Extreme Gamma Rays

The highest-energy gamma ray photon ever recorded was recently observed by the Large High Altitude Air Shower Observatory (LHAASO) on Haizi Mountain, Sichuan province, China, during its first year of operation.

1.42 ± 0.13 PeV

That is 1.4 petaelectronvolts = 1.4 × 1015 eV! The origin of this fantastically energetic photon hasn’t been localized, but possible candidates are the Cygnus OB2 young massive cluster (YMC), the pulsar PSR 2032+4127, or the supernova remnant candidate SNR G79.8+1.2.

The LHAASO observatory, in China, observes ultra high-energy light using detectors spread across a wide area that will eventually cover more than a square kilometer. Institute of High Energy Physics/Chinese Academy of Sciences

How much energy is 1.4 PeV, actually?

We can calculate the frequency of this photon using

\textup{E}=h\nu


where
h = Planck’s constant = 4.135667696 × 10-15 eV·Hz-1
ν = the photon’s frequency
E = the photon’s energy

Solving for ν, we get

ν = 3.4 × 1029 Hz

Next, we’ll calculate the photon’s wavelength using

c=\lambda \nu

where
c = the speed of light = 299792458 m·s-1
λ = the photon’s wavelength

Solving for λ, we get

λ = 8.9 × 10-22 m

To give you an idea of just how tiny 8.9 × 10-22 meters is, the proton charge radius is 0.842 × 10-15 m, so 1.9 million wavelengths of this gamma ray photon would fit inside a single proton! An electron has an upper limit on its radius—if it can be said to have a radius at all—between 10-22 and 10-18 m. So between 1 and 2000 wavelengths of this gamma ray photon would fit inside a single electron.

Using Einstein’s famous equation E = mc2 we can find that each eV has a mass equivalent of 1.78266192 × 10-36 kg. 1.4 PeV then gives us a mass of 2.5 × 10-21 kg. That may not sound like a lot, but it is 1.5 million AMUs (Daltons), or a mass comparable to a giant molecule (a protein, for example) containing ~200,000 atoms.

This and other extremely high energy gamma ray photons are not directly detected from the Earth’s surface. The LHAASO detector array in China at 14,500 ft. elevation detects the air shower produced when a gamma ray (or cosmic ray particle) hits an air molecule in the upper atmosphere, causing a cascade of subatomic particles and lower-energy photons, some of which reach the surface of the Earth. It is the Cherenkov photons produced by the air shower secondary charged particles that LHAASO collects.

References
Conover, E. (2021, June 19). Record-breaking gamma rays hint at violent environments in space. Science News, 199(11), 5.
https://www.sciencenews.org/article/light-energy-record-gamma-ray

Z. Cao et al. Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ-ray Galactic sourcesNature. Published online May 17, 2021. doi: 10.1038/s41586-021-03498-z.

James Clerk Maxwell

Today we celebrate the 190th anniversary of the birth of Scottish mathematician and physicist James Clerk Maxwell (13 Jun 1831 – 5 Nov 1879). Between 1864 and 1873, Maxwell developed four important mathematical equations that describe the behavior of electric and magnetic fields and their interrelated nature. He showed that any oscillating electric charge produces an electromagnetic field, and that this electromagnetic field propagates outward from the oscillating charge at the speed of light. He then correctly deduced that light itself is an electromagnetic phenomenon, and proposed that since electric charges can oscillate at any frequency, there should be a whole spectrum of electromagnetic waves of which visible light is only a small part. We now know that the electromagnetic spectrum does include many other types of “light”, namely gamma rays, x-rays, ultraviolet, infrared, microwave, and radio waves. They are all exactly the same phenomenon, differing only in their properties of frequency, wavelength, and energy.

Why No New Einstein?

In the June 2005 issue of Physics Today there is an article by Lee Smolin with the provocative (or evocative) title, Why No ‘New Einstein’? That year marked the 100th anniversary of Albert Einstein‘s annus mirabilis (year of wonders), in which the 26-year-old Swiss patent examiner submitted and had published revolutionary papers on the photoelectric effect, Brownian motion, special relativity, and matter-energy equivalence in a prominent German physics journal, Annalen der Physik. These papers were so important that they completely changed the course of physics and led to great opportunities for Einstein to further develop his career as a physicist.

