Andromeda'sDynamics in Expanding Universe

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  The differential equation, defining the motion of two isolated bodies in space, is obtained by equating the gravitational force between the two bodies to the rate of change of their relative velocity. It could actually provide us with a better estimate of time needed for the motion of galaxies in our example. However, since we do not know the strength of the gravitational force between individual galaxies, we cannot determine the exact magnitude of their acceleration at the 2.5 Mlyr separation point and thus accurately determine their previous behavior. Instead, let us examine a few hypothetical examples, which in our case will be more than sufficient to demonstrate our point.

Consider at first the case when both galaxies existed but were widely separated in space a long time ago and had initially a negligible approach velocity. This is a somewhat unrealistic example because of the very large distance of separation. However, this example provides for a simple solution of our differential equation. Keep in mind that we are ultimately interested only in the behavior of the two galaxies in their proximity.

Our previously selected initial conditions of our first hypothetical example can now be introduced into the differential equation, which will help us to understand the behavior of the two initially widely separated bodies in space in greater detail. The results show that in this case the time required for celestial motion is directly proportional to the 3/2 power of their distance of separation. Therefore, we can state that if it will take 4.5 Gyr for the two galaxies to merge from a distance of 2.5 Mly, then it will take them 12.7 Gyr to merge from a distance of 5 Mly. By the same token, it will take the two galaxies roughly 23.4 Gyr to merge from an initial separation in space of 7.5 Mly. The two galaxies of our local group, a part of the Virgo Super-cluster, are separated from surrounding large galaxies by at least this distance.

This result appears to indicate that in this example, the interval of time required for the galaxies to move from a separation of only 7.5 Mly to reach their present position of 2.5 Mly apart is greater than the total life span allowed by the theory of the expanding universe. These are very serious timing discrepancies, which will require further investigation.

The same differential equation can be used also to obtain more accurate information on velocity. It shows that in this particular case the approach velocity between two isolated bodies in space is inversely proportional to the square root of their distance of separation. Thus, with the approach velocity of 100 to 140 km/sec at their present distance of 2.5 Mly, the velocity at the 5 Mly separation point in space had to have been approximately 71 to 99 km/sec. The approach velocity at a distance of 7.5 Mly had to have been approximately 58-81 km/sec. As we have shown above, this event would have taken place an extremely long time ago, thus implying that it had to have taken our two galaxies a very long time to reach their present approach velocity.

A few more hypothetical questions also come to mind on the subject of celestial motion. These new questions deal with celestial motion events taking place in space where individual bodies were located closer to each other to begin with and were initially at rest. The resulting motions due to gravitational forces would have to be much more time-consuming than in the previous case of two isolated bodies already in motion. For example, how much time would it take Andromeda galaxy to reach our galaxy, just 2.5 Mly away, if the initial approach velocity between the galaxies were almost zero? We sidestepped the effect of gradual reduction in the initial approach velocity for the two galaxies and went directly to the more interesting subject of near zero initial velocity.

Clearly, it would take them significantly longer to merge than the previously estimated value of 4.5 Gyr for the two galaxies already in motion at a present rate of about 100 to 140 km/sec. In this instance, even maintaining present velocity at a constant value, that is disregarding the effect of the additional acceleration with time or distance, it would take only slightly longer than 4.5 Gyr for the two galaxies to merge. This observation alone implies that to reach their present approach velocity of 100 to 140 km/sec, the two galaxies had to have been moving and continuously accelerating towards each other for a very long period of time, confirming our earlier statement.

Let us now examine the behavior of our two galaxies when both of them originated much closer to each other in space, thus effectively increasing the acceleration force acting between them. This would be a more realistic case for the origins of the two galaxies in an isolated area of space. In the first of these examples, let us assume that the beginnings of the Andromeda galaxy was located at a distance of only 20 Mly away from our galaxy and both of them were initially at rest.

In this case the differential equation states that if Andromeda’s velocity was 100 to 140 km/sec at a separation point of 2.5 Mly, then its approach velocity at the 5 Mly separation would have been approximately 65 to 92 km/sec. Similarly, their approach velocity at the 7.5 Mly separation point would have been approximately 49 to 68 km/sec. As expected in both cases, the approach velocities were significantly lower than in our previous example. This result indicates that our earlier estimates of 12.7 and 23.4 Gyr time required for the galaxies to merge after passing the separation points of 5 and 7.5 Gyr were significantly underestimated.

The same calculations can be repeated for our second example. In this case, only 10 Mlyr may have separated the young galaxies initially. Their corresponding relative velocities at the 5 Mlyr and at 7.5 Mly separation points would have been 58 to 81 km/sec and 33 to 47 km/sec respectively. The effect of a significant velocity reduction between two initially closely spaced galaxies becomes evident, implying that at start-up of the merging process, it takes much longer for the galaxies to cover same distances than in the previous examples. These time spans become increasingly greater the closer were their origins.

