22 March 2005 AST 2010: Chapter 16 1 Analyzing Starlight.

22 March 200522 March 2005 AST 2010: Chapter 16AST 2010: Chapter 16 11

Analyzing StarlightAnalyzing Starlight


Image of stars in the direction of the center of the Milky Way Galaxy, taken by the Hubble Space Telescope

How do the How do the stars appear stars appear different?different?


Not All Stars are AlikeNot All Stars are AlikeStars appear different inStars appear different in

brightnessbrightness, , from very bright from very bright to very faint to very faint

colorcolor, , from red to blue-whitefrom red to blue-white

sizesize

A good A good constellationconstellation for for seeing star seeing star colorscolors in the in the winter sky is winter sky is OrionOrion (the (the hunter) hunter)

BetelgeuseBetelgeuse, a , a red super- giant red super- giant starstar

RigelRigel, a blue super-, a blue super-giant stargiant star


Betelgeuse


Brightness of Stars (1)Brightness of Stars (1)The total amount of energy at all wavelengths that a The total amount of energy at all wavelengths that a star emits is called its star emits is called its luminosityluminosity

NoteNote: this is how much energy the star : this is how much energy the star gives offgives off each each second, second, NOTNOT how much energy ultimately reaches our how much energy ultimately reaches our eyes or telescopeeyes or telescopeThe The luminosityluminosity of a star is perhaps of a star is perhaps its most important its most important characteristiccharacteristic

The amount of a star’s energy that actually reaches a The amount of a star’s energy that actually reaches a given area each second here on Earth is called the given area each second here on Earth is called the star’s star’s apparent brightnessapparent brightnessIf all stars had the same If all stars had the same luminosity, their apparent luminosity, their apparent brightnesses would tell us brightnesses would tell us how how farfar they are from us they are from us

The The inverse-square law inverse-square law of light of light propagation: the apparent brightness of a light source propagation: the apparent brightness of a light source decreases as the square of the distance from itdecreases as the square of the distance from it


Brightness of Stars (2)Brightness of Stars (2)The The inverse-square lawinverse-square law implies that implies that

a star will appear 4 times a star will appear 4 times fainter if an observer’s fainter if an observer’s distance from it is distance from it is doubled, 9 times fainter if doubled, 9 times fainter if the distance is tripled, the distance is tripled, etc.etc.

In reality, stars generally In reality, stars generally do do not have the same not have the same luminosityluminosity

In other words, they are In other words, they are notnot “ “standard bulbsstandard bulbs””Consequently, distance is Consequently, distance is the among the most difficult quantities to measure in the among the most difficult quantities to measure in astronomyastronomy


Stars’ Apparent Magnitudes (1)Stars’ Apparent Magnitudes (1)A star’s A star’s apparent brightnessapparent brightness is described using is described using the the magnitudemagnitude system system

The system was devised by the Greek The system was devised by the Greek astronomer astronomer HipparchusHipparchus around 150 B.C. around 150 B.C. He put the brightest stars into the He put the brightest stars into the first-first-magnitudemagnitude class, the next brightest stars into class, the next brightest stars into second-magnitudesecond-magnitude class, and so on, until he class, and so on, until he had all of the visible stars grouped into had all of the visible stars grouped into six six magnitudemagnitude classes classesExamplesExamples: a star of the : a star of the 11stst magnitude appears magnitude appears 2.52.5 times brighter than a star of the times brighter than a star of the 22ndnd magnitude, whereas a star of the magnitude, whereas a star of the 22ndnd magnitude magnitude appears appears 40 40 times brighter than a star of the times brighter than a star of the 66thth magnitude magnitude


Stars’ Apparent Magnitudes (2)Stars’ Apparent Magnitudes (2)Thus, the Thus, the smaller the magnitudesmaller the magnitude, the , the brighterbrighter the the object being observed! object being observed!

The old magnitude-system was based on how bright a The old magnitude-system was based on how bright a star appeared to the unaided eyestar appeared to the unaided eye

Today’s magnitude system (based on more accurate Today’s magnitude system (based on more accurate measurements) goes beyond Hipparchus' original measurements) goes beyond Hipparchus' original range of magnitudes 1 through 6 range of magnitudes 1 through 6

Very bright objects can have a magnitude of 0, or even a Very bright objects can have a magnitude of 0, or even a negative numbernegative number

Very faint objects have magnitudes greater than +10 Very faint objects have magnitudes greater than +10


Stars’ Colors and TemperaturesStars’ Colors and TemperaturesA star is a ball of dense, hot gas that emits a A star is a ball of dense, hot gas that emits a continuous spectrumcontinuous spectrum of radiation of radiation

