of 1 ID: 279236
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Chapter 3Continuous Spectrum of Light 3.1 Stellar Parallaxd(pc) = 1/p” where p” is the parallax in arc seconds d(pc) is the distance in parsecs 1 pc =3.26 light years and is the distance at which a star would have a parallax of 1”Slide2
Stellar ParallaxSlide3
Chapter 3.2The Magnitude ScaleApparent Magnitude – Invented by Hipparchus. The brightest stars were 1st magnitude and the faintest, 6th magnitude. The lower the number, the brighter the star. Norman Pogson discovered that a difference of 5 magnitudes corresponds to a factor of 100 in brightness. A difference of 1 magnitude corresponds to a brightness ratio of 1001/5 ~ 2.512.Slide4
The Magnitude ScaleApparent Magnitude – A first magnitude star is 2.512 times brighter than a 2nd magnitude star, etc. Apparent magnitude, m, for the sun -26.83. Faintest object detectable, m = 30. Faintest star a person with 20/20 vision can see is ~6th magnitude.Slide5
The Magnitude ScaleAbsolute Magnitude – This is the apparent magnitude a star would have if it were 10 parsecs or 32.6 light years distant.Slide6
Radiant FluxA star’s brightness is the total amount of starlight energy/second at all wavelengths (bolometric) incident on one square meter of detector pointed at the star. This is called the radiant flux, F and is measured in watts/m2. Slide7
LuminosityLuminosity, L is the total amount of energy emitted by a star into space.Slide8
Inverse Square Law The relationship between a star’s luminosity L, and its radiant flux, F is:where r is the distance to the star.Slide9
Inverse Square LawKnowing the values for the sun’s luminosity, L and using 1 AU for the average Earth-sun distance, for r, the solar flux, F received by the Earth from the sun is:F = 1365 W/m2, This is also known as the solar constant.Slide10
Distance ModulusA measure of the distance to a star is called its distance modulus, or m – M. m – M = 5log10(d) – 5 = 5 log10 (d/10 pc)Remember, that M is the magnitude a star would have if it were 10 pc (parsecs) distant.Slide11
Distance ModulusThe distance modulus is a logarithmic measure of the distance to a star. Here’s a listing of m, M, and m – M of notable stars:Star Name m M m – M Sirius -1.5 1.4 -2.9 Alpha Centauri A 0.0 4.4 -4.4 Alpha Centauri B 1.4 5.8 -4.4 Proxima Centauri 10.7 15.1 -4.4 Sun -26.75 4.83 -31.58Slide12
Distance ModulusExample to calculate the M of Proxima Centauri:m – M = 5 log10 (d/10 pc)M = m - 5 log10 (d/10 pc)For Proxima Centauri, d = 1.295 pc, m = 10.7 (it’s a red dwarf).M = 10.7 - 5log10 (1.295/10) = 15.1Slide13
Chapter 3.4Blackbody RadiationA blackbody is defined as an object that does not reflect or scatter radiation shining upon it, but absorbs and reemits the radiation completely. It is a kind of ideal radiator, which cannot really exist. However, stars and planets behave as if they were blackbodies.Blackbody radiation depends only on its temperature and is independent of its shape, material and construction.Slide14
Latest Spectrum of SN2014JSlide15
Blackbody RadiationThis figure shows the blackbody spectrum of an object has a certain peak, and goes to shorter wavelengths as the temperature increases.Slide16
The Planck Functionwhere h = Planck’s constant = 6.626 x 10-34J sand the units of Bl(T) are W m-3 sr-1Slide17
Wien’s LawNotice that the peak of a BB curve goes to shorter and shorter wavelengths as T increases. This is Wien’s Law.lmaxT = 0.0029 m KSlide18
Chapter 3.4Blackbody RadiationRemember this animation site?http://www.astro.ubc.ca/~scharein/a311/Sim.htmlIt has a great blackbody simulation/animation!Slide19
Wien’s LawExample: 3.4.1What is lmax for Betelgeuse? Its temperature is 3600 K.which is in the IR.Slide20
Wien’s LawExample: 3.4.1Similarly for Rigel. What is lmax for Rigel? Its temperature is 13,000 K.which is in the UV.Slide21
Chapter 3.6Color IndexThe Johnson - Morgan UBV Filter SystemSlide22
Chapter 3.6Color IndexThe Johnson - Morgan UBV Filter SystemApproximate central wavelengths and bandwidths are:Band < λ > ( A) ∆λ ( A) U 3600 560 B 4400 990 V 5500 880Slide23
Color IndexColor index is related to a star’s temperature. Figure below is from http://csep10.phys.utk.edu/astr162/lect/stars/cindex.htmlSlide24
Returning to The Planck Functionwhere h = Planck’s constant = 6.626 x 10-34J sand the units of Bl(T) are W m-3 sr-1Slide25
Exploring the Planck FunctionLet’s investigate this function.The exponent in the denominator is sometimes written as b. And b = hc/lkT, has no units, ie. it is dimensionless.h = 6.626068 x 10-34 joule sec k =1.38066 x 10
-23
joule deg
-1
c
=
2.997925 x 10
8
m/s
T
= object temperature in KelvinsSlide26
Example Using the Planck FunctionLet’s do an example with this function. Consider an object at 213 K and let’s compute the emitted radiance at 10 microns. Everything is in SI units, i.e. meters and joules. We have that b =,Notice that all of the units cancel.The denominator of the Planck function is e6.77-1 = 870.3Slide27
Example Using the Planck FunctionThe numerator becomes2(6.63×10−34 Js)(3.0×108 m/s)2 (1.0×10−5 m)−5 =119.3×107 Jm−3s−1steradian−1The full Planck function becomesB
=119.3×10
7
/
870.3 = 0.137
×10
7
Jm
−3
s
−1
steradian
−
1
and the units of
B
l
(T) are W m
-3
sr
-1Slide28
Back to Color Indices and the Bolometric CorrectionA star’s U – B color index is the difference between its UV and blue magnitudes.A star’s B – V color index is the difference between its blue and visual magnitudes.The difference between a star’s bolometric magnitude and its visual magnitude is its bolometric correction BC.A bolometric magnitude includes extra flux emitted at other wavelengths. The magnitude adjustment that takes into account this extra flux is the bolometric correction.mbol – V = Mbol – MV = BCSlide29
Color Indices and the Bolometric CorrectionOne can associate an absolute magnitude with each of the filters.U – B = MU – MBB – V = MB – MVThe difference between a star’s bolometric magnitude and its visual magnitude is: mbol – V = Mbol – MV = BCSlide30
Bolometric CorrectionThe significance of the bolometric correction is that, the greater its value, either positive or negative, the more radiation the star is emitting at wavelengths other than those in the visible part of the spectrum.This is the case with very hot stars, where most of their radiation is in the UV. The BC would be negative.This is also the case with very cool stars, where most of their radiation is in the IR. The BC would be posative.The BC is least with sun-like stars, since most of their radiation is in the visible part of the spectrum. The BC would ~ 0.Slide31
Example Using Bolometric CorrectionFor Sirius, U = -1.47, B = -1.43, V = -1.44U – B = -1.47 –(-1.43) = -0.04B – V = -1.43 – (-1.44) = 0.01This shows that Sirius is brightest at UV wavelengths, which is what you would expect, since T = 9970 K.which is in the UV part of the electromagnetic spectrum. The bolometric correction for Sirius is BC = -0.09. Apparent bolometric magnitude is: mbol = V + BC = -1.44 + (-0.09) = -1.53BC is negative for a hot star like Sirius. BC is positive for a cool star like Betelgeuse.