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Home , Stellar parallax

Astronomy 110: SURVEY OF

9. Properties of

1. Distances & other parameters

2. The Hertzsprung-Russell diagram

3. clusters & Distance measurements are critical to understanding stellar properties. Stars span an enormous range of , temperature, and size, and these parameters are profoundly related to each other. Studying clusters of stars born at the same time provides clues to the lives of stars. 1. DISTANCES & OTHER PARAMETERS

a. The Scale of the

b. How Far to the Stars?

c. Luminosity and Brightness The Scale of the Solar System

Kepler and later astronomers made good scale models of the Solar System, but they didn’t know its true size.

Planet a (AU) P (yr) Mercury 0.387 0.241 S Venus 0.723 0.615 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.857 Saturn 9.537 29.424

To find the value of one AU, a measurement of the actual distance (in km) to any would suffice. Method: Theory

Observe P from points 1, 2 separated by baseline, b.

D 1

b θ P 2 θ to distant star

Suppose that from point 1 the planet lines up with a distant star, while from point 2 the angle between the planet and star is θ. Parallax Method: Theory

How many triangles? 360° N = θ D

b θ C Circumference P C of big circle? θ 360° C ≃ b θ Radius of big circle? 1 360° D ≃ b That’s the distance to P! 2π θ The Distance to Mars

On October 1, 1672, Mars lined up with a bright star:

Paris (Europe) Cayenne (South America) Wikipedia: Giovanni Cassini

Mars was then 0.43 AU from Earth. Cassini used the known distance between the two observing points and the measured parallax angle to find this distance in km:

7 8 DMars ≃ 6.0×10 km ⇒ 1 AU ≃ 1.38×10 km Measuring the AU

1. Transits of Venus: 1761, 1769, 1874, 1882 — inconclusive due to effects of atmosphere 2. Observations of Mars: 1877 1 AU = 1.49×108 km 3. Observations of Eros: 1930 1 AU = 1.4960×108 km 4. Radar measurements: 1958 and since 1 AU = 1.49597871×108 km How Far to the Stars?

We need a much larger baseline to measure Dec June stellar distances! The Earth’s orbit gives a baseline of b = 2 AU Stellar Parallax

Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the .

Parallax of a Nearby Star Stellar Parallax

Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the Sun. Parallax Calculations

The parallax angle p is half the total shift:

1 360° 2p D ≃ Dec June 2π p AU

Stars are far away, so D p is measured in arc- sec (1˝ = 1°/3600). p Define a new distance AU unit, the (pc): 360 × 3600 1˝ 1 pc = AU = 3.09×1013 km ⇒ D ≃ 2π p pc 1. Suppose star B is twice as far away as star A.

A. Star B has 4 times the parallax angle of star A. B. Star B has 2 times the parallax angle of star A. C. Both stars have the same parallax angle. D. Star A has 2 times the parallax angle of star B. E. Star A has 4 times the parallax angle of star B. 2. If we could measure stellar from Mars instead of Earth, would nearby stars move in ovals which are

A. the same size as seen from Earth, because the stars are just about as far from Mars. B. larger than seen from Earth, because Mars has a larger orbit. C. smaller than seen from Earth, because Mars is a smaller planet. Nearest Known Stars

Most too dim 3.50 pc = 11.4 ly to see without 3.50 pc = 11.4 ly a telescope! 3.22 pc = 10.5 ly

3.65 pc = 11.9 ly

2.63 pc = 8.6 ly

1.32 pc = 4.3 ly

3.62 pc = 11.8 ly

Wikipedia: Nearest stars A Stellar Distance Scale

1. Distances on Earth are determined by surveying techniques. 2. Parallax measurements at two points on Earth yield distances to other (now checked by radar). 3. These distances set the scale for the Solar System, and fix our distance to the Sun: 1 AU = 1.496×108 km. 4. Parallax measurements at two (or more) points on Earth’s orbit yield distances to nearby stars. At each step, known distances are used to find unknown distances. 3. Suppose we found an error in our calculation of the AU, and the correct value was 10% larger. How would this change our values for stellar distances?

A. Stellar distances would be unchanged. B. Stellar distances would increase by 10%. C. Stellar distances would decrease by 10%. Luminosity and Brightness

Absolute Luminosity (L) is the energy a star radiates per unit time.

26 L⊙ = 3.8×10 watt

Apparent Brightness (B) is the energy received per unit time and unit area.