We must point out that in our very first example, it was assumed that the Andromeda galaxy originated very far away from our galaxy. The equations of motion showed that in order to cover a long distance with low initial acceleration, the galaxies eventually converged at an optimum speed and quickly traversed the 7.5 and 5 Mly separation points in space. For this reason, all the new time spans produced by the reduced approach velocity of our two galaxies traversing same distances, but now originating anywhere reasonably close from each other, would have to be more time consuming than we previously reported. However, it appears that our two galaxies originated a long time ago separated by a substantial distance.

The important point here is to show that in all of these hypothetical examples, the time it took for the two approaching galaxies to cover just relatively short distances was very long and was encroaching on the time limit imposed by the theory for the expanding universe. Note that these events were supposed to have taken place between just two galaxies in a relatively small, but isolated area of our universe, which presumably initially consisted of some homogeneous and isotropic distribution of matter.

  For all of these reasons, it is very difficult to comprehend how stars, much less distant galaxies at the fringes of our presently observable universe, could have formed in the time span estimated to be approximately 0.4 to 0.8 Gyr, as reported by Wilson, et al., (2004). The photograph of the Hubble Ultra Deep Field (HUDF) by Windhorst & Yan (2004) shows a collection of some very distant galaxies. Approximately 100 of these galaxies were circled for ease of identification. They were located in an area of space extending 3.6 Mly across (Windhorst 2008). It is important to note that these few early galaxies were randomly scattered and widely separated from each other in the universe that shortly before consisted only of some homogeneous and isotropic distribution of small particles. 

Considering the fact that this distribution of galaxies was observed in the very early universe, so very soon after the Big Bang. It would have been much more reasonable if we have found many more than 100 smaller galaxies closer-together in the same area of space. Actually the separation between individual galaxies in the deep field of space is even greater than it appears, as their photographs are projected onto a plane. That is, the separation between two galaxies, which appear to be on a collision course in the photograph, could be found to be quite distant from each other when their redshift differential is taken into account. 

By the end of 2009 it was reported that a few new galaxies were observed in the previously photographed HUDF. These new galaxies, observed in the near-infrared light were only 0.6 Gyr old (Villard et al. 2009). The new photograph referred to as HUDF09 showed galaxies approximately 13 Glyr away with some of them redshifted to z = 8.6 and hopefully others to be observed all the way to z = 10 (Villard 2009). In fact, in January 2011, it was reported that one galaxy was found to be some 13.2 Glyr from Earth (Villard et al. 2011). This fully assembled galaxy appears as a small red dot in the photograph and represents thus far the most distant object found in space in our universe, designated as UDFj-39546284. Its light was emitted some 0.48 Gyr after the Big Bang. 

We continue to look very deep into space in the direction of HUDF in an attempt to reach the origins of our expanding universe and we have successfully penetrated very deep into space. In our last effort we managed to find a tiny galaxy which is said to be very young (only 0.48 Gyr), 13.2 Gly away from Earth. With the velocity of light of 300,000 km/sec, 13.2 Gly represents truly an astronomic distance in space. As Massimo Stiavelli, the HUDF project leader pointed out: "Hubble takes us to within a stone's throw of the big bang itself" (Savage, et al. 2004).

However, it is important to point out that as we continue to reach deeper into space, we keep finding only occasional tiny galaxies. This observed unusual distribution of galaxies in the very early universe makes us stop and ask these questions: What specific celestial bodies other than galaxies are we looking for? And what exactly are we expecting or hoping to find in space as we approach the 13.7 Gyr age limit of our expanding universe?

 

In January of 2010 a new photograph of a portion of the Southern Field, known as Great Observatories Origins Deep Survey (GOODS) showed a few new and not previously observed galaxies dating back to 0.65 Gyr after the Big Bang (Villard et al. 2010). These distant galaxies in the GOODS-S/ERS photograph are said to be blue and in their formative years. It is now believed that the first galaxies in our universe were formed in the first few hundred million years after the Big Bang (McKee2005). The report by Villard et al. (2010) provides some interesting insights into the early GOODS universe. By looking into the direction of the GOODS field, however, the universe appears to be essentially identical to that looking towards the HUDF and that, on a macroscopic scale, our 13 Gyr universe appears to be homogeneous and isotropic.

When observing distant HUDF and the GOODS field in an expanding universe, a few questions come to mind. First of all, 13 Gyr ago a galaxy existed 13 Gly away in the presently observable HUDF. Because this galaxy exhibited redshift in its signals, it was concluded that at that time, this galaxy was receding from our galaxy following the expansion of space. This is a widely recognized explanation for the redshift of signals in space. Likewise, another galaxy was glowing at the same time 13 Gyr ago, 13 Gly away in the GOODS field and was also receding from our galaxy. 

