How Difficult Would It Be For Advanced Extraterrrestrials To Get To Earth?

In the wake of the recently disclosed Pentagon UFO files, many have inquired regarding the difficulty of actual ETs making it to our planet. In fact, this question has been explored in papers published in peer-reviewed astronomical journals over the past 40 years. One doesn't need a tremendous amount of savvy to dredge these papers up either.

For example, the diffusion of an advanced alien civilization based on applying known diffusion wave front equations to their spread (together with very pragmatic assumptions) was the basis for the paper ‘Galactic Civilizations: Population Dynamics and Interstellar Diffusion’ by William Newman and Carl Sagan, in Icarus, Vol. 46, June 1981, page 293.

The authors began with a standard diffusion equation, treating the spread of any colonizing civilization similarly to any medium that diffuses – for example, viruses, or general infections, or even human populations (say in the early colonization of the New World).. The basic diffusion equation used was (p. 301, eqn.12):

d(r)/dt = DIV (D(x,t,r) · grad r(x,t)

where, r (x,t) describes the population density at time t, and position x, and D is the diffusion coefficient in terms of x, t and r. The preceding equation is then tweaked and used as the basis for future refinements.

Rather than weary the casual reader with the dozens and dozens of equations leading to the Results section (page 314), I will simply commence at that section and then go from there.

The authors' first major computation is of N’, the steady state number of extant advanced civilizations in the Milky Way. This is essential to obtain because it is one of the key variables used to compute the mean distance between advanced civilizations in the Milky Way:

L _M = (2.5 x 10 ¹¹  /N’) ^1/3

Where the numerator refers to the number of  stars estimated in the galaxy, and N the estimated civilization-bearing stars. The result is in parsecs, assuming the mean separation between stars in the galaxy is 1pc = 3.26 light years. (Bear in mind while our region near the outer rim is sparse with stars, the interior third of the Milky Way is teeming with them, very densely packed)

Based on a star –planet formation factor, f * ≈  1, and a mean lifetime for an advanced civilization of 10⁶ years, the authors obtain: N’ = f(10⁶) = 10⁶ , or one million advanced civilizations in the Milky Way alone.

(* Note: my inclination is actually to increase f  to  ≈ 2, based on the discovery of more than 950 actual extra-solar planets, which were unknown at the time Newman and Sagan published their paper. This would yield double the number of advanced civilizations, but we will retain the more conservative estimate)

Then, the mean distance between advanced civilizations in the Galaxy is:

L_M = (2.5 x 10 ¹¹  /10⁶ ) ^1/3  = 63 pc = 205 Light years

Readers may well not appreciate this, but this is literally “next door neighbors” in terms of the galaxy!

The authors’ next task is to obtain the velocity of the colonization wavefront which they give as (Eqn. (79), page 316):

V = (v  _j )(D g) ^1/2

Here, (v _j ) is a dimensionless constant of order unity(1), and g ≈  0.1 (based on the rate of migration of human populations today (Newman and Sagan estimated 0.01 /yr, but that was nearly 30 years ago before the age of globalization). The diffusion coefficient, D, they (very) conservatively estimate at: D ≈ (2 x 10 ^-8 pc ² /yr).

Thus, the colonization wave velocity would be:

V = (1)[ (2 x 10 ^-8 pc ² /yr) (0.1 /yr)] ^1/2 = 6.3 x  10 ^-9 pc/ yr

But the authors adjust this value (with "bias") i.e. toward younger civilizations - using historic Earth colonization rates-   to: 3 x  10 ^- 4 pc/ yr.  I removed some of that bias using a statistical algorithm, leading to the slower  colonization wave rate of : 

V =   4.4 x  10 ^-5 pc/ yr

Which would imply 1.4 x  10⁶   or 1.4 million years  (instead of 210,000 yrs.) before the colonization wave reached Earth, assuming a 63 pc distance to the planet of the nearest advanced colonizers.  (The lifetime of these advanced colonizer civilizations is assumed to be greater than 30 million years. In other words, they all would have had to survive their critical nuclear energy development phase.)

Now, before anyone gets too ecstatic, bear in mind:

1) Sagan and Newman based their diffusion coefficient on relatively low travel speeds (v much less than c) since anything near v ~ c would be enormously expensive in terms of shielding, propulsion (page 312). They opted then for speeds far below relativistic (e.g. ≈ 40,000 km/h).

2)They deliberately assumed a “random walk” diffusion with directional bias “away from population centers".

I personally suspect the first is way too conservative and ignores the sort of ingenuity and enterprise that may well apply to a truly advanced civilization which is also space faring. And again, just because we can’t imagine humans attaining relativistic speeds, doesn’t mean advanced aliens couldn’t. So, just a shift (reduction) of the base travel time to about one ten thousandth of what the authors use enhances the diffusion wave speed, V to 0.004 pc/yr.

