# Do Earth Lavas and Lunar Lavas Flow Simultaneously?

A former collaborator recently contacted me with an interesting possible correlation he’d found. I’ll describe his correlation by posing a few relevant questions:

1. Are massive volcanic events on Earth periodic?

The geologic record on Earth presents multiple episodes of concentrated emplacements of basaltic magma near and lava on its surface. These “Large Igneous Provinces” (LIPs) include the Deccan Traps in India, the Siberian Traps in Russia, and the Central Atlantic Magmatic Province spread across the continental coasts of the Atlantic Ocean. All three of these LIPs have been incriminated in a mass turnover in the Earth’s ecology – for example, the Siberian Traps lava flows occurred around the same time as the greatest extinction event since the Paleozoic, the Permian-Triassic cataclysm.

There have been attempts to show that these episodes happen at roughly regular time intervals, but these attempts are accepted by only a small subset of the geologic community. Were these events truly periodic, it would represent something like the pulse of the Earth. What could possibly cause the Earth to pump massive amounts of basaltic magma towards its surface over and over, on a regular schedule?

2. Does the Solar System’s motion through the Milky Way galaxy affect deep planetary processes? Or, anything else on the planets for that matter?

It has been shown that our Solar System passes up and down through the plane of the galaxy while orbiting the galactic center, and that the time between crossings takes anywhere from 26 to 37 million years. Some statisticians have suggested that a hypothesized periodicity in mass ecologic transformation of ~26 Myr could coincide, and be caused by, this galactic period.

My friend passed me one paper that suggested various other effects on the Earth due to these galactic passages. The author, Michael Rampino, attributed these effects to interaction of dark matter particles in the core of the Earth. Rampino posits that, were dark matter composed of the mooted Weakly Interacting Massive Particles (WIMPs), these WIMPs could be captured in the Earth’s gravity well, collide, and be mutually annihilated within the core, causing the release of potentially enormous amounts of heat (>= 1019 W). This amount of heat generated in the Earth’s core could raise the core’s temperature hundreds of degrees K within only a few thousand years.

That amount of heat could certainly drive mantle plumes to the Earth’s surface, and generate emplacements of massive amounts of basalt.

3. Are Lunar volcanic events connected with terrestrial LIP emplacements?

Whether they are or not, Braden et al. (2014) catalogue emplacement dates of Lunar basaltic volcanism over the past 100 million years. Here is where my friend’s coincidence occurs.

Lunar events:
• 18 Myr (+/- 1 Myr) — “Sosigenes IMP,” covering 4.5 km2
• 33 Myr (+/- 2 Myr) — “Ina,” covering 1.7 km2
• 58 Myr (+/- 4 Myr) — “Cauchy-5 IMP,” covering 1.3 km2

Earth LIP events:
• 15.3–16.6 Myr — “Columbia River Flood Basalts”
• 29.5–31 Myr — “Ethiopian and Yemen traps”
• 54–57 Myr — “North Atlantic Tertiary Volc. Prov. 2”

These seem pretty regular – the Lunar events occur about 3 million years after the corresponding Terrestrial events. Of course, for comparison, the Siberian Traps LIP, which is the largest basaltic emplacement event known on Earth, appears to only have lasted 2 million years.

4. ## The big question

My first reaction was that large-scale periodic processes are suspicious. My geology thesis advisor once mentioned that the two big “flashy” geologic paper topics are either periodic events or biggest things ever. Maybe that was what informed by knee jerk. It’s interesting that one source Rampino cites as critical to these kinds of periodicities, specifically periodicity in geomagnetic reversals, was my advisor’s husband Tim Lutz.

But my friend’s question isn’t really about periodic processes. There is a deeper issue here.

Statistical coincidence is not correlation, especially when the data set is small (e.g. three terrestrial-lunar coincidences). However, the human mind is wired to look for coincidences like this, because it thirsts for evidence of hidden causes. No true cause of physical phenomena can be perceived by the senses. The cause always must be inferred by witnessing sensible events that shouldn’t happen without the cause. Strange coincidences can be just the thing that betrays a hidden cause.

For example, you are able to read this article because of a principle called light. You can’t see light. Light is a principle that generates the relationship between the observer and the observed that we call “seeing”. It took a lot of work by a lot of creative people (Huyghens, Fresnel, Planck, and Einstein to name a few) to clothe the principle of light with the appropriate geometry and mathematics, so we can understand how it works. You can see the geometric and mathematical descriptions of light, but you still can’t see light. Because the math and geometry can generate predictions about the effects of light, we know that light is a real principle that exists.

The human mind is designed to hunt for, and understand, these hidden principles that cause sensible artifacts to exist.

Rampino identified several apparently linked processes – passage of the solar system through the galactic plane, and the periodicity of emplacement of terrestrial LIPs, terrestrial extinctions, and impact cratering – and suggested a possible hidden cause: dark matter annihilation. My former collaborator identified another possible linked process: basalt flows on the Moon happen with the same frequency as those on the Earth. This certainly doesn’t prove that dark matter causes basaltic upwellings, but may indicate that the cause of these deep geologic process is located outside of either celestial body.

Maybe, in this way, the planets are functioning as something like seismometers, recording the action of something unseen, which acts according to our stellar system’s distance from the galactic plane. Stone telescope, indeed!

# The Cosmic Ray Threat: Is Our Sun Shutting Down?

### It’s been raining cats and dogs!

The quietest spot in the solar system is on the dark side of the full moon. On these nights, the moon blocks out all the sunlight, as well as all the radio and other electromagnetic radiation from the Earth. It’s the most serene spot in the solar system to do astronomy. But, things have been getting louder there recently.

Earlier this year, Schwadron et al. reported on observations by the Lunar Reconnaissance Orbiter’s CRaTER instrument (abstract printed below). This instrument was specially designed to measure cosmic ray intensity when the Sun is shielded behind our moon. The report states that cosmic ray intensity is now the highest it has been since we started measuring cosmic rays, and it’s getting more intense faster than expected.

Cosmic rays are electrically charged atomic nuclei, hurtling through space at incredible speeds. There are two flavors of these little morsels. One type comes from the sun, and are called solar energetic particles, or SEPs. The other type are generally thought to have been blasted out of supernovae, and then accelerated around the Milky Way and other galaxies by intense intergalactic magnetic fields. These are called galactic cosmic rays, or GCRs.

Both types of speed demon are so small and so fast that a few may have shot through your body in the time it took to read this sentence. But sometimes, those cosmic rays hit other atoms. When they do, the effects can range from cosmic ray showers, to lightning, cloud formation, malfunctioning Toyotas, heart attacks, cancer, or even evolution.

Schwadron et al. showed that, if the hail of specifically galactic cosmic rays keeps intensifying at the rate it has over the past five years, it could become a dramatic risk to our astronauts.

### The details

In 2009, the Lunar Reconnaissance Orbiter (LRO) launched with an instrument designed to study the cosmic ray environment around the moon. This instrument, called the Cosmic Ray Telescope for the Effects of Radiation (CRaTER), was outfitted specifically to model the cosmic ray effects on humans, both with and without shielding.

In late 2013 through 2014, a series of articles came out that detailed the initial findings. One of these papers, Does the worsening galactic cosmic radiation environment observed by CRaTER preclude future manned deep space exploration?, by Schwadron et al., definitively warned that it was looking pretty bad for the astronauts.

They combined cosmic ray measurements made by CRaTER with those made by the Advanced Composition Explorer (ACE) spacecraft to build a picture of the environment going back to about the year 2000. They then used a model to relate the GCR flux to the strength of the solar cycle, as indicated by sunspot number, going back to about 1950. Combining these two sets of data (observation plus model), they were then able to make a forecast about the GCR flux for the coming solar minimum, depending on just which minimum we end up with (more on this below).

They noted that, based on GCR flux measured by ACE during the previous solar minimum (~2009), male astronauts would have reached their recommended limit of GCR exposure within 400 days, and female astronauts would have reached theirs within 300. Based on forecasts of the next solar minimum (~2019), the CRaTER observations indicated exposure times would decrease by about 20%: about 320 days for male astronauts, and about 240 days for female. Given about six months to travel from Earth to Mars, and then six months back, a crew would easily exceed their GCR dose rates and enter dangerous territory.

In the latest paper, Update on the worsening particle radiation environment observed by CRaTER and implications for future human deep-space exploration, Schwadron et al. revisit this prediction, since we’re almost in the middle of solar minimum. Their conclusion? The 2014 paper overestimated the friskiness of our sun, and underestimated the intensity of GCRs, by about 10%. In other words, astronauts will be able to spend even less time than expected in deep space, because the cosmic ray environment was getting worse faster than expected.

