IB Physics

Option F - Astrophsyics

Galaxies and the Expanding Universe

galactic types / galactic motion / hubble's law

Galactic Types

The Milky Way galaxy is a spiral shaped galaxy consisting of over 400 billion stars. Gas and dust are arranged into three general components as shown by the picture below. The size of our galaxy is the order of magnitude 100 000 ly and it rotates around its centre in 200 - 300 million years.

The halo is a roughly spherical distribution which contains the oldest stars in the Galaxy. The Halo consists of the oldest stars known, including about 146 Globular Clusters, believed to have been formed during the early formation of the Galaxy with ages of 10-15 billion years from their H-R Diagrams. The halo is filled with a very diffuse, hot, highly-ionized gas. The very hot gas in the halo produces a gamma-ray halo. Investigations of the gaseous halos of other spiral galaxies show that the gas in the halo extends out to hundreds of thousands of light years. Studies of the rotation of the Milky Way show that the halo dominates the mass of the galaxy, but the material is not visible, now called dark matter.

The nuclear bulge and Galactic Center. The nuclear bulge is the central, spherical part of a spiral galaxy. It is surrounded by a disk-shaped mass of stars with spiral arms. The Nuclear Bulge appears as a distinct, massive disk-like complex of stars and molecular clouds which is, on a large scale, symmetric with respect to the Galactic Centre. It is distinguished from the Galactic Bulge by its flat disk-like morphology, very high density of stars and molecular gas, and ongoing star formation.

The disk, which contains the majority of the stars, including the sun, and virtually all of the gas and dust The disk of the Galaxy is a flattened, rotating system which contains the Sun and other intermediate-to-young stars. The sun sits about 2/3 of the way from the center to the edge of the disk (about 25,000l.y.). The sun revolves around the center of the galaxy about once every 250 million years.

Hubble Classification of Galaxies

All bright galaxies fall into one of three broad classes according to their shape:

Spiral Galaxies

Ordinary Spirals are classified by relative strength of the central bulge & tightness of the spiral arms. Types are Sa which is string bulge and tight with indistinct arms, Sb is intermediate type and Sc is small bulge and loose with well-defined arms. Barred Spirals feature a strong central stellar bar. Its bar rotates as a unit. Spiral arms emerge from the ends of the bar. There is ongoing star formations in the disk. It is supported by relatively rapid rotation.

Elliptical Galaxies

Elliptical galaxies do not have disks, spiral arms or dust lanes. Their brightest stars are red and they are classified by the degree of flatness. E0 are circular and E7 are the flattest. Star formation ended in these galaxies billions of years ago. They are supported by random motions of stars with some very slow rotation.

Irregular Galaxies

Show an irregular, often chaotic structure. They has lots of young blue stars. There is moderate rotation in Irregulars, but very chaotic motions as well. There is often a great deal of on-going star formation.

Many galaxies near each other form galactic clusters which in turn form superclusters, which make up the known universe.

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Galactic Motion

Distribution of Galaxies in the Universe

Galaxy groups and clusters are the largest gravitationally-bound objects. They form the densest part of the large scale structure of the Universe. In models for the gravitational formation of structure with cold dark matter, the smallest structures collapse first and eventually build the largest structures, clusters of galaxies. Clusters are then formed relatively recently between 10 billion years ago and now. Groups and clusters may contain from ten to thousands of galaxies. The clusters themselves are often associated with larger groups called superclusters.

Clusters are larger than groups, although there is no sharp dividing line between a group and a cluster. When observed visually, clusters appear to be collections of galaxies held together by mutual gravitational attraction. However, their velocities are too large for them to remain gravitationally-bound by their mutual attractions, implying the presence of either an additional invisible mass component, or an additional attractive force besides gravity. X-ray studies have revealed the presence of large amounts of intergalactic gas known as the intracluster medium. This gas is very hot, between 107K and 108K, and hence emits X-rays in the form of bremsstrahlung and atomic line emission. The total mass of the gas is greater than that of the galaxies by roughly a factor of two. However this is still not enough mass to keep the galaxies in the cluster. Since this gas is in approximate hydrostatic equilibrium with the overall cluster gravitational field, the total mass distribution can be determined. It turns out the total mass deduced from this measurement is approximately six times larger than the mass of the galaxies or the hot gas. The missing component is known as dark matter and its nature is unknown. In a typical cluster perhaps only 5% of the total mass is in the form of galaxies, maybe 10% in the form of hot X-ray emitting gas and the remainder is dark matter.