Here are some excerpts from Smolin’s article.

“Many of Einstein’s contemporaries testified that he was not unusually talented mathematically. Instead, what enabled him to make such tremendous advances was a driving need to understand the logic of nature, tied to a breathtaking creativity and a fierce intellectual independence.”

“Perhaps a lesson might be learned from the fact that this one person, who was initially unable to find an academic job, did more to advance physics than most of the rest of us [physicists] put together have since.”

“It follows that new Einsteins are unlikely to be easily characterized in terms of research programs that have been well explored for decades. Instead, a new Einstein will be developing his or her own research program that, by definition, will be one that no senior person works on.”

“Are our universities, institutes, and foundations doing all they can to identify and promote individuals who have the creativity and intellectual independence that characterize those who contribute most to physics? I say that they are not.”

“People with the uncanny ability to ask new questions or recognize unexamined assumptions, or who are able to take ideas from one field and apply them to another, are often at a disadvantage when the goal is to hire the best person in a given well-established area.”

“It is easy to write many papers when you continue to apply well-understood techniques. People who develop their own ideas have to work harder for each result, because they are simultaneously developing new ideas and the techniques to explore them. Hence they often publish fewer papers, and their papers are cited less frequently than those that contribute to something hundreds of people are doing.”

Marfa Lights

Yes, I’ve seen the Marfa lights. Bernie Zelazny and I were coming back from doing a star party for a culinary group at El Cosmico in Marfa on April 7, 2011 when we decided to stop at the Marfa lights viewing station just off of US 67/90. For the first couple of minutes (Thursday evening around 11:00 p.m. or so) we saw nothing, but then, sure enough, a slowly moving white light appeared near a small tower with red lights, providing a good point of reference for the motion. The light gradually changed brightness, sometimes brighter, sometimes dimmer, moving left to right, then disappeared. Soon, another would appear: sometimes higher, sometimes lower, usually moving to the right, but sometimes to left. My first thought: distant headlights. Sometimes, more that one could be seen at the same time.

Quickly, I ran back to my car to get the 15 x 70 binoculars and binocular mount (an Orion Paragon Plus) and set them up to view the Marfa lights, which by now were happening frequently. When viewing each Marfa light through these powerful binoculars, the first thing I noticed is that I was not able to focus! No matter how I changed the focus of the binoculars, I could do no better than to see a round amorphous blob of light.

Next, I decided to see if any of the fixed distant lights would focus. First the red tower lights. Nope, red blobs. Then a distant ranch light to the left of the light dome of Ojinaga/Presidio. Nope, a while blob. Then, another distant ranch light. Another white blob. Then some distant headlights on US 67/90 near Marfa heading toward Alpine. The headlights were too far away to resolve, and in the binoculars they, too, were an unresolvable white blob. Next I moved the binoculars up a few degrees to look at some stars. Perfect focus! Back down to the ground lights and Marfa lights: out of focus blobs!

So, it appears to me that some atmospheric phenomenon is defocusing and distorting terrestrial lights in the distance. Perhaps some sort of superior mirage. I think the most likely explanation for the Marfa lights is distant vehicle headlights.

Next steps in the investigation of this curious phenomenon: Use a micrometer eyepiece in a low-power rich-field telescope to measure the angular sizes of the Marfa light blobs, as well as the angular sizes of the blobs from identifiable terrestrial lights. Determine the distance to the terrestrial light sources in the daytime (if possible) using triangulation. Better yet, determine the great circle distance to each terrestrial light source by obtaining GPS coordinates of each of those light sources, and the Marfa lights viewing station. Even better would be to shine a mobile light source at the Marfa lights viewing station from various GPS-determined locations at different distances on an evening when the Marfa lights are visible. Determine if the size of each known light blob is a function of distance. Using this information, estimate the distance to the Marfa light sources.

Also, note whether the angular size of each Marfa light is related to its altitude above the horizon.

More ideas: Take a series of 30-second digital camera exposures over the course of an evening to determine if the Marfa lights take preferred paths. The results might support or refute the vehicle headlights hypothesis. Determine if the Marfa lights paths change from night to night or during the course of one night.