Why was their prediction so far off?

### What’s up with the Sun?

“That’s a very good and a very hard question,” said Nathan Schwadron, principal investigator for the CRaTER experiment. “I am not sure why the dose rates are going up so quickly. [But] I suspect two issues:

“1) The magnetic fields in the solar system are weakening more rapidly than we anticipated. This has the effect of allowing more radiation into the solar system.

“2) The drift of cosmic rays has changed dramatically due to a recent reversal in the dominant polarity of the magnetic field within the solar system. This is a natural solar cycle effect, but may be accentuated due to the weak strength in the magnetic field.”

[emphasis by pjm]

Every 11 years or so, the sun goes through a cycle. This cycle is observed through increasing and decreasing numbers of sunspots, magnetic field strength, and other forms of solar emanations. Humans have observed this cycle since about the 1600s, and these observations form one of the longer records of continuous human measurement. Right now, in mid-2018, we’re at the tail end of Cycle 24. Solar minimum is predicted to hit around 2020.

The flux of GCRs follows this cycle. During solar maximum, the GCR flux is low. During minimum, it’s high. When the charged GCRs pass through the Sun’s far flung magnetic field, they experience a torque. The net effect of this torque is that the GCRs don’t get very deep into the solar system before getting redirected back out again.

When the solar magnetic field is strong, during solar maximum, only a few, very high speed GCRs make it to the Earth. When the field is weak, during solar minimum, more GCRs can get to us, including lower energy ones.

At this point, it may appear that an increasing GCR flux is just a normal result of the approach to solar minimum, though the current minimum may be some kind of really deep minimum, and it’s approaching super fast. However, that is not the only story about the sun.

### What’s down with the sun?

Back in 2011, the sun was nearing the top of its cycle, solar maximum. At that time, I filmed a pedagogical video on a prediction that was made by three sets of researchers. They forecasted that, based on observation and theory, the sun was going into a severe quiet period. I followed that video with a few additional pieces to expand on the concept.

William Livingston and Matthew Penn observed the strength of magnetic fields within sunspots from 1992 through 2009. It is well known that, in the vicinity of a strong magnetic field, spectral lines can split into multiple lines – this is the so-called Zeeman effect. This splitting in the Fe I 15,648.5 Å line can be used to estimate the strength of the magnetic field. Livingston et al. showed that the strongest magnetic field found in the smallest sunspots was about 1500 Gauss. They also showed that the average strength of magnetic field in the sunspots was trending down over time. They forecasted that, based on that trend, the next solar cycle may not produce a magnetic field stronger than 1500 G – in other words, the sun may not have enough oomph to produce sunspots during Cycle 25.

A second group, the Global Oscillation Network Group (GONG) studies sound waves on the sun. Ripples of gas on the sun, observed as a wiggling Doppler effect on spectral lines, can be analyzed to reveal processes deep within the sun’s interior. A periodic feature the GONG group has identified using these helioseismic studies is called the Torsional Oscillation. This is a specific latitude band of gas inside the sun that rings with its own frequency. As the solar cycle progresses, these two bands start around the mid-latitudes (~55° N, ~55° S) and move toward the equator. Frank Hill et al. demonstrated that about halfway through the progression of this feature to the equator, a new torsional oscillation begins. The strength of these two bands can be a predictor of the strength of the next solar cycle. However, they also showed that the torsional oscillation had not yet started in 2010, well past the equivalent starting point during the previous cycle. Hill et al. concluded that Cycle 25 would be at least very late in starting, and possibly very weak.

The third indication came from observations of triply ionized iron spectra within the solar corona, by Richard Altrock of the Air Force Research Laboratory. I did an interview with Dr. Altrock back in 2011 on his observations, but here is the summary. Triply ionized iron is a good tracker of the sun’s corona.  Around solar maximum, features appear in the corona at high North and South latitude.  These features then progress quickly to the two poles up to solar maximum, and then disappear.  Thus, this “Rush to the Poles” is a good indication of the progression of a solar cycle.  As seen in Altrock’s diagram below, the Rush to the Poles for solar cycle 24 has barely started at a spot congruent to three previous cycles.  This suggested that the next cycle would, at the very least, start very late.

The sum total of these three sets of observations is that Cycle 25 will be late, weak, and possibly nonexistent.  In other words, the sun could be headed for a Grand Solar Minimum, something we have not witnessed since the late 17th Century. The Maunder Minimum was a period during which the sun sprouted virtually no sunspots. John Eddy, who named the period after E. W. Maunder, reexamined not only the history of sunspot observations, but also anecdotal evidence like stories of auroral activity. This event lasted some 70 years, and happened to coincide with an uncharacteristically cold period in Europe. Since then, the solar cycle has picked up and popped out sunspots every 11 years or so.

### Grand Solar Minimum?

The CRaTER observations appear to support the Grand Minimum forecast. If this is the near future, what will it look like?

Every year or so, I check in on the sun. It has been very quiet lately. And I wonder, when will my kids next see a sun full of sunspots? Ten years? Seventy years? The measurements and analysis by the CRaTER team seem to suggest the latter.

However, it’s a different world now, and things have changed in the past seven years since the Grand Minimum forecast. The sun is a crafty beast, and it is not following the forecast. Please stay tuned for the next part in this series…

### ABSTRACT

Over the last decade, the solar wind has exhibited low densities and magnetic field strengths, representing anomalous states that have never been observed during the space age. As discussed by Schwadron et al. (2014a), the cycle 23–24 solar activity led to the longest solar minimum in more than 80 years and continued into the “mini” solar maximum of cycle 24. During this weak activity, we observed galactic cosmic ray fluxes that exceeded the levels observed throughout the space age, and we observed small solar energetic particle events. Here, we provide an update to the Schwadron et al (2014a) observations from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) on the Lunar Reconnaissance Orbiter (LRO). The Schwadron et al. (2014a) study examined the evolution of the interplanetary magnetic field, and utilized a previously published study by Goelzer et al. (2013) projecting out the interplanetary magnetic field strength based on the evolution of sunspots as a proxy for the rate that the Sun releases coronal mass ejections (CMEs). This led to a projection of dose rates from galactic cosmic rays on the lunar surface, which suggested a ∼ 20% increase of dose rates from one solar minimum to the next, and indicated that the radiation environment in space may be a worsening factor important for consideration in future planning of human space exploration. We compare the predictions of Schwadron et al. (2014a) with the actual dose rates observed by CRaTER in the last 4 years. The observed dose rates exceed the predictions by ∼ 10%, showing that the radiation environment is worsening more rapidly than previously estimated. Much of this increase is attributable to relatively low-energy ions, which can be effectively shielded. Despite the continued paucity of solar activity, one of the hardest solar events in almost a decade occurred in Sept 2017 after more than a year of all-clear periods. These particle radiation conditions present important issues that must be carefully studied and accounted for in the planning and design of future missions (to the Moon, Mars, asteroids and beyond).

# Don’t be lazy, dare to be Semantic! The Free Code Camp Tribute Project

Chingu Cohorts is a fantastic subgroup of Free Code Camp. They set up collaborative programming experiences among members of FCC on a roughly monthly schedule to help them develop their professional coding abilities. I have been taking part for the last two months or so, and have met great people, put together a solid project (/pengo), and generally learned a ton.

This round, I signed up for the FCC Speedrun. The goal is to complete all the FCC projects in five weeks. I may not acheive that goal, but set a few additional goals for myself.

1. Create a standard “boilerplate” semantic webpage structure that will get improved each project.
2. Learn to do unit testing, and test driven development in general.
3. Come to love CSS.
4. Develop a sustainable workflow that I can apply in a professional setting.

I just completed the first project – the Tribute Page. Two aspects I’ll discuss here are semantic design and using JavaScript for static webpages, i.e. “why use JavaScript for static webpages, Peter!?”

## Semantics

Semantics is a fancy name for the proper user of HTML in a webpage. Semantics means using the right tags for the right situation. It helps someone read the code and figure out what’s what, but also helps automated web crawlers identify specific pieces of information. HTML5 introduced many new tags, like <article> and <figure> that offer more descriptive markup. When designing webpages, I usually find I need tags that don’t exist. Tags like or – not the “ that shows up in the page tab, but a title splash area. But, it’s ok in these cases to just add either class or id attributes, or to just be creative. For example, my title splash zone is denoted as a special <section> above the main <article>.

<section>
<span>(March 15, 1925 - April 26, 2014)</span>
<h2>Linked the deep ocean with prehistoric life</h2>
</section>
<article>
<section>
It is said that old warriors never die, they just fade away.
...