A hypothetical question comes to mind: What would the present HUDF observer see if he were to look in the direction of our galaxy and even beyond? Would he not see our galaxy, moving away from him and radiating in space 13 Gyr ago and 13 Gly away, just as we have been observing his? In an expanding universe, which is homogeneous, there is no center and no observer can occupy a preferential position in space (Wright 2013). Therefore, we can state that the present HUDF observer must have an identical view of the universe and also of our galaxy (as it existed 13 Gyr ago), when looking in our direction. There would be no difference between who the observer is and who is being observed.

The HUDF observer might be puzzled by his inability to look deeper into space beyond our galaxy, just as we are presently unable to look deeper beyond the HUDF galaxy. However, today we do know what existed 13 Gyr ago near our galaxy and even  beyond our galaxy, in the direction away from the HuDF observer. By looking today in any direction we fail to see any observable difference in space near our galaxy or anywhere else, extending all the way up to a distance of 13 Gly outward from Earth - that is, visible all the way to the HUDF galaxy and the GOODS galaxy. 

On the basis of this observation and realizing that homogeneity must exist in space at all times, even in an expanding universe (Wright 2013), we can safely conclude that such conditions had to have existed near our galaxy 13 Gyr ago. That is, what the present HUDF observer can see in front of our galaxy 13 Gyr ago, should be essentially the same what today’s GOOD’s observer is able to see what existed just in front of our galaxy 13 Gyr ago.  

We can now state with a fairly high degree of confidence as to what the present HUDF observer should find immediately behind our galaxy. Eventually, he should be able to see the same distribution of galaxies behind our galaxy, similar to the ones he was able to find in front and to all sides of our galaxy. These new galaxies would only be farther away, probably to a distance of no less than what is observable to both sides of our galaxy’s field and so on into deeper space, all the way to the GOOD observer’s galaxy.

We can now state that this argument should also be applicable to our galaxy’s observer, trying to look deeper into space beyond the HUDF galaxy or the GOODS observer’s galaxy. The areas of the universe beyond currently-observable HUDF and the GOODS field would also have to be populated by many other galaxies, looking very much like similar areas just in front of them, all the way for the next 13 Gyr of distant space.

Since we know the size of our presently observable universe as it existed 13 Gyr ago and we recognize that continuity in space exists between our observable universe and those of the HUDF and the GOODS galaxies observers’ universes (and even others beyond), our common universe must have been “enormous.” That was 13 Gyr ago with the universe still rapidly expanding at that time. Could we suppose that this term “enormous”, used by Filippenko (1998) to describe the size of the expanding universe 13 Gyr ago, implies an indefinable universe?

These findings lead us to believe that the estimate of the reported time span of approximately 0.4 to 0.8 Gyr allotted for the formation of new galaxies in the distant universe, from an initially uniform distribution of matter, may not be reasonable. This implies that the model of our 13.7 Gyr old expanding universe may be suspect. In an expanding universe, the area of distant space 12.7 Gly away, as shown in the HUDF photograph, was only 3.6 Mly across (Windhorst 2008). In the steady state model of the universe, this distance would be almost three times greater and the observed distribution of distant galaxies in the HUDF would not be any different than that in the near field of our universe (Saharian2009).

In the very early expanding universe, which was presumably homogeneous and isotropic, near zero velocity and acceleration conditions had to have existed in space between individual particles of expanding matter. As we have demonstrated in our Andromeda examples, it would have required a very long period of time to initiate motion of these particles, even in an inherently unstable medium. With no obvious mechanism in place to form organized galaxies directly from an initially uniform distribution of smaller particles in space, stars would have to have been formed first, followed by galaxies as a result of some momentary local non-uniformity may be caused by some “quantum fluctuations” in space. Each process, sequentially, would have required a significant amount of time to complete.

For this reason, it would have been very unlikely to form this particular distribution of approximately 100 randomly scattered and widely separated galaxies in the reported interval of time of approximately 0.4 to 0.8 Gyr. It does not matter how small and distorted these galaxies might appear, they are still completely assembled and functioning galaxies. Because of the uniformity existing in space, the time it takes to assemble galaxies in the distant universe and their behavior in general should not be any different than in our vicinity, as long as the galaxy-forming process is the same.

One explanation for the observed distribution of these early, distant galaxies was given as: “Galaxies evolved so quickly in the universe that their most important changes happened within a billion years of the big bang.” (Savage, et al. 2004). Again, no other explanation was given in the article as to why or how this behavior of matter in the very early expanding universe came about. Further observations reaching even deeper into space, where we would expect to find many more of the widely separated galaxies exhibiting greater redshifts, may help us to confirm that we are presently looking at a very small portion of an infinitely large Steady State universe.