Clusters typically have the following properties.

  • They contain 50 to 1000 galaxies, hot X-ray emitting gas and large amounts of dark matter
  • The distribution of these three components is approximately the same in the cluster.
  • They have total masses of 1014 to 1015 solar masses.
  • They typically have a diameter of 2 to 10 Mpc (see 1 E23 m for distance comparisons).
  • The spread of velocities for the individual galaxies is about 800-1000 km/s.

Super Clusters

Superclusters are large groupings of smaller galaxy groups and clusters, and are among the largest structures of the cosmos. The existence of superclusters indicates that the galaxies in our Universe are not uniformly distributed; most of them are drawn together in groups and clusters, with groups containing up to 50 galaxies and clusters up to several thousand. Those groups and clusters and additional isolated galaxies in turn form even larger structures called superclusters.

Superclusters can range in size up to several 108light years. No clusters of superclusters are known, but the existence of structures larger than superclusters is debated (see Galaxy filament). Interspersed among superclusters are large voids of space in which few galaxies exist. Even though superclusters are the largest structures confirmed, the total number of superclusters leave possibilities for structural distribution; the total number of superclusters in the universe is believed to be close to 10 million.

Superclusters are frequently subdivided into groups of clusters called galaxy clouds.

Red Shift of Light from Different Galaxies

In physics and astronomy, redshift is a phenomenon in which the visible light from an object is shifted towards the red end of the spectrum. It is an observed increase in the wavelength, which corresponds to a decrease in the frequency of electromagnetic radiation, received by a detector compared to that emitted by the source. The corresponding shift to shorter wavelengths is called blueshift.

The phenomenon goes by the same name even if it occurs at non-optical wavelengths (e.g. gamma rays, x-rays and ultraviolet). At wavelengths longer than red (e.g. infrared, microwaves, and radio waves) redshifts shift the radiation away from the red.

Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left). Wavelength increases up towards the red and beyond, (frequency decreases)

Redshift typically occurs when a light source moves away from an observer, analogous to the Doppler shift which changes the frequency of sound waves. While observing this redshift has a number of terrestrial uses (e.g. Doppler radar and Radar guns), it is famously employed in astronomy where it is used as a diagnostic in spectroscopic astrophysics to determine information about the dynamics and kinematics (i.e. movement) of distant objects. This redshift phenomenon was first predicted and observed in the nineteenth century as scientists began to consider the dynamical implications of the wave-nature of light. There is also a gravitational redshift which happens due to the time dilation that occurs in general relativity near massive objects. Most famously, redshifts are observed in the spectra from distant galaxies, quasars, and intergalactic gas clouds to increase proportionally with the distance to the object. This is generally considered to be one of the major forms of evidence that the universe is expanding, as predicted by the Big Bang model.

A redshift can be measured by looking at the spectrum of light that comes from a single source (see idealized spectrum illustration top-right). If there are features in this spectrum such as absorption lines, emission lines, or other variations in light intensity, then a redshift can in principle be calculated. This requires comparing the observed spectrum to a known spectrum with similar features. For example, the atomic elementhydrogen, when exposed to light, has a definite signature spectrum that shows features at regular intervals. If the same pattern of intervals is seen in an observed spectrum occurring at shifted wavelengths, then a redshift can be measured for the object. Determining the redshift of an object therefore requires a frequency- or wavelength-range. Redshifts cannot be calculated by looking at isolated features or with a spectrum that is featureless or white noise (random fluctuations in a spectrum).

Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy it is customary to refer to this change using a dimensionless quantity called z. If λ represents wavelength and f represents frequency (note, λf = c where c is the speed of light), then z is defined by the equations:

After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. According to the mechanisms section below, there are some basic interpretations that follow when either a redshift or blueshift is observed. For example, Doppler effect blueshifts (z < 0) are associated with objects approaching (moving closer) to the observer with the light shifting to greater energies. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, Einstein effect blueshifts are associated with light entering a strong gravitational field while Einstein effect redshifts imply light is leaving the field.

