Cosmic Distance Ladder

What’s Up There in the Universe

Measuring the Distances• There is no one single

method that works in all distance scales.

• Measuring the distance is a hard problem in astronomy.

• Infact there is succession of methods whose domain of validities overlap.

• Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

• We need to calibrate each method in the domain of overlap.

Distances of Planets

• Kepler’s third law give only the ratios of the distances:

• Although by the 17th century astronomers could calculate each planet's relative distance from the Sun in terms of the distance of the Earth from the Sun, an accurate absolute value of this distance had not been calculated.

P2=ka3

Astronomical Unit

• Astronomical Unit (AU): Average distance between the Earth and the Sun.

• Appropriate unit for giving distances in the Solar System.

• No constant of proportionality if P is measured in years and a is measured in AU.

P2=a3

Conjunction

Conjunction: two celestial bodies appear near one another in the sky. Mostly one of the objects is the Sun and the other is one of the planets

2004 Transit of Venus

• The duration of such transits is usually measured in hours (the transit of 2004 lasted six hours).

• occur in a pattern that repeats every 243 years, with pairs of transits eight years apart separated by long gaps of 121.5 years and 105.5 years.

Transit of Venus

• It does not occur very often because the plane of the orbit of the Earth is tilted by 3.4°.

Three consecutive days of close conjunction between the Moon and Venus.

Solar Paralax by Venus Transit

• The technique is to make precise observations of the slight difference in the time of either the start or the end of the transit from widely separated points on the Earth's surface.

• The distance between the points on the Earth can then be used as to calculate the distance to Venus and the Sun.

Measuring Venus transit times to determine solar parallax

AU

• The astronomical unit is precisely determined with the transit method.

• Also by radar ranging.• 1AU=150 Million km=1.51013 cm• The Earth is actually 147 104 753 km

away from the Sun on the 29th of December and 152 091 803 km away from the Sun on the 30th of June.

• The currently accepted value of the AU is 149 597 870 691 30 metres.

Distances of planets

• Once 1AU is determined, the distances of all planets can be found from Kepler’s third law.

• Actually not a law, an emprical relation that has to be explained by the underlying physics.

Distances of Stars

• How do we know the distances of stars?

• Parallax!

Stellar Parallax

• Different orbital positions of the Earth causes nearby stars to appear to move relative to the more distant stars.

• The annual parallax is defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun.

Parallax and distance• Only direct measure of distance astronomers

have for objects beyond solar system is parallax– Parallax: apparent motion of nearby stars against

background of very distant stars as Earth orbits the Sun

– Requires images of the same star at two different times of year separated by 6 months

Earth’s Orbit

Foreground star

“Background” star

Caution: NOT to scaleA

B (6 months later)

Apparent Position of ForegroundStar as seen from Location “B”

Apparent Position of ForegroundStar as seen from Location “A”

Parallax as a Measure of Distance

• P is the “parallax”• typically measured in arcseconds• Gives measure of distance from Earth to nearby star (distant stars

assumed to be an “infinite” distance away)

Image from “A” Image from “B” 6 months later

Background star P

Parsec

• The parsec is the distance for which the annual parallax is 1 arcsecond.

• A parsec equals 3.26 light years.

• Distance (in parsecs) is simply the reciprocal of the parallax angle (in arcseconds): d=1/p

Examples:

• Parallax angle = 0.5 arcsecond=>d=2 pc

• Proxima Centauri has a parallax of 0.771 arcsecond. This implies that its distance is d= 1.295 pc.

Example

• The Sun has a parallax of 90 degrees• Proxima Centauri has p=0.77233

thus it is at a distance of d=1.295 pc 

Bessel (1838)

• Successfully measured the parallax of the star 61 Cygni.

• This was considered as the conclusive evidence that the Earth was in motion.

Astronomical Angular “Yardsticks”

• Easy yardstick: your hand held at arms’ length– fist subtends angle of 5°– spread between extended index finger and thumb

15°

• Easy yardstick: the Moon– diameter of disk of Moon AND of Sun 0.5° = ½°½° ½ · 1/60 radian 1/100 radian 30 arcmin =

1800 arcsec

Distance Units

• Light Year (ly): the distance light can travel in one year = 9.46E17 cm=6.324X104 AU

• Parsec (pc) = 3.26 ly = 3.08X1018 cm• Astronomical Unit (AU) = 149.6E13

cm

Limits of Parallax Method

• Refraction caused by the atmosphere limits the accuracy to 0.01 arcseconds.

