Evidence for the Big Bang and the Expansion of the Universe Part-3 - Completely Remote Sensing, GPS, and GPS Tutorial
Evidence for the Big Bang and the Expansion of the Universe Part-3

Now, to more detail: Distance measurements obtained for nearby bodies, e.g., in our own Milky Way galaxy, can be made on visible stars whose magnitudes can be directly ascertained. One technique is that of parallax observations. While not fully explained here, the gist of this technique can be sensed by this simple experiment: Hold your index finger first about 6 inches in front of your nose and rapidly alternately close your left eye and then right one repeatedly. Your finger will appear to shift back and forth relative to a fixed background, perhaps seeming to displace several inches. Now, put your finger full out (about 24 inches) and do the same thing. Note that the displacement is now less. This is the parallax effect (first discussed in Section 11). The amount of shift decreases with increasing distance and that distance can be determined by simple trigonometry.

As used to measure stars within about 100 parsecs (326 light years), the left and right eye positions are proxied by the positions at opposite points in the Earth's elliptical orbit six months apart. A star's apparent shift relative to distant background stars, even though proportionately much smaller than that of the finger experiment, is sufficient to provide an accurate distance measure for stellar bodies close to Earth.

The standard candle method requires use of objects (stars; galaxies) whose intrinsic luminosity L is known. At some distance d, the L (in watts) is spread over a sphere of area A = 4πd2. What is actually measured is brightness b; b = L/A. The distance d is then calculated as d = (L/4πb.

Approximate distances to closer host galaxies containing separable stars rely on determining the intrinsic luminosity of certain types of individual stars. One class is the so-called pulsating stars, i.e., those whose luminosities vary systematically over periods of days to several months. These include stars that have used up nearly all of their Hydrogen fuel and are enroute off the Main Sequence towards then becoming Red Supergiants. During this phase of their history, their atmospheres expand rapidly with a rise in luminosity, only to revert back to their previous state during a cycle whose time is that of a regular period. What happens is this: the star in its more compact state has a specific internal pressure; at some point the nuclear processes cause the star to expand, increasing its diameter by a factor around 2. The pressure gradient decreases until a condition is reached in which gravity now reverses the process causing contraction. The expansion-contraction repeats at its characteristic, nearly constant time period (in Earth days) for a long time before a particular pulsating star evolves into a more stable Red (Super)Giant. Most stars showing this phenomenon have initial masses from 5 to 20 times that of the Sun. More massive stars have longer periods of expansion-contraction and are also more luminous to start with.

One class of periodically pulsing star groups are the RR-Lyrae stars whose periods are in hours to a single day. More important are the Cepheid Supergiant stars. Cepheids were first discovered by astronomer Henrietta Leavitt in 1912 in the nearby Magellanic Clouds; she then showed them to have regular, pulsating variations in luminosity proportional to their pulse periods (in so doing, determined that the brighter the star, the longer its period P). Cepheids flare up to peak brightnesses, then dim down, over periods of days to weeks. Using the parallax method, the distances to some of these were independently fixed and their absolute magnitudes M were calculated. Since these distances varied (within the Milky Way and in the Magellanic Clouds), the various M values could be associated with their corresponding periods in the cycle, thus establishing the M-P relationship. Of course, Cepheids having the same values of M but located at widely varying distances from Earth will experience an apparent decrease in brightness m depending on distance (and subject to the 1/d2 relation that defines the falloff in brightness with distance). These ideas are illustrated for one type of Cepheids (δ-Cephei) and for the more general case:.

Once absolute luminosity for a given Cepheid is calibrated from this relation, the drop in apparent (observed) brightness m from that value owing to its specific distance d can then be included in the following equation to determine that distance to this star:

m - M = 5(log d/10)

In the 1920s, Edwin Hubble firmly established the relation that the longer the period, the greater is the increase in the intrinsic (absolute) brightness in a Cepheid. He applied this pulse cycle approach to these stars in different galaxies and over a range of distances. It was Hubble's use of primarily Cepheid-derived distances that led to his first major hypothesis of an expanding Universe, after also introducing the redshift relation. Some of the values he used were not highly accurate (but were later corrected) so that his initial postulated rates of expansion were considerably off-the-mark.

The Cepheid variable star method works well out to a distance of 50 million light years (roughly, out to Virgo). For galaxies farther away, other methods of measuring distances to them (such as the rich cluster-brightest galaxy indicator which gives usable approximations out to 10 billion l.y.) have been worked out and applied (these have varying degrees of accuracy.