At the bottom of the page, I put a standard footer that will appear (better and better!) in each project. Each is inside its own <div> and placed appropriately using specific class attributes.

HTML:

<footer>
<div class="github"><a href="https://github.com/peterjmartinson/chingu-fcc-speedrun-challenge/tree/master/frontend/tribute-page">FCC : Tribute 1.0</a></div>
</footer>


CSS:

footer .copyright {
width: 32%;
text-align: left;
}

footer .github {
width: 33%;
text-align: center;
}

width: 32%;
text-align: right;
}


## JavaScript

I chose to put only the footer in index.html, but the rest of the page is injected from app.js.

var output = '';

output += '<section>';
...
var tag = document.getElementById("app");
tag.innerHTML = output;


Why? There are a couple reasons, besides the fact that I like doing things the hard way, to learn. First, reusability. All future pages can use the same basic index.html and CSS, but will need their own .js file. Ultimately, all these pages will be loaded dynamically into a portfolio page, and I think it will be useful to have them already JavaScripted. Second, proof of principle. I’m not using a framework because I want to force myself to get deep into JavaScript. I’ll use some jQuery, but want to try to limit that to AJAX stuff and whatever may get crazy across sundry browsers. Third, testing. Though there is no test here, I want to begin implementing unit tests, which means you need your pages to be slapped in with JavaScript.

That’s it. Go see the finished product in CodePen, and the source code at GitHub.

# Don’t return the call – Callback instead!

Callbacks took me a while to understand, while they are a fundamental part of JavaScript, and especially Node.js. The concept finally clicked while working on a Slack slash command with the Chingu Penguins cohort, called Pengo. The key take away is that there are two categories of functions – those that use return, and those that use callbacks. A function that sends a HTTP request needs a callback, while one that does internal operations can simply use return.

When the Slack user invokes /pengo, one of several useful programming tips is recalled from a MongoDB database on mLab. The steps required are:
1. receive POST request from Slack
2. Request document from mLabs database
3. Receive quote response from the database
4. Format the quote in a JSON object
5. Send the JSON object back to Slack

The place callbacks clicked for me is step 3. pengo.js sends the request to a function, getQuote.atRandom(), which queries the database and serves the response back to pengo.js to play with. The problem is that it may take time for the database query to run, and the getQuote.atRandom() may complete before the query is finished.

My initial construction of getQuote.atRandom() was the following:

atRandom : function() {
Quote.count({}, function(err, N) {
if (err) callback(err);
var id = Math.floor(Math.random() * N);
Quote.find({ quote_id : id }, function(err, result) {
if (err) return err;
else return result;
});
});
}


Now, if pengo.js calls the function with var quote = getQuote.atRandom();, quote will always end up undefined. This is because the return statement is reached before the database query finishes its run. The solution here is to use a callback.

Callbacks are functions within other functions that fire off when the parent function has completed. JavaScript is designed to pause the parent function until a response returns after a request was sent. In other words, you dump the return statement and replace it with a callback.

The way I implemented this is as follows. First, replace the return with a callback. Note, you just call it callback:

atRandom: function(callback) {
Quote.count({}, function(err, N) {
if (err) callback(err);
var id = Math.floor(Math.random() * N);
Quote.find({ quote_id : id }, function(err, result) {
if (err) callback(err);
else callback(null, result, id);
});
});
}


Notice a few things. The callback accepts multiple parameters, but the first is designated for any error conditions. If there’s no error, set the first parameter to null. The savvy reader will also notice that, while my function implements a callback, it also invokes two callbacks, because there are two calls to the database.

Second, do the business in pengo.js within the callback function:

getQuote.atRandom(function(err, quote) {
if (err) console.error(err);
//
// 'quote' is now the response object
// do with it what you will!
//
var data = quote.text;
response.send(data);
});


The guts of this statement is within the function, or callback, which waits until the HTTP request has completed before running.

It’s a slight difference in how to write a function (using callback instead of return), but the returns are great.

# Earth Atmosphere, on the Moon!

Terada et al. have demonstrated that oxygen from the Earth can be transported to the Moon’s surface. The core of their study reports the observation of high-speed (1-10 keV) oxygen ions, O+, by Japan’s Kaguya (SELENE) lunar orbiter. These high-speed O+ ions are only observed when 1) the Earth is between the Sun and the Moon, and 2) Kaguya is between the Earth and the Moon. This zone is where the Earth’s magnetic field excludes the Sun’s solar wind and channels the ions that have left the Earth. Terada et al. show that the composition of this terrestrial stream of oxygen is composed of 16O poor oxygen, similar to the isotopic weight of atmospheric ozone. It also matches a hitherto mysterious oxygen signature found in several lunar samples returned by the Apollo missions.

A consequence of this finding is that the entire lunar surface can be contaminated with biogenic terrestrial oxygen, which has been produced by photosynthesis over a few billion years (with an estimate of 4×1036 O+ ions for about 2.4 billion years after the Great Oxygenation Event).

The implications are fascinating. Photosynthesis appears to have begun 2.4-2.7 billion years ago, and created the massive oxygen instability in our atmosphere (~20% O). Since that time, the Earth has been puffing this oxygen into nearby interplanetary space, where a good amount could get sucked up by the Moon’s surface. Over time, that sequestered oxygen would get buried by weathered lunar powder, thus creating an incredibly stable geologic (selenologic?) record of the Earth’s changing atmosphere. Whether that record could actually be teased out is debatable (and is questioned by Terada et al.), but perhaps deep core samples could provide a clear signal. In general, this work is another reminder that life on Earth has really been life in the Solar System. Sending people back to the Moon to study its rocks is a clearly indispensable step in understanding life’s interaction with both its home planet and its solar environment.

## ABSTRACT

For five days of each lunar orbit, the Moon is shielded from solar wind bombardment by the Earth’s magnetosphere, which is filled with terrestrial ions. Although the possibility of the presence of terrestrial nitrogen and noble gases in lunar soil has been discussed based on their isotopic composition , complicated oxygen isotope fractionation in lunar metal (particularly the provenance of a 16O-poor component) re­mains an enigma . Here, we report observations from the Japanese spacecraft Kaguya of significant numbers of 1–10 keV O+ ions, seen only when the Moon was in the Earth’s plasma sheet. Considering the penetration depth into metal of O+ ions with such energy, and the 16O-poor mass-independent fractionation of the Earth’s upper atmosphere , we conclude that biogenic terrestrial oxygen has been transported to the Moon by the Earth wind (at least 2.6 × 104 ions cm−2 s−1) and implanted into the surface of the lunar regolith, at around tens of nanometres in depth. We suggest the possibility that the Earth’s atmosphere of billions of years ago may be preserved on the present-day lunar surface.

Biogenic oxygen from Earth transported to the Moon by a wind of magnetospheric ions
Kentaro Terada, Shoichiro Yokota, Yoshifumi Saito, Naritoshi Kitamura, Kazushi Asamura, Masaki N. Nishino
Nature Astronomy 1, Article number: 0026 (2017)

# The First Law of Galactic Rotation

Nota Bene:  One of the authors, Stacy McGaugh, pointed out to me that he considers the principle described below as the Third Law of Galactic Rotation.  If you would like to know why, please go read his fascinating article on the law, as well as his articles on the other two laws.

The online magazine Quanta recently published a hot button article called “The Case Against Dark Matter”. The gist of the article is that a flurry of papers and lectures were presented over the last months of 2016 that call into question the existence of dark matter. One of the papers stood out to me, so I’ll review it here. It is called Radial Acceleration Relation in Rotationally Supported Galaxies, composed by Stacy McGaugh, Federico Lelli, and James Schombert. The abstract is reprinted below, after I summarize what I think is understated by the word extraordinary in the paper.  To be clear, for me, this appears to be the kind of discovery that will usher in a new view of the universe, as the Michelson-Moreley results motivated a similar paradigm shift in the early 20th Century.

## The relationship

The authors compiled two sets of observations into one database called SPARC – Spitzer Photometry and Accurate Rotation Curves. One set, at wavelength 3.6 μm, was obtained from observations with the Spitzer Space Telescope. The other set, at wavelength 21 cm, was compiled from decades of observations with arrays of radio telescopes like New Mexico’s Very Large Array. The 3.6 μm observations see stars, and are used to measure the amount of stellar mass in galaxies. The 21 cm observations see dark dust and gas in galaxies due to a spectral line in neutral hydrogen, and is used to create rotation curves for the galaxies.

