the birth & death of stars part 1 are stars similar to our sun? how far away are they? what do...

The Birth & Death The Birth & Death of Stars Part 1of Stars Part 1

•Are Stars similar to our Sun?•How far away are they?•What do they do?

Astronomy 12

The Birth & Death The Birth & Death of Stars Part 1of Stars Part 1

Learning Outcomes (Students Learning Outcomes (Students will…):will…):

•Describe and apply Describe and apply classification systems and classification systems and nomenclature used in the nomenclature used in the classification of starsclassification of stars

•Use parallax to determine Use parallax to determine distancedistance

•Calculate luminosityCalculate luminosity•Describe nuclear fusion Describe nuclear fusion

(what stars “do”)(what stars “do”)

Stars – What are they?

Stars are great Stars are great balls of hot balls of hot

gas held gas held together by together by their own their own gravity.gravity.

If stars were not If stars were not so hot, the gas so hot, the gas would collapse would collapse

into a small into a small dense body.dense body.

Life on Earth Life on Earth depends on the depends on the

Sun. Nearly all of Sun. Nearly all of our energy comes our energy comes

from the Sun, from the Sun, even coal and oil. even coal and oil. This could be true This could be true

for other for other extrasolar extrasolar planets!planets!

Stars – Why are they important?

Near the center of Near the center of the Sun nuclear the Sun nuclear

fusionfusion generates generates energy and this energy and this

energy flows energy flows outward towards outward towards

the surface where it the surface where it is radiated into is radiated into

space as space as heatheat and and lightlight and other and other

forms offorms ofelectromagnetic electromagnetic

radiationradiation..

Stars – What do they do?

Nuclear Fusion and the Sun

Stars create energy through nuclear fusion.

In this process, 2 nuclei (mostly hydrogen) combine to produce a single, larger nucleus which creates energy.

In large enough quantities, nuclear fusion can be used as an energy source. To get large enough quantities, atoms must be heated to 1.5 x 107K (the heat of the Sun)!

1.5 x 107K = 15,000,000 K OR 14,999,726°C

Nuclear Fusion

The Sun radiates energy at the rate of 3.9x1026W (watts) and has been doing so for several billion years.

The fusion reaction in the Sun is a multistep process in which (typically) hydrogen is burned into helium.

Hydrogen is the “fuel” Helium is the “product”

Nuclear Fusion

2 protons (1H) combine to form a deuteron (2H), a positron (e+) and a neutrino (v). 1H + 1H 2H + e+ + v

The positron quickly reacts with an electron (e-) and both particles annihilate, their mass energy appearing as two gamma-ray photons (γ). e+ + e- γ + γ

Nuclear Fusion

The deuteron (2H) collides with another proton (1H) and forms a 3He nucleus and a gamma ray (γ). 2H + 1H 3He + γ

Two 3He nuclei may eventually (within ten thousand years) find each other. 3He + 3He 4He + 1H + 1H

The Sun’s Nuclear Energy – When will it run out???

The Sun has been creating nuclear energy for about 5 billion years.

There is enough Hydrogen left to continue this process for another 5 billion years.

What about nuclear fusion that creates other atoms???

If the core temperature increases to about 1 x 108K then energy can be produced by burning helium to make carbon.

As a star evolves and becomes hotter than 1 x 108K, other elements can be formed by other fusion reactions.

This only works for elements up to the iron-56. At this point, more energy would be consumed than produced.

Nuclear Fusion Review Questions

1) What is the fuel for nuclear fusions (in most cases)?

2) What is the product? 3) What is the largest atom that can

be used in nuclear fusion? Why? 4) What is the overall equation for

nuclear fusion? 5) How long will the Sun’s life be in

total?

1) Hydrogen 2) Helium 3) Iron- 56 because at this point,

more energy would be consumed than produced.

4) ** See slide 10 5) 10 billion years

There are lots of stars in There are lots of stars in the universe…and a lot of the universe…and a lot of

different stars!different stars!

Panorama view of the sky Panorama view of the sky

Classifying Stars:Classifying Stars:The Four Basic Characteristics The Four Basic Characteristics

of a Starof a StarLuminosityLuminositySizeSizeMassMassSurface Surface TemperatureTemperature

To discover these characteristics, distance to a star must be determined…use parallaxparallax!!