Recession Speed of galaxies Using the Simplified Red Shift Equation

In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us. In fact, he found that the Universe was expanding - with all of the galaxies moving away from each other. This phenomenon was observed as a redshift of a galaxy's spectrum. This redshift appeared to be larger for faint, presumably further, galaxies. Hence, the farther a galaxy, the faster it is receding from Earth. You can see this trend in Hubble's data shown in the images above. The velocity of a galaxy could be expressed mathematically as

v = H x d

where v is the galaxy's radial outward velocity, d is the galaxy's distance from Earth, and H is the constant of proportionality called the Hubble constant.

The exact value of the Hubble constant is still somewhat uncertain, but is generally believed to be around 65 kilometers per second for every megaparsec in distance. (A megaparsec is given by 1 Mpc = 3 x 106 light-years). This means that a galaxy 1 megaparsec away will be moving away from us at a speed of 65 km/sec, while another galaxy 100 megaparsecs away will be receding at 100 times this speed. So essentially, the Hubble constant reflects the rate at which the Universe is expanding.

So to determine an object's distance, we only need to know its velocity. Velocity is measurable thanks to the Doppler shift. By taking the spectrum of a distant object, such as a galaxy, astronomers can see a shift in the lines of its spectrum and from this shift determine its velocity. Putting this velocity into the Hubble equation, they determine the distance. Note that this method of determining distances is based on observation (the shift in the spectrum) and on a theory (Hubble's Law). If the theory is not correct, the distances determined in this way are all nonsense. Most astronomers believe that Hubble's Law does, however, hold true for a large range of distances in the Universe.

It should be noted that, on very large scales, Einstein's theory predicts departures from a strictly linear Hubble law. The amount of departure, and the type, depends on the value of the total mass of the universe. In this way a plot of recession velocity (or redshift) vs. distance, which is a straight line at small distances, can tell us about the total amount of matter in the universe and may provide crucial information about the mysterious dark matter.

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Hubble's Law

Hubble’s law states that the general trend for recessional velocities for galaxies is directly proportional to the distance from Earth.

In Mathematical terms:

v ∝ d

where v = recessional velocity and d = distance from Earth

alternatively

v = Hod

where Ho is a constant known as the Hubble constant.

Due to the uncertainties in determining the distance from Earth, the value of Ho is not known to any degree of precision and under constant debate and review. It should also be noted it is a general trend in line with the expanding universe and relative movement of individual galaxies may deviate from the overall general trend.

The SI for Hubble constant is s-1 but the unit of km s-1 Mpc-1 is often used.

To determine the Hubble constant, it must be remember that it is a genral trend and therefore must be obtained from a large a sample as possible.

The two values that need to be determined for each galaxy according to the mathematical expression of Hubble’s law, are, v (recessional velocity) and d (distance from Earth).

The recessional velocities can be measured for the red shift of known absorption lines (for example of hydrogen) and applying the formula for recessional velocity, that is,

The distances of galaxies is however more difficult to measure but the most common method will be to measure the apparent magnitudes of Cepheid variable found in the galaxies and using the general luminosity-period relation of Cepheid variables to estimate the absolute magnitude of the star and hence determine, using the relationship absolutes magnitudes M, apparent magnitude m and distance d

The distance for Earth can be determined (with limitations on accuracies).

The data points of observations can then be plotted on a recessional velocity versus distance plot with the gradient of the line of best fit through the origin give a estimation of the value for the Hubble constant Ho.

The uncertainties, especially in the distance measurements, means that Hubble’s constant cannot be determined with any great certainty and is under constant debate and review by astronomers.

As Hubble’s law states that the recessional velocity / distance is a constant, and if we make the consideration if the universe has been undergoing constant expression, we can use the Hubble constant to work out when the galaxies are all in one point and hence when the Universe began in the Big Bang or the age of the universe.

Using the formula relating time, distance and constant speed, Time = distance / speed

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