The best among these is the Type Ia supernova explosion (discussed in more detail on the next page). This occurs when a white dwarf star has a larger binary companion. Material stripped from the larger star accumulates around the dwarf until a critical mass (~1.4 solar masses) is attained, at which point it explodes releasing luminant energy of a narrow range of L. (Details about White Dwarfs are presented on this Wikipedia website). Thus it qualifies as a standard candle star. This explosion is a Type Ia supernova that is so bright that it is readily detected in very distant galaxies. This plot show the relation of luminosity to time history of Type 1a and Type II supernovae:

This next diagram was shown first on page 20-1. It is repeated as a summary of some of the Cosmic Ladder methods:

As earlier stated, cosmic distances are used to relate redshift values to recessional velocities. When redshifts begin to exceed about 1, the speeds of the objects concerned begin to approach relativistic values, i.e., they are ever larger fractions of the speed of light. Thus, although the actual speeds continue to increase, the incremental rate of velocity increase itself decreases (slope asymptote approaches 0). This gives rise to a redshift vs recessional speed curve that is like this:

From Astronomica.com

Another relationship: z = 1/R(tem) - 1 describes the redshift in terms of the Scale Factor R pertinent to tem which refers to the particular time when the light was emitted . This relationship can also be cast in the following way:

Dnow/Dthen = Rnow/Rthen = z + 1 = λrec/λem,

in which Dnow is the distance to the emitter when the light is received and Dthen refers to the distance in the past when light left the emitter.

A plot of z + 1 versus r/R (the distance out to any galaxy ratioed to the distance out to a Universe's edge, set at the Scale Factor R) shows the exponential character of this curve (generalized here):

We see a redshift (towards longer wavelengths) because the Universe had a different Scale Factor when the light left the emitter. The redshift is due to the relative expansion of space (increasing "D's" [for distance]) rather than actual speeding up of more distant galaxies. Look at the two circle drawing shown earlier on page 20-8. Note the S-like curl that represents part of a wavelength train. It has a shorter wavelength in the left circle; as the circle expands with its enlarged coordinates, note that the wavelength on the right is now longer.

Before new data from the HST and other observing systems were acquired, the prior estimates of the value of H0) had fallen between 50 to 100 km/sec/Megaparsecs (a parsec is 3.26 l.y). (In some expressions of H, megaparsecs are replaced by 1 million (106) light years; thus 75 km/sec/Mpc = 23 km/sec/106 l.y.) One goal of the Hubble Telescope is to better zero in on the most accurate value of H0 - essential to an accurate estimate of the Universe's age. From most recent best estimates, a range of H0 (value at the present time) between 65 and 79 km/sec/Mpc is considered the most likely to contain the eventual most accurate value (still being sought).

A good discussion of some of the above information on the Hubble Law is found at these two Wikipedia-1 and Wikipedia-2 sites.

Cosmic Ages: The Age of the Universe

The Hubble constant H0 provides a direct way of estimating the time from the Big Bang (Universe's "birth") to the present. Currently, 13.69 (rounded to 13.7) billion years (using H0 = 71.4 km/sec/Mpc, based on WMAP data [see below on this page]), with an uncertainty of +/- 10%, is the most widely accepted value.

The general relation for the Universe's age (since the Big Bang) is given by the expression:

t0 = 1/H0
.

This formula is deceptively simple. Just putting in a value for H0 yields a number that is not years as such. The proper units must be included. Here we will run through the calculation that leads to the end-result age for a value of H0 = 71 km/s/Mpc (s = sec; Mpc must be converted into mega-light years). In the actual calculations, when H units (in the Mpc mode) are adjusted to give an answer in billions of years, the formula becomes:

Age t0 (years) = 979.3 x 109/H0

Inserting 71 km/s/Mpc into the formula yields an age of 13.7 billion years.

Most textbooks on Cosmology and relevant Internet sites do not show the details of the calculations in regard to units involved. This is done here:

Age of Universe (109 years) = 1/H0 (Mpc x sec/km) x (3.09 x 1019 km/1 Mpc) x (1 yr/3.155 x 107 sec)

The bold letters refer to units that cancel out.

The lower the value of H0, the larger is t0 and thus the Universe becomes older; smaller H0 yield younger ages.

