Lesson 6: Properties of Stars, Patterns Among Stars, Star Clusters

Question 1

What is brightness? What is Luminosity? How do the two relate to each other?

Answer 1

• Luminosity: amount of power a star radiates (energy per second = watts)
• Apparent brightness: Amount of starlight that reaches Earth (energy per second per square metre)

The relationship between apparent brightness and luminosity depends on distance

Question 2

What is the inverse-square law? Give the Formula

Also,
[Exam] How would the apparent brightness of Alpha Centauri change if it were three times farther away?

Answer 2

Inverse square law: The apparent brightness is inversely proportional to the square of the distance

• inversely proportional: As one gets bigger, one gets lower
  □ As the apparent brightness increases than distance decreases

Brightness = Luminosity / 4π (Distance)2

Answer:
It would be 1/9 as bright
3^2 = 9 …… 1/9

Question 3

How would the apparent brightness of the star Sirius change if it were 5x farther away?

Answer 3

Answer: It would be 1/25 as bright
5^2 = 25 …… 1/25

Question 4

If two stars of equal luminosity were being observed by an astronomer on Earth, but one of the stars was 10x farther away than the other, how much dimmer would that
star appear?

Answer 4

Brightness = Luminosity / 4π (Distance)2

Answer: it would appear
10^2 = 100
would appear 1/100 as dimmer

Question 5

What is parallax? Why do stars exhibit parallax shift?

Answer 5

Parallax: is the apparent shift in a position of a nearby object against a background of more distance objects

• The apparent positions of the nearest stars shift by about an arcsecond as the Earth orbits the Sun
• More distant stars shift even less than closer stars

Question 6

How can we use parallax shift to measure the distance to a star?

give the formula

Answer 6

d (in light years) = 3.26 x 1/p(in arcseconds)

Question 7

Define: the parallax angle, parsecs

define parasecs and connect the rest of the terms

Answer 7

Parsecs: a unit of difference, if there was a star and its parallax shift was one arc second (shifts a tiny angle), it would be at a distance that we define as a parsecs

Question 8

What is the range in largest possible stellar luminosity? What is the smallest?

Answer 8

• Most luminous stars: 10^6 LSun
• Least luminous stars: 10^−4 LSun

Question 9

What does the word ‘spectra mean? What is the electromagnetic spectrum?

Answer 9

• to describe the rainbow of colours in visible light after passing through a prism
  it has come to apply to the entire electromagnetic spectrum

Question 10

How do we measure stellar temperatures? How is this related to thermal radiation?

Answer 10

• Every object emits thermal radiation with a spectrum that depends on temperature

1. Hotter objects emit more light per unit area at all frequencies
2. Hotter objects emit photons with a higher average energy

Question 11

What temperature is the hottest possible star? What is the coolest?

Answer 11

Hottest stars: 50,000 K (gives off most ultra violet light)
Least luminous stars: 3000 K (gives off most infared light)

Question 12

What is an absorption line? What is an emission line? How do these relate to the specific atom doing the absorption/emitting?

Answer 12

• An atom can absorb or emit one photon (light) depending on its type and state

Absorption line: some material has absorbed photons at a wavelength in the spectrum
Emission lines: some material is emitting photons at a wavelength in the spectrum

Question 13

How does temperature affect a spectra’s emission or absorption lines?

Hint: what do the lowest vs. the highest temperatures create?

Answer 13

The level of ionization also reveals a star’s temperature

• Lowest temperature - element are more solid (molecules, neutral metals)
• Highest temperature - elements are more gas/plasma (ionized helium, neutral helium, hydrogen)

Question 14

How would you define ‘spectral type’ when referring to stars? What are the 7 different spectral types? What is the order of these spectral types in descending temperature?

Answer 14

(Hottest) O, B, A, F, K, G, M (Coldest)
○ Only Bold Astronomers Fight Green Killer Martians

Question 15

How would you measure the mass of a star? Hint: you need Kepler’s 3rd law
Also, what does mass determine about a Star?

state the law and what are the three observables to get mass

Answer 15

• Mass is the key factor that determines a star’s life

Kepler’s 3rd law:
More distant planets orbit the Sun at slower average speeds, obeying the relationship
* More distant orbits have longer periods.