Finally, I’d suggest using the same kind of wide-field spectroscopic equipment used to obtain meteor spectra to determine the spectral characteristics of the Marfa lights. This would tell us much about their chemical composition, temperature, and origin.

Space Travel Under Constant 1g Acceleration

The basic principle behind every high-thrust interplanetary space probe is to accelerate briefly and then coast, following an elliptical, parabolic, or mildly hyperbolic solar trajectory to your destination, using gravity assists whenever possible. But this is very slow.

Imagine, for a moment, that we have a spacecraft that is capable of a constant 1g (“one gee” = 9.8 m/s2) acceleration. Your spacecraft accelerates for the first half of the journey, and then decelerates for the second half of the journey to allow an extended visit at your destination. A constant 1g acceleration would afford human occupants the comfort of an earthlike gravitational environment where you would not be weightless except during very brief periods during the mission. Granted such a rocket ship would require a tremendous source of power, far beyond what today’s chemical rockets can deliver, but the day will come—perhaps even in our lifetimes—when probes and people will routinely travel the solar system in just a few days. Journeys to the stars, however, will be much more difficult.

The key to tomorrow’s space propulsion systems will be fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2. This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2. You cannot get any more energy than this out of any conceivable on-board power or propulsion system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion system by a few percent.

How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey? Using the equations below, you can calculate this easily.

Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

Maximum velocity is reached at the halfway point (when you stop accelerating and begin decelerating) and is given by

The energy per unit mass needed for the trip (one way) is then given by

How much fuel will you need for the journey?

hydrogen fusion into helium gives: Efusion = 0.008 mfuel c2

matter-antimatter annihilation gives: Eanti = mfuel c2

This assumes 100% of the fuel goes into propelling the spacecraft, but of course there will be energy losses and operational energy requirements which will require a greater amount of fuel than this. Moreover, we are here calculating the amount of fuel you’ll need for each kg of payload. We would need to use calculus to determine how much additional energy will be needed to accelerate the ever changing amount of fuel as well. The journey may well be analogous to the traveler not being able to carry enough water to survive crossing the desert on foot.

Now, let’s use the equations above for a journey to the nearest stars. There are currently 58 known stars within 15 light years. The nearest is the triple star system Alpha Centauri A & B and Proxima Centauri (4.3 ly), and the farthest is LHS 292 (14.9 ly).

I predict that interstellar travel will remain impractical until we figure out a way to harness the vacuum energy of spacetime itself. If we could extract energy from the medium through which we travel, we wouldn’t need to carry fuel onboard the spacecraft.

We already do something analogous to this when we perform a gravity assist maneuver. As the illustration below shows, the spacecraft “borrows” energy by infinitesimally slowing down the much more massive Jupiter in its orbit around the Sun and transferring that energy to the tiny spacecraft so that it speeds up and changes direction. When the spacecraft leaves the gravitational sphere of influence of Jupiter, it is traveling just as fast as it did when it entered it, but now the spacecraft is farther from the Sun and moving faster than it would have otherwise.

Reference: https://www.daviddarling.info/encyclopedia/G/gravityassist.html

Of course, our spacecraft will be “in the middle of nowhere” traveling through interstellar space, but what if space itself has energy we can borrow?

Multiverse

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.2 Issue H: The possible existence of multiverses
If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist; and this can help explain the fine-tuned nature of many parameters whose values are otherwise unconstrained by physics.  As discussed in the previous section, there are a number of ways in which, theoretically, multiverses could be realized.  They provide a way of applying probability to the universe (because they deny the uniqueness of the universe).  However, there are a number of problems with this concept.  Besides, this proposal is observationally and experimentally untestable; thus its scientific status is debatable.

My 100-year-old uncle—a lifelong teacher and voracious reader who is still intellectually active—recently sent me Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, published by Vintage Books in 2014. I could not have had a more engaging introduction to the concept of the Multiverse. Tegmark presents four levels of multiverses that might exist. They are

Level I Multiverse: Distant regions of space with the same laws of physics that are currently but not necessarily forever unobservable.

Level II Multiverse: Distant regions of space that may have different laws of physics and are forever unobservable.

Level III Multiverse: Quantum events at any location in space and in time cause reality to split and diverge along parallel storylines.