2 B⊙ = 1366 watt / m Brightness: Inverse-Square Law

Energy conservation implies that the same luminosity passes through each sphere. Sphere of radius D has area A = 4πD2

Thus, brightness is inversely proportional to (distance)2:

L L B = = A 4πD2 The Sun and αCen Compared

αCen appears much fainter: αCen is much further away:

-8 2 16 Bα = 2.8×10 watt / m Dα = 1.32 pc = 4.1×10 m

2 11 B⊙ = 1366 watt / m D⊙ = 1 AU = 1.49×10 m

What about their ?

2 26 Lα = Bα (4πDα ) = 5.9×10 watt

2 26 L⊙ = B⊙ (4πD⊙ ) = 3.8×10 watt

αCen is about 50% more luminous than the Sun! 4. How would αCen’s apparent brightness change if it was 3 times further away?

A. It would be 1/3 as bright. B. It would be 1/6 as bright. C. It would be 1/9 as bright. D. It would appear the same. E. It would be 3 times as bright. Neighbors of the Sun

A few nearby stars are more luminous than the Sun, but most are much less luminous; of the 150 nearest stars: Number From (L⊙) To (L⊙) Examples of Stars

10 100 4 : 50 L⊙

1 10 14 αCen: 1.5 L⊙

0.1 1 25 τCet: 0.46 L⊙ 0.01 0.1 21 0.001 0.01 57 0.0001 0.001 29 DISTANCES & OTHER PARAMETERS: REVIEW 1. Parallax equation: (a) number of triangles, (b) circumference of circle, (c) radius of circle. D b θ 1 360° P D ≃ b 2π θ 2. Brightness and luminosity: — brightness is what we observe; it has units of energy per unit time per unit area. — luminosity is what a star puts out; it has units of energy per unit time. 2. THE HERTZSPRUNG-RUSSELL DIAGRAM

a. Interpreting Stellar Spectra

b. The

c. Beyond the Main Sequence Stars have different luminosities and colors. — luminous stars may be red or blue — dim stars are generally red

SWEEPS ACS/WFC Color Composite Types of Spectra: Review

Black Body Spectrum Black-Body (Thermal) Radiation

Any opaque object (black body) with a temperature T > 0 K emits light (radiation). As the temperature goes up, this light gets brighter and bluer.

Relationship Between Temperature and Luminosity Properties of Thermal Radiation

• Higher temperature ⇒ more light at all wavelengths • Higher temperature ⇒ peak shifts towards blue Types of Spectra: Review

Black Body Spectrum

Emission Spectrum

Black Body + Absorption Spectrum Spectral Lines: Review n = ∞ 13.6 eV

Each electron orbit has a n = 6 13.2 eV n = 5 13.1 eV definite energy level. n = 4 12.8 eV

In hydrogen, orbit n has energy n = 3 12.1 eV 1 2.9 eV En = ( 1 - 2 ) × 13.6 eV n 2.6 eV 434 nm

1.9 eV where an eV is an energy unit. 486 nm

To jump from orbit to orbit 656 nm takes a photon with exactly the right amount of energy. n = 2 10.2 eV Stellar Spectra

In stars, the lower produces a black-body spectrum, while cooler gas above creates dark lines.

Black Body + Absorption Spectrum

Text

Stars exhibit a tremendous variety of spectra — why?

Stellar Spectra Interpreting Stellar Spectra

Stars have different spectra almost entirely because they have different surface temperatures!

Stellar Spectra and Temperatures

Composition plays a minor role — almost all stars are mostly hydrogen and helium, just like the Sun. Spectral Types

Hydrogen T > 30000 K OOld T ~ 20000 K BBread T ~ 9000 K AAnd T ~ 6800 K FFruit T ~ 5500 K GGet T ~ 4200 K KKinda T < 3500 K MMoldy

Ionized Titanium Sodium Titanium Calcium Oxide Oxide Spectral Types

Hydrogen T > 30000 K Most H atoms are ionized. T ~ 20000 K

Most H atoms T ~ 9000 K at n = 2 level. T ~ 6800 K T ~ 5500 K Most H atoms at n = 1 level. T ~ 4200 K T < 3500 K

Ionized Titanium Sodium Titanium Calcium Oxide Oxide Plotting the HR Diagram

The HR diagram shows surface temperature on the horizontal axis and luminosity on the vertical axis. The Main Sequence

Most stars in the Sun’s neighborhood fall along a roughly diagonal line on an HR diagram.

This line is called the main sequence. Nature of the Main Sequence

All main-sequence stars produce energy in the same way as the Sun, by fusing hydrogen to form helium in their cores.