(Only need two out of the three)
1. Orbital period (p)
2. Orbital separation (a or r=radius)
3. Orbital velocity (v)

Question 16

What are Eclipsing Binaries? Spectroscopic binaries

Answer 16

Eclipsing Binary: binary star system in which the orbital plane of the two stars lies so nearly in the line of sight of the observer

• one star moving infront of the other star in relation to the observer

Spectroscopic Binary: two close stars moving in an orbit

• determine the orbit by measuring Doppler shifts
• spectrum can be blushifted or redshifted depending on direction

Question 17

What’s the most massive star that can exist? Why can’t it get larger?
What’s the least massive star that can exist? Why can’t it get smaller?

Answer 17

Most massive stars
* 100MSun
* their luminosity is so great that the radiation pressure prevents the accretion of further mass

Least Massive stars:
0.08 MSun
* Brown dwarfs (failed stars, not star nor planet) are not massive enough to build up the pressure in the central regions to allow nuclear fusion of hydrogen into helium

Question 18

What is the HR diagram? What is the main sequence?

Answer 18

• An H-R diagram plots the luminosities and temperatures of stars
• Most stars fall somewhere on the main sequence of the H-R diagram (where fusion occurs)

Question 19

What role does mass play in the luminosity and temperature of a star? What about the how long the star lives? How are these represented on the HR diagram?

Luminosity, size, colour, and lifetimes of high & low mass stars

Answer 19

Generally:
Smaller mass stars are cooler and dim, red
○ Live longer
Larger mass stars are hotter and brighter, blue
○ Shorter life

Question 20

WHY is mass the property of a star that ultimately determines temperature, luminosity, and lifetime?

describe the effects of a high mass star

Answer 20

The more massive the star, the hotter it is inside

At higher temperatures in the core, the nuclear fusion reactions generate **energy much faster ** (more luminous)
- the faster it burns, therefore **shorter the lifetime **

Question 21

What are giants/super giants? What are white dwarfs? Are they on the main sequence? Why or Why not?

Answer 21

Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence

• All stars become larger and redder after exhausting their core hydrogen: **giants and supergiants **
• (low-mass) Most stars end up small and white after fusion has ceased: white dwarfs

Question 22

Compare open clusters vs globular clusters

Answer 22

Open Clusters
* Young stars
* Bright blue stars
* Thousands of stars
* In milky arms
Irregularly shaped

Globular Clusters
* Old stars
* Bright red stars
* Millions of stars
* In milky way Halo and bulge
Symmetrical (circular ball of stars)

Question 23

What is the significance of the main sequence turn-off?

Answer 23

• Massive blue stars die first, followed by white, yellow, orange, and red stars
• The main sequence turnoff point of a cluster tells us its age
  (because each star(s) mass has its own lifetime and clusters do too since they’re primarily one type of star)

Question 24

What is luminosity? What does the LSun mean?

Explain meaning: Sirius can be written as 25 LSun

Answer 24

Luminosity: the total amount of energy at all wavelengths that it emits per second

Ex. the luminosity of Sirius is about 25 times that of the Sun. Use the symbol LSun to denote the Sun’s luminosity; Sirius can be written as 25 LSun

Question 25

What is the magnitude scale? Where did it originate?

(because the sun is closer!)

Hint: Sun has around a -25 apparent mag. and Sirius has around -1 mag.

Answer 25

Photometry: The process of measuring the apparent brightness of stars - founded by Hipparchus
He sorted the stars into six brightness categories, each of which he called a magnitude

• the larger the magnitude, the fainter the object you are observing.

Question 26

Why are negative apparent magnitudes possible?

Answer 26

Measurements showed that we receive about 100 times more light from a first-magnitude star than from a sixth-magnitude star.

Question 27

How does colour relate to approximate temperature of a star?

Answer 27

Blue colors dominate the visible light output of very hot stars and Red colours dominate the visible light output of cool stars

Question 28

What is the primary reason stellar spectra look different?

Answer 28

The primary reason that stellar spectra look different is because the stars have different temperatures

Question 29

Why don’t we see hydrogen absorption lines in the spectra of BOTH the hottest and coldest stars?