Level IV Multiverse: Space, time, and the Level I, II, and III multiverses all exist within mathematical structures that describe all physical existence at the most fundamental level.

There seems little question that our universe is very much larger than the part that we can observe. The vast majority of our universe is so far away that light has not yet had time to reach us from those regions. Whether we choose to call the totality of these regions the universe or a Level I multiverse is a matter of semantics.

Is our universe or the Level I multiverse infinite? Most likely not. That infinity is a useful mathematical construct is indisputable. That infinite space or infinite time exists is doubtful. Both Ellis and Tegmark agree on this and present cogent arguments as to why infinity cannot be associated with physical reality. Very, very large, or very, very small, yes, but not infinitely large or infinitely small.

Does a Level II, III, and IV multiverse exist? Tegmark thinks so, but Ellis raises several objections, noted above and elsewhere. The multiverse idea remains quite controversial, but as Tegmark writes,

Even those of my colleagues who dislike the multiverse idea now tend to grudgingly acknowledge that the basic arguments for it are reasonable. The main critique has shifted from “This makes no sense and I hate it” to “I hate it.”

I will not delve into the details of the Level II, III, and IV multiverses here. Read Tegmark’s book as he adroitly takes you through the details of eternal inflation, quantum mechanics and wave functions and the genius and tragic story of Hugh Everett III, the touching tribute to John Archibald Wheeler, and more, leading into a description of each multiverse level in detail.

I’d like to end this article with a quote from Max Tegmark from Mathematical Universe. It’s about when you think you’re the first person ever to discover something, only to find that someone else has made that discovery or had that idea before.

Gradually, I’ve come to totally change my feelings about getting scooped. First of all, the main reason I’m doing science is that I delight in discovering things, and it’s every bit as exciting to rediscover something as it is to be the first to discover it—because at the time of the discovery, you don’t know which is the case. Second, since I believe that there are other more advanced civilizations out there—in parallel universes if not our own—everything we come up with here on our particular planet is a rediscovery, and that fact clearly doesn’t spoil the fun. Third, when you discover something yourself, you probably understand it more deeply and you certainly appreciate it more. From studying history, I’ve also come to realize that a large fraction of all breakthroughs in science were repeatedly rediscovered—when the right questions are floating around and the tools to tackle them are available, many people will naturally find the same answers independently.

References
Ellis, G.F.R., Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Tegmark, Max. Our mathematical universe : my quest for the ultimate nature of reality. New York: Alfred A. Knopf, 2014.

“You passed your exam in many parallel universes—but not in this one.”

The Laws of Physics and the Existence of Life

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

The first requirement is the existence of laws of physics that guarantee the kind of regularities that can underlie the existence of life.  These laws as we know them are based on variational and symmetry principles; we do not know if other kinds of laws could produce complexity.  If the laws are in broad terms what we presently take them to be, the following inter alia need to be right, for life of the general kind we know to exist:

  • Quantization that stabilizes matter and allows chemistry to exist through the Pauli exclusion principle.

  • The neutron-proton mass differential must be highly constrained.  If the neutron mass were just a little less than it is, proton decay could have taken place so that by now no atoms would be left at all.

  • Electron-proton charge equality is required to prevent massive electrostatic forces overwhelming the weaker electromagnetic forces that govern chemistry.

  • The strong nuclear force must be strong enough that stable nuclei exist; indeed complex matter exists only if the properties of the nuclear strong force lies in a tightly constrained domain relative to the electromagnetic force.

  • The chemistry on which the human body depends involves intricate folding and bonding patterns that would be destroyed if the fine structure constant (which controls the nature of chemical bonding) were a little bit different.

  • The number D of large spatial dimensions must be just 3 for complexity to exist.

It should not be too surprising that we find ourselves in a universe whose laws of physics are conducive to the existence of semi-intelligent life.  After all, we are here.  What we do not know—and will probably never know: Is this the only universe that exists?  This is an important question, because if there are many universes with different laws of physics, our existence in one of them may be inevitable.  If, on the other hand, this is the only universe, then the fantastic claims of the theists, or at least the deists, become more plausible.

