Chapter 12 - Galaxy Distances and Hubble's Law

Measuring Cosmic Distances

• We measure distances using a chain of interdependent techniques:
- Radar Ranging
- Parallax
- Standard Candles
- Main-Sequence Fitting
- Cepheid Variables
- Distant Standard Candles
- Hubble's Law

Radar Ranging

• Radio waves are transmitted from Earth, and bounce off Venus
• Radio waves travel at the speed of light
• We can calculate the distance from the round-trip travel time
• Good within a couple of AU

Stellar Parallax

d (in parsecs) = 1 / p (in arcseconds)

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

Standard Candles

• Almost all astronomical objects used as physical distance indicators belong to a class that has a known luminosity
• By comparing this known luminosity to an object's observed brightness, the distance to the object can be computed using the inverse-square law

Main-Sequence Fitting

• Idea: use the entire main sequence as a standard candle
• Because all main-sequence stars of a particular spectral type should have about the same luminosity, we can use the apparent brightness of a star cluster's main sequence to calculate the distance

Cepheid Variables

• Any star that varies significantly in brightness with time is called a variable star
• Some stars vary in brightness because they cannot achieve proper balance between power welling up from the core and power radiated from the surface
• Such a star alternately expands and contracts, varying in brightness as it tries to find a balance

Cepheid Variable Stars

• Most pulsating variable stars inhabit an instability strip on the H-R diagram.
• The most luminous ones are known as Cepheid variables.
• All Cepheid variables of a particular period have about the same luminosity
- By measuring the period, we can determine the luminosity and thus the distance

Distant Standard Candles

• Idea: using white dwarf supernovae as standard candles
• Should have nearly the same luminosity because they result from an exploding white dwarf which has reached 1.4M_sun mass limit
• Rare in each individual galaxy, but several have been detected in galaxies within about 50 million l.y. from the Milky Way
• About 10 billion solar luminosities at their peak
• The apparent brightness of a white dwarf supernova tells us the distance to its galaxy (up to 10 billion light-years)

Milky Way vs the Universe

• 1920, The Great Debate was a National Academy of Sciences gathering to argue the nature of the Milky Way
- Is the Milky Way the entire universe and the other "spiral nebulae" are inside the Milky Way?
- Is the Milky Way just one of the galaxies in the universe, and the "spiral nebulae" are other galaxies that are outside of the Milky Way?
• Before Hubble, some scientists argued that "spiral nebulae" were entire galaxies like our Milky Way, while others maintained they were smaller collections of stars within the Milky Way
• The debate remained unsettled until Edwin Hubble finally measured their distances

Hubble's Discovery

• Hubble used a 100 inch telescope (largest at the time) to see what looked like individual stars in Andromeda that had a variable brightness
• The distance to these Cepheid variables in Andromeda is further than any star in the Milky Way, so Andromeda had to be a separate galaxy
• Hubble settled the debate by measuring the distance to the Andromeda Galaxy using Cepheid variables as standard candles

Galactic Redshift

The spectral features of virtually all galaxies are redshifted, which means that they're all moving away from us

Hubble's Law

• In 1929, by matching the distances of galaxies with the spectrum, Hubble found that the more distant a galaxy, the more redshifted its spectrum
• The more distant the galaxy, the faster it moves away from us
• Hubble's Law: velocity = H0*distance
• The velocity is the speed at which the galaxy is moving away from us
• H0 is Hubble's Constant
- H0≈ 22 km/s per million light years
• Today, Hubble's Law is the most useful technique for determining the distance to the far away galaxies

How does Hubble's Law tell us the age of the universe?

• The expansion rate appears to be the same everywhere in space
• The universe has no center and no edge (as far as we can tell)

Expansion of the Universe

• One example of something that expands but has no center or edge is the surface of a balloon
• Expansion stretches photon wavelengths, causing a cosmological redshiftdirectly related to lookback time.

Reminder: How do galaxies move within the Universe?

• Edwin Hubble discovered that galaxies are carried along with the expansion of the universe
• But how did Hubble figure out that the universe is expanding?
- All galaxies outside our Local Group are moving away from us.
- The more distant the galaxy, the faster it is racing away.