This reduces the time to encounter to 1.57 x 10 ⁴ yrs. or just over 15,700 years. A blink of an eye.

Thus, if the alien colonizers commenced a journey in our general direction from about 3ky before the Holocene geological era, then they’d be roughly 700 years away from finding us. (Give or take 1000 years in terms of uncertainties). This means the colonizers may well be “right around the corner”. Or may even have already entered our terrestrial environment.

The conclusion here is that any of the strange craft we've seen in the released Pentagon files could well be craft from an advanced civilization, based on fine tuning the Sagan- Newman diffusion wave equations.  This doesn't prove the unusual craft seen in the released Pentagon video, e.g.  https://youtu.be/Ce6ZevfbIK0

is an actual alien craft, only that this hypothesis can't be excluded. Especially in light of the Sagan-Newman paper, especially with factors tweaked after the emergence of the exoplanet discovery era. 

Solving The Mystery Of Stellar Motions In The 'Hercules Stream' Of Our Galaxy

Polar view of Milky Way galaxy showing L4, L5 Lagrangian points and the solar neighborhood.

As I noted from an earlier (May 15, 2011) post, analysis of the motions in the spiral galaxies like the Milky Way is not easy or straightforward.     As an example, assume the (polar) coordinates for a galactic rotating frame are given as (r, φ) with:

dφ/dt = dΘ/dt - W _p

where W_p is the angular velocity of the rotating frame for the galaxy. Then orbits are described by a Hamiltonian (recall the Hamiltonian adds kinetic and potential energies of the system):

H = ½(p_r² + p_φ²/r²) + V(r) - p_φ W_p

where the p_r, p_φ  are the particle momenta referred to the associated coordinates, and V(r) is the gravitational potential. The point is that H can change depending on the coordinates, and what is presented for the previous frame as H = E - J W_p (with simplification, p_φ = J) may well be different for another frame.

Such considerations enter into investigating the cause of the motion of the so-called "Hercules stream".  This is a group of stars (about 10 percent in the solar neighborhood) which exhibits an oddly distinctive collective motion. It includes stars that are moving away from the galaxy center while actually falling behind the galaxy's general  rotation.

What this means is that the group's average orbital angular speed is less than the angular speed of the galaxy (e.g.   W  <  W _p )

According to standard theories of stellar evolution, new stars typically condense with other new stars out of the same dense, cool region of dust and gas. Hence, since stars are born more or less at the same time they "inherit" the motion at that position of the galaxy coincident with their birth place.  The problem is that the Hercules stream is different with spectroscopic observations revealing stars of widely varying ages. How can this be? Whatever the basis of the streaming motion it operates across vast scales of time and space.

One suspect is the dense central bar of stars (see highlighted in graphic) from which two of the galaxy's spiral arms sprout. The solar neighborhood lies beyond the orbit of the ends of the bar, but the Sun (and stars of the Hercules stream) are close enough to feel the bar's gravitational influence. As the stars orbit the galaxy they oscillate toward and away fro the galactic center.

The number c of epicycle oscillations per orbit about the galactic center is given by the ratio of the star’s epicycle frequency (k_o)  to its orbital angular speed, W.

Or:   c =  k_o / W  

If it happens that the star's radial oscillation resonates with the bar's rotation the star can end up with an extra 'kick' away from the galactic center.  The resonance, the outer Lindblad resonance, has been invoked to explain the Hercules stream but more recent observations have identified flaws.  In fact one major flaw in that since the bar rotates more slowly than originally thought the outer Lindblad resonance is too distant to be the stream's primary mover.

Recognition of this disparity has been incorporated in a new dynamical model proposed by Angeles Perez - Villegas and colleagues at the Max Planck Institute  Their model has succeeded in not only re-creating the positions and velocities of the Hercules stream but also revealed the cause of the unusual motion.

It turns out the stream's stars are orbiting two local maxima, identified as the L4 and L5 Lagrange points. (See diagram at top).  The Lagrange points mark positions where the combined gravitational pull of the two large masses provide precisely the centripetal force required to orbit with them.  In this case,  the masses are the galaxy central bar, and the Hercules stream.  The key point to note is that the L4 and L5 points are in the bar's effective gravitational potential, V(r) = - GMm/r.

Note more specifically that the L4 and L5 points are situated on the bar's perpendicular bisector close to the distance where stars co-rotate with the bar.  In the Perez -Villegas et al model the majority of stars in the Hercules stream originate from the inner part of the galaxy where stars tend to be older than the Sun. Then their looping orbits, i.e. around L4 and L5, take them all the way into the solar neighborhood but not much beyond it. 

Mysterious Radio Bursts Detected - Of Alien Origin?

The Parkes 64 m radio telescope which detected the strange radio bursts.

