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Distance Measuring

Techniques and The Milky Way Galaxy

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Measuring distances to stars is one of the biggest

challenges in Astronomy.

If we had some standard “candle”, some star with a

known luminosity, then we could observe its apparent

magnitude, get a distance modulus and determine its

distance.

It turns out that there is a type of star that can be used

as a standard for measuring distance. This star type is

called a pulsating variable.

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Such stars are normal stars with varying luminosity.

They are not pulsars (which are neutron stars)

[and neutron “stars” are hot neutron spheres, not stars]

There are two main types of pulsating variables:

RR Lyrae and Cepheids.

These stars have varying luminosity because they are

not in hydrostatic equilibrium and their size varies

periodically.

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RR Lyrae and Cepheids in the “instability strip”after leaving the Main Sequence.

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RR Lyrae variables are normal stars of one solar

mass or less in size, averaging ~0.6 Msun.

After leaving the Main Sequence, becoming red giants,

and starting to burn helium, they go through about a

million year period of instability as they settle onto the

horizontal branch.

They all have pulsation periods of about one-half day

to one day.

They all have about the same peak luminosity which

makes them good prospects for “standard candles”.17

All RR Lyrae stars have approximately the same

peak luminosity ( ~100 times that of the Sun).

Once a star is identified as an RR Lyrae, its absolute

magnitude is known, and its distance can be

determined [ m – M = log(d) – 5 + A ]

Cepheids have luminosities that are proportional to

the length of their periods.

Longer periods correlate with higher luminosities.

Cepheids are 10 to 100 times brighter than RR Lyrae

stars.

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RR Lyrae stars are smallerstars with shorter periods.

A Cepheid variable star with a period of about 3 days.

A Cepheid showing minimumand maximum brightness in

this offset.

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Cepheids are larger normal stars, from about 3 to 18

solar masses.

These stars have evolved off of the Main Sequence

and have started burning helium in non-degenerate

cores.

They are not in hydrostatic equilibrium and are

unstable. Their photospheres expand and shrink.

Cepheids have a broader range of periods from about

one day to over three months.

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Relationship between luminosity and period

for Cepheids.22

By using the correlation between luminosity and

period, the period is determined and the absolute

magnitude (or luminosity) can be read from the graph.

The apparent magnitude is easily measured and,

using this with the absolute magnitude ( m - M), the

distance to the Cepheid variable can be determined.

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RR Lyrae variables have been an important part of

determining distances to other objects in our Milky

Way galaxy, and have helped to determine our

galaxy’s structure.

RR Lyrae variable stars are often found in globular

clusters and the distances to the globular clusters

have been determined using these stars.

Cepheid variables are bright enough to see them

not only in our galaxy, but in other galaxies, and

allow distance measurements as great as

~ 25 Mpc (Million [“Mega”] parsecs).

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Harlow Shapley used RR Lyrae variables to measure

the distance to globular clusters and was the first to

understand the true size and shape of the Milky Way

halo (announced in 1918).

About 150 globular clusters have been found, their

positions calculated, and their distribution plotted.

They are distributed within roughly a sphere of radius

40 kpc around the center of the Milky Way galaxy.

After many years of effort by a large number of

dedicated people, a 3-dimensional structure of the

entire Milky Way galaxy began to take shape.

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In the early 20th century, there was a big debate about

whether or not the Milky Way galaxy constituted the

entire universe.

Shapley argued that the spiral nebulae were part of the

Milky Way.

Edwin Hubble, in 1925, discovered Cepheid variables

in the Andromeda spiral, M31, and was able to

determine its distance as 800 kpc, well outside of the

Milky Way galaxy. This proved that M31 was a separate

galaxy similar to ours.

26The great Andromeda galaxy M31 at 800 kpc

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A sample of the distribution of globular clusters in the Milky Way galaxy. 28

Artist’s conception of the Milky Way galaxy showingthe main populations of stellar objects.

Galactic disk is

~ 500 pc

thick

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8.5

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Stellar Populations

Stars can be assigned to different stellar populations, according to the “metal” abundances (Z values) of elements seen in stellar atmospheres.

