Reading assignment for:

THURSDAY 9/24: Chapters 5.1, 5.2 (not in detail), 5.3, 5.4 (not in detail)

Homework assignment #1 due NOW

The Continuous Spectrum of Light - Part II

If the star is at a distance d from the instrument:

Incident energy flux on the detector (a.k.a., apparent brightness)

If the star is at a distance d from the instrument:

Incident energy flux on the detector (a.k.a., apparent brightness)

a.k.a. the inverse square law of light

If the star is at a distance d from the instrument:

Incident energy flux on the detector (a.k.a., apparent brightness)

a.k.a. the inverse square law of light

NOTE 1: this law is true only without interstellar absorption

NOTE 2: by measuring

Assuming no interstellar absorption:

monochromatic apparent magnitude

i.e., the apparent magnitude depends on both the intrinsic luminosity and the distance of the star

Assuming no interstellar absorption:

monochromatic apparent magnitude

ABSOLUTE MAGNITUDE M: For an absolute comparison of intrinsic brightness, it is common to discuss the magnitudes of stars would have IF they were all at the same distance of d=10 pc, i.e., M = m(@d=10pc):

i.e., the apparent magnitude depends on both the intrinsic luminosity and the distance of the star

NOTE: Mbol is not directly measurable. To obtain the total energy radiated from a star requires making a bolometric correction

In bolometric units:

a.k.a. the inverse square law of light

Solar irradiance

Given the Sun and another star:

Photometric systems of magnitudes:

1. Photographic system: mpg=mvisual for A0 stars (Vega)

Photometric systems of magnitudes:

1. Photographic system: mpg=mvisual for A0 stars (Vega)

2. Photometric system: UBVU=mU, B=mB (similar to photographic plate magnitude), V=mVzero-point determined using the sequence of standard stars (A0 spectral type stars)For Vega (A0 star, Tsurface=10,000K), U-B=B-V=0

Photometric systems of magnitudes:

1. Photographic system: mpg=mvisual for A0 stars (Vega)

2. Photometric system: UBVU=mU, B=mB (similar to photographic plate magnitude), V=mVzero-point determined using the sequence of standard stars (A0 spectral type stars)For Vega (A0 star, Tsurface=10,000K), U-B=B-V=0

3. Spectro-Photometric system

Effective frequency

Photometric systems of magnitudes:

1. Photographic system: mpg=mvisual for A0 stars (Vega)

2. Photometric system: UBVU=mU, B=mB (similar to photographic plate magnitude), V=mVzero-point determined using the sequence of standard stars (A0 spectral type stars)For Vega (A0 star, Tsurface=10,000K), U-B=B-V=0

3. Spectro-Photometric system

4. AB system (this has become the standard magnitude system):

Apparent brightness

The smaller (or more negative) the color index, the bluer a star is. The color index is independent on distance of the star.

Astronomers measure the apparent magnitude (m) and the distance (d) of a star. The absolute magnitude (M) is computed by mentally moving the star at a distance d=10pc. The absolute magnitude is then converted to an absolute bolometric magnitude (Mbol) using the bolometric correction (BC).

Astronomers measure the apparent magnitude (m) and the distance (d) of a star. The absolute magnitude (M) is computed by mentally moving the star at a distance d=10pc. The absolute magnitude is then converted to an absolute bolometric magnitude (Mbol) using the bolometric correction (BC).

The BC depends on the spectral type of the star; known the spectral type, I can derive its absolute bolometric magnitude Mbol given BC (tabulated as a function of different spectral types) and MV.