The Geometry The Geometry of Parallaxof Parallax

d (in Parsecs) = 1 (AU)

p (in arcseconds)

p

1 parsec (pc) = 3.26 ly

http://www.astronomynotes.com/starprop/s2.htm



Parallax from a Different Parallax from a Different PlanetPlanet

If we lived on Mars, orbiting 1.5 If we lived on Mars, orbiting 1.5 times farther away from the times farther away from the Sun, the parallax would beSun, the parallax would be

1.1. the same as from Earththe same as from Earth

2.2. 1.5 times smaller than from 1.5 times smaller than from EarthEarth

3.3. 1.5 times bigger than from 1.5 times bigger than from EarthEarth

Journal Formula

Symbolsd = distance in parsecs p = angle in arcseconds

Unitspc = 1 parsec = 3.26 light years (ly)1 light year = the distance that light

travels in a vacuum in one Julian year (365.25 days)

= 9,460,730,472,580.8 km

sec

1

arcd

Suppose a star has a parallax of 0.01 arc Suppose a star has a parallax of 0.01 arc seconds. How many parsecs away is it?seconds. How many parsecs away is it?

distance (in parsecs) = 1 / pdistance (in parsecs) = 1 / p

Answer: 100 parsecs

Journal: Example 1Journal: Example 1

d = 1 (AU)

0.01

Suppose a star has a distance of 12 Suppose a star has a distance of 12 parsecs. How many arcseconds is parsecs. How many arcseconds is its angle?its angle?

Answer: 0.083333 arcseconds

Journal: Example 2Journal: Example 2

08333.012

1

1

Re

1

p

p

dp

arrange

pd

Category 1

LUMINOSITY

Apparent or Visual Brightness (m)Apparent or Visual Brightness (m)……Brighter objects have Brighter objects have smallersmaller magnitudes than fainter objectsmagnitudes than fainter objects..

Luminosity

Luminosity (absolute brightness) depends on distance and apparent brightness

Luminosity is the amount of electromagnetic energy a body radiates per unit of time.

2

1

rI

Luminosity Luminosity depends

on: 1) size of the star

(bigger = more luminous!)

2) distance to the star (closer = more luminous!)

3) intervening matter (dust and gas can absorb light – reduces luminosity and increases redness)

Calculating Luminosity

If we know the distance to the star we can measure luminosity:

L = 4πfd2 where… the distance d to the star (m), the Flux f of the star (W/m2) where flux

measures light intensity the luminosity L of the star (Watts) 1 Parsec = 3.08568025 × 1016

meters

Example 1: Finding Luminosity

What is the luminosity of our Sun which has a flux of 1360 W/m2 and a distance of 4.84813×10-6 parsecs?

Step 1: Change distance to m

m11

166-

10495977899.1

pc

m x103.08568025pc)x10(4.84813

Step 2: L = 4πfd2

L = 4π (1360)(1.495977899 x 1011)2

L = 3.82 x 1026 Watts

Luminosity

By definition (using more accurate measurements):

Lsun = 3.9 x 1026 W However, we can measure astronomical

luminosity in Solar luminosity units, where

Lsun = 1 Solar luminosity unitSolar luminosity units = L© (this should

be a circle with a dot!)

Example 2: Changing into Solar Luminosity Units

If a star has a luminosity of 1.3 x 1010 Watts, what is its luminosity in Solar luminosity units?

unitsL

Lstar

17

2610

103.3

Watts109.3

unit luminositySolar 1 Watts)103.1(

There is a Big Range of There is a Big Range of Stellar Luminosities Out Stellar Luminosities Out

there!there!

StarStar

Luminosity Luminosity (in units of (in units of

solar solar Luminosity)Luminosity)

SunSun 11Proxima CentauriProxima Centauri 0.00060.0006

Rigel (Orion)Rigel (Orion) 70,00070,000Deneb (Cygnus)Deneb (Cygnus) 170,000170,000

Example 3: Finding Distance from Luminosity

You have a 100 W lightbulb in your laboratory. Standing at a distance of d from the lightbulb, you measure flux of the lightbulb to be 0.1 W/m2. How can you use this information to determine the distance from you to the lightbulb?

1) Rearrange

2) Sub in values

3) Solve for d92.8

58.79

58.79

1.0**4

100

4

2

2

2

d

d

d

d

f

Ld

Example 4: Finding Flux Find the flux of the star Arcturus if it is 11.25 pc

away from Earth and its Solar luminosity is 114.

Step 1: Change luminosity into Watts 114 Solar luminosity units x ( 3.9x1026 Watts )

1 Solar luminosity unit 4.446 x 1028

Step 2: Change distance into metres 11.25 pc x (3.0856802 x 1016m)

1 pc 3.47 x 1017 m

Example 4: Finding Flux

Find the flux of the star Arcturus if it is 11.25 pc away from Earth and its Solar luminosity is 114.

Step 3: Rearrange equation, sub in values, solve for f

28

17

28

2

/10936.2

)1047.3(4

)10446.4(

4

mWf

f

d

Lf

Luminosity

The luminosity of stars ranges from 0.01 Lo to 1 x 106 Lo.