You may wonder why I call the human race semi-intelligent.  Rest assured, I am not being sarcastic or sardonic.  I say “semi-intelligent” to call attention to humanity’s remarkable technological and scientific achievements while also noting our incredible ineptness at eradicating war, violence, greed, and poverty from the world.  What is wrong with us?

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Infrasound and Meteors

Humans typically can hear sound waves in the range 20 Hz to 20,000 Hz. Frequencies below 20 Hz are called infrasound and frequences above 20 kHz are called ultrasound. The speed of sound in dry air at a temperature of 20˚ C (68˚ F) and an atmospheric pressure of 1 bar (slightly less than the average air pressure at sea level) is 343 m/s. Dividing the speed of sound by the frequency (in Hz) gives us the wavelength of the sound waves: 17 m (56 ft.) at 20 Hz, and 17 mm (0.67 in.) at 20 kHz.

Meteoroids enter the Earth’s atmosphere (thus becoming meteors) at hypersonic velocities, 35 to 270 times the local speed of sound (Mach 35 to Mach 270). Only a small portion of the total energy of the incoming meteoroid is transformed into visible light: most of the energy dissipated goes into acoustic shock waves. If the meteoroid is on the order of a centimeter (0.4 inches) or larger, infrasound waves are generated that can be detected on the ground, albeit after a delay of many seconds to minutes.

Infrasound waves can travel long distances, but higher frequencies are attenuated due to spreading losses and absorption over much shorter distances. There are many natural and man-made sources of infrasound waves, so identifying an incoming meteoroid as the source of the infrasound requires that we also “see” and record the meteoroid optically (the “meteor”), through radar, or VLF radio emissions from the meteoroid’s ionization trail in the Earth’s atmosphere. Ideally, all of these methods should be used at each observing station to best characterize the size and kinetic energy of each incoming meteoroid.

Infrasound detectors are not yet an off-the-shelf commodity. Chaparral Physics (http://chaparralphysics.com) is one good source, but seeing as they do not list any prices you know the equipment will be expensive.

An infrasound detector is basically an extremely sensitive microphone that can detect tiny changes in air pressure. A peak sensitivity around 1 Hz is probably a good place to start for detecting meteors. Meteors large and/or energetic enough to be detected on the ground are rare, not even one a day for a given station, so automated recording will be necessary.

Finally, it is important to know that louder sounds that we cannot hear (infrasound and even ultrasound) can sometimes have adverse physical and psychological effects on humans. The cause can be as simple as a malfunctioning piece of mechanical or electrical equipment, or as nefarious as a sonic weapon. It would be advantageous to have a readily available and affordable infrasound and ultrasound detector to detect problem emissions.

For example, you might want an

  • Infrasound detector that maps 0.02 Hz – 20 Hz to the 20 Hz – 20 kHz audible range
  • Ultrasound detector that maps 20 kHz – 20 MHz to the 20 Hz – 20 kHz audible range

References
Silber, Elizabeth A. (2018). Infrasound observations of bright meteors: the fundamentals. WGN, Journal of the International Meteor Organization, 46:2.


Cold Matters

Our current best estimate for the age of the universe (as we know it) is 13.799 Gyr ± 21 Myr. The Great Flaring Forth (GFF) occurred 13.8 billion years ago, and the universe has been expanding and cooling ever since.

The background temperature of the universe is today 2.72548 ± 0.00057 K. “K” stands for Kelvin, a unit of temperature named after William Thomson, 1st Baron Kelvin (1824-1907) – Lord Kelvin – who championed the idea of an “absolute thermometric scale”. A temperature in Kelvin is equivalent to the number of Celsius degrees above absolute zero. Put into terms we may be more familiar with, the cosmic background temperature is -270.42452° C, or -454.764136° F. While in the absence of nearby stars or other energy sources, the universe is certainly cold, scientists have artificially produced temperatures as low as 100 pK (1 picoKelvin = 10-12 K).

Using Wien’s displacement law, we can calculate the wavelength of electromagnetic radiation where the background universe is brightest.

\lambda _{max}=\frac{2.8977729\ \pm \ 0.0000017\ mm\cdot K}{T_{K}}=\frac{2.8977729\ \pm \ 0.0000017\ mm\cdot K}{2.72548\ \pm\ 0.00057 K}=\\1.0632\pm0.0002\ mm

So, we see here that the background universe is “brightest” in the microwave part of the radio spectrum, at a peak wavelength around 1 mm. Using the relationship between frequency and wavelength, c = νλ, we can determine the microwave frequency where the background universe is brightest.

