Chapter 15:Chapter 15:

Surveying the StarsSurveying the Stars

How can we Study the Life Cycles of Stars?

A star can live for millions to billions of years.A star can live for millions to billions of years.• we will never observe a particular star evolve from birth to deathwe will never observe a particular star evolve from birth to death• so how can we study stellar evolution?so how can we study stellar evolution?

The key is that all stars were not born at the same time.The key is that all stars were not born at the same time.• the stars which we see today are at different stages in their livesthe stars which we see today are at different stages in their lives• we observe only a brief moment in any one starwe observe only a brief moment in any one star’’s lifes life• by studying large numbers of stars, we get a by studying large numbers of stars, we get a ““snapshotsnapshot”” of one of one

moment in the history of the stellar communitymoment in the history of the stellar community• we can draw conclusions just like we would with human census data…we can draw conclusions just like we would with human census data…

we do stellar demographics!we do stellar demographics!

The stars we observe also have different masses.The stars we observe also have different masses.• by counting stars of different masses, we can determine how long by counting stars of different masses, we can determine how long

stars of a given mass remain in a certain stage of lifestars of a given mass remain in a certain stage of life

Classification of StarsStars were originally classified based on:Stars were originally classified based on:

• their brightnesstheir brightness• their location in the skytheir location in the sky

This classification is still reflected in the names of the This classification is still reflected in the names of the brightest stars…those we can see with our eyes:brightest stars…those we can see with our eyes:

Orionis

Geminorum

Order of brightness within a constellation

Latin Genitive of the constellation

Classification of StarsThe old classification scheme told us little about a starThe old classification scheme told us little about a star’’s true s true

(physical) nature.(physical) nature.• a star could be very bright because is was very close to us; not a star could be very bright because is was very close to us; not

because it was truly brightbecause it was truly bright• two stars in the same constellation might not be close to each two stars in the same constellation might not be close to each

other; one could be much farther awayother; one could be much farther away

In the 20In the 20thth Century, astronomers developed a more Century, astronomers developed a more appropriate classification system based on:appropriate classification system based on:• a stara star’’s s luminosityluminosity• a stara star’’s s surfacesurface temperaturetemperature

Since these properties depend on a starSince these properties depend on a star’’s mass and its stage s mass and its stage in life:in life:• measuring them allows us to reconstruct stellar life cyclesmeasuring them allows us to reconstruct stellar life cycles

Luminosity of Stars

Apparent brightnessApparent brightness refers to the amount of a refers to the amount of a starstar’’s light which reaches us s light which reaches us per unit areaper unit area..

• the farther away a star is, the fainter it the farther away a star is, the fainter it appears to usappears to us

• how much fainter it gets obeys an how much fainter it gets obeys an inverse inverse square lawsquare law

• its apparent brightness decreases as the its apparent brightness decreases as the (distance)(distance)22

App Bright = L / 4d2

Luminosity – the total amount of power radiated by a star into space.

The apparent brightness of a star depends on two things:• How much light is it emitting: luminosity (L) [watts]• How far away is it: distance (d) [meters]

Apparent Brightness

The Inverse Square Law for Light What Determines Apparent Brightness?

Measuring Distances to Stars

parallax – apparent wobble of a star due to the Earth’s orbiting of the Sun

Measuring Distances to Stars

This is a right triangle

sin p = 1 AU/ d

if p << 1; sin p p

d = 1 AU/ p

convert p into arcsec

d = 206,265 AU/ p

Measuring Distances to Stars

d = 1 / pIf p is in arcsec and d is in parsecs

A star with a parallax of 1 arcsec is 1 parsec distant

let’s define1 parsec 206,265 A.U. = 3.26 light years

The Brightness of StarsThe Brightness of Stars

Astronomers still use an ancient method for measuring stellar brightness which was proposed by the Greek astronomer Hipparchus (c. 190 – 120 B.C.)

This scale runs backwards:The bigger the number, the fainter the starBrightest stars are #1, next brightest are #2, etc.

The Modern Magnitude System

apparent magnitude

• brightness of a star as it appears from Earth

= -2.5 log (app bright)

• each step in magnitude is 2.5 times in brightness

absolute magnitude

• the apparent magnitude a star would have if it were 10 pc away

Colors of StarsColors of Stars

Stars come in many different colors.

The color tells us the star’s temperature according to Wien’s Law.

Bluer means hotter!

Spectral Type Classification System

O B A F G K M• Our Best Astronomers Feel Good Knowing More• Oh Boy! An F Grade Kills Me!• Oh Be A Fine Girl (Guy), Kiss Me!