Cosmological Principle

- The universe looks about the same no matter where you are within it.
• Matter is evenly distributed on very large scales in the universe.
• It has no center or edges.
• The cosmological principle has not been proven beyond a doubt, but it is consistent with all observations to date.

How does expansion affect distance measurements?

• Distances between faraway galaxies change while light travels
• Astronomers think in terms of lookback timerather than distance
• The Cosmological Horizonmarks the limits of the observable universe.
• It is a horizon in time rather than space. Since looking far away means looking back in time, there must be a limit -the beginning of the universe!

How does Hubble's Law tell us the age of the universe?.

• Hubble's constant tells us the age of universe because it relates the velocities and distances of all galaxies
Age = Distance / Velocity ~ 1/H0
• Looking at further galaxies is the same as looking further back in time

Which kind of stars are best for measuring large distances?
A. high-luminosity stars
B. low-luminosity stars

A. high-luminosity stars

Your friend leaves your house. She later calls you on her cell phone, saying that she's been driving at 60 miles an hour directly away from you the whole time and is now 60 miles away. How long has she been gone?
A. 1 minute
B. 30 minutes
C. 60 minutes
D. 120 minutes

C. 60 minutes

You observe a galaxy moving away from you at 0.1 light-years per year, and it is now 1.4 billion light-years away from you. How long has it taken to get there?
A. 1 million years
B. 14 million years
C. 10 billion years
D. 14 billion years

D. 14 billion years

A standard candle is ________.

a light source of known luminosity

What is a Cepheid variable?

a type of very luminous star that makes an excellent standard candle

What two observable properties of a Cepheid variable are directly related to one another?

the period between its peaks of brightness and its luminosity

Given that white dwarf supernovae are such good standard candles, why don't we use them to measure the distance to all galaxies?

They are rare events, so we have observed them in only a tiny fraction of all galaxies.

If we say that a galaxy has a lookback time of 1 billion years, we mean that ________.

its light traveled through space for 1 billion years to reach us

Which of the following is an important starting assumption in models of galaxy formation?

Some regions in the universe start out denser than others.

Why are collisions between galaxies more likely than collisions between stars within a galaxy?

Relative to their sizes, galaxies are closer together than stars.

Using the technique of main-sequence fitting to determine the distance to a star cluster requires that ________.

we have telescopes powerful enough to allow us to identify the spectral types of main-sequence stars of many masses in the cluster

Suppose we observe a Cepheid variable in a distant galaxy. The Cepheid brightens and dims with a regular period of about 10 days. What can we learn from this observation?

We can learn the distance to the galaxy.

In 1924, Edwin Hubble proved that the Andromeda Galaxy lay far beyond the bounds of the Milky Way, thus putting to rest the idea that it might have been a cloud within our own galaxy. How was he able to prove this?

By observing individual Cepheid variable stars in Andromeda and applying the period-luminosity relation

Why are white dwarf supernovae more useful than massive star supernovae for measuring cosmic distances?

White dwarf supernovae all have roughly the same true peak luminosity, while massive supernovae come in a wide range of peak luminosities.

Does Hubble's law work well for galaxies in the Local Group? Why or why not?

No, because galaxies in the Local Group are gravitationally bound together.

What is the best way to determine a galaxy's redshift?

Take a spectrum of the galaxy, and measure the difference in wavelength of spectral lines from the wavelengths of those same lines as measured in the laboratory.

Which statement below correctly describes the relationship between expansion rate and age for the universe?

The faster the rate of expansion, the younger the age of the universe.

What does cosmological redshift do to light?

stretches its wavelength

Why can't we see past the cosmological horizon?

Beyond the cosmological horizon, we would be looking back to a time before the universe was born.

We can study how galaxies evolve because ________.

the farther away we look, the further back in time we see

Interactions among galaxies also are thought to influence a galaxy's type in at least some cases. Which of the following does not support the idea that interactions can shape galaxies?

the fact that more distant galaxies have larger redshifts

Why are Cepheid variables important?

Cepheids variables are pulsating stars whose pulsation periods are directly related to their true luminosities. Therefore they can be used as distance indicators.