The spectrum is very similar to that of radiation emitted by a The spectrum is very similar to that of radiation emitted by a blackbody blackbody

The most intense color of a star is related to its The most intense color of a star is related to its surface temperature by surface temperature by Wien’s lawWien’s law

The higher the temperature, the shorter the wavelength of the The higher the temperature, the shorter the wavelength of the most intense color most intense color

Thus Thus BlueBlue colors dominate the light output of very colors dominate the light output of very hothot stars stars CoolCool stars emit most of their visible radiation at stars emit most of their visible radiation at redred wavelengthswavelengths

Our Sun’s surface temperature is about 6,000 K, with Our Sun’s surface temperature is about 6,000 K, with the dominant color being a slightly the dominant color being a slightly greenish yellowgreenish yellow

Hottest stars can have surface temperatures of 100,000 K, Hottest stars can have surface temperatures of 100,000 K, whereas coolest stars have surface temperatures of about whereas coolest stars have surface temperatures of about 2,000 K2,000 K


Star’s Color Star’s Color Temperature Temperature


Determining Star’s TemperatureDetermining Star’s TemperatureTo determine the exact color of a star, astronomers To determine the exact color of a star, astronomers usually observe its brightness through usually observe its brightness through filtersfilters

A A filterfilter allows only a narrow allows only a narrow range of wavelengths range of wavelengths (colors) to pass through(colors) to pass through

Two commonly used Two commonly used filters are filters are

a a blueblue ( (BB) filter that lets ) filter that lets through only a narrow through only a narrow band of blue wavelengthsband of blue wavelengthsa “a “visualvisual” (” (VV) filter ) filter that lets through only colors around the green-yellow bandthat lets through only colors around the green-yellow band

The colored light transmitted by each filter has its own The colored light transmitted by each filter has its own brightness, usually expressed in brightness, usually expressed in magnitudesmagnitudes

The relative brightness of the transmitted colors can tell if the The relative brightness of the transmitted colors can tell if the star is hot, warm, or coolstar is hot, warm, or cool


B-V Color IndexB-V Color IndexA A B-V color indexB-V color index is defined as the difference is defined as the difference in in magnitudemagnitude between the B and V bandsbetween the B and V bands

A hot star has an A hot star has an index of around 0 or index of around 0 or a negative a negative number, while a number, while a cool star has an cool star has an index close to 2.0index close to 2.0

Other stars are Other stars are somewhere in betweensomewhere in between


Spectra of StarsSpectra of StarsTo analyze starlight, one can also use To analyze starlight, one can also use spectroscopyspectroscopy, instead , instead of filters of filters In general, the In general, the spectra of different stars look differentspectra of different stars look different

The primary reason is that stars The primary reason is that stars have different temperatureshave different temperatures

Most stars are very similar in composition to the SunMost stars are very similar in composition to the SunHydrogen is the most abundant element in starsHydrogen is the most abundant element in stars

In the In the hottesthottest stars, the hydrogen atoms are completely stars, the hydrogen atoms are completely ionized (no longer have their electrons attached) due to the ionized (no longer have their electrons attached) due to the high temperature and, consequently, they cannot produce high temperature and, consequently, they cannot produce hydrogen hydrogen absorption linesabsorption lines in the spectra in the spectraIn the In the coolestcoolest stars, the hydrogen atoms are all in lowest stars, the hydrogen atoms are all in lowest state and, consequently, hydrogen transitions that can state and, consequently, hydrogen transitions that can occur do not produce occur do not produce absorption linesabsorption lines in the visible in the visible spectrumspectrumOnly stars with Only stars with intermediate surface temperaturesintermediate surface temperatures (not too (not too hot, not too cool — about 10,000 K) have spectra with hot, not too cool — about 10,000 K) have spectra with hydrogen lineshydrogen lines


How Absorption Line is ProducedHow Absorption Line is Produced


Spectral ClassesSpectral ClassesAstronomers sort stars according to the Astronomers sort stars according to the patterns of lines seen in their spectra into patterns of lines seen in their spectra into seven principal seven principal spectral classesspectral classes

From hottest to coldest, the classes are From hottest to coldest, the classes are designated O, B, A, F, G, K, and Mdesignated O, B, A, F, G, K, and M

O B A F G K M


Spectral Class

Characteristics of Spectral Lines

O Ionized helium and metals; hydrogen very weak

B Neutral helium, ionized metals; hydrogen stronger

A Hydrogen strongest; singly-ionized metals

F Ionized metals; hydrogen weaker

G Ionized and neutral metals; hydrogen very weak

K Neutral metals; molecular lines begin to appear

M Molecular titanium-oxide dominant, neutral metals


Spectral Classes L and TSpectral Classes L and TSince 1995, astronomers have discovered objects Since 1995, astronomers have discovered objects cooler than those in class M, but they are cooler than those in class M, but they are notnot considered true stars because they are not massive considered true stars because they are not massive enoughenough

