Cosmology, Galaxies and Expansion of the Universe (Senior 6 Physics): free lessons | Ganzaa

Cosmology, Galaxies and Expansion of the Universe

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Senior 6 · Physics

Cosmology, Galaxies and Expansion of the Universe

5 lessons

Lesson 1 of 5

Cosmology, the Milky Way and Galaxies

25 min

One galaxy, or billions?

On a clear, moonless night far from town lights, a faint band of light arches across the sky. In 1610 Galileo turned his telescope on it and saw that it is made of countless faint stars. For three more centuries, many astronomers believed this band, our Galaxy, was the whole universe. The faint spiral "nebulae" seen through telescopes were thought to be clouds inside it. The question was settled in 1924, when Edwin Hubble found pulsating stars of a known type in the Andromeda nebula and showed it to be so far away that it had to be a separate system of stars, a galaxy like our own. Today we know of hundreds of billions of galaxies. This unit follows the path astronomers took: from our own Galaxy, to the stars and how we measure them, to the expanding universe and its age.

What is cosmology?

Cosmology is the study of the universe as a whole: what it contains, how it is arranged on the largest scales, how it began and how it has changed. Its distances are so large that astronomers use special units.

Unit	Definition	In metres
astronomical unit (AU)	mean Earth–Sun distance	$1.496 \times 10^{11}$
light-year (ly)	distance light travels in a year	$9.46 \times 10^{15}$
parsec (pc)	distance at which 1 AU subtends 1 arcsecond (Lesson 3)	$3.09 \times 10^{16}$ = 3.26 ly

Object	Approximate distance
Sun	1 AU (8.3 light-minutes)
Proxima Centauri, the nearest star after the Sun	4.2 ly (1.30 pc)
centre of the Milky Way	26 000 ly (8 kpc)
Andromeda Galaxy	2.5 million ly (0.77 Mpc)
Virgo Cluster of galaxies	54 million ly (16.5 Mpc)

Because light takes time to arrive, looking far away means looking back in time: we see the Andromeda Galaxy as it was 2.5 million years ago.

Worked example 1: the light-year and looking back

(a) Calculate the light-year in metres ( $c = 3.00 \times 10^{8}\,\mathrm{m\,s^{-1}}$ , 1 year $= 3.16 \times 10^{7}\,\mathrm{s}$ ). (b) Express the distance to the Andromeda Galaxy, 2.5 million ly, in metres and in megaparsecs. (c) How old is the light we see from it?

Solution

(a) $1\,\mathrm{ly} = (3.00 \times 10^{8})(3.16 \times 10^{7}) = 9.46 \times 10^{15}\,\mathrm{m}$ .

(b) $d = 2.5 \times 10^{6} \times 9.46 \times 10^{15} = 2.4 \times 10^{22}\,\mathrm{m}$ . In parsecs: $\frac{2.37 \times 10^{22}}{3.09 \times 10^{16}} = 7.7 \times 10^{5}\,\mathrm{pc} = 0.77\,\mathrm{Mpc}$ .

Our Galaxy, the Milky Way

Figure 1.1: The Milky Way seen edge-on (schematic, not to scale in thickness).

The Milky Way is a barred spiral galaxy containing a few hundred billion stars, together with gas and dust. Most of the stars, gas and dust lie in a thin, flat disc about 100 000 light-years across and about 1000 light-years thick, where the spiral arms are and where new stars are still forming. The disc surrounds a central bulge of older stars, crossed by a bar. Around everything is a faint, roughly spherical halo of old stars and about 150 globular clusters, each a ball of hundreds of thousands of old stars. At the very centre is a black hole of about 4 million solar masses, Sagittarius A*. The Sun lies in the disc, about 26 000 light-years from the centre, which is why we see the disc from inside as a band of light around the sky.