50,000 K 3,000 K Temperature

(L)

Spectral Types of Stars

Spectral Types of Stars

Spectral Types of Stars

Spectral types are defined by the:Spectral types are defined by the:• existence of absorption lines belonging to various elements, ions, & existence of absorption lines belonging to various elements, ions, &

molecules in a starmolecules in a star’’s spectrums spectrum• the relative strengths of these linethe relative strengths of these line

However, spectral type is not determined by a starHowever, spectral type is not determined by a star’’s composition.s composition.• all stars are made primarily of Hydrogen & Heliumall stars are made primarily of Hydrogen & Helium

Spectral type is determined by a starSpectral type is determined by a star’’s surface temperature.s surface temperature.• temperature dictates the energy states of electrons in atoms temperature dictates the energy states of electrons in atoms • temperature dictates the types of ions or molecules which existtemperature dictates the types of ions or molecules which exist• this, in turn, determines the number and relative strengths of absorption lines this, in turn, determines the number and relative strengths of absorption lines

in the starin the star’’s spectrums spectrum• this fact was discovered by Cecilia Payne-Gaposchkin in 1925this fact was discovered by Cecilia Payne-Gaposchkin in 1925

Masses of Stars

MassMass is the single most important property of any star. is the single most important property of any star.• at each stage of a starat each stage of a star’’s life, mass determines…s life, mass determines…

• what its luminosity will bewhat its luminosity will be• what its spectral type will bewhat its spectral type will be

The mass of a star can only be measured directly by …The mass of a star can only be measured directly by …• observing the effect which gravity from another object has on the observing the effect which gravity from another object has on the

starstar

This is most easily done for two stars which orbit one This is most easily done for two stars which orbit one another…a binary star!another…a binary star!

Binary Stars(two stars which orbit one another)

Optical doublesOptical doubles• two unrelated stars which are in the same area of two unrelated stars which are in the same area of

the skythe sky

Visual binariesVisual binaries• a binary which is spatially resolved, i.e. two a binary which is spatially resolved, i.e. two

stars are seen (stars are seen (e.g.e.g. SiriusSirius))

Binary Stars

Spectroscopic binariesSpectroscopic binaries• a binary which is spatially unresolved, i.e only one star is a binary which is spatially unresolved, i.e only one star is

seen; the existence of the second star is inferred from the seen; the existence of the second star is inferred from the Doppler shift of lines.Doppler shift of lines.

Binary Stars

Eclipsing binariesEclipsing binaries• a binary whose orbital plane lies along our line of a binary whose orbital plane lies along our line of

sight, thus causing sight, thus causing ““dipsdips”” in the light curve. in the light curve.

Binary Stars

• The stars orbit each other via gravity.The stars orbit each other via gravity.• So the laws of Kepler & Newton apply!So the laws of Kepler & Newton apply!• Remember NewtonRemember Newton’’s version of Keplers version of Kepler’’s s

Third Law:Third Law:

PP2 2 = 4 = 42 2 aa33 / G (m / G (m11 + m + m22))• If you can measure the orbital period of the If you can measure the orbital period of the

binary (binary (PP) and the distance between the stars ) and the distance between the stars ((aa), then you can calculate the sum of the ), then you can calculate the sum of the masses of both stars (masses of both stars (mm11 + m + m22).).

Mass transfer in close binary systems can produce unusual double stars

Close binary systems are where only a few Close binary systems are where only a few stellar diameters, or less, separate the starsstellar diameters, or less, separate the stars

Mass can be dramatically transferred between Mass can be dramatically transferred between the starsthe stars- detached binary - detached binary (no mass transfer)(no mass transfer)

- semidetached binary- semidetached binary(material can flow across (material can flow across along a path called the Roche lobe)along a path called the Roche lobe)

- contact binary - contact binary (the two stars share a common (the two stars share a common envelope of material)envelope of material)

The Hertzsprung-Russell Diagram

• What is the Hertzsprung-Russell (HR) diagram?• What are the major features of the HR diagram?• How do stars differ along the main sequence?• What determines the length of time a star spends on the

main sequence?• What are Cepheid variable stars and why are they

important to astronomers?

Our goals for learning:

The Hertzsprung-Russell Diagram

MV

Spectral type

bright

faint

hot cool

• A very useful diagram for understanding stars• We plot two major properties of stars:

• Temperature (x) vs. Luminosity (y)• Spectral Type (x) vs. Absolute Magnitude (y)

• Stars tend to group into certain areas

HOT COOL

BRIGHT

FAINT

The Main Sequence (MS)

90% of all stars lie on the main sequence!

Stellar Luminosity• How can two stars have the same temperature, but vastly How can two stars have the same temperature, but vastly

different luminosities?different luminosities?

• The luminosity of a star depends on 2 things:The luminosity of a star depends on 2 things:• surface temperaturesurface temperature• surface area (radius)surface area (radius)

• L = L = T T44 4 4 R R22

The stars have different sizes!!The stars have different sizes!!

The largest stars are in the upper right corner of The largest stars are in the upper right corner of the H-R Diagram.the H-R Diagram.