The rotation curves represent the original problem Dark Matter was invented to solve. According to Kepler’s laws of planetary motion, as modified by Newton’s law of gravitational force, the speed of an orbiting object depends on how much mass is within the orbit. More mass = faster object. For rough point masses, like the objects in our Solar System, the orbits are determined by how far they are from the central star. In a galaxy, things get more complicated because the mass is distributed. As you go further away from the center, more and more stars and other matter end up within your orbit, thus increasing your orbital speed. This increase of mass with distance is tempered by the fact that the amount of stars and gas gets less as you approach the edge of the galaxy. Therefore, the speed of orbiting objects should drop off as you leave the galaxy.

Exactly the opposite is found. The 21 cm observations have shown that the orbital velocity of gas usually speeds up as you leave the galaxy, thus implying that the amount of matter, in fact, goes up as you leave the galaxy! But, to date, nobody has actually observed the mass. This missing mass got the apt name Dark Matter in the 1930s by astronomer Fritz Zwicky. Over 80% of matter, based on these galactic rotation curves as well as other observational evidence, is this dark matter. Other theories that don’t invoke dark matter have been invented – such as the Modified Newtonian Dynamics of Mordehai Milgrom – but none has had the success enjoyed by dark matter.

In the future, the work by McGaugh et al. might be seen as the silver bullet that killed dark matter. Using both sets of observations, they calculate the centripetal acceleration exerted on the objects in over 150 galaxies. Centripetal acceleration can be calculated in two ways: one way requires knowledge of orbital velocity, the other way requires knowledge of mass. McGaugh et al. get the mass with the 3.6 μm observations, which can be converted from luminosity to mass quite directly. This gives them $g_{bar}$, the centripetal acceleration due to observed mass. Then they get the orbital velocity from the 21 cm observations, via the rotation curves. This gives them $g_{obs}$, the centripetal acceleration observed to exist. Then, these are plotted against each other:

The relationship is absolutely extraordinary! It’s not directly proportional, but follows a slight curve toward the center of the galaxy. What is remarkable is that the exact same relation holds for all galaxies in the study, and is not dependent on galactic type. They map the relationship to a relatively simple equation

$g_{obs} = \mathcal{F}(g_{bar}) = \frac{g_{bar}}{1-e^{\sqrt{g_{bar}/{g_{\dagger}}}}}$

which only requires one parameter for the fit, $g_{\dagger}$.

Why is this extraordinary? It does NOT mean that observed mass causes what we see in the rotation curve – there is still something missing. However, it shows that there is a simple, absolute, relationship between the rotation curve and the observed mass. In other words, in a given galaxy, using this new law, if you are given the distribution of observed, not dark, matter, you can produce the galaxy’s rotation curve. There is absolutely no need to invoke invisible mass.

## The First Law

Kepler developed his laws after hundreds of hours of observational, computational, and hypothetical work. With these laws, the orbits of any object in the solar system can be completely determined (disregarding important small deviations). There is no concept of gravitational force in Kepler’s laws, only geometry, time, and motion. The laws hold for every stellar system.

McGaugh et al. have found a new law that applies to galaxies. And, they are not blind to this law’s significance. In a more extensive paper published in the Astrophysical Journal, Lelli et al. state

The radial acceleration relation describes the local link between baryons and dynamics in galaxies, encompassing and generalizing several well-known galaxy scaling laws. This is tantamount to a Natural Law: a sort of Kepler law for galactic systems. A tight coupling between baryons and DM [dark matter] is difficult to understand within the standard ΛCDM cosmology. Our results may point to the need for a revision of the current DM paradigm.

One difference between Kepler’s laws and this new galactic law, is that Kepler believed he had found the causes of his laws. Later on, his causes were tossed out by the new theory of Newtonian gravitation. McGaugh et al. have not yet settled on a cause for their newfound relationship. However, they do hint at some possibilities:

Possible interpretations for the radial acceleration relation fall into three broad categories: (1) it represents the end product of galaxy formation; (2) it represents new dark sector physics that leads to the observed coupling; (3) it is the result of new dynamical laws rather than dark matter. None of these options are entirely satisfactory.

I’ll conclude by drawing another parallel. Case Western University, home of two of this paper’s authors, was host to another critical observational result. In 1887, Albert Michelson and Edward Morely performed an interferometry experiment there to measure the Earth’s velocity through the ether. They famously returned a “null” result. Almost 30 years later, Albert Einstein shocked the world by declaring, based on Michelson and Morely’s result, that the ether – a fundamental substance of physics since the Enlightenment – does not exist.  Never again could theory or experiment rely on belief in the existence of the ether.  Case Western may, again, be the source of a critical result that will provide reason to both discard a fictional substance and provoke a new paradigm shift in our view of the cosmos.

But, maybe not.  If this discovery doesn’t kill dark matter, then dark matter’s place in the universe is about to become much stronger.  Either way, we now have a new, first law of galactic rotation.

## ABSTRACT

We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.

# Echoes of Ancient Cataclysm Heard Through FOSSILS

To paraphrase Jon Stewart, the United States after the presidential election is the same as it was before.  However, the Earth is certainly not the same since it was showered by the flotsam of numerous supernova explosions around 2 million years ago.  In this post, which is a followup to this one, we review a paper which purports to present evidence of those long ago supernovae as recorded in microfossils at the bottom of the ocean.  The paper’s abstract is at the end of this blog post.

First, what are microfossils?  In the present case, they are the remains of bacteria which populate the ocean floor.  Usually, the remains left behind by bacteria are anomalous chemical signals, such as the banded iron formations made by photosynthesizing bacteria.  Since bacteria are single celled creatures, they rarely leave fossils of their actual body parts (organelles).  However, some bacteria do produce hard internal structures that can get left behind.  One incredible type of bacteria does leave actual fossils are called Magnetotactic Bacteria (MTB).  These bacteria ingest iron from ocean water and manufacture tiny magnets within their single-celled bodies, which they can then use to orient to the Earth’s magnetic field.  When the bacteria die, these little magnets, called magnetosomes, remain as microscopic chains of magnetite.  Unambiguous fossils of these little guys can be found going back to almost a billion years.

Ludwig, et al., perform analyses on MTB and other iron microfossils from two oceanic drill cores from the Pacific Ocean.  Most of the iron within the microfossils is made up of typical 58Fe, but the analysis presented here demonstrates a spike in 60Fe within these magnets around 2-2.5 Million years ago (Ma).  As stated before, 60Fe is most likely produced by supernova explosions, but it can also be delivered to the Earth by meteorites.  Ludwig, et al., isolate supernova-specific 60Fe via a careful chemical leaching technique which draws out only secondary iron oxides and microscopic grains, thus leaving any potential micrometeorite particles in the discarded residue.  The leached material was then analyzed by accelerator mass spectrometry.  They found a clear spike in the ratio 60Fe/Fe around 1.8-2.6 Ma in both samples, and attributed the spike to the debris of multiple supernova explosions.

As noted previously, the supernovae were probably associated with the formation of the so-called Local Bubble.  According to the authors:

The Local Bubble is a low-density cavity ~150 parsecs (pc; 1 pc = 3.09×1016 m) in diameter, within the interstellar medium of our galactic arm, in which the solar system presently finds itself.  It has been carved out by a succession of ~20 [supernovae] over the course of the last ~ 10 Ma, likely having originated from progenitors in the Scorpius-Centaurus OB star assocation, a gravitationally unbound cluster of stars ~50 pc in radius.

A future Stone Telescope post will discuss the possible relationship between the Local Bubble supernovae and the Pliocene-Pleistocene geologic boundary, but for now let’s consider two aspects of this story:  1) the use of geology for historical astronomy, and 2) the plight of the magnetotactic bacteria.

## Geology as a temporal telescope

Typical presentations of astronomy compare looking through a telescope to traveling in a time machine.  Lightspeed is finite, and the closest star to our solar system is a few light years away.  Just like Han Solo’s 12 parsec Kessell Run is strange, since a parsec is a unit of distance and not a unit of time, a light year is a unit of distance, not time – it is how far an object would travel in one year if traveling at the speed of light.  Say something happens 100 light years (ly) away from the Earth.  The absolute soonest that we would know anything about that is 100 years after it happened, when its radiation finally reaches our planet.  Therefore, looking through a telescope, we see objects as they were long ago.

However, when you see an object through a telescope, you are not looking at a stop-motion picture.  What you see is changing.  For example, Johannes Kepler saw a supernova in 1609.  Astronomers have located the remnant of this supernova, which is now a cloud of plasma much larger than the original star.  It’s about 13,000 ly away, which means the actual supernova occurred about 13,407 years ago.  In other words, when we look at the remnant today, we are seeing it as it was 407 years after Kepler observed the explosion.  To see what Kepler saw, we need to read his famous book on the subject.  There is no other physical evidence to see through the telescope.

