StarsFlux and LuminosityBrightness of stars and the magnitude scaleAbsolute magnitude and luminosityDistance modulusTemperature vs heatTemperature vs colorColors/spectra of stars

Flux and luminosityLuminosity - A star produces light the total amount of energy that a star puts out as light each second is called its Luminosity.Flux - If we have a light detector (eye, camera, telescope) we can measure the light produced by the star the total amount of energy intercepted by the detector divided by the area of the detector is called the Flux.

Flux and luminosityTo find the luminosity, we take a shell which completely encloses the star and measure all the light passing through the shellTo find the flux, we take our detector at some particular distance from the star and measure the light passing only through the detector. How bright a star looks to us is determined by its flux, not its luminosity. Brightness = Flux.

Flux and luminosityFlux decreases as we get farther from the star like 1/distance2

Brightness of starsThe brightness of a star is a measure of its flux.Ptolemy (150 A.D.) grouped stars into 6 `magnitude groups according to how bright they looked to his eye.Herschel (1800s) first measured the brightness of stars quantitatively and matched his measurements onto Ptolemys magnitude groups and assigned a number for the magnitude of each star.

Brightness of starsIn Herschels system, if a star is 1/100 as bright as another then the dimmer star has a magnitude 5 higher than the brighter one.Note that dimmer objects have higher magnitudes

Little Dipper (Ursa Minor)

Guide to naked-eye magnitudes

Consider two stars, 1 and 2, with apparent magnitudes m1 and m2 and fluxes F1 and F2. The relation between apparent magnitude and flux is:Apparent MagnitudeFor m2 - m1 = 5, F1/F2 = 100.

Flux, luminosity, and magnitude

Distance-Luminosity relation:Which star appears brighter to the observer?d10dL10LStar 1Star 2

Flux and luminosity

Star 2 is dimmer and has a higher magnitude.

Flux and luminosity

Star 2 is dimmer and has a higher magnitude.

Absolute magnitudeThe magnitude of a star gives it brightness or flux when observed from Earth.To talk about the properties of star, independent of how far they happen to be from Earth, we use absolute magnitude.Absolute magnitude is the magnitude that a star would have viewed from a distance of 10 parsecs.Absolute magnitude is directly related to the luminosity of the star.

Absolute Magnitude and LuminosityThe absolute magnitude of the Sun is M = 4.83.The luminosity of the Sun is L = 3.861026 W.Note the M includes only light in the visible band, so this is accurate only for stars with the same spectrum as the Sun.

Absolute magnitude, M, is defined asAbsolute Magnitudewhere D is the distance to the star measured in parsecs.For a star at D = 10 parsecs, 5log10 = 5, so M = m.If we can figure out the absolute magnitude of a star, then we can determine its distance using the apparent magnitude. The distance modulus is defined as

Is Sirius brighter or fainter than Spica:

as observed from Earth [apparent magnitude] Intrinsically [luminosity]?

Sun

Which star would have the highest magnitude?Star A - 10 pc away, 1 solar luminosityStar B - 30 pc away, 3 solar luminositiesStar C - 5 pc away, 0.5 solar luminositiesStar D - Jennifer Lawrence

Stars: Temperature and ColorTemperature vs heatTemperature vs colorColors/spectra of stars

TemperatureTemperature is proportional to the average kinetic energy per molecule

lower Thigher Tk = Boltzmann constant = 1.3810-23 J/K = 8.6210-5 eV/K

Temperature vs. HeatTemperature is proportional to the average kinetic energy per molecule

Heat (thermal energy) is proportional to the total kinetic energy in boxlower Thigher Tsame Tless heatmore heat

Wiens lawCooler objects produce radiation which peaks at lower energies = longer wavelengths = redder colors.Hotter objects produce radiation which peaks at higher energies = shorter wavelengths = bluer colors.

Wavelength of peak radiation:Wien Law max = 2.9 x 106 / T(K) [nm]

A objects color depends on its surface temperatureWavelength of peak radiation:Wien Law max = 2.9 x 106 / T(K) [nm]

What can we learn from a stars color?The color indicates the temperature of the surface of the star.

UBVObservationally, we measure colors by comparing the brightness of the star in two (or more) wavelength bands.This is the same way your eye determines color, but the bands are different.

Use UVRI filters to determine apparent magnitude at each color

The ratio of fluxes in two bands translates to the difference in magnitudes, or a color, e.g. B V = mB mV.Stellar temperature follow an approximate, empirical relation: T ~ 9000 K/[(B-V) + 0.93]

The spectrum of a star is primarily determined byThe temperature of the stars surfaceThe stars distance from EarthThe density of the stars coreThe luminosity of the star

Stars are assigned a `spectral type based on their spectraThe spectral classification essentially sorts stars according to their surface temperature.The spectral classification can also use spectral lines.

Spectral typeSequence is: O B A F G K MO type is hottest (~25,000K), M type is coolest (~2500K)Star Colors: O blue to M redSequence subdivided by attaching one numerical digit, for example: F0, F1, F2, F3 F9 where F1 is hotter than F3 . Sequence is O O9, B0, B1, , B9, A0, A1, A9, F0, Useful mnemonics to remember OBAFGKM:Our Best Astronomers Feel Good Knowing MoreOh Boy, An F Grade Kills Me(Traditional) Oh, Be a Fine Girl (or Guy), Kiss Me

QuestionWhich is cooler, a star with spectral type G2 or a star with spectral type A6?

Classifying starsWe now have two properties of stars that we can measure:LuminosityColor/surface temperature

Using these two characteristics has proved extraordinarily effective in understanding the properties of stars the Hertzsprung-Russell (HR) diagram

HR diagram

Absolute Bolometric Magnitude and LuminosityThe bolometric magnitude includes radiation at all wavelengths.The absolute bolometric magnitude of the Sun is Mbol = +4.74.

Bolometric CorrectionIt is difficult to measure the radiation from a star at all wavelengths. However, if one knows the temperature and the magnitude in one band, then one can integrate the blackbody spectrum over all wavelengths.

We typically estimate the bolometric magnitude using the V-band magnitude and a color to estimate the temperature.Bolometric correction = BC = Mbol - MV.