A star’s place along the main sequence is fixed by its mass. Measuring Stellar Masses: Review

For any two masses M and m orbiting each other, Newton’s version of Kepler’s Law III states:

m P2 4π2 = a3 G(M + m) M

Wikipedia: Kepler’s Laws

This provides a way of ‘weighing’ stars — we observe a pair of stars orbiting each other (a double-star) and solve this equation to get their masses. Stellar Lifetimes Along the Main Sequence

The main sequence is also a sequence of life- times.

High-mass stars must have hotter cores to balance , so they use up hydrogen faster. The Main Sequence: Summary

Mass is the key property of a main-sequence star: other basic properties are all determined by mass.

Low Mass High Mass

low luminosity high luminosity

low temperature high temperature

long lifetime short lifetime Giants and Supergiants

Some stars are not part of the main sequence; they are relatively cool but very luminous.

These stars must have enormous radii to give off so much energy. White Dwarfs

Other stars are hot but very dim.

These stars must have tiny radii to give off so little energy. Stellar Radii THE H-R DIAGRAM: SUMMARY a. Interpreting Stellar Spectra — spectra differ mostly because of temperature. b. The Main Sequence — on the main sequence, stars are arranged by mass. c. Beyond the Main Sequence — giants and dwarfs have very different radii. Main Sequence Lifetimes

• 1 M⊙ star: L = L⊙ 10 — lifetime: T⊙ ≈ 10 yr

4 • 10 M⊙ star: L ≈ 10 L⊙ 10 × fuel; use at 104 × rate 4 7 ⇒ T ≈ (10/10 ) T⊙ ≈ 10 yr

• 0.1 M⊙ star: L ≈ 0.003 L⊙ 0.1 × fuel; use at 0.003 × rate 11 ⇒ T ≈ (0.1/0.003) T⊙ ≈ 3×10 yr 3. STAR CLUSTERS & STELLAR EVOLUTION

a. Nature of Star Clusters

b. Cluster HR Diagrams

c. Cluster Distances Nature of Star Clusters

Open clusters Globular clusters Two Types of Clusters

1. Globular Clusters — old, ‘metal’-poor stars — contain 105 to 106 stars — found in halo of

2. Open Clusters — young, ‘metal’-rich stars — contain 100 to 104 stars — found in disk of Milky Way Cluster Formation

Star clusters form in massive interstellar gas clouds. — cloud well-mixed ⇒ stars have similar composition — rapid formation ⇒ stars have similar ages

Star Cluster R136 Bursts Out Dynamics

Clusters are held together by mutual gravity of stars.

Simulated Star Cluster

High-mass cluster stars tend to form pairs and eject smaller stars. This eventually disrupts open clusters. Cluster HR Diagrams

The Pleiades (M45) All the stars in a cluster have the same age, so HR diagrams for cluster stars tell us about:

• cluster ages

• stellar evolution

• cluster distances Evolution of HR Diagrams

High-mass stars burn out first; low-mass stars die later.

So as a cluster ages, the lifetime: 107 yr main sequence ‘burns 8 down’ in order. lifetime: 10 yr

lifetime: 109 yr

lifetime: 1010 yr

(Note: this animation also shows stars after they leave the main sequence.) Using the H-R Diagram to Determine the Age of a Star Cluster Evolution of HR Diagrams

High-mass stars burn out first; low-mass stars die later.

So as a cluster ages, the main sequence ‘burns down’ in order.

Instead of plotting stars, we represent them with a line of constant age. Using the H-R Diagram to Determine the Age of a Star Cluster The Pleiades: A Young Cluster

Using the H-R Diagram to Determine the Age of a Star Cluster

Pleiades and Stardust M67: An Older Cluster

Using the H-R Diagram to Determine the Age of a Star Cluster

Star Cluster Messier 67 Cluster HR Diagrams Compared

Globular Cluster M4

Clusters have a range of ages; giant and dwarf stars appear at different stages of cluster aging process. 106 Cluster Distances 106 Pleiades 105 All stars in a cluster are 104 at the same distance. 103 Plot apparent brightness 102 instead of luminosity. 10 1 ent brightness ppar Main seq. in Hyades a 0.1 appears ~9 × brighter 10-2

than in Pleiades; why? 10-3

10-4 Pleiades are ~3 × more 10-5 distant than Hyades! 30000 10000 3000 surface temperature A Cluster Distance Scale

1. Parallax measurements at two (or more) points on Earth’s orbit yield distances to nearby stars. 2. Nearby stars are used to measure luminosity of main sequence. 3. Main sequence luminosity is used to get distance to Hyades & Pleiades (also checked by parallax). 4. Improved main sequence luminosities yield distances to other clusters throughout (and beyond!). At each step, known distances are used to find unknown distances.