AAAB/nicbVDLSsNAFJ3UV62v+Ni5GSyCCwmJFuxGKLpxI1SwD2hCmEwm7dBJJsxMhBqKv+LGhYK49Tvc+TdO2yy09cCFwzn3cu89QcqoVLb9bZSWlldW18rrlY3Nre0dc3evLXkmMGlhzrjoBkgSRhPSUlQx0k0FQXHASCcYXk/8zgMRkvLkXo1S4sWon9CIYqS05JsHt37uihi2T10ecjW+rFn1c9+s2pY9BVwkTkGqoEDTN7/ckOMsJonCDEnZc+xUeTkSimJGxhU3kyRFeIj6pKdpgmIivXx6/RgeayWEERe6EgWn6u+JHMVSjuJAd8ZIDeS8NxH/83qZiupeTpM0UyTBs0VRxqDicBIFDKkgWLGRJggLqm+FeIAEwkoHVtEhOPMvL5LOmeXULMe5q1UbV0UeZXAIjsAJcMAFaIAb0AQtgMEjeAav4M14Ml6Md+Nj1loyipl98AfG5w9NjpRJ

MV,� = 4.83

Blackbody radiation:

Any object with a temperature above absolute zero emits light at all wavelengths with varying degrees of efficiency. An ideal blackbody is an object that absorbs all of the light energy incident upon it, and reradiates this energy with the characteristic spectrum. The radiation emitted by a blackbody is called blackbody radiation. Stars, planets, and humans are blackbodies, to a rough first approximation.

Blackbody radiation:

Any object with a temperature above absolute zero emits light at all wavelengths with varying degrees of efficiency. An ideal blackbody is an object that absorbs all of the light energy incident upon it, and reradiates this energy with the characteristic spectrum. The radiation emitted by a blackbody is called blackbody radiation. Stars, planets, and humans are blackbodies, to a rough first approximation.

Considering the power (energy per unit of time) radiate per unit of area per unit of wavelength by a surface in thermodynamic equilibrium (i.e., having already integrated the specific intensity over the solid angle):

Planck’s function

Blackbody radiation:

Any object with a temperature above absolute zero emits light at all wavelengths with varying degrees of efficiency. An ideal blackbody is an object that absorbs all of the light energy incident upon it, and reradiates this energy with the characteristic spectrum. The radiation emitted by a blackbody is called blackbody radiation. Stars, planets, and humans are blackbodies, to a rough first approximation.

Considering the power (energy per unit of time) radiate per unit of area per unit of wavelength by a surface in thermodynamic equilibrium (i.e., having already integrated the specific intensity over the solid angle):

Planck’s function

AAACHnicbVDNSsNAGNz4W+tf1KOXxSJ4Kkkp6EVoFcRjBWsLTQyb7aZdupuE3Y1QQvogXnwVLx4URPCkb+M2zUFbBxaGmW/49hs/ZlQqy/o2lpZXVtfWSxvlza3tnV1zb/9ORonApI0jFomujyRhNCRtRRUj3VgQxH1GOv7ocup3HoiQNApv1TgmLkeDkAYUI6Ulz6z3rrzUERw6TIf6KHPPnUAgnOYiEYMsm1E5wfy+NnGazSzzzIpVtXLARWIXpAIKtDzz0+lHOOEkVJghKXu2FSs3RUJRzEhWdhJJYoRHaEB6moaIE+mm+XUZPNZKHwaR0C9UMFd/J1LEpRxzX09ypIZy3puK/3m9RAVnbkrDOFEkxLNFQcKgiuC0KtingmDFxpogLKj+K8RDpMtRutCyLsGeP3mRdGpVu1617Zt6pXFR9FECh+AInAAbnIIGuAYt0AYYPIJn8ArejCfjxXg3PmajS0aROQB/YHz9AD47ow8=

[F�] =erg

s cm2 Å

AAACGXicbZDLSgMxFIYz9VbrbdSlm2ARXNWZUtCNUBSkywrWFjpjyaSZNjTJDElGqMP0Ldz4Km5cKIhLXfk2ppeFtv4Q+PjPOZycP4gZVdpxvq3c0vLK6lp+vbCxubW9Y+/u3aookZg0cMQi2QqQIowK0tBUM9KKJUE8YKQZDC7H9eY9kYpG4kYPY+Jz1BM0pBhpY3Xsk/ZVJ/Ukh55IMv/cCyXC6cQgspdlU1QjzO/Ko9pDlnXsolNyJoKL4M6gCGaqd+xPrxvhhBOhMUNKtV0n1n6KpKaYkazgJYrECA9Qj7QNCsSJ8tPJYRk8Mk4XhpE0T2g4cX9PpIgrNeSB6eRI99V8bWz+V2snOjzzUyriRBOBp4vChEEdwXFKsEslwZoNDSAsqfkrxH1kstEmy4IJwZ0/eRGa5ZJbKbnudaVYvZjlkQcH4BAcAxecgiqogTpoAAwewTN4BW/Wk/VivVsf09acNZvZB39kff0AuLShQw==