The Sun is not nearly as bright as the most luminous stars but is brighter than most stars.

The Sun is gradually becoming more luminous (about 10% every 1 billion years). The Sun used to be fainter in the past, which is possibly the reason life on Earth has only existed for about 1 billion years on land.

Category 2

SIZE!

Stellar SizeStellar Size

Stars are very spherical so we Stars are very spherical so we characterize a star’s size by its characterize a star’s size by its radius.radius.

We always compare to our Sun!We always compare to our Sun!

R

Stellar Radii vary in sizefrom ~1500 RSun for a large Red Giant to 0.008 RSun for a WhiteDwarf.

Size Equation

L = 4πR2s T4,

Where L is the luminosity in Watts R is the radius in meters s is the Stefan-Boltzmann constant

T is the star's surface temperature in Kelvin NOTE: R is often given in Solar radii

(radius of Sun)

4281067.5

Km

Wx

Example 1

Find the Luminosity of Zeta Puppis which has a temperature of about 38,000 K and a radius of 18 Ro. Then change this into Solar luminosity units.

Step 1: Change units R = 18 x (6.955 x 108 m) = 1.2519 x 1010 m Step 2: Plug into equation L = 4πR2s T4

L = 4π(1.2519 x 1010)2(5.67 x 10-8) (25000)4

L = 2.328 x 1032 W L = 597,038 Lo

Example 2

Find the radius of a new star, SBUTLER, that has a luminosity of 5Lo and a temperature of 25,000K.

Step 1: Change units 5Lo x (3.9 x 1026

Watts/1Lo) = 1.95 x 10 27

Step 2: Rearrange equation

L = 4πR2s T4 mR

xR

sT

LR

83702962

)25000)(1067.5(4

10x95.1

4

48

27

4

Category 3

MASS!

Mass

Stars fall into a narrow mass range because below 0.08 Solar masses, nuclear reactions

cannot be sustained AND greater than 100 Solar masses stars are

unstable.

High mass stars burn their fuel at higher rates and live shorter lives than low-mass stars.

How do you weigh a How do you weigh a star?star?

By observing the star and anything By observing the star and anything that orbits it (maybe even another that orbits it (maybe even another star)star)

Use Kepler’s Laws of Planetary Use Kepler’s Laws of Planetary Motion and Newton’s Law of Motion and Newton’s Law of Gravitation to determine massGravitation to determine mass

Formula – A “metric” version of Kepler’s Law!

Where: M = mass of star in kg N = mass of planet in

kg a =distance from star

to planet in m (average)

G = gravitational constant

(6.673 × 10-11m3 kg-1 s-

2) P = period of the orbit

in seconds

NGP

aM

)(

42

32

What do I have to know?

How to change from a mass in kg to a mass in Solar mass units

Change 15 Mo into kg. Change 1.52 x 1035 kg into Mo.

Category 4

SURFACE TEMPERATURE

The Sun

Although nuclear fusion needs heat of 1.5 x 107K (core), the surface temperature of the Sun is about 5,700 K.

The temperature of stars are between 3,000K to 30,000 K.

How do you measure the How do you measure the surface temperature of a surface temperature of a

star?star?• Every element (when heated) will emit lines that Every element (when heated) will emit lines that

lie along the visible light spectrum a.k.a. R-O-lie along the visible light spectrum a.k.a. R-O-Y-G-B-I-VY-G-B-I-V

• Stars are mostly composed of hydrogen (and some helium)

Spectral Types of StarsSpectral Types of Stars

Spectral types are defined by the:Spectral types are defined by the:• existence of spectral lines belonging to existence of spectral lines belonging to

various elements, ions, & molecules in various elements, ions, & molecules in a star’s spectruma star’s spectrum

• the relative strengths of these linesthe relative strengths of these lines However, spectral type is not However, spectral type is not

determined by a star’s composition.determined by a star’s composition.• all stars are made all stars are made primarilyprimarily of of

Hydrogen & HeliumHydrogen & Helium

Reason for Spectral TypesReason for Spectral Types

Spectral type is determined by a star’s Spectral type is determined by a star’s surface temperaturesurface temperature..

Astronomers use Kelvin (K) as temperature unit…

272 K = 0 oC298 K = 30 oC1000 K = 727 ºC

Spectral Type Classification Spectral Type Classification SystemSystem

O B A F G K M

Oh Be A Fine Girl/Guy, Kiss Me!

50,000 K 3,000 K Temperature

Stellar ClassificationStellar Classification

AnalogyAnalogyMake a plot that shows the general Make a plot that shows the general

relationship between height and relationship between height and weight for humans.weight for humans.

- now add to your plot the population of basketball players who are very tall and very thin.