Population I (young) stars: Z > 0.01 (metal-rich)`

Population II (old) stars: Z < 0.001 (metal-deficient)

Disk Population (old) stars: intermediate between I and II Populatons, closer to the galactic plane.

Recall that “Z” is the fractional part of the composition for elements heavier than helium.

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• Open cluster – relatively new stars, a few hundred to a few thousand, in a loose association, all formed around the same time. Pop I stars. Some of the stars are massive.

• Globular cluster – extremely compact, spherically symmetric, 30 pc diameter balls of up to a million old stars, none of them massive. Pop II stars. All formed around the same time.

• Disk Population – Metallicity increases closer to the disk. Both Pop II and disk population stars are very old.

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Artist’s rendition of the Milky Way galaxy showing the

approximate position of our Sun in the disk. The halo

is not displayed in this view.

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Spiral Structure of the Milky Way Galaxy

• The spiral arms are visible because O and B stars

are formed there, along with open clusters.

Emission nebulae glow due to the uv radiation from

the hot stars.

• Spiral arms are regions of higher density gas and

dust, called spiral density waves. The

compression of this gas triggers the formation of

new stars.

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NGC 4603

spiral galaxy

Distance:

100 million

lightyears

or

~30 Mpc

Similar to the

Milky Way

galaxy

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“Southern pinwheel”

galaxy.

Spiral galaxy M83

at a distance of

~4.5 Mpc

Similar to our own

Milky Way galaxy.

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More on the galactic bulge

• The bulge is not simply an extension of the disk, but a separate component of the galaxy.

• The number of stars in the bulge is ~10 billion.

• The gas density at the center of the bulge is high and there is much star formation activity there.

• Some heavier elements are detected there which means there have been Type II supernovae that have distributed these elements.

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More on the galactic halo

• In the roughly spherical (40 kpc diameter) there are about 150 globular clusters and many single high velocity stars with orbits that are different than the disk.

• The ages of the globular clusters range from 11 to 13 billion years.

• There is very little gas and practically no dust in the halo, and few elements heavier than helium. Pop II.

• There are no young hot stars and no star formation.

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More on the galactic disk

• The gas and dust in the disk is found primarily

in the spiral arms.

• Most of the massive, hot stars are being

formed in the spiral arms.

• Stars in the disk tend to be Population I

stars, which are young and have some

heavier elements (i.e., higher metal

abundance).38

Spiral arms must not be tied to the material of the disk

because the disk rotates and would wind up the spirals

in a few million years and they would disappear.

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Spiral density waves in the gas and dust ofthe disk cause new stars to form there. 40

How star formation

propagates in the

spiral arms.

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Galactic Coordinates

(Local Standard of Rest)42

North

Galactic

Pole (NGP)

Sun

Galactic

center

star

Lat

Long

Galactic equator

around disk

Galactic Coordinates

(Local Standard of Rest)

Rotation

of galaxy

Angle between the galacticequator and the celestial

equator is 62.6o

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North

Galactic

Pole (NGP)

Sun

Galactic

center (0,0,0)

starLat

Galactic equator

around disk

Galactic Coordinates

(galactocentric system)

Rotation

of galaxy

Long

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Some facts about the Milky Way galaxy

• It consists of over 100 billion stars.

• Diameter is ~120,000 light-years ( ~40 kpc).

• Thickness of the spiral disk is about 500 pc.

• The central bulge is about 4 kpc thick.

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• The spiral arms contain new stars, open clusters,

and much gas and dust.

• The galaxy is surrounded by a large halo of old

individual stars and globular clusters. The halo is

about 80 kpc in diameter.

• At the center, we have the nucleus of the

galaxy……

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Central portion of the Milky Way galaxy

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The galactic center

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Infrared

image

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Artist’s renditionof Sagittarius A

at the center ofour galaxy,

based on actualdata.

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Sagittarius A overview

• Sgr A is a supermassive black hole at the center of

the Milky Way galaxy.

• Mass is about 4 million solar masses.

• Size is smaller than the Earth’s orbit around the Sun

(i.e., Rs is less than 1 AU).

• It rotates once every 11 minutes.