How do astronomers use the Hubble Constant (H0) to estimate the age of the universe?

The inverse of H0 is the approximate age of the universe.

Based on current estimates of the value of Hubble's constant, how old is the universe?

12 to 15 billion years old

How do observations of galaxies at different distances help us learn about galaxy evolution?

Observations of different distances show galaxies of different ages and therefore different stages of evolution.

Which of these galaxies is most likely to be oldest?

a galaxy in the Local Group

Which set of star-position measurements is most likely to show the largest parallax shift for nearby stars?

measurements made 6 months apart

Which kind of object is the best standard candle for measuring distances to extremely distant galaxies?

a white dwarf supernova

When the ultraviolet light from hot stars in very distant galaxies finally reaches us, it arrives at Earth in the form of

visible or infrared light.

Why do virtually all the galaxies in the universe appear to be moving away from our own?

because observers in all galaxies see a similar phenomenon due to the universe's expansion

When we observe a distant galaxy whose photons have traveled for 10 billion years before reaching Earth, we are seeing that galaxy as it was when the universe was about

4 billion years old.

When we observe a distant galaxy whose photons have traveled for 10 billion years before reaching Earth, we are seeing that galaxy as it was when the universe was

4 billion years old.

The most distant galaxies that astronomers have observed are much easier to see in infrared light than in visible light. Explain why that is the case.

Since our universe is expanding away from us, the light wavelengths are red-shifted, which means light is shifted towards the infrared portion of the spectrum. With time, the wavelengths of light become longer and come off as redder, making it easier to see them with infrared.

The following diagrams represent a balloon analogy for the expansion of the universe. Each diagram shows two balloons: The small pink balloon represents the universe at an early time and the large red balloon represents the universe at some later time. The black dot on each balloon represents a galaxy. Rank the diagrams based on how much the galaxy has expanded in size (due to the overall universal expansion) from the early time to the later time in each case, from most expansion to least expansion. If you think that two (or more) of the diagrams show galaxies that have expanded by the same proportion, indicate this equality by dragging one diagram on top of the other(s).

all balloons in center (on top of each other) because galaxies aren't expanding

The following diagrams are similar to those in Part A, except this time each one shows two galaxies: "your galaxy" and a second galaxy. Rank the diagrams based on how far the second galaxy has moved away from your galaxy due to expansion of the universe between the early time and the later time, starting at the left with the one that has moved the largest distance and moving to the one that has moved the smallest distance at the right.

Largest distance are the dots farthest apart to dots closest together (smallest)

The following diagrams are similar to those from Part B, with each diagram showing the position of "your galaxy" and another galaxy at an early and later time in the history of the universe. Rank the diagrams based on the speed at which the other galaxy is moving away from your galaxy as the universe expands, from fastest to slowest.

fastest are the dots farthest apart to dots closest together (slowest)

The following diagrams are similar to those from parts B and C, with each diagram showing the position of "your galaxy" and another galaxy at an early and later time in the history of the universe. In this case, however, the location of the other galaxy can vary on which side of your galaxy it is from one diagram to another. Rank the diagrams based on the speed at which the other galaxy is moving away from your galaxy as the universe expands, from fastest to slowest. If two (or more) of the diagrams show galaxies moving at the same speed, show this equality by dragging one diagram on top of the other(s). (Hint: Notice that two of the diagrams show the galaxies separated by one distance and two of the diagrams show them separated by a different distance; that is, there are only two different distances shown among the four diagrams.)

The two with points farthest apart are fastest (on top of each other); and the two with points closest together are slowest (on top of each other)

Which of the following statements best describes what astronomers mean when they say that the universe is expanding?

The average distance between galaxies is increasing with time.

Note that an observer located at the Local Raisin would see Raisins 1, 2, and 3 all move away from her during the video. What would an observer located at Raisin 2 see?

Raisin 1 and Raisin 3 both move away from her.

The table in the video shows you the speeds of Raisins 1, 2, and 3 as measured from the Local Raisin. Suppose instead that you measured speeds as seen from Raisin 2. An observer at Raisin 2 would measure __________.