[F⌫ ] =erg

s cm2 Hz

Continuous spectrum

Blackbody curve(Plank’s eq.)

Total power (energy per unit of time) radiated per unit of area, i.e., the surface flux:

Total power (energy per unit of time) radiated per unit of area, i.e., the surface flux:

AAACDHicbZBPS8MwGMZT/875r+rRS9gQPI12DPQiDAXxOMG5QVtHmqVbWJKWJBVGqWcvfhUvHhTEqx/Am9/GbOtBNx8I/Hje9+XN+4QJo0o7zre1tLyyurZe2ihvbm3v7Np7+7cqTiUmbRyzWHZDpAijgrQ11Yx0E0kQDxnphKOLSb1zT6SisbjR44QEHA0EjShG2lg9u+JdBmd+JBHOMl9ySOQgz2eoHjC/q+d5z646NWcquAhuAVVQqNWzv/x+jFNOhMYMKeW5TqKDDElNMSN52U8VSRAeoQHxDArEiQqy6S05PDJOH0axNE9oOHV/T2SIKzXmoenkSA/VfG1i/lfzUh2dBhkVSaqJwLNFUcqgjuEkGNinkmDNxgYQltT8FeIhMsFoE1/ZhODOn7wInXrNbdRc97pRbZ4XeZTAIaiAY+CCE9AEV6AF2gCDR/AMXsGb9WS9WO/Wx6x1ySpmDsAfWZ8/JP+bkA==

[F ] =erg

s cm2

Total power (energy per unit of time) radiated per unit of area, i.e., the surface flux:

AAACDHicbZBPS8MwGMZT/875r+rRS9gQPI12DPQiDAXxOMG5QVtHmqVbWJKWJBVGqWcvfhUvHhTEqx/Am9/GbOtBNx8I/Hje9+XN+4QJo0o7zre1tLyyurZe2ihvbm3v7Np7+7cqTiUmbRyzWHZDpAijgrQ11Yx0E0kQDxnphKOLSb1zT6SisbjR44QEHA0EjShG2lg9u+JdBmd+JBHOMl9ySOQgz2eoHjC/q+d5z646NWcquAhuAVVQqNWzv/x+jFNOhMYMKeW5TqKDDElNMSN52U8VSRAeoQHxDArEiQqy6S05PDJOH0axNE9oOHV/T2SIKzXmoenkSA/VfG1i/lfzUh2dBhkVSaqJwLNFUcqgjuEkGNinkmDNxgYQltT8FeIhMsFoE1/ZhODOn7wInXrNbdRc97pRbZ4XeZTAIaiAY+CCE9AEV6AF2gCDR/AMXsGb9WS9WO/Wx6x1ySpmDsAfWZ8/JP+bkA==

[F ] =erg

s cm2Stefan-Boltzmann law and constant

Lower Temperature

Peak @ longer wavelengths; less energy emitted per unit of area

Monochromatic luminosity:

Monochromatic luminosity:

Luminosity:

Monochromatic luminosity:

Luminosity:

This relation is used to estimate stellar radii by measuring the luminosity L and knowing the surface temperature Teff.

Monochromatic luminosity:

Luminosity:

This relation is used to estimate stellar radii by measuring the luminosity L and knowing the surface temperature Teff.

Effective temperature Teff is defined as the temperature of a blackbody with the same radiated power per unit of area F (1st definition of temperature)

Monochromatic luminosity:

Luminosity:

This relation is used to estimate stellar radii by measuring the luminosity L and knowing the surface temperature Teff.

