The Cosmic Distance Scale Laura A. Whitlock / Sonoma State U Rohnert Park, CA.

The Cosmic Distance Scale

Laura A. Whitlock / Sonoma State U Rohnert Park, CA

Outline

A quick review of notation and unitsAn examination of Distance

• Measuring inside our solar system• Measuring to “nearby” stars• Measuring distant objects• Measuring the Universe

Remember: Big or small, numbers are given meaning in our Universe!

Quick Review of Scientific Notation

Powers of Ten

Scientific Notation• 10n means 10 x 10 x 10 x 10 … [n times]• 10-n means 1/(10 x 10 x 10 ….) [n times]

There are 1010 – 1011 stars in our Galaxy, and a similar number of galaxies in the Universe

And remember...

To Multiply & Divide

10a •10b = 10 a + b

10a ÷10b = 10 a - b

How Many Grains of Sand?If Earth were made of sand, would it contain more or less than a googol

(10100) grains of sand?

Draw a 1 cm segment. Mark pencil points along the segment to get an estimate of the number of tightly packed grains of sand in 1 linear cm.

Calculate the number of grains of sand in 1 cubic km.

(Remember: 100 cm = 1 m , 1000 m = 1 km)

Earth’s radius is about 6400 km. Use the equation for the volume of a sphere {V = (4/3)r3} to calculate the number of grains in a sandy Earth.

A Quick Tour from the Unimaginably Tiny to the

Incomprehensibly Big

QuickTime™ and aIntel Indeo® Video R3.2 decompressor

are needed to see this picture.

…an oldie, but a goodie!

Units for Time and Distance

Kilometer (km) = .621 miles

Light-year (lt-yr) = The distance light travels in one year in a vacuum.

1 lt-yr = 9.5 x 1012 km

Parsec = 3.3 light-years (Mpc = 1,000 pc)

arc-second = (1 degree/3600)

Radar (the replacement method for Kepler’s Law, P2 ~ a3)

Parallax

Cepheid Period/Luminosity Relationship

Supernovae

Redshift and Hubble’s Law

Radar Measurements• Beam travels at speed of light, c

• Measure the time it takes beam to leave Earth, bounce off planet (or whatever), and return to Earth.This represents the time for the beam, traveling at c, to cover twice the distance between Earth and the target object.

2d = c t

d = ct/2d

But...

Radar techniques are only feasible for objects inside our solar system.

The Nearest Stars

Distance to Alpha or Proxima Centauri is~4 x 1013 km(~4.2 light-years)

Distance between Alpha and Proxima Centauri is ~23 AU

The Solar Neighborhood

Some stars are within about

2 x 1014 km(~ 20 light-years)

Distances to Nearby Stars

Parallax : determined by the change of position of a nearby star with respect to the distant stars, as seen from the Earth at two different times separated by 6 months.

ParallaxGold standard for astronomical distances. It is based on measuring two angles and the included side of a triangle

The parallax of a star is one-half the angle

Astronomers usually say the Earth-Sun distance is 1 astronomical unit, where 1 au = 1.5x1013 cm, and measure small angles in arc-seconds. Arc-seconds are often denoted by , just like inches. But don’t be confused!

parallax angleD = Earth-Sun distance

parallax

Approximation!

Historical Note

The first stellar parallax (of the star 61 Cygni) was measured by Friedrich Wilhelm Bessel (1784-1846) in 1838. Bessel is also known for the Bessel functions in mathematical physics.

Parallax

Parallax to Proxima Centauri

is only0.76

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So...

Only the nearest stars to us have a measurable parallax.

CepheidsCepheid variable stars are pulsating stars, named after the brightest member of the class, Delta Cephei.

Cepheids are brightest when they are hottest, close to the minimum size. Since all Cepheids are about the same temperature, the size of a Cepheid determines its luminosity.

Thus there is a period-brightness relationship for Cepheids.

Since it is easy to measure the period of a variable star and they can be very bright, Cepheids are wonderful for determining distances to galaxies!

Cepheid VariablesHenrietta Leavitt studied variable stars that were all at the same distance (in the LMC or SMC) and found that their pulsation periods were related to their brightnesses

L =K P1.3

Polaris (the North Star)

is not constant, it

is a Cepheid variable!

Distances to CepheidsDistance to closest Cepheid (Delta Cephei) in our Galaxy can be found using parallax measurements. This determines K in the period-luminosity relation (L = KP1. 3)

Since the period of a Cepheid is related to its absolute brightness, if you observe its period and the apparent brightness, you can then derive its distance (to within about 10%)

Apparent Brightness =

Absolute Brightness

4 distance2

If no Cepheids can be seen...

Life Cycles of Stars

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Supernova…Going out with a Blast!