The first reported (before 1995) HST-derived ages fell between 8-12 Ga, anomalously low compared with pre-HST reported ranges of 12 - 18 Ga. This was especially confusing in that separate evidence and theoretical calculations indicate some distant galaxies might well be 14 Ga and possibly older. This Age Paradox - stars seemingly older than the Big Bang's start time - proved particularly troubling to cosmological theorists for several years. The problem was minimized with further studies of nearby globular clusters which contain very old stars. These clusters formed along with the organization of the oldest galaxies around which the clusters are tied by gravity within the galactic halos. Data from the Hipparcos astronomical satellite led to a redetermination of globular cluster luminosities, and correlative rates of fuel consumption. From this new information the average ages of clusters was reduced by 14% so that their oldest stars (Red Giants) could not be older than the 13 Ga cited above. This, together with the more refined 13-14 billion year Hubble age (see below), obviates the discrepancy posed by the Paradox. One consequence of this most recent age estimate is that the farthest galaxies whose distances from Earth is said to be 13.4 billion l.y. must lie near the observable edge of the Universe. One galaxy has now been found at 13.23 b.l.y, and in time more will be detected that are even farther away (older).

Over the past 7 years, observational data analyzed by HST Teams whose prime task is to try to pin down the Universe's age using a better determined Hubble constant suggested in May of 1999 a best estimate for the Hubble constant of 70 km/sec/Mpc. (That number also coincides with the local expansion rate based on redshift-distance measurements for galaxies near the Milky Way.) For the H0 range they arrived at, an age of 13.97 billion years would result - a value reasonably close to the more recent WMAP results. The age uncertainty represents an accuracy variation to within +/- 10% for the value of this constant. Their value depends on analysis of redshifts in 18 galaxies within 67 million l.y. from Earth; in these they have found up to 800 Cepheid variable stars which are considered reliable indicators of large distances. From the combined determinations for the 18 galaxies, this best estimate of expansion rate gives an increase in velocity of 256,000 km/hr (160,000 mph) for every 3.3 million l.y. farther out the stellar entity (galaxy or individual stars) is from Earth.

A group of astronomers associated with Marshall Space Flight Center colleagues have used 38 galaxy clusters spread over distances from 1.4 to 9.3 million light years observed by the Chandra (X-ray) Observatory space telescope combined with radio telescope data to obtain intrinsic luminosity data from which distances can be calculated. Using these, they derived a value for H0 of 77 (+/- 15%) which translates into an age of 12.7 billion years for the Universe.

Many astronomers disputed the above age specifications based on the galaxy distance model, citing older ages according to their calculations and their interpretation of H values using different inputs. In the late 1990s most cosmologists (e.g., Alan Sandage and associates) had accepted a small range of values of H0 that yield ages centered on 14 Ga; those ages are now close to the preferred "best estimate" of 13.7 Ga (see above). However, a vital note of caution: As more galaxies at great distances from Earth are detected and measured astrometrically, so that their intrinsic brightnesses, distances, and redshifts are known with notable accuracy, the value of H0 could be recalculated to a lower number. This would mean an older Universe (greater than 14 Ga) and would mean that the oldest galaxies now detected lie inside the limits of the knowable Cosmos. Said another way: there may be considerably more space beyond our present observable Universe, which is where our time horizon now extends, and this additional outer volume would likely contain galaxies. This can be assessed when/if we can see the outermost, already detected galaxies in such detail that we can specify how primitive or early they are in their evolution. If they appear to be in the first stages of formation, if we know enough about their rates of growth, and if galaxies indeed to form within the first billion years after the Big Bang, then these galaxies are probably near the edge of the expanding Universe, with little or no space beyond. This does not rule out an infinite Universe, if it is destined to continue expanding into an infinite future.

However, the Hubble Age also can be modified depending on whether the Universe is open, closed, or flat, and may be influenced by the type of space involved (see below). In the absence of gravity the value of tH is 1/H0. The Hubble age for a Universe with flat expansion varies as the relation tH = 0.67/H0 (this applies to the Einstein-DeSitter Universe [see below]). For an open Universe, tH falls between 1 and 0.67 but 1 is usually chosen; an open Universe seems the best model at this time. For a closed Universe, tH can be less than 0.67. These several cases for ages that are less than 1/H seemingly point to Universes that began less than ~14 billion years ago. But, if the ages of the most distant galaxies, now only estimated from distance-brightness relations, prove to be around that value, then the resulting paradox - parts are older than the whole - will need to be explained away. To some extent, resolving this paradox can help to specify the type of Universe that actually exists, since age-incompatible situations would seem to argue against the types that don't fit.