In geology, the physical evidence is still there!  We can, in a sense, pick chunks of that astronomical event up off of our planet’s crust.  Our planet is a net that captures the stuff of cosmic phenomena, and preserves it for future scientists to study.  In the present case, those little magnetotactic bacteria caught pieces of supernovae and incorporated them into their tiny bodies, which are preserved to this day for us to find.

## Those little bacteria

But, what do the bacteria care?  They were just huffing up iron ions they found in the sludge at the bottom of the ocean.  Could they tell the difference between the usual 58Fe and that rare delicacy 60Fe?  Maybe they couldn’t, but maybe they could.

Vladimir Vernadsky famously emphasized that different organisms are characterized by different atomic weights of specific elements within their bodies.  The calcium in a horse would have a different atomic weight than the calcium in a mushroom, which means a different ratio of calcium isotopes.  Vernadsky believed that organisms sought out and selected specific isotopes of elements with which to build their bodies.  That as just a brief indication, maybe the magnetotactic bacteria could tell the difference between the usual fare and the exotic 60Fe.

Maybe the 60Fe made slightly better magnets?  Biological functions have been shown to respond slightly due to isotope variations, for example in ATP synthesis.  If there was some type of advantage in taking in 60Fe, perhaps this lent an evolutionary advantage to those bacteria that could tell the difference?

But, even if they couldn’t tell the difference, they were organisms that tasted of the supernovae.  Perhaps other organisms felt the effect of those supernovae as well.  But that’s an investigation for next time.

## ABSTRACT

Massive stars (M≳10 M⊙), which terminate their evolution as core-collapse supernovae, are theoretically predicted to eject >10−5M⊙ of the radioisotope 60Fe (half-life 2.61 Ma). If such an event occurs sufficiently close to our solar system, traces of the supernova debris could be deposited on Earth. Herein, we report a time-resolved 60Fe signal residing, at least partially, in a biogenic reservoir. Using accelerator mass spectrometry, this signal was found through the direct detection of live 60Fe atoms contained within secondary iron oxides, among which are magnetofossils, the fossilized chains of magnetite crystals produced by magnetotactic bacteria. The magnetofossils were chemically extracted from two Pacific Ocean sediment drill cores. Our results show that the 60Fe signal onset occurs around 2.6 Ma to 2.8 Ma, near the lower Pleistocene boundary, terminates around 1.7 Ma, and peaks at about 2.2 Ma.

# Echoes of Ancient Cataclysm Heard Through Ocean Rock

Although I should be joining the angst against our newly elected president, this paper fell into my lap. It precisely represents the purpose of my blog, and so reviewing it is probably a better way to spend my time than yelling at idiots on facebook.

A neat paper just went up on arxiv.org: The Link Between the Local Bubble and Radioisotopic Signatures on Earth. It came to my attention via the Astrobiology Web, where they published the abstract. I’ll throw up the abstract below, after a quick summary of the paper and its predecessor.

## Quick Summary

The iron isotope 60Fe is quite rare in nature. It’s only created during cataclysmic events – yes, more cataclysmic than the 2016 presidential election. Think supernovae, or worse. It has a half-life of about 2.6 million years (Myr), which means that none of the 60Fe generated 4-5 Million years ago (Ma) during the creation of our solar system is left. We know it existed, though, because its echo is preserved in its daughter isotope, 60Ni. This isotope of nickel is also quite rare, is found in super old Earth crust, and is created only as the decay product of 60Fe. Thus, any 60Fe we find in the crust today must have salted the Earth only a few million years ago.

An earlier paper by Wallner, et al., Recent near-Earth supernovae probed by global deposition of interstellar radioactive 60Fe, presented mass spectrometer analysis of eight portions of ancient ocean crust scattered around the world, each containing tiny amounts of <sup>60</sup>Fe. This 60Fe was most likely produced by supernova explosions within the last 10 Myr or so. It just so happens that astronomers have found possible evidence of these explosions, in the bodies of stars and matter within the Scorpius Centaurus Association, which stretches from Antares in Scorpius all the way down to include the Southern Cross. These supernovae likely inflated a cavity within the local Orion Spur, a dense part of the Milky Way’s interstellar medium. In fact, evidence of this cavity has been explored for the past few decades, and it has the name Local Bubble – our solar system has been traveling inside this cavity for at least the past 10 Myr. Hence, the 60Fe found by Wallner, et al., sounds like an echo of this supernova chorus that sang out so near our planet a few million years ago.

The authors go further in the arxiv.org paper: Feige, et al.. Here, several stars from the Scorpius Centaurus Association are identified as potential precursors to the Local Bubble supernovae. Tracing the stellar trajectories back in time, Feige et al. create a synthetic history of the Local Bubble to model what Earth’s environment may have encountered. They find that, according to the model, the best fit to the 60Fe signal found in the Earth’s crust occurs at about the time our solar system passed through the shell of the expanding bubble, 2-3 Ma. They note that the oceanic drill cores also indicate a supernova signal around 6.5-8.7 Ma, which they will attempt to model in the future.

It should be noted that Wallner, et al., are not the first to identify live 60Fe in the Earth’s rock. Other researchers have found such deposits in the single domain magnet chain fossils of magnetotactic bacteria, again, in the same rough date range (~3 Ma). The transition from Pliocene to Pleistocene also occurred around this time, and may have had some direct causal relationship with the supernovae that peppered the Earth with 60Fe. Maybe we’ll investigate some of these loose ends in future posts!

## Abstract

Traces of 2-3 Myr old 60Fe were recently discovered in a manganese crust and in lunar samples. We have found that this signal is extended in time and is present in globally distributed deep-sea archives. A second 6.5-8.7 Myr old signature was revealed in a manganese crust. The existence of the Local Bubble hints to a recent nearby supernova-activity starting 13 Myr ago. With analytical and numerical models generating the Local Bubble, we explain the younger 60Fe-signature and thus link the evolution of the solar neighborhood to terrestrial anomalies.

# Master’s Research Paper, Part 1

This is a reproduction of the first part of the paper I wrote for my Master of Arts degree in geology.

# On the Magmatic Plumbing and Differentiation of a Shallow Mafic Intrusive System: Morgantown Pluton, its Birdsboro Dike, and the Nearby Jacksonwald Syncline, Newark Basin, Pennsylvania, U.S.A.

Peter Martinson
Candidate for Master of Arts
West Chester University of Pennsylvania
1 December 2014

ABSTRACT

Geochemical, petrological, and structural clues are used to determine how magma filled and differentiated within the main sill of Morgantown Pluton, its Birdsboro Dike, and the nearby Jacksonwald Syncline. Whole rock geochemistry and ESEM-EDS analysis of zoning patterns shows that 1) basalt flows at the top of the Jacksonwald Syncline experienced vertical differentiation, 2) Birdsboro Dike experienced horizontal differentiation that cannot be explained through simple fractional crystallization of the original liquid therein, and 3) the southern sill of Morgantown Pluton was a site of accumulation of orthopyroxene phenocrysts as well as filter pressing-driven expulsion of evolved liquid. Measurement of plagioclase-plagioclase-pyroxene dihedral angles within samples from the southern sill (~97° at the bottom to ~92° at the top) show that the bottom cooled slower than the top of the sill, suggesting magma recharges from the bottom. Preliminary measurement of plagioclase aspect ratios in one sample from the top sill (2.79±0.05) indicates a cooling time of about 30 years. Models of crystallization pathways of parental liquid compositions using alphaMELTS suggest the magma that intruded the system was not a pure liquid, but a slurry that contained already crystallized orthopyroxene phenocrysts which had formed in the magma prior to intrusion. A specific hypothesis evaluated is as follows: Magma intruded the southernmost portion of Morgantown Pluton first, but the magma did not sit long in this lowest sheet before encountering a Paleozoic tear fault discontinuity, ascending there into the Birdsboro Dike, and finally erupting onto the Earth’s surface as the Jacksonwald Lava. After the initial intrusion was complete, magma differentiated mainly as a result of gravitational settling of the orthopyroxene phenocrysts down the dike back into the sill, collapse of roof sections from the sill, and filter pressing of evolved liquid from the sill up into the dike.