Six years ago, radio astronomers were baffled on detecting 4 energetic bursts of radio waves that lasted only a few milliseconds. Their bafflement was engendered by being unable to associate the bursts with a specific object.  Now, more recently, we find in the July 5 issue of Science, that Dan Thornton of University of Manchester and colleagues also reported 4 mysterious bursts.

Interestingly, they exhibited energies similar to the 2007 events,  and also resembled them in appearing only once. While researchers still aren't sure what might have caused such a signal they know it wasn't a fluke. The parameters for the radio telescope and the observed events all check out and conform to radio astronomy physics.  So we do know in order to be detected at all,  radio waves must fall within certain physical limits, i.e. brightness temperature, received flux, solid angle etc. One also needs to look at properties of the antenna -receiver such as beam width, gain, antenna temperature, etc. Since all the detected parameters were within conformance to standard radio physics we know the bursts aren't flukes.

In the Science paper, the radio astronomers reported scanning the sky with the 64 m Parkes radio telescope in New South Wales, Australia (see image).  They'd actually been searching for the rapidly spinning compact remnants of once massive stars as well as other transient radio sources. In the first case, one expects a supernova would have erupted leaving a neutron star (at least) in its wake. (The 4 newly observed bursts originated in the high latitudes of the Southern hemisphere, and roughly 40 degrees south of the Milky Way's disk.)

The first order of business was to determine the distance of the events. We know as radio wavelength radiation propagates through gas and dust it impacts electrons which smear the signal. The four strange burst emissions showed such a smearing, indicating the bursts were from space and not from Earth. Also, since the point of origin was 40 degrees off from the galaxy's disk the researchers concluded the burst originated outside the Milky Way. Following a computation of how much material the radiation had to travel through, they estimated the bursts' distance at between 5.5 and 10.5 billion years.

As for the energy signature, it was astounding. Each of the four bursts released as much energy in its brief emission time as the Sun puts out in 3,000 years.  So what is the source?

Could it be an advanced alien civilization which has somehow managed to exploit the energy of powerful astronomical objects to dispatch brief, but energetic signals? Granted, this hypothesis can't be totally excluded, since one must recall E.A. Milne's rubric of always dealing with physical proposals by using the concept of a bead on a wire and never letting the bead get to one end (certainty) or the other (impossibility). However, if the distance calculation for the events holds up - it is doubtful aliens are the source. At such immense distances, in effect looking that far back in time, it is improbable advanced alien civilizations existed.

In an article appearing 25 years ago, in The Journal of the Barbados Astronomical Society, I also argued against the likelihood of extra-terrestrials using radio signals to communicate. In order to communicate, say over thousands (or even hundreds) of light years' distance, information is transmitted. It requires energy to do this. Interestingly, a relation between energy and information is available. It can be written as:

E = 0.693 kT

Here, E is the energy associated with transmission of 1-bit of information. T is the temperature of the environment in which it is sent (say the radio transmitting antenna) and k is a physical constant known as the Boltzmann constant. Imagine an alien civilization sending the equivalent of a small novel to humans. This would be approximately 10²⁰  bits of information. The associated energy would be about 0.3 (three tenths) of a Joule.  The energy required, from a practical standpoint, would be much, much larger - maybe 100 million times larger. Why? Because in the process of pure transmission (over light years distance) a significant fraction of signal dilutes. So, at least 30 million Joules would be needed, to have it get to Earth in a useful form.

Arguably, aliens genuinely interested in contact would not waste time or effort with anything so puny as a small novel. It is more probable, if they went to the trouble of first contact (as in the film 'Contact') they'd send a lot of information. Say, equal to an alien encyclopedia of mathematics, or their most prevalent language. In this case, the information content soars to billions of megabytes, and the energy accordingly. For one million megabytes (10¹²    bits) the aliens are looking at an energy for transmission on the order of 3 x 10¹⁹  Joules.

It is well to realize that time factors into this as well. If the aliens kept the transmission going for at least one hour (Earth time), 3 x 10¹⁹   kilowatts of power are needed (assuming the aliens are able to sustain a rate of energy conversion of 1 Joule per second). In the civilization classification scheme of the late Russian astrophysicist I.S. Kardashev, this would put them at a bit beyond Type I, but not quite Type II. Kardashev's three-class scheme is:


I: Able to harness the equivalent power of the planet Earth

II: Able to harness the power equal to a typical star (10²³  kw)

III: Able to harness the power equal to a typical galaxy (10³³  kw)


While the burst energies appear to be close to the last category, there is one problem: no decipherable or intelligible communication was recorded. In this case, it leaves a powerful astronomical object as the likely source.

The astronomers themselves, in their Science paper, propose the most convincing cause is a neutron star known as a magnetar.  Thornton and colleagues suggest some 1,000 of these magnetar bursts occur across the sky every year. We will wait for confirmation to see if this is in fact, the best explanation