All of this rotates. The Sun moves around the centre at about 230 km s⁻¹; the gravitational pull of the matter inside its orbit provides the centripetal force. Setting $\frac{GMm}{r^2} = \frac{mv^2}{r}$ gives the mass inside the orbit:

$M = \frac{v^2 r}{G}$

Worked example 2: the Galactic year and the Galaxy's mass

The Sun orbits the Galactic centre at radius 26 000 ly with speed 230 km s⁻¹. Find (a) the time for one orbit, (b) the mass inside the Sun's orbit in kilograms and in solar masses ( $G = 6.67 \times 10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}$ , $M_\odot = 1.99 \times 10^{30}\,\mathrm{kg}$ ).

Solution

$r = 26\,000 \times 9.46 \times 10^{15} = 2.46 \times 10^{20}\,\mathrm{m}$ .

(a) $T = \frac{2\pi r}{v} = \frac{2\pi \times 2.46 \times 10^{20}}{2.30 \times 10^{5}} = 6.72 \times 10^{15}\,\mathrm{s} = \frac{6.72 \times 10^{15}}{3.16 \times 10^{7}} = 2.1 \times 10^{8}$ years. The Sun has gone round about 20 times since it formed 4.6 billion years ago.

(b) $M = \frac{v^2r}{G} = \frac{(2.30 \times 10^{5})^2 \times 2.46 \times 10^{20}}{6.67 \times 10^{-11}} = 1.95 \times 10^{41}\,\mathrm{kg}$ , or $\frac{1.95 \times 10^{41}}{1.99 \times 10^{30}} = 9.8 \times 10^{10}$ , about $10^{11}$ solar masses.

Condition: this treats the mass inside the orbit as if it were concentrated at the centre, which is exact only for a spherical distribution; for a flattened disc it is an estimate.

Types of galaxies

In 1926 Hubble sorted galaxies by their appearance into a scheme often drawn as a "tuning fork" (Figure 1.2). The diagram is a classification, not an evolutionary sequence.

Figure 1.2: Hubble's classification of galaxies.

Type	Shape	Stars and gas	Example
elliptical (E0 to E7)	smooth ellipsoid; the number gives the flattening, $10\left(1 - \frac{b}{a}\right)$ for axes $a \ge b$	old, reddish stars; very little gas or dust, so few new stars; from dwarfs to the largest galaxies known	M87
lenticular (S0)	disc and bulge but no arms	little gas	NGC 5866
spiral (Sa to Sc)	disc with spiral arms around a bulge; Sa has the largest bulge and tightest arms	young blue stars, gas and dust in the arms; old stars in the bulge	Andromeda (Sb)
barred spiral (SBa to SBc)	arms start from the ends of a central bar	as spirals	NGC 1300, the Milky Way
irregular (Irr)	no regular shape, often after a close encounter	much gas, active star formation	Large Magellanic Cloud

Clusters of galaxies and the cosmic web

Galaxies are not scattered evenly; gravity gathers them into groups and clusters.

The Local Group contains more than 50 galaxies within about 10 million light-years. Most are dwarfs; the two giants are the Milky Way and Andromeda, with the smaller spiral M33 third. Andromeda is approaching us at about 110 km s⁻¹ relative to the Milky Way.
Clusters such as the Virgo Cluster contain hundreds to thousands of galaxies, many of them ellipticals, bound by gravity and filled with hot gas that emits X-rays.
Groups and clusters gather into superclusters, arranged in long filaments and sheets around huge, nearly empty voids: the cosmic web, the largest structure in the universe.

Evidence for dark matter

The speed of stars and gas orbiting a spiral galaxy can be measured from the Doppler shift of their spectral lines. If almost all the mass were in the visible disc, then beyond it $M$ would be constant and $v = \sqrt{\frac{GM}{r}}$ would fall as $\frac{1}{\sqrt{r}}$ , like the planets' speeds around the Sun. Instead, the measured speeds stay nearly constant far beyond the visible disc (Figure 1.3). Since $M = \frac{v^2r}{G}$ , constant $v$ means the enclosed mass keeps growing in proportion to $r$ . Most of a galaxy's mass is therefore in a large, invisible halo of dark matter, which neither emits nor absorbs light and is detected only by its gravity. Galaxy clusters show the same: their galaxies move far too fast to be held together by the visible matter alone.

