Let us now look into the details of the concept of "redshift". Redshift is analogous to, but not the same as, the familiar Doppler shift as applied to sound. Increases in recessional velocities are associated with changes in the wavelength of light being received, such that as the velocity becomes greater the wavelength becomes longer, i.e, moves to higher values (say, from 0.4 to 0.6 Ám in the visible; wavelengths in other regions of the EM spectrum also are shifted towards greater values). This change is very much like the Doppler effect studied in Introductory Physics: this shows the influence of motion towards or away from the observer of a signal of some given wavelength, resulting in a systematic wavelength shift. One manifestation of a wavelength shift's effect, which can be experienced in everyday life on Earth, is exemplified by an audible phenomenon - recall the sound of a whistle or horn on a fast-moving train as it approaches and then moves past where you are stopped at a crossing. Or, perhaps more familiar is the change in pitch of a steady ambulance siren as it approaches you and then falls systematically as the ambulance recedes after passing (lower frequencies). This wavelength shortening (higher pitch) on approach and lengthening (lower pitch) with recession is called the Doppler effect, which results from velocity and/or position changes (relative motions) between moving source and stationary receiver.
In a sense, the lengthening of wavelength as light sources (mostly galaxies) recede from Earth at progressively increasing velocities and distances is seemingly analogous to the above Doppler effect. But, strictly speaking, this familiar effect as observed by us on Earth is not the same as applies to cosmic distances (although it is a good approximation for nearby galaxies in relative motion away from our observing location).
As applied to more distant objects seemingly moving away from us during Universe expansion, the wavelength shift actually results from a different mechanism known as the Cosmological Redshift. From a relativistic standpoint, while Dopplerlike in its consequences, the cosmological redshift is analogous to the "stretching" of light caused by the progressive increases in distance resulting from the continuous expansion of (curving) space. This in turn results in proportional increases in recessional velocities (thus in the formula for velocity v = d/t, it is the d that changes with respect to steady time progression) with increasing distance from Earth (recall the rubber band analogy on page 20-8).
The causative influence of expansion resulting in a stretching or elongation of wavelength is evident in this diagram:
A recently reported observation of a type of galactic body called a HERO (Hyper Extremely Red Object) may be the result of this cosmological redshift. Check these two images:
On the left, the object is not detected in visible light; but it appears as a red blotch in the near Infrared. The object, at least 10 billion light years from Earth, has been found to be speeding away from us at nearly the speed of light. One interpretation considers this object to be red (from a large proportion of older stars) at the time its light left the source 10 b.y. ago . But another considers this object to be composed in large part of bright, bluish stars, perhaps even farther away (13 billion l.y.) but owing to the cosmological redshift the light as received has been stretched to near Infrared wavelengths (but assigned red in this false color rendition).
Redshift phenomena are effectively studied from the spectral states of starlight (see page 20-7). As a star or galaxy emitting radiation recedes from an observing (measuring) spectrometer (somewhere on or near the Earth), the wavelength associated with a particular line will be shifted towards the red (longer wavelength-lower energy end of the visible spectrum) and even into the near Infrared. What is measured is the displacement (δλ/λ = the incremental wavelength shift ratioed to its initial wavelength λ) of this line to a new apparent wavelength relative to its [rest state] wavelength in a spectrum obtained by exciting the element on Earth in an emission or absorption spectrometer. Before modern electronic measuring methods, the spectra were commonly recorded on a photographic plate showing multiple lines that result from the spectral spread of wavelengths characteristic of all detected elements) representing an element in its ground or some excited state in the visible. The diagram below shows four sets of spectra, for hydrogen, with the bottom representing a star in the Milky Way, and each successive spectrum upwards representing galaxies at increasing distances from Earth. The leftward shifts are towards longer wavelengths.
This next illustration shows telescope images and spectra from five galaxies at increasing distances from Earth.
This oft-cited diagram, traceable to Hubble's work, can be misleading without some interpretation. To pick out and thus intrepret these spectra, start with the Virgo galaxy example (top right). The top and bottom lines are the same emission spectra for this spectral interval (unspecified as to Angstrom units; the lines are white instead of black because the photographic plate is printed as a negative) obtained by spectroscopic analysis on Earth of a sample containing elements observed in stars . The two leftmost lines are the H and K spectra for the excited Ca++ state. The spectrum from the galaxy appears as a long lenticular white smear in the middle between the two reference spectra. The vertical arrow points to the now shifted H and K line pair, which here appear black because they are absorption rather than emission lines. In the spectral image second from the top, the horizontal arrow leads to the position of the line pair (which does not reproduce well on this page) for a galaxy in Ursa Major, now shifted notably to the right. In the three succeeding spectal images, the horizontal arrow carries to the position of the two (hard to see) dark H and K lines after each greater redshift. From these observed shifts, the recessional velocities listed under each spectral image have been calculated. These could be plotted on the distance-recessional velocity diagram above, and would fall within the general distribution shown thereon.
Today, the spectra are more commonly recorded as continuous tracings on a strip chart. The next figure shows a spectrogram recorded by a Kitt Peak National Observatory telescope in which the top spectrum (obtained at rest in the laboratory) has peaks for three Hydrogen lines at 4340 A (in the blue); 4860 A (green) and 6552 A (red). The next four are spectra from distant quasars at progressively greater distances.