Local Raisin speed = 4.0 cm/hr; Raisin 1 speed = 2.0 cm/hr; Raisin 3 speed = 2.0 cm/hr

The following statements describe ways in which the analogy might apply to the real universe. Which statements are correct?

- The raisins stay roughly the same size as the cake expands, just as galaxies stay roughly the same size as the universe expands.
- An observer at any raisin sees more distant raisins moving away faster, just as an observer in any galaxy sees more distant galaxies moving away faster.
- The average distance increases with time both between raisins in the cake and between galaxies in the universe.

Based on what you've learned from the raisin cake analogy, which two properties of distant galaxies do astronomers have to measure to show that we live in an expanding universe?

their distances and speeds

Today, the evidence that we live in an expanding universe is extremely strong because astronomers have measured the motions of millions of galaxies. Nevertheless, in science, we must always remain open to the possibility that some future observation could call even our most strongly supported theories into question. Which of the following hypothetical observations would not be consistent with what we expect in an expanding universe?

You discover an extremely distant galaxy that is moving toward us.

Radar, the first link in the cosmic distance chain, is used to establish the baseline distance necessary for the second link, parallax. What baseline distance must we know before we can measure parallax?

the Earth-Sun distance

Which cosmic distance measurement techniques are considered standard candle techniques?

- main-sequence fitting
- white dwarf supernovae (distant standards)
- Cepheids

Suppose that Cepheids did not exist and there were no other standard candle technique that worked at the same distances. Which statement would be true?

We would not be able to measure the distances of distant galaxies.

Why do we use Hubble's law to estimate the distances of most distant galaxies, rather than using white dwarf supernovae in all cases?

We have not observed white dwarf supernovae in most galaxies.

Imagine that radar had never been invented and that we instead had to rely on a less reliable method of measuring distances in our solar system. If that method led us to underestimate the Earth-Sun distance by 10%, how would it affect other measurements in the distance chain?

They would all be off by the same 10%.

Which technique is the most useful for measuring the distance to a galaxy located 10 million light-years away?

Cepheids

Before we can use parallax to measure the distance to a nearby star, we first need to know __________.

the Earth-Sun distance

Which of the following is a valid way of demonstrating parallax for yourself?

Hold up your hand in front of your face, and alternately close your left and right eyes.

What is the cause of stellar parallax?

Earth's orbit around the Sun.

The more distant a star, the __________.

smaller its parallax angle

Approximately what is the parallax angle of a star that is 20 light-years away?

0.16 arcsecond

Suppose that a star had a parallax angle of exactly 1 arcsecond. Approximately how far away would it be, in light-years?

3.3 light-years

To get started, click on the blue Cepheids link on the main screen of the Interactive Figure. The Interactive Figure (in red) shows a graph of the Cepheid period-luminosity relation. This graph indicates that __________.

Cepheids with longer periods have higher luminosities

A Cepheid with a period of 30 days has an average luminosity that is about __________ times the luminosity of the Sun.

10,000

Next, click the label on the bottom of the Interactive Figure that reads Cepheids as Standard Candles to bring up the next screen. Read the instructions that appear in the upper left hand corner and study the animation.
What actually causes a Cepheid to vary in apparent brightness?

The Cepheid varies in radius, and its luminosity is greater when its radius is larger.

From here, click the Next button in the Interactive Figure to bring up the screen that shows a Cepheid light curve in the upper left.
What is the approximate luminosity of the Cepheid whose light curve is shown in the graph?

8000 LSun

Notice that the window with the light curve also has a box that tells you the average apparent brightness of the Cepheid, which shows a value of 1.3×104. (The units are shown in the box, but you only need to focus on the numerical value.) Based on this apparent brightness and the luminosity you found in Part D, what is the approximate distance to this Cepheid?

2 million light-years

Which of the following three-step processes correctly describes how we use Cepheids as a tool to make cosmic distance measurements?
In all cases, assume that the Cepheid's apparent brightness has been carefully measured through observations.

Step 1: Measure the period of the Cepheid's brightness variations.
Step 2: Use the period-luminosity relation to determine the Cepheid's luminosity.
Step 3: Calculate the Cepheid's distance from its luminosity and apparent brightness.