Effective temperature Teff is defined as the temperature of a blackbody with the same radiated power per unit of area F (1st definition of temperature)

Monochromatic flux for an observer at a distance d: Energy of starlight with wavelength between arriving per second on the unit of surface of detected aimed at the star. AAACI3icbZDNSsNAFIUn9a/Wv6hLN4NFcFWSUlAXQtGNywrWFpoYJpNJO3QmCTMToYT4Km58FTcuFIobF76L0zQLbb0w8HHOvdy5x08YlcqyvozKyura+kZ1s7a1vbO7Z+4f3Ms4FZh0ccxi0feRJIxGpKuoYqSfCIK4z0jPH1/P/N4jEZLG0Z2aJMTlaBjRkGKktOSZF4PQyxzBocP0UIByGJTkXjqhQDgrXCKGeT5H+YT5QzPPPbNuNayi4DLYJdRBWR3PnDpBjFNOIoUZknJgW4lyMyQUxYzkNSeVJEF4jIZkoDFCnEg3K07M4YlWAhjGQr9IwUL9PZEhLuWE+7qTIzWSi95M/M8bpCo8dzMaJakiEZ4vClMGVQxnecGACoIVm2hAWFD9V4hHSAejdKo1HYK9ePIy9JoNu9Ww7dtWvX1V5lEFR+AYnAIbnIE2uAEd0AUYPINX8A4+jBfjzZgan/PWilHOHII/ZXz/AHBapUY=

[f�d�] =erg

s cm2

AAACDHicbZDNSsNAFIUn/tb6F3XpZmgRBKEkUtBl0Y3LCtYWmlBuJpN26GQSZiZCCe3aja/ixoWCuPUB3Pk2TtsstPXAwMe593LnniDlTGnH+bZWVtfWNzZLW+Xtnd29ffvg8F4lmSS0RRKeyE4AinImaEszzWknlRTigNN2MLye1tsPVCqWiDs9SqkfQ1+wiBHQxurZldyTMfa4mQhhAiKcFHwWFjDu2VWn5syEl8EtoIoKNXv2lxcmJIup0ISDUl3XSbWfg9SMcDoue5miKZAh9GnXoICYKj+f3TLGJ8YJcZRI84TGM/f3RA6xUqM4MJ0x6IFarE3N/2rdTEeXfs5EmmkqyHxRlHGsEzwNBodMUqL5yAAQycxfMRmABKJNfGUTgrt48jK0z2tuvea6t/Vq46rIo4SOUQWdIhddoAa6QU3UQgQ9omf0it6sJ+vFerc+5q0rVjFzhP7I+vwBEGObgA==

� and �+ d�

Position in wavelength of the maximum (peak) of the blackbody radiation:

Position in wavelength of the maximum (peak) of the blackbody radiation:

Wien’s displacement law

Position in wavelength of the maximum (peak) of the blackbody radiation:

Wien’s displacement law

NOTE:

Rayleigh-Jeans law (the long wavelength tail of the blackbody radiation curve

Wien’s Law

Wavelength of the peak increases with decreasing temperature

COLOR INDICES

COLOR INDICES

mU =

COLOR INDICES

mU =

mB = BmV = V

COLOR INDICES

mU =

mB = BmV = V

mU-mB = U-B

COLOR INDICES

mU =

mB = BmV = V

mU-mB = U-B

mB-mV = B-V

COLOR INDICES

mU =

mB = BmV = V

mU-mB = U-B

mB-mV = B-V

NOTE: the color does not depend on (R/d)2 because this term cancels out in the above equationThe color is solely dependent on the temperature of a model blackbody star

The hotter are star, the smaller (or more negative) the B-V color, hence the bluer the star

Stars are not perfect blackbodies!

Reading assignment for:

THURSDAY 9/24: Chapters 5.1, 5.2 (not in detail), 5.3, 5.4 (not in detail)

The Interaction of Light & Matter