Regions of the H-R Diagram

Stellar Luminosity Classes

Stellar Luminosity Classes

Class I includes all the Class I includes all the supergiantssupergiants

Class V includes the Class V includes the main sequence starsmain sequence stars

e.g., the Sun is a G2 Ve.g., the Sun is a G2 V

If you know the spectral If you know the spectral type and luminosity type and luminosity class you can also class you can also use this to measure use this to measure the distance to stars the distance to stars millions of light years millions of light years awayaway

Stellar Masses on the H-R Diagram

Mass-Luminosity RelationMass-Luminosity Relation

L m3.5

for main sequence stars only

We use binary stars to measure directly the masses of stars of every type. This leads to the:

As one moves to the upper-left of the main sequence:• stars become more massive • stars become even much more luminous• stars become fewer in number

There is a relationship between mass and luminosity for main-sequence

stars

Bigger is brighter!

Mass–Luminosity RelationAll main sequence stars fuse H into He in their cores.All main sequence stars fuse H into He in their cores.Luminosity depends directly on mass because:Luminosity depends directly on mass because:

• more mass means more weight from the starmore mass means more weight from the star’’s outer layerss outer layers• nuclear fusion rates must be higher in order to maintain nuclear fusion rates must be higher in order to maintain

gravitational equilibriumgravitational equilibrium

Lifetime on the Main Sequence

How long will it be before MS stars run out of fuel? i.e. Hydrogen?

How much fuel is there? M

How fast is it consumed? L M3.5

How long before it is used up?

M/L = M/M3.5 = M-2.5

Lifetime on the Main Sequence

• O & B Dwarfs burn fuel like a bus!O & B Dwarfs burn fuel like a bus!• M Dwarfs burn fuel like a compact car! M Dwarfs burn fuel like a compact car!

• Our Sun will last 10Our Sun will last 101010 years on the Main years on the Main Sequence Sequence • MS Lifetime MS Lifetime = 10 = 1010 10 yrs / Myrs / M2.52.5

Lifetime on the Main Sequence

So for example:

B2 dwarf (10 M) lasts 3.2 x 107 yr

F0 dwarf (2 M) lasts 1.8 x 109 yr

M0 dwarf (.5 M) lasts 5.6 x 1010 yr

But the Universe is 1.37 x 1010 yr old!

Every M dwarf that was ever created is still on the main sequence!!

Cepheid Variables

Henrietta Leavitt(1868-1921)

She studied the light curves of variable stars inthe Magellenic clouds.

Same distance

Cepheid Variables

The brightness of the stars varied in a regular pattern.

Cepheid Variables

prototype: Cephei

F - G Bright Giants (II) whose pulsation periods (1-100 days) get longer with brightness (MV = -2 to -6)

Distance Indicator!!

Cepheid Variables

Cepheids enable Cepheids enable astronomers to estimate astronomers to estimate

vast distancesvast distances

This period-luminosity This period-luminosity relationship is important relationship is important because if an astronomer because if an astronomer can find a Cepheid and can find a Cepheid and measure its period, she can measure its period, she can determine its luminosity and determine its luminosity and absolute magnitude.absolute magnitude.

Comparing the absolute and Comparing the absolute and apparent magnitudes allows apparent magnitudes allows for the distance to be for the distance to be calculated.calculated.

Cepheids enable astronomersCepheids enable astronomersto estimate vast distancesto estimate vast distances

This period-luminosity relationship is important This period-luminosity relationship is important because if an astronomer can find a Cepheid because if an astronomer can find a Cepheid and measure its period, she can determine its and measure its period, she can determine its luminosity and absolute magnitude.luminosity and absolute magnitude.

Comparing the absolute and apparent magnitudes Comparing the absolute and apparent magnitudes allows for the distance to be calculated.allows for the distance to be calculated.

The Instability Strip

There appears to be an almost vertical region on the H-R Diagram where all stars within it (except on the Main Sequence)

are variable.

They pulsate due to partial ionization!

Open Clusters

• 100100’’s of starss of stars• 101066 - 10 - 1099 years old years old• irregular shapesirregular shapes• gas or nebulosity is gas or nebulosity is

sometimes seensometimes seen

Pleaides (8 x 107 yrs)

Globular Clusters

101055 stars stars 8 to 15 billion years 8 to 15 billion years

old (10old (101010 yrs) yrs)spherical shapespherical shapeNO gas or nebulosityNO gas or nebulosity

M 80 (1.2 x 1010 yrs)

Clusters are useful for studying stellar evolution!

• all stars are the same distanceall stars are the same distance• use apparent magnitudesuse apparent magnitudes

• all stars formed at about the same timeall stars formed at about the same time• they are the same agethey are the same age

Plot an H-R Diagram!Plot an H-R Diagram!

Pleiades H-R Diagram

Globular Cluster H-R Diagram

Palomar 3

Cluster H-R Diagrams Indicate Age

• All stars arrived on the MS at All stars arrived on the MS at about the same time.about the same time.

• The cluster is as old as the most The cluster is as old as the most luminous (massive) star left on luminous (massive) star left on the MS.the MS.

• All MS stars to the left have All MS stars to the left have already used up their H fuel and already used up their H fuel and are gone.are gone.

• The position of the hottest, The position of the hottest, brightest star on a clusterbrightest star on a cluster’’s main s main sequence is called the sequence is called the main sequence turnoff pointmain sequence turnoff point..

Older Clusters have Shorter Main Sequences