L9 HR Diagrams

8/2/2019 L9 HR Diagrams

1/23

Tim OBrien PHYS 10191 Introduction to Astrophysics & Cosmology 1

Lecture 9

Hertzsprung-Russell diagrams

(also known as colour-magnitude diagrams)


2/23


HR / Colour-Magnitude Diagrams First plotted by Hertzsprung and

Russell in 1911/1913, a plot of

brightness against colour (magnitudeagainst colour index) where colourrelates to temperature

Note, if we plot apparent magnitude

then the plot will be affected by how faraway the stars are. We should try toplot absolute magnitude if we know it.

Think of it as a plot of luminosity

versus temperature (albeittemperature increases to the left!) Often known as a

Hertzsprung-Russell or HR diagram

Brightness (Luminosity)

Colour index

Temperature

RedBlue


3/23


The brightest stars This is a HR diagram for the brightest

stars in the sky (apparent mags brighterthan V=4)

Here plot their

absolutemagnitude

But these are

untypicalstars (theyare bright)


4/23


The nearest stars All stars closer than 12 parsecs

This is likely tobe a moretypical sample

(stars thathappen to benear the Sun)


5/23


The nearest stars All stars closer than 12 parsecs

This is likely tobe a moretypical sample

(stars thathappen to benear the Sun)

This diagonal bandis known as themain sequence asabout 90% of starsin a random samplelie along it


6/23


Nearest & Brightest Combine on same axes

As we shall see,

the fact this is

not a scatterdiagram is

telling us

somethingvery interesting

The Sun: MV=+4.8, B-V=+0.65


7/23


Interpreting the HR Diagram Usually plotted with magnitudes on the axes

this is log of brightness Take logs of both sides of the Stefan-Boltzmannlaw L=4R2T4 :log10L = 4log10T+log10(4R

2)

The HR diagram is a plot of log10L (y axis)versus log10T(x axis ; minus because itincreases to left)

So, for stars with the same radius, Ris constantand they lie along straight lines of the formy = 4x +ci.e. sloping from upper left down to lower right


8/23


Interpreting the HR Diagram Stars at lower left

are small and hot

Stars at upperright are large andcool

Hence we can tellwhether a star is adwarf or a giant

-4

-2

0

2

4

6

Log10

Lum

inosity/L

sun

5x1031042x1045x104

Temperature / K (log scale)

Sun


9/23


Interpreting the HR Diagram Stars at lower left

are small and hot

Stars at upperright are large andcool

Hence we can tellwhether a star is adwarf or a giant

-4

-2

0

2

4

6

Log10

Lum

inosity/L

sun

5x1031042x1045x104

Temperature / K (log scale)

Sun

Supergiants

Giants Sizeincreases


10/23


Dwarfs & Giants

White Dwarfs

Giants

Supergiants


11/23


Cluster HR Diagrams Stars in a cluster are all at

about the same distance socan use apparent magnitudes

Open clusters- Sometimesknown as galactic clusters,loose structures containingabout 100 to 1000 stars of

similar chemical compositionto the Sun, brightest of whichare blue. Irregularly shaped,ranging in size from 1-20parsecs (pc). Almost athousand are known in ourGalaxy, confined mainly to thedisc. Examples include thePleiades (the famous 'Seven

Sisters') and Praesepe.

Praesepe (The Beehive)1 degree x 1 degree field fromDigitized Sky Survey


12/23


Cluster HR Diagrams HR diagram for Praesepe

Most stars on main sequence a few in giantregion and perhaps in white dwarf region


13/23


Cluster HR Diagrams Globular clusters-Very

different to open clusters.Centrally condensed, virtually

spherical, and contain about100,000 to 1,000,000 stars,the brightest of which are red.Typically about 40 pc across.

About 150 known in ourGalaxy distributed roughlyspherically about the centre ofthe galaxy and outside thedisc. The stars are typically

underabundant in heavyelements by a factor of 10-1000 in comparison to theSun.

Globular cluster M30.5 degree x 0.5 degree field fromDigitized Sky Survey


14/23


Cluster HR Diagrams HR diagram for M3

Far more complex we will see how tounderstand these features in terms of the age ofthe stars in the cluster


15/23


What is the main sequence? Can measure masses and luminosities of

main-sequence stars in binary systemsTight relationship fittedby a power-law

L Mwhere ~4( ranging from ~3-5)

[ Also radius R M0.62and temperatureT M0.65 ]


16/23


The main sequence

is a sequence of mass

High mass(high luminosity)

Low mass(low luminosity)


17/23


Lifetime on the main sequence Assume star has energy reserves that scale with its

mass i.e. E M Rate at which energy used (energy output per

second) relates to luminosity and L M4

Therefore lifetime scalesas t= E/L M/M4 M-3

High-mass stars are bright,hot and very short-lived they live fast and die young

10 billion years

1 billion years

100 million years

10 million yrs


18/23


Lifetime on the main sequence

High mass these stars will run outof fuel first


19/23


After the main sequence1. This section ofthe main sequence

has already run outof fuel

2. The stars that were at thetop left of the main sequencehave moved to occupy theseareas of the HR diagram

3. The turn-off

point can be usedto estimate theage of the cluster

4. Theoretical modelscan be used to calculatewhere stars would be at

a certain age this iscalled an isochrone(here 10 Gyrs) initiallythey lie on the Zero AgeMain Sequence, the

ZAMS


20/23


Turn-off points Each isochrone

represents a group ofstars of differentmasses but all thesame age

Individual stars sit onmain sequence, at apoint determined bytheir mass, until they

run out of fuel. Starsat top left run out offuel first.

Age of group of stars


21/23


Distances & ages of clusters Determine distance and age of three clusters using

Java applet on Blackboard website

Open the HR diagrams of Star Clusters Java appletand select the data for the Hyades cluster from the

drop-down menu at bottom left. Plot the ZAMS on the same graph by selecting it in the

second drop-down menu. Use the slider bar to offset the ZAMS vertically to

match the magnitudes of the Hyades stars and soobtain an estimate for the distance modulus. You canalso set this by entering a value in the text field - notethat the values for the distance modulus are in 0.01

mags.

Example in lecture The Hyades Cluster.Try the other clusters at home.


22/23


Distance The vertical difference in magnitudes between the ZAMS

and the unevolvedlower section of the Hyades main

sequence is simply due to the distance of the Hyades. Ifthe cluster were at the canonical distance of 10 parsecsused to define absolute magnitudes then the two mainsequences would lie on top ofone another. The fact that theHyades main sequence lies atfainter apparent magnitudesthan the ZAMS means it mustbe farther away than 10 parsecs.

I estimate a vertical difference of3.18 mags. Distance modulusequation is m-M = 5log d 5.Here m-M = 3.18, so d = 43 pc.


23/23


Age Estimate age from best-fitting

isochrone. I estimate it as a little older than 500

Myrs, say 600 Myrs. Note the goodfit of the 500 Myr isochrone to thelower m-s and how it lies just belowthe observed m-s at the bright (left)end. Whereas for the 1000 Myr

isochrone the turn-off point is clearlywell beyond the observed m-s at thebright end.

Perryman et al (1998) derive 625 +/-50 Myr from Hipparcos

measurements(http://adsabs.harvard.edu/abs/1998A&A...331...81P) in good agreementwith our estimate here. (Note theyalso obtain a distance estimate of46.3 +/- 0.3 pc, close to ours).

500 Myr

1000 Myr

L9 HR Diagrams

Documents

Transcript of L9 HR Diagrams