Just when it seemed that astronomers have finally firmly fixed the value of the Hubble constant so that the Universe's age and size can be considered as accurate, a new set of data - if confirmed by additional observations - have cast doubt on the best number for H0 and hence for estimates of Universe age and size. A group of astronomers led by Dr. Kris Stanek of Ohio State Universe have spent years developing a new technique for determining distances to galaxies and stellar objects that would avoid several steps in the process - hence reducing errors. Their method involves determining the mass of mutually orbiting binary stars, which allows calculation of intrinisic brightness that is compared with apparent brightness, from which distance is then established. They used two large bright stars in M33, the Triangulum galaxy. Their method came up with a distance from Earth of 3.0 x 106 l.y. Previously that galaxy had been rated as 2.6 million light years away.

If, after repeated testing and detailed assessment by fellow astronomers, their method holds up and becomes accepted as the best distance estimater, this could imply that the 15% greater distance the OSU team found for M33 is valid for other galaxies at various distances. The value for H0 would need to be adjusted downward by 15% and thus cosmic age and size of the Universe would need to be increased by 15%. At the moment, the "jury is still out" on this new result.

Nevertheless, from the above, variations in the chosen value for H0 have a major, definitive influence on two fundamental cosmological parameters that scientists seek to know "exactly" - the size of the observable Universe and the age of the Universe. This notion is brought home by considering the consequences of changing the H0 value, as is done in this figure:

The question to ask in interpreting these H curves is which one leads to a younger Universe; which Universe is smaller? Check the conclusion by clicking on this asterisk *.

The essential factors determining the Universe's age are its overall density (mass and energy) and the value of the Deceleration Parameter (related to the Hubble Scale Factor), as discussed elsewhere on this page. These specify the rate of expansion which in turn reveals how long it takes for galaxies to get to the farthest reaches of observable space Observable space is defined as the limits or horizon defined as the farthest bodies that have emitted radiation which has had time since the beginning of the Universe to travel to Earth's observing stations. This will be marked by the first vestiges of materials capable of emitting detectable radiation during the early moments of the Big Bang. So far, detectors covering optical and other spectral regions have not yet picked out these oldest sources, so the currently observable Universe presently is smaller than the total observable Universe.

The Hubble equation specifies that the fastest receding objects must be farthest away; conversely, those near the Milky Way are the slowest moving. Thus, in an expanding Universe, with all galaxies ultimately drawing apart from each other, those progressively farther away must travel at proportionately greater speeds, but at the same rates in all directions, to preserve an overall uniformity of spatial relations during these expansive movements. As a general rule, the greater the lookback time, the smaller was the size of the Universe at such times, and the hotter and denser is the early expansion status of matter and energy. (Lookback time connotes the idea that the farther out in space one looks, the further back in time [earlier] is the event or stage of development associated with objects [e.g., galaxies] when light left them; a large Lookback time means a younger age]).

Because most galactic measurements made on distant galaxies show red rather than blue shifts (the latter are seen for mostly nearby galaxies moving towards us [Andromeda is approaching Earth at ~360,000 kph] or can be noted in individual spiral galaxies as one arm moves towards Earth), this evidence for overall (net) recession is the principal proof for the Big Bang expansion model. The redshift is related to recessional velocities (ratioed with respect to the speed of light) by an exponential curve in which the velocities rise rapidly towards infinity as that speed in approached. Most measurements of z from less distant galaxies afford numbers between 0 and 1 (for example, z = 0.1 represents a distance of about 1 billion light years). Farther out galaxies showing redshifts of 1.2 correspond to ages in light years of about 8 billion years; HST has now observed many galaxies with z's up to 2+. Distant quasars, some about 10-11 billion l.y away, have shifts of 3 - 4 or higher (at an observed age much earlier in Big Bang time). Several galaxies have measured z values of 5-6 and one now has a value of z = ~10 (reaching to about 90% of the speed of light); these are thus formed during the first billion years of the Universe.

Here is an image obtained during the Sloan Digital Sky Survey (SDSS) showing a galaxy with a redshift of 5.82 that is unusually bright (a quasar is inferred as the cause).

Recessional velocities as a function of distance of cluster galaxies from Earth as the observational frame of reference can be calculated from the Hubble equation and z values. Choosing a Hubble constant that gives 14 Ga as the age of the Universe, a galaxy recedes an additional 25 km/sec for each million l.y. further out one looks through space. For a cluster in the Virgo Constellation, at a distance of 78 million light years, the recessional velocity is ~ 1200 km/sec. For the Bootes cluster, at 2.5 billion l.y., the velocity has increased to 22000 km/sec. Galaxies whose distance is about 5 billion l.y., attain velocities approximately one-third the speed of light (100000 km/sec). The most distant observed sources (mainly quasars) reach recessional velocities approaching light speed. The same type of velocity distribution would be ascertained at any other observational point (such as set up by the distant galaxy "civilization" referred to earlier) in the Universe.