The displacement of a spectral line owing to redshift can be used to calculate the Cosmological Redshift value z associated with a source simply from the rest wavelength of a given line and the observed wavelength of the same line displaced by the source's motion.
The Cosmological Redshift z is given as:
Using the z value, the velocity v of receding motion of the source is given by:
Since the redshift is velocity dependent, its magnitude is a direct indication of the rate of recession, i.e., the larger the shift, the greater the velocity. The redshift z is a number that represents the fraction by which spectral lines from a luminous source shift towards longer wavelengths. Values of z range from less than one for closer sources and have risen for the most distant sources (early time galaxies) to numbers around 6.
If instead the source advances towards the observer, the shift will be towards the blue (shorter wavelengths). Since it is postulated in the Big Bang model that all sources are apparently moving away from one another, a blueshift would seem anomalous. However, this occurs, for example, when spectra are acquired from a rotating spiral galaxy in which arms on one side (from the center) may indeed be moving away but the other side must be approaching from opposite directions. Likewise, some galaxies in a local group may appear to be moving towards Earth towards Earth, but the entire group is still receding relative to our galaxy.
Another mechanism can cause redshifts, namely, the effects of gravity on radiation. This gravitational redshift is a consequence of General Relativity. When light leaves a massive gravitational source, such as a White Dwarf, gravity causes a shift towards a longer wavelength (conversely, light passing into a huge gravitational field will undergo a blueshift). The massive body thus slows down photons representing a range of energies as these escape from it, causing a loss in their energies that results in reducing their frequencies and increasing their wavelengths. This effect has been observed for light grazing supermassive bodies, including Black Holes. Overall, the effect is localized or confined to individual bodies, and normally the shift is very small, so that even the cumulative effects of light reach Earth from the outermost reaches of Space are quite small compared with the motion-induced Cosmological Redshifts related to expansion. Nevertheless this local redshift must be accounted for when individual receding galaxies are used in determining the cosmological-scale redshifts.
There is another, more general effect of gravity, shown in the plot below, which shows the redshift curve for a Universe with maximum gravity influence versus no gravity at all. The ordinate is distance in billions of light years. This range of possibilities is pertinent to the accelerating Universe model discussed on the next page.
Most redshifts measured so far include the lower values of z obtained by examining a range of "normal" galaxies at distances from Earth under about 7 billion light years.
As stated above, most redshifts are observed to fall within the range of a fraction of 1 to about 3. These are all associated with galaxies that are less than 10 billion years (in lookback time) from Earth. This is evident in this plot:
As galaxies lying beyond 10 billion light years are observed, their redshifts begin to rise at more rapid rates. Thus:
The ordinate denotes relative age: The present time is given by "1", with nearby galaxies that appear most fully evolved (to us in the present time) having very low redshifts. The exponental drop in the curves (the red curve applies to a Universe with 70% Dark Matter; the blue curve described a Universe without Dark Energy [Cosmological Constant = 0]) shows that the maximum rate of increase in the value of 'z' occurred when the Universe was less than a relative 0.2.
Higher redshifts have been found for galaxies that are strong radio sources and even larger values (around z = 5 to 6.5) from very distant quasars (mainly those which display their effects in the first two billion years of Universe history). Values of 'z' increase rapidly towards infinity for Universe events older than the first stars. For instance, at the time of Recombination (page 20-1) z = 1000. This is the general relationship as tied to major cosmological entities:
The most distant galaxies are hard to observe but their redshifts can be greater than 10. Theory permits calculations of redshifts from the Recombination Era back through the first minute of the Big Bang. These values have been taken from Joseph Silk's The Big Bang (3rd Ed, page 68): At Universe age of 2 billion years, z = 5; Decoupling at 380000 yrs, z = 103; Radiation Era, 1st minute after the BB: z = 109; Hadronic Era, at t = 10-10sec, z = 1010sec; Planck time, at 10-43sec, z = 1032 ;
Now with this overview of redshifts, the reader is encouraged to work through a review on this Wikipedia website.
To calibrate and then apply the redshift to estimate R (Scale Factor; previous page), and to calculate the Hubble contant H, the distances to the stellar bodies each with a specific redshift must be determined. Over the last century various methods of estimating distances have been developed. A good, in-depth review of the principal methods used in distance determination is found at Ned Wright's Cosmology site.Some of these methods will be discussed in this subsection. Use of multiple methods applicable at different distances is called the Cosmic Distance Ladder. We will start with an overview given in these two illustrations and a summation:
This is a synopsis of most of the distance measuring methods:
1) .For the Solar System: Radar is the most accurate measuring method.
2) For nearby stars: The parallax method, using either Earth's orbit to occupy different positions or an orbiting satellite, to determine how far away are stars in the Milky Way Galaxy; works well out to about 3000 light years.
3) For some stars farther out in the Milky Way: The standard candle method uses stars whose true luminosity L can be determined.
4) For stars out to the edge of the Milky Way: The Cepheid Variable star method is employed.
5) For many more distant galaxies out to several hundred million light years: The Tully-Fisher method utilizes measured brightness and galaxy rotation (using the Doppler effect).
6) For galaxies out to about 10 billion light years: This depends on observations of White Dwarf supernovae, whose intrinsic brightness is well known.
Some of these methods have accuracies of +/- 10% or better.