Figure 1.3: A typical spiral-galaxy rotation curve (schematic).

Definition

A galaxy is a huge system of stars, gas, dust and dark matter held together by its own gravity. A cluster of galaxies is a group of hundreds to thousands of galaxies bound by gravity. Dark matter is matter that does not emit, absorb or reflect light and is detected only through its gravitational effects. Example: the flat rotation curve of the Milky Way shows that most of its mass is dark matter.

Worked example 3: weighing the dark halo

In a galaxy, gas clouds orbit at 220 km s⁻¹ both at 10 kpc and at 50 kpc from the centre. (a) Find the mass enclosed within each radius, in solar masses (1 pc $= 3.09 \times 10^{16}\,\mathrm{m}$ ). (b) The visible stars and gas total about $6 \times 10^{10}$ solar masses. What fraction of the mass within 50 kpc is dark?

Solution

(a) At 50 kpc: $r = 50 \times 10^{3} \times 3.09 \times 10^{16} = 1.54 \times 10^{21}\,\mathrm{m}$ ; $M = \frac{(2.20 \times 10^{5})^2 \times 1.54 \times 10^{21}}{6.67 \times 10^{-11}} = 1.12 \times 10^{42}\,\mathrm{kg} = 5.6 \times 10^{11}\,M_\odot$ . At 10 kpc, with the same $v$ , $M$ is five times smaller: $1.1 \times 10^{11}\,M_\odot$ .

(b) Dark fraction $= \frac{5.6 \times 10^{11} - 0.6 \times 10^{11}}{5.6 \times 10^{11}} = 0.89$ : about 90% of the mass within 50 kpc is dark.

Warning

Common mistakes. (1) Treating the light-year as a unit of time: it is a distance. (2) Reading the tuning fork as a life history (ellipticals do not turn into spirals). (3) Thinking the Milky Way is the universe, or that "galaxy" and "solar system" mean the same thing: the Solar System is one star and its planets, inside one galaxy among hundreds of billions. (4) Using $M = \frac{v^2r}{G}$ with $v$ in km s⁻¹ or $r$ in ly: convert to SI first.

Tip

A ladder of sizes to remember, each step roughly a thousand times or more: Solar System (hours of light) → nearest stars (a few years of light) → Milky Way (100 000 ly) → Local Group (millions of ly) → clusters and the cosmic web (tens to hundreds of millions of ly).

Galaxies, part 1: Crash Course Astronomy #38, presented by Phil Plait. Watch how Hubble settled whether the spiral nebulae were inside the Milky Way, and how galaxies are classified.

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Practice

Convert 1.00 pc into light-years and into astronomical units (1 AU = $1.496 \times 10^{11}\,\mathrm{m}$ ).
Describe the structure of the Milky Way, naming its three main parts and the position of the Sun.
An elliptical galaxy's image has axes in the ratio $\frac{b}{a} = 0.70$ . What is its Hubble type?
State two differences between elliptical and spiral galaxies.
A star orbits a galaxy's centre at 8.0 kpc with speed 200 km s⁻¹. Find its orbital period in years.
Light from a galaxy in the Virgo Cluster left it 54 million years ago. How far away is the galaxy, in metres?
Explain how the rotation curves of spiral galaxies provide evidence for dark matter.
Keza says: "Andromeda is coming towards us at 110 km s⁻¹, so it will hit us in $\frac{d}{v}$ years." Calculate $\frac{d}{v}$ and evaluate her reasoning.