- now add the population of obese children

•The plot would show a cluster of people that would have similar “middle-of-the-road” height/weight ratios•It would also show a smaller cluster of “very tall and very thin” AND a smaller cluster of “very short and very fat”

•The plot would show a cluster of people that would have similar “middle-of-the-road” height/weight ratios•It would also show a smaller cluster of “very tall and very thin” AND a smaller cluster of “very short and very fat”

Weight

Height

Most people in the world

Very Tall,Very Thin

Very Short,Very Fat

?

?

How can we classify starsHow can we classify stars

1) Collect information ona large sample of stars.

2) Measure their luminosities

3) Measure their surface temperatures(need their spectra)

The Hertzsprung-Russell The Hertzsprung-Russell DiagramDiagram


HOT COOL

BRIGHT

FAINT


The Main Sequence ~90% of all stars

are in the main sequence (MS)

~90% of all MS stars are cooler spectral types than the Sun (i.e., at the lower MS)

All MS stars fuse H into He in their cores.


Mass-Mass-Luminosity Luminosity Relation:Relation:

L M3.5

For example, if the mass of a star is doubled, its luminosity increases by a factor 23.5 ~ 11.

Mass of MS StarL M3.5

The relation is for main sequence stars only!


Red Giants

- Red Giant starsare very large, cooland quite bright.

e.g., Betelgeuse is100,000 times moreluminous than the Sunbut is only 3,500K onthe surface. It’s radiusis 1,000 times that of the Sun.


Supergiants

•Very bright•Very hot

Size of Star:


White Dwarfs

- White Dwarfsare hot, but sincethey are so small,they are not veryluminous.

Main Main Sequence Sequence LifetimeLifetime

All M-S stars have temperatures sufficient All M-S stars have temperatures sufficient to fuse H into He in their cores.to fuse H into He in their cores.

Luminosity depends directly on mass:Luminosity depends directly on mass: more mass = more pressure from upper layersmore mass = more pressure from upper layers fusion rates must be high to maintain fusion rates must be high to maintain

equilibriumequilibrium Lifetime Lifetime (Amt of Fuel)/(Rate of Burning) (Amt of Fuel)/(Rate of Burning)

M / L M / L M / M M / M3.53.5 1 / M 1 / M2.52.5

Higher mass stars have shorter lives!Higher mass stars have shorter lives!


Lifetimeof Star

Shorter

Longer

More mass,more fuel,very fast burning.

Less mass,less fuel,slow, steady burning.

ThinkThinkSUV vs Honda CivicSUV vs Honda Civic

MassMass(M(MSunSun))

LuminosityLuminosity(L(LSunSun))

Surface Surface TemperatTemperature (K)ure (K)

RadiusRadius((RRSunSun))

Main Main sequence sequence lifespan lifespan

(yrs)(yrs)

0.100.10 3×103×10-3-3 2,9002,900 0.160.16 2×102×101212

0.500.50 0.030.03 3,8003,800 0.60.6 2×102×101111

0.750.75 0.30.3 5,0005,000 0.80.8 3×103×101010

1.01.0 11 6,0006,000 1.01.0 1×101×101010

1.51.5 55 7,0007,000 1.41.4 2×102×1099

33 6060 11,00011,000 2.52.5 2×102×1088

55 600600 17,00017,000 3.83.8 7×107×1077

1010 10,00010,000 22,00022,000 5.65.6 2×102×1077

1515 17,00017,000 28,00028,000 6.86.8 1×101×1077

2525 80,00080,000 35,00035,000 8.78.7 7×107×1066

6060 790,000790,000 44,50044,500 1515 3.4×103.4×1066

•As mass of a M-S star increases, luminosity, surface temperature and As mass of a M-S star increases, luminosity, surface temperature and

radius (size)radius (size) increaseincrease

•As mass of a M-S star increases, life span on M-S As mass of a M-S star increases, life span on M-S decreasesdecreases

Review Questions:Review Questions: The H-R The H-R DiagramDiagram1.1. Where are most stars?Where are most stars?

2.2. What is the common What is the common characteristics of MS characteristics of MS stars?stars?

3.3. What determines the What determines the location of a star in the location of a star in the MS?MS?

4.4. Where do you find the Where do you find the largest stars? largest stars?

5.5. The smallest?The smallest?6.6. The most massive one?The most massive one?7.7. The coolest stars?The coolest stars?8.8. How do we know the age How do we know the age

of a star?of a star?

1. MS, 2. H He, 3. M, 4. upperright, 5. lowerleft, 6. upperleft, 7. lowerright, 8. normally we don’t

the birth & death of stars part 1 are stars similar to our sun? how far away are they? what do...

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