Distance Ladder

Pre-class ProblemYou stand are looking

at “famous local landmark” from two positions on either side of the “other famous local place”. You see that it moves relative to more distant landmarks. The angle it moves through is X degrees. Work out the distance between the two landmarks.

Unit Learning Goals

Understand 3 different ways astronomers measure distances in the Universe

- parallax- variable stars- Type Ia supernovae

Understand some of the techniques used by astronomers to study the accelerating Universe and Dark Energy

Lecture 1Understand “astronomical triangulation” – the

parallax method

Calculate a parsec – an important quantity for astronomers

Understand Cepheid variables

Know the methods and limits of both methods

Homework: problems plus research on RRLyrae stars

Pre-class ProblemYou stand are looking

at “famous local landmark” from two positions on either side of the “other famous local place”. You see that it moves relative to more distant landmarks. The angle it moves through is X degrees. Work out the distance between the two landmarks.

Parallax Method

Eyes Finger Distant Objects

Parallax Method1. Star appears at B2. Star appears at A

Observation 6 months apart on opposite sides of the Sun shows a nearby star moving relative to the more distant stars

Parallax MethodFrom trig we know:

For small angles using radians

Therefore we can measure the distance to the star if we know the angle

1AU

Aside on Angles

x

QuestionQuick question: what would you see at 1 and 2?

What would you see at position 3?

A B

1 2

3

Distant Stars

C D

ParsecDistance for which the

parallax angle is 1 arcsecond

What is the angular change on the sky?

Calculate a parsec in:meters, AU, lightyears

Input into Google Dochttp://tinyurl.com/cu569uj

Earth – Sun distance = 1.5x1011m1ly = 3x108m/s x 60 x 60 x 24 x 365.25

Homework Question:Distance to nearest stars

1. Barnard’s star is 1.83pc away, what is its parallax angle? What is the change in position on the sky? Its apparent magnitude in V is 9.54, what is its absolute magnitude? What does that tell you about the star? Where is it on an HR diagram?

2. What does the parallax method assume about the motions of stars in our Galaxy relative to the Sun? What is proper motion?

Remember to draw diagrams, label quantities you use and show all the steps in your workings

Homework Question:Hipparcos (1989) and Gaia (2013) are 2 satellites for

measuring distances using parallax. Why are astronomers going into space for these measurements?

Using the information below, explain why Gaia will be a great improvement on the Hipparcos catalogue

For giant stars (M=0), Sun-type stars (M=4.8) and red dwarfs (M=11) what is the maximum distance in pc that Hipparcos and Gaia will provide?. The Milky Way is 16 kpc in size; what does this tell you about the mission?

Why will Gaia help in the study of binary stars?Limiting mag Position

accuracy

Hipparcos 12.4 0.002 arcsec

Gaia 20 200 micro-arcsec

Variable StarsWe can see

these in external galaxies

RRLyrae stars on homework

Cepheid variablesin class

Cepheid VariablesLuminous variable star

Period relates to luminosity

You have all seen a Cepheid variable star!

Which has the brightestabsolute magnitude?

Which has the dimmestabsolute magnitude?

What do we know abouttheir apparent magnitudes?

A

B

C

D

Homework Question:Sketch an HR diagram with a main sequence.

Show the region where you’d find Cepheids.

Hubble measured Cepheids in external galaxies. This is one of his graphs. Measure the periods and get luminosities for the stars

Homework QuestionResearch RR Lyrae stars.

Summarize: what type of star they are; the relationship that allows them to be used as distance indicators; including a lightcurve sketch; what luminosity/distance range they can be used for; how their use compares to Cepheids. Add them to your HR diagram along with the Cepheids.

Class SummaryDescribed the parallax method

For nearby stars we can measure their positions 6 months apart and use that to get their distances

Use Cepheid variables to measure distances to external galaxiesEvolved starsRelationship between the period of their brightness change and luminosity

Lecture 1 Recap

Measuring distances in the Universe is difficult

Parallax method for nearby stars

Cepheid and RR Lyra star variables are visible in external galaxies

Can only get to nearby galaxies

Lecture 2Understand Type Ia supernovae which are a

probe for the most distant universe

Study of SNe Ia lead to the discovery of dark energy

Homework: group project to summarise other techniques to characterise dark energy

Type Ia SupernovaeCan shine brighter than

a galaxy for a couple of months

See them across vast distances: most distant z=1.9.

One of the most powerful tools in cosmology

What are SNe Ia?Still an active area of research

White dwarf star reaches about 1.4M and explodes

Two competing theories: one, the other, or both?

How Do We Do Cosmology?

Same mass = same energy

Same energy = same absolute magnitude

We can use their apparent magnitude to measure their distance modulus which is related to distance

d tells us about the content of the universe – matter, radiation etc

Questions1. I observe a Type Ia supernova at magnitude 18.

Its absolute magnitude is -19.3. What distance away is it?

A 29 Mpc B 290 kpc C 290Mpc D 2900 Mpc`

2. A Typa Ia supernova goes off in the LMC (50 kpc) away. Will it be observable with the naked eye? A Yes B No

Supernova CosmologyNot all supernovae

have exactly the same brightness. Mark Phillips in 1993 found a way round this.

Make a correction to the peak magnitude based on the width of the lightcurve

Supernova Cosmologyd depends on the

matter/energy content of the universe

Too much energy and it expands forever. Not enough and it collapses in on itself.

Use observations of the SNe to “weigh” the universe

Discovery of Dark EnergyIn 1990s, 2 groups were using supernovae to populate these diagrams

They were really surprised that supernovae were fainter than they should have been in the distance universe

This means the universe must have been expanding faster in recent cosmic times than in the past

Velocity

Dis

tance Where the SN

should have been

Where are we now?

Many more supernovae to measure the distances in the universe

Much more precise understanding of what the universe is made of.

Limits for SN CosmologyWe need to understand more about the SN

explosions

Limited by our understanding of simple things like a galaxy calibration star, or the spectrum of our filters

Getting to 1% precision on measurements is going to be a bit challenge

new surveys in the local universe

Does dark energy vary with time? More distant supernovae will tell us. How do we get the data?

Future Projects

WFIRST – NASA IR space missionWill find distant supernovae for cosmology

LSST – 8m survey telescopeWill find thousands of transientsper night

Group Homework Get into groups of 4

Read the article http://onlinelibrary.wiley.com/doi/10.1111/j.1468-4004.2006.47420.x/abstract

Each person makes notes for the rest of the group on one of the topics: ISW, weak lensing, baryon acoustic oscillations, cluster counts

Theory behind the technique, measurements made, current and future projects etc…

Next week you will compare notes and EVERY PERSON will submit THEIR OWN summary article of the tools to measure dark energy plus whatever notes they provided the rest of the group

You will submit a brief report on the contributions of other members of your group as well as self-assessment