Crab Nebula

Observed by Chinese astronomers in 1054 AD

Age determined by tracing back exploding filaments

Crab pulsar emits 30 pulses per second at all wavelengths from radio to TeV

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Crab Nebula

Radio/VLA Infrared/Keck

Crab Nebula

Optical/HST WFPC2Optical/Palomar

Crab Nebula and Pulsar

X-ray/Chandra

Distances to Supernovae

Supernova 1987A in LMC

D = 47 kpc

Brightest SN in modern times, occurred at t0

Measure angular diameter of ring,

Measure times when top and bottom of ring light up, t2 and t1

Ring radius is given by R = c(t1-t0 + t2-t0)/2

Distance = R /

Distances to Supernovae

Type Ia supernovae are “standard candles”

Occur in a binary system in which a white dwarf star accretes beyond the 1.4 Mo limit and collapses and explodes

Decay time of light curve is correlated to absolute luminosity

Good to 20% as a distance measure

But to really “measure the Universe”...

Historical Note

Edwin Hubble discovered

that the Universe is expanding!

What Hubble Found

Compared to modern measurements, Hubble’s

results were off by afactor of ten!

The Hubble constant

Ho = 558 km s -1 Mpc -1

is the slope of these graphs

Hubble’s Law

v = Ho * d Ho is called the Hubble constant. It is generally believed to be around 65 km/sec/Mpc…plus or minus about 10 km/sec/Mpc.

Note: The further away you are, the faster you are moving!

Implications of Hubble’s Law

To get a rough idea of how far away a very distant object is from Earth, all we need to know is the object's velocity.

The velocity is relatively easy for us to measure using the Doppler effect,or Doppler shift.

Distance = velocity/(Hubble constant)

Doppler Shift

Wavelength is shorter when approaching

Stationary waves

Wavelength is longer when receding

What It Looks Like

Comparison of laboratory to blue-shifted object

Comparison of laboratory to red-shifted object

Doppler Shift / Redshift

Redshift, z, is a non-relativistic approximation to the Doppler shift

=

vc

=z =

Hubble’s Law Revisited

v = Ho d = cz

where v = velocity from spectral line measurementsd = distance to objectHo = Hubble constant in km s-1 Mpc -1 z is the redshift

Space between the galaxies expands while galaxies stay

the same size

ExampleA certain absorption line that is found at 5000Å in the lab is found at 5050Å when analyzing the spectrum of a particular galaxy. We then conclude that this galaxy is moving with a velocity v = (50/5000) * c = 3000 km/sec away from us.

Putting it altogether now, if the object is moving away from us at 3000 km/ sec, its distance from us (according to the Hubble’s Law) is

d = v/Ho = 3000/65 = 46 Mpc or 1.4 x 108 light-years

And so the Universe is...

v = H0d and d =vt

Solving for t, we find the age of the Universe is:

t ~ 1/H0

If H0 = 65 km/s/Mpc, then the age of the Universe is

~ 16 x 109 yr or 16 billion years

Books and Slides

Mitton, Jacqueline and Mitton, Simon, Scholastic Encyclopedia of Space, Scholastic Inc., 1998.

Fraknoi, Andrew, A Grand Tour of the Universe Slide Set, Astronomical Society of the Pacific.

Videos Powers of Ten: $39.95 through the Astronomical Society of the Pacific

Catalog. http://www.aspsky.org/catalog/vt110.html

or

write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112

Cosmic Voyage: $29.95 through the Astronomical Society of the Pacific Catalog. http://www.aspsky.org/catalog

or

write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112

Web Cosmic Distance Ladder – 3 labs -

http://www.astro.washington.edu/labs/Distance_Ladder.html

Extragalactic Cosmic Distance Scale -

ttp://www.uq.edu.au/~phjross/ph227/galaxy/candles.htm

Cosmic Distance Ladder I: Parallax - http://209.52.189.2/article.cfm/astronomy/11999

Cosmic Distance Ladder II – Stars as Standard Candles -

http://209.52.189.2/article.cfm/astronomy/13217

More Web Seeing is Believing! – Determining the Distance to Venus

http://www.amtsgym-sdbg.dk/as/venus/ven-dist.htm

Stellar Parallax Lab

http://einstein.uhh.hawaii.edu/spacegrant/lab2/lab2.html

More Web

Cosmic Distance Scale

http://csep10.phys.utk.edu/astr162/lect/cosmology/cosmicd.html

Cepheid Variables and the Cosmic Distance Scale Lab

http://einstein.uhh.hawaii.edu/spacegrant/lab4/lab4.html

Wrap Up…at long last!

Presentation will appear at http://perry.sonoma.edu/nbsp/materials/

distances.html

The Cosmic Distance Scale Laura A. Whitlock / Sonoma State U Rohnert Park, CA.

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