\nu =\frac{c}{\lambda }=\frac{299,792,458\ m/s}{1.0632\times 10^{-3}\ m}=281.97\pm 0.05\ GHz

Microwaves at this frequency are in the extremely high frequency (EHF) radio band, above all our allocated communications bands (275-3000 GHz is unallocated).

Of course, a significant amount of emission occurs either side of the peak, particularly at longer wavelengths and lower frequencies. (The background universe radiates with an almost perfect blackbody spectrum.)

There are several ways to define the wavelength/frequency of maximum brightness. The above is one. Depending on the method we choose, the peak wavelength lies between 1.0623 and 3.313 mm, and the peak frequency between 90.5 and 282.0 GHz.

A Warm Day on Pluto

The coldest weather I’ve ever experienced occurred January 30-31, 2019. Here in Dodgeville, Wisconsin, I measured a low temperature the morning of Wednesday, January 30, 2019 of -31.0° F and a high that day of -14.4° F. It was even colder the following night. On Thursday, January 31, 2019 the low temperature was -31.9° F.

Thanks to the National Weather Service, we had advance notice of the arrival of the Arctic polar vortex that was to bring the coldest weather to Wisconsin in a generation. Concerned about the effect this would have on my observatory electronics, I started running my warming room electric heater continuously from 8:30 p.m. CST Monday, January 28 until 9:45 a.m. CST Friday, February 1. Of course, I left the warming room door open to the telescope room to ensure that some of the heat would reach the telescope and its associated electronics.

During this time, I made a number of temperature measurements from an Oregon Scientific weather station inside the house, connected by 433 MHz radio frequency signals to temperature sensors inside the observatory and on the north side of my house.

Here are those observations:

And here is graph plotting both temperatures at each time:

Air (north side of house) and Observatory (inside the observatory) temperatures January 28-February 1, 2019.

And here is a plot of the temperature difference vs. the outside Air temperature:

Temperature difference vs. Air temperature with a linear regression line

There seems to be a general trend that the colder it was outside the observatory, the bigger was the temperature difference between inside the observatory and outside the observatory. Why is that? The electric heater is presumably putting out a constant amount of heat, so you might think that the temperature difference would remain more or less constant as the temperature goes up and down outside. It doesn’t.

There are a number of factors influencing the temperature inside the observatory. First, there is the thermal mass of the observatory itself, and some heating of the inside of the observatory should occur when the sun is shining on it. There is the wind speed and direction to consider. There may be some heating through the concrete slab from the ground below. It seems to me that thermodynamics should be able to explain the general downward trend in ΔT as the outside air temperature increases. Can you help by posting a comment here?

You’ll notice three outliers in the graph above where ΔT is quite a bit lower than the regression line. The points (-22.0,16.6) and (-10.5,10.1) were consecutive measurements just 76 minutes apart (8:32 a.m. and 9:48 a.m.), the first readings I made after the lowest overnight temperature of -31.9° F on 1/31. The point (8.2,7.6) was my first reading on 1/28 at 8:42 p.m., soon after turning the space heater in the observatory on. The points (-16.4,25.2), (-17.9,26.0), (-19.5,26.3), (-25.1,27.2), and (-26.9,27.4) all are above the regression line and are consecutive readings between 8:29 p.m. on 1/29 and 3:20 a.m. on 1/30 before the -31.0° F low on the first really cold night.

My weather station keeps track of the daily high and low temperatures, but not the time at which those temperatures occur. On 1/30 when the outside low temperature of -31.0° F was recorded, the low inside the observatory was -4.0° F (though not necessarily at the same time). ΔT = 27.0°. The high temperature that day was -14.4° F and 6.4° F inside the observatory (ΔT = 20.8°). The next night, 1/31, the low temperature was -31.9° F and -6.2° F inside the observatory (ΔT = 25.7°).

So, despite the many factors which influence the temperature differential between outside and inside the observatory, the clear trend of smaller ΔT at warmer outside temperature begs for an explanation. Can you help?