I. INTRODUCTION

Morgantown Pluton is a layered mafic intrusion which lies at the southern corner of Berks County, PA. It is one part of a much larger complex of 200±4 Ma mafic intrusions (Marzoli et al. 1999; Blackburn et al. 2013) that spreads across the Atlantic coasts of North and South America, North Africa, and Europe, collectively called the Central Atlantic Magmatic Province (CAMP). In Eastern North America, the CAMP is represented as a network of igneous sheets and dikes that crop out in basins of Triassic-aged sedimentary rock and conglomerate. These Mesozoic basins are roughly parallel to the Atlantic coast, and were formed during the initial rifting of Pangaea and the opening of the Atlantic Ocean. The intrusion of enormous masses of diabase into the basins coincides precisely with the end-Triassic mass turnover of marine fauna identified by Raup & Sepkoski (1982), one of the big five Phanerozoic mass extinctions (Blackburn et al. 2013).

The intrusions within the Eastern North America (ENA) portion of the CAMP have the surface expression of diabase rings. Drilling within the rings has established that the intrusions are actually continuous sheets, perhaps comparable to the saucer-shaped sills of Karoo Basin, South Africa (Hotz 1952; Polteau et al. 2008). The upturned edges of saucer-shaped sills have been shown to be capable of delivering flood basalt to planetary surfaces, but many dikes are present as well in the ENA basins. The strike of these dikes is not random, but rather has been found to vary systematically along the basins – northeast-southwest in the north, to northwest-southeast in the south (King 1961, 1971).

Geochemical analysis of dikes, chill margins, and basalt flows was used to demonstrate that the rocks share a common tholeiite ancestry (Weigand & Ragland 1970; Smith et al. 1975). They can be broken into three subfamilies: 1) an olivine-normative tholeiite, 2) a high-Ti quartz-normative tholeiite (1.0-1.2 wt% TiO2), and 3) a low-Ti quartz-normative tholeiite (0.65-0.85 wt% TiO2). Local variations within any diabase body can deviate strongly from the basic types, though the variations came about through differentiation of a magma matching one of the types. The high-Ti quartz normative (HTQ) tend to be the most compositionally diverse, containing orthopyroxene cumulates, iron rich ferrogabbros, and granophyres, in addition to typical diabase.

Perhaps the most famous of the HTQ mafic sheets is the Palisades Sill, a beautifully exposed, 300 m thick, 70 km long tablet of black rock rising, cliff like, along the west bank of the Hudson River. Based on an analysis of layering within the sill, Shirley (1987) proposed that differentiation within the Palisades magma was driven by plumes of crystallizing mush that fell from the roof to the floor. The resulting cumulate pile compacted and drove residual liquid out and upwards. Further evidence for compaction and recrystallization of roof-derived plumes that resulted in modal layering was attained by Dickson & Philpotts (2001) and Dickson (2006). Besides vertical differentiation, Gottfried & Froelich (1985) has documented that lateral differentiation within the sheets is more common, and more extreme. Corroborating evidence was found for the York Haven sheet, just west of Morgantown Pluton, by Mangan et al. (1975). Several roof-to-floor sections obtained throughout the York Haven sheet revealed three major regions – an orthopyroxene-cumulate dominated region to the southeast, an iron and granophyre rich region towards the northwest, and more typical diabase in between. This lateral differentiation has been interpreted as due to lateral flow segregation of orthopyroxene and other early cumulate phases during emplacement, followed by gravitational settling, and ending with late-term hydrothermal alteration. One implication of this theory is that orthopyroxene cumulate zones are located near the original conduits from which deep magma intruded the sedimentary basins.

Morgantown Pluton, though no less interesting than its two siblings, lies mostly hidden from view, both physically and in the literature. Pennsylvania geologic maps made before 1980 do not even present the pluton as one connected body (Smith 1893). Outcrops of the Morgantown Pluton are scattered among sometimes precarious roadcuts and a few diabase quarries. Otherwise, evidence of its presence is betrayed by weathered boulders dug up by landowners and construction crews. There are no known outcrops that run from roof to floor. However, there are exposures where diabase meets country rock at a quarry in the northern part of the pluton, but this portion of the pluton is a nearly vertical chamber called the Birdsboro dike. At most other locations, elevation of outcrop above or below the contacts must be estimated.

The pluton lies quite close to a small basalt flow, though their relationship is somewhat cryptic. The Palisades Sill outcrop is also located to the south and east of a series of extensive basalt flows, collectively called the Watchung Basalt. Based on geochemical affinities and an observed point of connection, some believe magma that fed the basalt flows first travelled through the sill (Puffer et al. 2012). The basalt flow near the Morgantown Pluton has no point of physical contact with other subsurface diabase, and lies atop a stack of related intrusions within the plunging Jacksonwald Syncline (Schlische & Olsen 1988).

Several aspects of Morgantown Pluton and the nearby Jacksonwald Syncline render them unique among their diabase siblings. The fold axis of the syncline is almost parallel to the Birdsboro Dike. The dike itself is peculiar in that it runs perpendicular to the average NE-SW dike trends in the Newark Basin (King 1961), and is over 200 m thick along its entirety. The dike marks the southwestern boundary of the Newark Basin, and Morgantown Pluton lies in a transition zone between that basin and the so-called Narrow Neck region. These facts present themselves as indications that an understanding of how Morgantown Pluton formed and how it is related to the syncline is necessary for understanding the formation of the Newark Basin as a whole, and could provide insights into the development of tectonic basins in general.

For the present report, petrological, geochemical, and structural evidence will be used to evaluate a hypothesis about the formation and relationship between the southern portion of Morgantown pluton, Birdsboro Dike, and the Jacksonwald basalt. That hypothesis is as follows: Before the magma which intruded the southern sill of Morgantown Pluton had time to begin crystallizing, it spread up Birdsboro Dike, an ancient tear fault, and spilled onto the surface of the Jacksonwald flood basalt. Subsequent inputs of magma were confined to the sill, and most chemical differentiation was due to the combination of crystal settling and consequent liquid displacement. The presentation of data which will help evaluate this hypothesis will be preceded by a more extensive description of the geography and geological setting of Morgantown Pluton, the Jacksonwald Syncline, and the enclosing Newark Basin.

II. GEOLOGIC SETTING

Morgantown Pluton and the Jacksonwald Syncline inhabit the southern end of the Newark Basin (Figure 1). More specifically, the northeastern border of the pluton is the ~20 km long, 200-300 m thick Birdsboro Dike, which itself forms the southwestern boundary of the basin (Figure 2). Thus, the Jacksonwald Syncline lies inside the Newark Basin, while the rest of the Morgantown Pluton lies in a transition region between the Newark Basin and its neighbor, the Narrow Neck. Let us first examine the geography of the pluton and the syncline, and then look at the structure of the basin surrounding the two.

Birdsboro Dike strikes an average of N50W and dips about 80° SW. The dike runs from just south of Reading, PA to a little east of St. Peters about 20 km to the southeast. Here, the pluton takes a sharp turn almost due west into a broad, 200-300 m thick sill that dips about 24° towards the north (Wood, 1980). This sill runs continuously for about 15 km west-southwest, until breaking into a somewhat chaotic region which steps alternating west and north for another 15 km to just south of Knauers, PA, where the pluton widens into what may be an offshoot subsill. It may be that this chaotic region represents a series of short sills interconnected by short dikes which allowed the magma to jog upsection to this offshoot subsill. The pluton continues north from the subsill to just east of Fritztown, PA, where it again takes a sharp turn towards the east. This portion of the pluton has been described as either a steeply south dipping sheet or a shallow dike, based both on its uniformity as well as on its aeromagnetic signature (MacLaghlan et al. 1972). This portion ends when it reaches the Schuylkill River, which is also where Birdsboro Dike begins.

The axis of the Jacksonwald Syncline and its associated igneous bodies lies about 5 km northeast of Birdsboro Dike. The syncline, which is parallel to the dike, and dips about 17° NW, contains a lava flow and three diabase intrusions. The first diabase intrusion lies concentric to the lava flow with about 1 km larger radius. The second diabase intrusion, Monacacy Hill, lies about 6 km towards the east-southeast of the first. The Monacacy Hill pluton appears more tabular and less folded than the prior two igneous bodies. The third and last diabase intrusion, Rattlesnake Pluton, lies about 4 km east of Monacacy Hill. This intrusion is flat along its upper margin, and curved along its lower, which suggests it was intruded into accommodation space already created by the folding of the syncline (Schlische & Olsen 1988).