Show answersHide answers

$\frac{3.09 \times 10^{16}}{9.46 \times 10^{15}} = 3.26\,\mathrm{ly}$ ; $\frac{3.09 \times 10^{16}}{1.496 \times 10^{11}} = 2.06 \times 10^{5}\,\mathrm{AU}$ .
A thin disc (spiral arms, gas, dust, young stars), a central bulge with a bar (old stars, central black hole), and a spherical halo (old stars, globular clusters, dark matter). The Sun is in the disc, about 26 000 ly from the centre.
$10 (1 - 0.70) = 3$ : type E3.
Ellipticals: smooth, no arms, little gas and dust, mainly old red stars, little star formation. Spirals: disc with arms, much gas and dust, young blue stars and ongoing star formation (any two).
$r = 8.0 \times 10^{3} \times 3.09 \times 10^{16} = 2.47 \times 10^{20}\,\mathrm{m}$ ; $T = \frac{2\pi r}{v} = \frac{2\pi \times 2.47 \times 10^{20}}{2.0 \times 10^{5}} = 7.8 \times 10^{15}\,\mathrm{s} = 2.5 \times 10^{8}$ years.
$d = 54 \times 10^{6} \times 9.46 \times 10^{15} = 5.1 \times 10^{23}\,\mathrm{m}$ .
Measured orbital speeds stay nearly constant far beyond the visible disc. With only visible matter, speeds there should fall as $\frac{1}{\sqrt{r}}$ . Constant $v$ requires enclosed mass $M = \frac{v^2r}{G}$ growing with $r$ , so there must be large amounts of unseen (dark) matter in a halo.
$\frac{d}{v} = \frac{2.37 \times 10^{22}}{1.1 \times 10^{5}} = 2.2 \times 10^{17}\,\mathrm{s} \approx 6.8 \times 10^{9}$ years. Her method assumes a constant speed in a straight line. In fact gravity speeds the galaxies up as they approach, and Andromeda also has some sideways motion, so the real time to a close encounter, from detailed models, is shorter, about 4 to 5 billion years, and a direct collision is likely but not certain.

Key points

Cosmology studies the universe as a whole. 1 ly $= 9.46 \times 10^{15}\,\mathrm{m}$ ; 1 pc $= 3.09 \times 10^{16}\,\mathrm{m} = 3.26\,\mathrm{ly}$ . Looking far means looking back in time.
The Milky Way: barred spiral, disc (about 100 000 ly), bulge, halo; the Sun is 26 000 ly from the centre and orbits in about 210 million years.
Hubble types: elliptical (E0 to E7), lenticular (S0), spiral (Sa to Sc), barred spiral (SBa to SBc), irregular.
Galaxies form groups (the Local Group), clusters and superclusters in a cosmic web. Flat rotation curves, $M = \frac{v^2r}{G}$ , reveal dark matter.

Sources and credits

25.2: The Architecture of the Galaxy, 25.4: The Mass of the Galaxy and 26.3: Types of Galaxies, from Astronomy 2e by Andrew Fraknoi, David Morrison and Sidney C. Wolff, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: ESO - Milky Way.jpg by ESO/S. Brunier, Wikimedia Commons, licensed under CC BY 4.0.
Photo: Andromeda Galaxy (with h-alpha) by Adam Evans, Wikimedia Commons, licensed under CC BY 2.0.
Image: Hubble2005-01-barred-spiral-galaxy-NGC1300.jpg, NASA, ESA and the Hubble Heritage Team (STScI/AURA), Wikimedia Commons, public domain.
Video: Galaxies, part 1: Crash Course Astronomy #38, CrashCourse, embedded from YouTube.

The three diagrams, the worked examples and the practice exercises are written by Ganzaa.

1One galaxy, or billions?

2What is cosmology?

3Our Galaxy, the Milky Way

4Types of galaxies

5Clusters of galaxies and the cosmic web

6Evidence for dark matter

One galaxy, or billions?

What is cosmology?

Our Galaxy, the Milky Way

Types of galaxies

Clusters of galaxies and the cosmic web

Evidence for dark matter