Objects with masses less than 7.2% of or our Sun’s mass Objects with masses less than 7.2% of or our Sun’s mass (0.072 M(0.072 MSunSun) are not expected to become hot enough for the ) are not expected to become hot enough for the nuclear fusion to take place nuclear fusion to take place

Those objects are called Those objects are called brown dwarfsbrown dwarfsThey are very faint and cool, emitting radiation in the infrared They are very faint and cool, emitting radiation in the infrared part of the spectrumpart of the spectrum

The warmer brown dwarfs are assign to spectral class The warmer brown dwarfs are assign to spectral class L, and the cooler ones to spectral class TL, and the cooler ones to spectral class T



Spectra of Stars in Different Spectral Spectra of Stars in Different Spectral ClassesClasses


Doppler Effect in Sound WavesDoppler Effect in Sound WavesCase (a)Case (a)

The source is moving The source is moving towards observer A towards observer A

Observer A sees a Observer A sees a compressed wave, and compressed wave, and hence a hence a shorter shorter wavelength wavelength (or a (or a higher higher frequencyfrequency))

Observer B sees a Observer B sees a stretched wave, and hence stretched wave, and hence a a longer wavelengthlonger wavelength (or a (or a lower frequencylower frequency))

Case (b)Case (b)The source is stationaryThe source is stationary

Observers A and B both Observers A and B both see see same wavelengthsame wavelength

SourceObserver A Observer B

v

(a)

SourceObserver A Observer B

(b)


Doppler Effect in StarlightDoppler Effect in StarlightThe motion of a star causes its spectral lines to shift The motion of a star causes its spectral lines to shift positionspositions

The shift depends on its speed and direction of motionThe shift depends on its speed and direction of motion

If the star is moving toward us, the wavelengths of its If the star is moving toward us, the wavelengths of its light get shorter light get shorter

Its spectral lines are shifted toward the shorter-Its spectral lines are shifted toward the shorter-wavelength (bluer) end of the spectrumwavelength (bluer) end of the spectrumThis is, therefore, called a This is, therefore, called a blueshiftblueshift

If the star is moving away If the star is moving away from us, the wavelengths of its from us, the wavelengths of its light get longer light get longer

Its spectral lines are shifted Its spectral lines are shifted toward the longer-wavelength toward the longer-wavelength (redder) end of the visible (redder) end of the visible spectrumspectrumThis is, thus, called a This is, thus, called a redshiftredshift


Doppler Effect in Stellar SpectraDoppler Effect in Stellar SpectraThe Doppler effect doesn’t affect the The Doppler effect doesn’t affect the overall color of an object, unless it is overall color of an object, unless it is moving at a significant fraction of the moving at a significant fraction of the speed of light (VERY fast!)speed of light (VERY fast!)For an object moving toward us, the red For an object moving toward us, the red colors will be shifted to the orange and colors will be shifted to the orange and the near-infrared will be shifted to the the near-infrared will be shifted to the red, etc. red, etc.

All of the colors shiftAll of the colors shift

The overall color of the object depends The overall color of the object depends on the combined intensities of all of the on the combined intensities of all of the wavelengths (colors)wavelengths (colors)


The Sun’s Spectral ShiftsThe Sun’s Spectral ShiftsThe Sun’s spectra at 3 speeds (0, 0.01c, 0.1c) The Sun’s spectra at 3 speeds (0, 0.01c, 0.1c)

The hydrogen-alpha line (at 656.3nm) is shownThe hydrogen-alpha line (at 656.3nm) is shown

The Doppler-shifted continuous spectrum of the Sun The Doppler-shifted continuous spectrum of the Sun moving at 0.01c is almost indistinguishable from that moving at 0.01c is almost indistinguishable from that of the Sun being at of the Sun being at restrest


Doppler Shift of Spectral LinesDoppler Shift of Spectral LinesThe Doppler shift of spectral lines is measurable even The Doppler shift of spectral lines is measurable even for slow speed for slow speed

Astronomers can detect spectral-line Doppler shifts for Astronomers can detect spectral-line Doppler shifts for speeds as small as speeds as small as 1 km/sec or lower 1 km/sec or lower (less than 3.3(less than 3.31010-6-6 c) c)


Doppler Effect in Stellar

Rotation

The broadening of spectral lines indicates that the star is rotating

The greater the broadening, the greater the speed of rotation

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22 March 2005 AST 2010: Chapter 16 1 Analyzing Starlight.

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