• d=1/p|d|=|p|/p2

• Reliable measurements, those with errors of 10% or less, can only be achieved at stellar distances of no more than about 100 pc.

• Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of ground-based observations.

• E.g. Hipparcos 0.001 arcseconds

Size of the Milky Way

Question:

• 100 pc is a small fraction of the size of the Galaxy (diameter 100.000 light years.)

• How do we know the distances of galaxies, clusters of galaxies etc if the parallax method does not work?

Great Debate (1920)

• Is the Galaxy the whole Universe?• Are the “spiral nebulae” other galaxies or

are they just gas clouds in the Galaxy?• A universe of stars or a universe of

galaxies?• Great Debate between Heber D. Curtis and

Harlow Shapley.• Even Einstein’s Universe (1916) was a

universe of stars.

Standard Candles

• A standard candle is an astronomical object that has a known luminosity.

• Luminosity=power (measured in Watts)• Or rather ergs/s (cgs system prefered

in astronomy).• Flux = Luminosity/4d2

• Measure the flux received on Earth and calculate the distance.

Woman Computers

A group of womencomputers a the Harvard CollegeObservatory circa 1890, directed byMrs. Williamina Fleming (standing).Photo credit: The Harvard CollegeObservatory

Cepheid Variables: A Standard Candle

• A cepheid variable is a young star of several solar masses and roughly 104L whose luminosity changes periodically.

• The period of a Cepheid variable is related to its intrinsic luminosity.

• Measuring the period of light fluctuations (easy) allows the object's absolute luminosity to be determined.

Cepheids as Variable Stars

Modern calibration of the Cepheid P-L relation in the Magellanic clouds, yields:

9.4)1(log96.2 PM I

here the period P is measured in days, and the magnitude is measured in the I band.

Henrietta Leavitt

• One of the woman computers at Harvard Observatory.

• Established of the period-luminosity relation for variable stars.

• Along with Annie Jump Cannon and Cecilia Payne-Gaposchkin, Leavitt represents an early generation of early female astronomers who, serving as astronomical “computers” doing meticulous and demanding work around the turn of the 20th Century, received little credit for their contributions until much later.

Photo Caption: Henrietta Leavitt at herdesk.Photo credit: The Harvard CollegeObservatory.

Through painstaking comparison of numerous photographic plates of the Magellanic Clouds, she identified thousands of variable stars.

Great Debate Solved (1924)

• Edwin Hubble determined a Cepheid Variable in Andromeda Galaxy.

• Used Leavitt’s method to find the distance.

• Andromeda is much distant than the estimated size of our galaxy!

Summary of Distance Ladder

Note that beyond the Virgo cluster, even very bright stars like Cepheidsbecome unresolved and we see only the integrated light from galaxies. Further away than this, we mustdetermine distances using the redshift of galaxies.

Some Elements of the Universe

Open Clusters• Few

thousand stars formed at the same time

• Gravitationally looselt bound

• Usually less than a few hundred million years old Pleiades Open Cluster

The Solar NeighborhoodThe 30 closest stars to the Sun:

Globular Clusters

• Spherical collection of stars

• Strongly bound by gravity

• Orbits the galactic core

• 150 currently known globular clusters in the Milky Way, with perhaps 10–20 more undiscovered

• Concentrated in the halo of the galaxy

• Old stars

Milky WayOur galaxy

Our Position in the Milky Way

Andromeda Galaxy:Our Neighbour

2.5 million light-years away

Local Group

A few million lightyears.

Galaxies do not stand alone.They are in groups

Abell

Super-Clusters

• Local group is a member of a supercluster called Virgo

• So galaxy clusters form superclusters.

Part of the Virgo super-cluster. Some 60 million lightyears.

Large Scale Structure• Large scale

structure is made up of superclusters.

• Each dot represents a supercluster.

• Superclusters form filaments and walls around voids.

Billions of lightyears.

Age of the Universe

The universe is about 13.7 Billion years old.

Spectrum