All known exposures of Morgantown Pluton exhibit some form of layering, about which more will be described below. However, one important fact derived from the layering should be stated here. Srogi et al. (2010) has shown that layering found on the walls of the Pennsylvania Granite Quarry, in the middle of the southern sill, dip conspicuously towards the north about 20°. Similar subhorizontal layering found throughout the pluton also exhibit a range of 15-20° dip either NNW or NNE. This uniformity of orientation suggests that the layering formed normal to the Earth’s gravitational field, and that the pluton was tipped towards the north after intrusion, and after solidification. The utility of this knowledge is that the northernmost portions of the pluton formed at a paleodepth about 5-6 km above the southernmost portions. Similarly, the plunge of the Jacksonwald Syncline places the base of the Rattlesnake Pluton about 4 km below the base of the basalt flow, and thus below the paleosurface.

This knowledge allows us to give a back-of-the-envelope estimate of the total volume of diabase within Morgantown Pluton, given a few reasonable assumptions. Assume that the southern sill is a disk exposed along its diameter. With a diameter of 15 km, thickness of 300 m, its volume will be 53 km3. Assume Birdsboro Dike is a tablet exposed along its long diagonal. If the diagonal is 20 km, thickness is 300 m and depth is 5 km, the volume will be 29 km3. The chaotic portion along the southwestern margin can be broken into several small sills and short dikes, which ends up having about the same volume as Birdsboro Dike, 29 km3. The northern portion is assumed to be a dike about 5 km deep, 300 m wide, and 12 km long, giving it a volume of 18 km3. Altogether, this gives Morgantown Pluton a rough volume of about 130 km3.

STRUCTURAL CONSIDERATIONS

Birdsboro Dike is peculiar because it is a dike as thick as a typical Newark Basin sheet (200-300 m), but what renders it so conspicuous is its orientation. King (1961) demonstrated that the dikes in and around the Newark Basin strike northeast, which reflects the regional stresses during the period of rifting. Birdsboro Dike lies almost orthogonal to this stress field. A cursory examination of the geologic map (Figure 1) reveals the striking alignment of the dike as a continuation of the south-east margin of the Newark Basin. Comparatively striking is the trend of the Jacksonwald Syncline, which runs exactly parallel to the Birdsboro Dike, again suggesting a structural kinship. The orientation of these two features suggests that the magma was responding to some factors other than the typical stresses associated with rifting. It may be instructive in our investigation of the Morgantown system’s origin and plumbing to summarize the current structural thinking about this region.

The most complete working model of basin evolution comes from Schlische (1992). In his view, the ~200 km long Newark Basin is a half-graben bounded on its north-west edge by a system of normal faults that dip towards the Atlantic coast. The basin began its life as a system of smaller synclines that plunged northwest and terminated against normal faults. These synclines grew and eventually merged into the larger half-graben (Figure 3). It may be that the local synclines observed in the Newark Basin today, like the Jacksonwald Syncline, were the original nuclei of the greater basin. As the basin floor tilted down against the border fault system, and the fault footwalls isostatically rose, sediment filled in from both sides. Repeated debris flows dumped mainly limestone fanglomerate at the base of the border fault system. Along the south-east margin lay the ridge of mountains formed during the Appalachian orogenesis, which delivered seasonal fluvial sediments into the basin. As the basin grew, fluvial sediment gave way to lacustrine deposition. Schlische suggests that local synclines and anticlines within the main basin (Figure 4) may have formed as short-wavelength corrugations due to both compression along the surface parallel to the basin margin, as well as to differential slip along the border fault system. After several kilometers of sediment accumulated, early Jurassic intrusive diabase dissected the sediment above the thinned basin crust. The entrainment of both diabase and lavas within the synclines suggests that the igneous event occurred long before the conclusion of folding. The extreme ends of the major basins served as axes of rotation that allowed the intrusion of magmatic dikes as accommodation features.

This construction offers at least two controls on the diabase that interest us in the present study. First, the model suggests that several of the sills and lava flows were folded along with the synclines, and thus were originally emplaced flat and only developed their currently observed curvature later. Schlische (1992; also Schlische and Olsen 1988) specifically treats the four igneous portions of the Jacksonwald syncline as follows. The lava flow and the intrusive diabase immediately below exhibit no thickening, or “ponding,” near the synclinal axis, which suggests that they were emplaced as relatively flat entities and folded afterwards. The two deeper intrusions, however, exhibit clear ponding, which suggests that they were emplaced as phacoliths into weakened zones along an already formed synclinal hinge. Second, the model suggests that Newark Basin as a whole functions as a long-wavelength plunging syncline, and that either end of this syncline could be host to steeply dipping igneous dikes intruded as accommodation dikes. While the northern end of the Newark Basin may or may not contain a steeply dipping dike (Puffer et al. 2009, Schlische 1992), the southern end certainly does – the Birdsboro Dike.

In broader context, tectonic processes pertinent to the formation of the Morgantown Pluton and the Jacksonwald syncline may predate the formation of the Newark Basin, and possibly control the basin’s extent. Wise & Faill (2002) define the Schuylkill Tectonic Zone (STZ) as an 8-10 km wide swath around the Schuylkill River roughly parallel to the Birdsboro dike and Jacksonwald Syncline, running from the northern edge of the Great Valley to the southeast edge of the Honeybrook formation (Figure 5). The abrupt offset of Silurian rocks at the north (the “plunge” north of Morgantown Pluton) as well as the isolation of the Little South Mountain Precambrian klippe suggest that this region is a broad right lateral transform zone. Wise (2013, 2014, personal communication) suggests that the STZ represents a reactivated tear fault inherited from the Paleozoic Alleghanian orogenesis, and that Birdsboro Dike itself may be a trace of this ancient fault. Wise & Faill (2002) demonstrate that a related pattern of seismicity called the Lancaster Seismic Zone (Armbruster and Seeber 1987; Figure 6), the most active seismic zone east of the New Madrid Seismic Zone, betrays the existence of the southern edge of a northern thrust block of Alleghanian origin which lies atop a deeper Alleghanian thrust block. This deeper block’s basement becomes exposed west of the Gettysburg Basin as the South Mountain formation, while the shallower basement rock is exposed as Little South Mountain, the Reading Prong, and the Honeybrook Upland. Wise (2014) suggests that basin dip and width may be controlled by the presence of this basement rock, since the steepest dipping and most narrow basin, the Narrow Neck, lies within the transition between upper block and lower block.

The existence of a hitherto unrecognized tear fault beneath the Birdsboro Dike may offer a control on length of the Newark Basin, as it could be the hinge against which the basin was allowed to slip. Such is suggested by sedimentary relations across Birdsboro Dike. South of the dike (inside Morgantown Pluton), the Hammer Creek sedimentary formation is present almost everywhere, while north of the dike the Hammer Creek crops out only at the southeastern end, underneath the younger Passaic Formation (Figure 7). This juxtaposition could occur if the sediments north of the dike dip northwestward more steeply than the southern sediments. This geometry would suggest that the region north of the dike is dropped down relative to the region south. Schlische apparently saw as much – a cross section in Schlische (1992) represents Birdsboro Dike as a steeply dipping normal fault with the down-dropped block on the north side, though nothing this clear is stated in the text (Figure 8).
Now, let us turn to a description of the petrology and rock types found within these igneous bodies.

ROCK DESCRIPTIONS

The diabase and basalt in Morgantown Pluton and the Jacksonwald Syncline generally correspond to the HTQ, York Haven type of tholeiite (Smith et al. 1975, Gottfried et al. 1991d). Chemical compositions of specific samples used in the present study will be detailed below, but in general, the chill margins have a TiO2 wt% of 1.15-1.23, and the lava has TiO2 wt% of 1.07-1.17. Within the pluton interiors, TiO2 can go down to 0.66 wt% (eg. southern sill), and up as high as 3.20 wt% (eg. the dike), though these wide variations likely reflect differentiation processes within the chambers. The diabase is dominated by intergranuar to subophitic grains of plagioclase and pyroxene, with late interstitial phases of biotite, quartz, K-feldspar, granophyre, and Fe-Ti oxides. Especially in the northern/upper portions of Morgantown pluton extensive hydrothermal alteration of pyroxene to amphibole and plagioclase to sericite occurs.

Pyroxene occurs throughout the pluton and lava as the clinopyroxenes augite (Ca > ~20 wt%) and pigeonite (5 wt% < Ca < 15 wt%). In the Jacksonwald Lava, augite phenocrysts are far more abundant towards the floor than the roof, though this has not yet been quantified. In Birdsboro Dike, the modal proportion of pyroxene to plagioclase is 22:50 (px:plag), while in the southern sill, the modal proportion is 53:42 (px:plag), where the pyroxene is divided between orthopyroxene and clinopyroxenes in the modal proportion 19:34 (opx:cpx). Euhedral, cumulate orthopyroxene is typically only found in the southern portions of Morgantown Pluton and the lower Jacksonwald plutons, but can reach almost 20 modal percent (26 wt%) in those regions. To date, unambiguous orthopyroxene phenocrysts outside of the southern portions have been found only in the possible subsill south of Knauers, where it only reaches 2% by volume in samples studied. Orthopyroxene found elsewhere takes the form of so-called inverted pigeonite, a product of exsolution from pigeonites, and never as cumulate phenocrysts.