As HST observations accumulate, it is becoming evident that, with its resolving power, structure in galaxies can still be recognized out to about 4 billion light years. Present evidence is that beyond a z value of 2.75 no well-formed spiral galaxies can be confirmed to exist (but at least some are likely). Those that lie farther out seem to be ellipitical or commonly "dismorphous" (no regular form). Since these are older, this implies that spiral galaxies may not develop until later in galactic evolution. Some of the earlier-formed spirals have one or more extra arms compared with younger ones (the Milky Way has 3 major ones).

The discussion in the above paragraphs is confined to redshift measurements that can be made from observable astronomical phenomena such as galaxies and quasars. There is another aspect which is more theoretical, namely, the redshifts in the earlier history of the Big Bang prior to the onset of the Decoupling Era (before which no direct observations is possible). At the initial Planck Time of 10-43, the redshift z is calculated to be 1032. After one minute - the beginning of the Radiation Era, z drops to 109. In the first 1-2 billion years after the B.B., the redshift decreases from about 30 to 6. The latter is near the maximum value determined so far by direct measurements - the galaxies with that value are about 13 billion l.y. away.

This systematic increase in redshift going back in time accompanies the expansion of the Universe. The process of enlarging space leads to a lengthening of the wavelength of light - hence the progressive rise in the redshift value of z. Photons that have to travel greater distances, from further out in the expanding Universe, appear as though they have decreased energy - hence longer wavelengths (Planck's Radiation Law), i.e., shifts from blue to red. Since redshift depends on the velocity of a receding object, it follows that the maximum velocities of galaxies are found in the outer reaches of the observable Universe. This is logical: if all matter/energy was concentrated at a singularity at the time of the Big Bang and then dispersed thereafter, those manifestations of matter such as the galaxies that are farthest from the observation point (for us, Earth) must have been traveling at the fastest speeds - in other words, if all matter started from the same point, matter now farthest away had to travel at the highest velocities.

There is also another theory which can, in principle, modify the implications of the observed redshifts, namely, that the velocity of light is not constant but has changed over time by gradually slowing down: this is the "tired light" concept which, while intriguing, has so far not been supported by data or observational proofs, although it does seem to have a relation to the expansion aspect of stretching light to longer wavelengths (paragraph above). It has its supporters; some cosmologists and quantum physicists have postulated that the current values of certain fundamental parameters have changed with time, having different values (especially in the early moments of the Big Bang) that evolve into their present numbers as the Universe grew. Even though evidence for this is presently lacking, this is not trivial or frivolous speculation but falls into the time-honored scientific methodology of proposing seemingly outlandish theorems or propositions capable of explaining some phenomena and then conducting experiments to confirm or deny the idea.

The age of the Universe is a fundamental value which cosmologists seek with great care and effort to establish accurately. What will help in settling on a "best value" would be an independent measurement using a technique other than the recessional velocity extrapolation. In April of 2002, a seemingly reliable second method has been reported. It is based on knowledge of the time involved in White Dwarf stars burning out their remaining fuel to reach a "glowing ember" state. Theory sets a fairly precise time span for this to occur. In the earliest stages of galaxy formation, Globular clusters will contain rapidly produced white dwarfs as large stars burn their Hydrogen over a brief time and then enter the Dwarf stage. The "embers" that are very old are hard to detect by telescopes. But, the Hubble ST has been used on a globular cluster near the Milky Way to search for these embers; by taking a long exposure image (cumulative 8 days, spread over 67 days) these faint White Dwarfs were detected, as shown in this set of images of stars within cluster M4:

As reported by Dr.Harvey Richer and his colleagues, calculations place the age of these White Dwarf "cinders" at between 13 and 14 billion years. By adding ~1 b.y. (typical time for the first Globular clusters to develop) to these values, this independent age assessment falls right within the same range now generally accepted from recession measurements. The two methods of determining Universe age, using a "ladder" approach to arrive at the final values, are shown schematically in this diagram:

Unless fatal flaws are discovered in either or both methods, it seems for now that an upper limit of 14 billion years will stand as the actual age of our Universe.

We can summarize the age information that includes key events in the Universe's early history by posting this diagram which includes some of these events (most of those were described on page 20-1):

Note that we can only look directly back at stars and galaxies, such as those that formed in the early Universe, to a time approximately 380,000 years after the Big Bang.

Source: http://rst.gsfc.nasa.gov/