Hubble's law expresses a relationship between __________.

the distance of a galaxy and the speed at which it is moving away from us

We can always determine the recession velocity of a galaxy (at least in principle) from its redshift. But before we can use Hubble's law, we must first calibrate it by __________.

measuring the distances to many distant galaxies with a standard candle technique

Suppose that you measure a galaxy's redshift, and from the redshift you determine that its recession velocity is 30,000 (3×104) kilometers per second. According to Hubble's law, approximately how far away is the galaxy?

1.4 billion light-years

Based on what you have learned, which of the following best describes the meaning of Hubble's constant (H0 )?

It describes the expansion rate of the universe, with higher values meaning more rapid expansion.

Consider the following hypothetical observations, some of which are real and some of which are fictional. For each observation, your job is to answer this question: If the observation were real, would it provide evidence for or against the idea that the universe is expanding? Sort each observation into the appropriate bin as follows:
Place an observation in the "Supports the expanding universe" bin if it would provide evidence that the universe is expanding. Place an observation in the "Contradicts the expanding universe" bin if it would provide evidence that would force us to reconsider the idea of an expanding universe. Place an observation in the "Neither supports nor contradicts" bin if it does not allow us to distinguish between a universe that is expanding and a universe that is not expanding.

Supports the expanding universe
- All galaxies in the Coma cluster of galaxies have redshifted spectra.
- Galaxies 200 million light-years away move away from us twice as fast as galaxies 100 million light-years away.
- The measured rate of expansion is the same in all directions.

Contradicts the expanding universe
- Irregular galaxies outside the Local Group are moving toward us.
- Galaxy speeds are faster in summer than in winter.
- Spiral galaxies move away from us 10% faster than elliptical galaxies at the same distances.

Neither supports nor contradicts
- The Andromeda Galaxy, a member of our Local Group, is moving toward us.

Consider the hypothetical observation "Irregular galaxies outside the Local Group are moving toward us." From Part A, this observation would contradict the idea of an expanding universe. Why?

Because Hubble's law predicts that all galaxies outside our Local Group should be moving away from us.

Consider the observation "The Andromeda Galaxy, a member of our Local Group, is moving toward us." Why doesn't this observation contradict the idea that the universe is expanding?

Because the galaxies of the Local Group are gravitationally bound together

We can in principle measure the expansion rate by studying galaxies in many different directions in space and at different times of year. If we compare such observations, we would find that the expansion rate is __________.

the same no matter when or in which direction we measure it

You learned about the general concept of parallax in Chapter 2, and the video offers a review of the basic ideas. To check your understanding of the concept, which of the following is a valid way of demonstrating parallax for yourself?

Hold up your hand in front of your face, and alternately close your left and right eyes.

Which of the following makes it possible for us to observe stellar parallax (from Earth)?

Earth's orbit around the Sun

Compared to a nearer star, a more distant star will have a __________.

smaller parallax angle

Suppose there was a star with a parallax angle of 1 arcsecond. How far away would it be?

3.26 light-years

A star with a parallax angle of 0.1 arcsecond is ________ away from us.

32.6 light-years

A star with a parallax angle of 0.01 arcsecond is ________ away from us.

326 light-years

A star with a parallax angle of 0.001 arcsecond is ________ away from us.
3260 light-years

3260 light-years

A star with a parallax angle of 0.0001 arcsecond is ________ away from us.

32,600 light-years

The GAIA spacecraft is capable of measuring parallax angles as small as about 0.00002 arcsecond (20 microarcseconds). Based on this fact, GAIA should in principle be able to measure the distances of stars located __________.

throughout the Milky Way Galaxy, but not in the Andromeda galaxy or other more distant galaxies

If I measure the recession velocities of 2 galaxies and galaxy A has a velocity twice that of galaxy B, how far away is B if A is 100 Mpc away? (Remember that V = H0 x D)

50 Mpc

galaxy A:
2(galaxy B's V) = H0 x 100
galaxy B's V = H0 x 50

Why are Cepheid variable stars good distance indicators?

They have a set period - luminosity relationship

What would you expect to find in the Halo of the Milky Way Galaxy?

Globular Clusters

The three types of galaxies are called:

Elliptical, Spiral and Irregular.