Chemical zoning of phenocrysts reflect the changing composition of a crystallizing magma. Zoning patterns are witnessed in both the pyroxenes and the plagioclase. Augite zoning ranges from about 79% to 55% enstatitic (Mg/(Mg+Fe) %). In the interior of Birdsboro Dike, this can get down to En30. Plagioclase compositions range from about 80% to about 40% anorthitic (Ca/(Ca+Na) %), but can get down to An25 in the dike interior. Based on zoning patterns, two distinct families of plagioclase have been recognized to exist in the dike and the sill of Morgantown Pluton. In the first family, normally zoned plagioclase, the highest anorthite composition is at the core and the lowest is at the rim. In the second family, oscillatory or reverse zoned plagioclase, lower anorthite cores (An65-An75) are surrounded by one or more rings of higher anorthite zones (~An80) which interzone with low anorthite zones. These phenocrysts are ultimately rimmed with anorthite compositions that compare with those of the first family (Srogi et al. 2010).

Layering within the pluton takes several forms (Srogi et al. 2010). In the southern sill, layering is defined by concentrations of plagioclase that form light-colored layers ranging from a few millimeters to a few centimeters thick that are immediately underlain by orthopyroxene rich, mafic layers. These subhorizontal layers dip north-northeast at ~20° on average, and appear to be curving and to branch or intersect with other plagioclase-rich layers. The cause of this layering is likely to be similar to that proposed for the Palisades Sill, in which rafts of crystallizing mush from the roof region sink to the floor (Dickson & Philpotts 2001). These subhorizontal layers are turned slightly upwards where they are crosscut by subvertical, mafic channels. It is believed that the subhorizontal layering originally exhibited an average dip of 0°, and that the current orientation was formed through post-magmatic tilting of the entire pluton towards the north. In Birdsboro Dike, layering is rhythmic and steeply dipping, parallel to dike margins. The layers are of approximately equal thickness and consistent in orientation and thickness over several meters. The cause of this layering is as-yet unknown, though it may have to do with thermal patterns set up as a byproduct of crystallization. Layering has also been found near one of the few exposed roof contacts in the western subsill portion of the pluton, and takes the form of repeated fine-grained selvages immediately underlain by coarse-grained granophyric lenses that grade back into medium-grained diabase (Martinson & Srogi 2014). These layers also exhibit a northward dip of ~20°, again suggesting post-solidification tilt of the entire pluton. It is quite likely that these layers were formed by a combination of rising evolved magma segregations and sudden quenching by outgassing events through the roof.

# Area and Volume

Let’s say you have two similar prisms, A and B. The surface area of A is 161 square centimeters, and its volume is 1331 cubic centimeters. The surface area of B is 250 square centimeters. Can you find the volume of prism B?

It seems like you need more information. You don’t even know how many sides the prism bases have! It turns out there’s a neat principle involving areas in general and volumes that we can use here, and we don’t need to know any specifics about the prisms beyond their similarity. The short answer is, volume is in sesquialterate ratio with surface area. The long answer is the rest of this post!

First, let’s get clear what prisms are, and what it means to have similar prisms.

A prism is a spatial object with two identical, flat faces (the bases) that, when cut anywhere along its length parallel to those faces, has identical cross sections throughout. The general image of a prism has two triangles for bases, and three rectangular faces connecting the triangles. Prisms like this made of glass are generally used to split white light into its spectrum of colors.

Here, light is passing through the identical faces, and the prism sits on one of its two triangular bases. In general, prisms can have any shape base, and any length of face. The simplest prism is actually the cylinder, about which we shall see more below.

Similar prisms are defined just like any other similar shapes. In a picture, they look identical unless they’re either right next to each other, or both compared with a known measure. Visually, the larger similar figure just looks like it’s just the smaller figure brought closer to you. In other words, all lengths found on one prism are in constant proportion with all comparable lengths on a similar prism.

Here, we have two similar rectangular prisms. The larger one has lengths $X, Y,$ and $Z$, while the smaller one has lengths $\alpha, \beta,$ and $\gamma$. Since they’re similar, each pair of comparable sides are proportional with each other. If our constant of proportionality is $\kappa$, then we have

$X = \kappa \alpha$
$Y = \kappa \beta$
$Z = \kappa \gamma$.

The surface areas of the two prisms are $2XY + 2YZ + 2ZX$ and $2\alpha\beta + 2\beta\gamma + 2\gamma\alpha$. The two volumes are $XYZ$ and $\alpha\beta\gamma$. Since the two prisms are similar, we can relate the surface areas with

$2XY + 2YZ + 2ZX = 2 \kappa\alpha \kappa\beta + 2 \kappa\beta \kappa\gamma + 2 \kappa\gamma \kappa\alpha = \kappa^2 (2\alpha\beta + 2\beta\gamma + 2\gamma\alpha)$

In other words, the surface area of the larger prism is equal to $\kappa^2$ times the surface area of the smaller one. There’s a similar relationship between the volumes

$XYZ = \kappa\alpha \kappa\beta \kappa\gamma = \kappa^3 \alpha\beta\gamma$,

or, the volume of the larger prism is $\kappa^3$ times the volume of the smaller one. More concisely,

$\frac{SA_{large}}{SA_{small}} = \kappa^2$
$\frac{V_{large}}{V_{small}} = \kappa^3$

The constant of proportionality, $\kappa$, can be thought of as a magnification or scaling factor. This means that, for example, if we double the size of a prism, the surface area gets $2^2=4$ times larger, while the volume gets $2^3=8$ times larger. In other words, surface area grows as a square, while volume grows as a cube.

We just did this for two similar rectangular prisms. Does this hold for all prisms? Remember the prism principle – two sides must be parallel and identical, the other sides just connect these two together. The main difficulty in determining surface area or volume in a prism lies in the shape of the two parallel bases. When you double an oddly shaped base’s sides, the area of the base does not double, but rather quadruple

Meno ran into this when he was trying to double the square for Socrates. Doubling area doesn’t follow from doubling side length. When you increase the length of a polygon’s side, the volume increases by the square. This is why a larger similar prism will always have a total surface area that is larger than that of a smaller prism by the square of the scaling factor. With volumes (I won’t try to draw this one), as you increase side length, you increase the volume by the cube. Try it with blocks.

Therefore, the shape of the prisms doesn’t matter. The ratio of volumes and the ratio of surface areas only depends on the scaling factor. In fact, we can use this to find a direct relationship between the surface areas and volumes:

$\frac{SA_{large}}{SA_{small}} = \kappa^2 \Rightarrow (\frac{SA_{large}}{SA_{small}})^{\frac{1}{2}} = \kappa$
$\frac{V_{large}}{V_{small}} = \kappa^3 \Rightarrow (\frac{V_{large}}{V_{small}})^{\frac{1}{3}} = \kappa$
or,
$(\frac{SA_{large}}{SA_{small}})^{\frac{1}{2}} = \kappa = (\frac{V_{large}}{V_{small}})^{\frac{1}{3}}$

This relationship, where the square of one side is equal to the cube of the other, is called a “sesquialterate ratio.” Some may remember this type of relationship from Kepler’s third law.

In any case, now we are able to solve our problem. The smaller prism has surface area 161 square centimeters and volume 1331 cubic centimeters, while the larger prism has surface area 250 square centimeters. To find the volume of the larger prism, we just rearrange our sesquialterate ratio

$(\frac{SA_{large}}{SA_{small}})^{\frac{1}{2}} = (\frac{V_{large}}{V_{small}})^{\frac{1}{3}}$
$(\frac{SA_{large}}{SA_{small}})^{\frac{3}{2}} = \frac{V_{large}}{V_{small}}$
$V_{small} (\frac{SA_{large}}{SA_{small}})^{\frac{3}{2}} = V_{large}$

Putting in the numbers,

$V_{large} = (1331 cm^3) (\frac{250 cm^2}{161 cm^2})^{\frac{3}{2}} = 2575.4 cm^3$

Pretty easy, right? Maybe not too easy. Still, the fact that volume and surface area know to always follow their sesquialterate relationship is another testament to our incredibly constructed universe!