Answer 29

• In the atmospheres of the hottest stars,** hydrogen atoms** are completely ionized. Because the electron and the proton are separated, ionized hydrogen cannot produce absorption lines.
• In the atmospheres of the coolest stars, hydrogen atoms have their electrons attached and can switch energy levels to produce lines. However, practically all of the hydrogen atoms are in the lowest energy state (unexcited) in these stars and thus have to absorb enough photons to lift itself (which doesn’t really happen, cannot produce absorb. lines)

Question 30

Who was Annie Jump Canon?

Answer 30

Annie Jump Cannon revised the star classification system, focusing on just a few letters from the original system: A, B, F, G, K, M, and O.

Question 31

What type of star has the strongest hydrogen absorption lines? The strongest neutral helium lines? What about absorption lines from molecules?

Answer 31

Strongest hydrogen absorption lines: A Star
The strongest neutral helium lines: B Star
Absorption lines from molecules: M Star

Question 32

What is a brown dwarf?

Answer 32

Brown dwarf: objects even cooler than M9-type stars; has a mass intermediate between stars and planets; can’t become hot enough for hydrogen fusion to take place; extremely faint and cool

Question 33

When was the first brown dwarf discovered?

Answer 33

The first brown dwarf was discovered in 1988

Question 34

What is the difference between a low-mass brown dwarf and a high-mass planet?

Answer 34

• The International Astronomical Union considers the distinctive feature to be deuterium fusion.

Although brown dwarfs do not sustain regular (proton-proton) hydrogen fusion, they are capable of fusing deuterium (a rare form of hydrogen with one proton and one neutron in its nucleus).

Question 35

How much more massive would Jupiter have to be to be considered a brown dwarf?

trick question

Answer 35

• If an object has enough mass to fuse deuterium (about 13 MJ ), it is a brown dwarf.

Question 36

Within 21 light-years of Earth, how many more M stars are there than A stars?

Answer 36

94 - M stars ( most common)
2 - A Stars (least common)

Question 37

Is the Sun more massive or less massive than the vast majority of stars?

Answer 37

Sun - G Star, therefore more massive
compared to 94 - M Stars

Question 38

About half of stars are in binary systems. Why is this important for measuring masses? Be able to describe the importance of Newton’s version of Kepler’s 3rd law

state both laws

Answer 38

Kepler’s 3rd Law:
* More distant orbits have longer periods.

Newton:
* any two objects orbiting a common center of mass

In our binary star situation, if two objects are in mutual revolution, then the period (P) with which they go around each other is related to the **semimajor axis **(D) of the orbit of one with respect to the other (relates to the common centre of mass)

Question 39

What is the difference between a “double star” and a true binary?

Answer 39

Astronomers call any pair of stars that appear to be close to each other in the sky double stars
True binary is when the stars are phsyically associated with each other

Question 40

What is a visual binary? Give an example of a visual binary system, and its discoverer.

Answer 40

Visual binary: A binary star system in which both of the stars can be seen with a telescope

One well-known binary star is Castor, located in the constellation of Gemini. By 1804, astronomer William Herschel

Question 41

What is a spectroscopic binary? Give an example of a spectroscopic binary system, and its discoverer.

Answer 41

Spectroscopic binary: is a star system that can only be seen as more than one star by looking at its spectrum

Edward C. Pickering discovered a second class of binary stars by examining the spectrum of Mizar stars

Question 42

What is the range of stellar masses possible, and why are there limits?

Answer 42

0.08 to 250 (or more) times the mass of the Sun

Question 43

What is the Mass-Luminosity Relation in stars?

Answer 43

Mass-luminosity relation: The more massive stars are generally also the more luminous.
There is a positive relationship

Question 44

Describe in detail the technique used to measure the
following characteristics of stars: surface temperature, chemical composition, luminosity, radial velocity, and mass

Answer 44

Surface temperature - determine the colour and the measure the spectrum to get spectral type

Chemical composition - determine which lines are present in the spectrum

Luminosity - measure the apparent brightness and distance

Mass - measure the period and radical velocity curves of the spectroscopic binary stars

Question 45

What are white dwarfs? Describe their characteristics on the H-R diagram

high temp and high luminosity… But how then can the overall star be dim?

Answer 45

• White dwarfs: stars that have a very small total surface area
  Less area to emit a lot of light