The Stars in the Brazilian flag are not randomly drawn. For instance, in the lower left area of the circle are six stars from the Canis Major constellation. This morning while the rest of the family either snored or dreamed, I walked the dog at an early hour under relatively dark skies. Thanks to our dim streetlamps and a waning moon. I was able to observe the fourth brightest star of Canis Major, designated as delta (δ). Named as such because δ is the fourth letter of the Greek alphabet, it also has the common name of Wezen. Deceivingly it only seems dimmer than the very bright Sirius, the alpha-dog star, because Sirius is a lot closer to the Earth.
How do we know how far away Wezen is?
Hold a finger close and directly in front of your nose. Close one eye. Close the other eye while opening the first one. The finger seems to move against the background. If you hold the finger further away and repeat the exercise, the finger still seems to move, but not as much. Similarly for a given star, if it can be observed from two distant viewpoints along earth’s orbit around the sun, the star, will seem to be in slightly different positions against the background of more distant stars. If the distance between viewpoints is known and the angle of apparent movement is measured, simple trigonometry can help us calculate the distance between our sun and the star. The problem is that the angle is extremely small—after all, any star is a lot further away than your finger can possibly be by a factor significantly larger than the ratio of the orbit’s diameter to that of your eye-separation. A small uncertainty in angle can be amplified into a large error in distance, limiting us to measurements of only “neighborhood stars”. For more distant stars, other techniques involving Cepheid variables and type 1a supernovae have to be used. But thanks to Hipparcos, a scientific satellite of the European Space Agency (ESA) especially devoted to astrometry, parallax measurements have improved recently and are definitely accurate enough for a Milky Way star at Wezen’s distance.
Given that there are 3600 arc seconds in a degree and setting the sun-earth distance at 1 astronomical unit (AU), tan p = 1/d or d = 1 ÷ tan (2.03 × 10-3/3600) = 1.02 × 108 AU.
1 light–year = 63240 AU, so Wezen is about 1.02 × 108 AU ÷ 63 240 AU/light year = 1607 or about 1610 light years away.
How do you get absolute luminosity from distance and apparent brightness?
Due to that distance, which is far greater than the 8.61 light years that separates us from Sirius, Wezen’s apparent brightness is only 1.83. Compared to the number line, the stellar brightness scale runs backwards. The dimmest stars have the largest positive values and the brightest have pronounced negative values.
To get the true or intrinsic brightness ( absolute magnitude) of Wezen, we can use the following formula:
M = m – 5 log (d/10),
where m = apparent brightness and d = the star’s distance from our sun in parsecs. Since there are 3.26 light years per parsec,
M = 1.83 – 5 log(1607÷3.26÷10) = – 6.63
That’s a lot more intrinsically bright than Sirius, which has an M value of +1.42. It is Sirius’ proximity to us that makes it the 2nd brightest star in the sky after our sun and puts its apparent brightness at – 1.47. If you imagine them to be both at Sirius’ distance from Earth, by doing the math you realize that Wezen would have an apparent brightness of – 9.52, which would be almost as bright as a half-moon.
Using Two Measurements To Learn About Wezen’s Nature
Now if you rely on one other measurement for Wezen, something even more startling will be revealed. Its color is yellow, and with spectroscopic analysis of the lines from its excited atoms, it is classified as F8Ia, which gives away its surface temperature.
If you then plot absolute magnitude versus spectral class for various stars you get astronomy’s equivalent of the “periodic table”. It’s called the Hertzsprung–Russell diagram and it reveals a star’s stage in its evolution.
Using F8 as its x coordinate (each class has 10 subdivisions, zero through 9, so F8 is close to G’s lower bound) and its absolute magnitude of -6.63 as its y coordinate, we end up with a coordinate point on the supergiants line on the instability strip.
Our sun’s class of G2 and absolute magnitude of 4.83 place it on the main sequence, which is why we are still alive. Notice however that the sun’s spectral class is telling us that its surface is actually a little warmer than Wezen’s. If Wezen’s luminosity is so much greater than that of the sun, Wezen has to be a lot bigger, but its energy is spread thinly over its large surface area. But with more mass, gravity is a lot stronger, driving Wezen’s core temperature exponentially higher. This accelerates its rate of fusion. To make a long story short, Wezen is only 10 million years old and has already stopped fusing hydrogen, whereas the sun has celebrated its 4.6 billionth birthday. Moreover, the sun will also stay on the main sequence long enough to double its present age.
It seems that Wezen has already started to expand. As it fuses helium, it will become a red supergiant and eventually go supernova within a mere 100 000 years. When that happens, in our night sky, Wezen will appear almost as bright as Sirius and brighter than every other star. It’s comforting to think that maybe our descendants will walk with their dogs early one morning and marvel at it.
A mineral is more pure than its parent rock. But compared to food additives, industrial compounds and pharmaceuticals, a mineral’s compound often hosts more elements. As a result it isn’t difficult to find a mineral whose atoms have a variety of cosmic origins.
Only a small percentage of elements on Earth are created in and around the planet by nuclear reactions, and even at that, they are only derivatives of atoms made elsewhere. The secondary creations result from the atmosphere’s interaction with cosmic rays, from the lithosphere’s minority of radioactive elements, from nuclear reactors and from scientific research—my favorite being the tanks that sit deep in abandoned mines collecting neutrinos from our sun and supernovae.
So where in space did the majority of constituents of the living-geological continuum originate and by what mechanism? Let’s look at the cosmic roots of the six elements of a mineral known as pezzottaite, discovered in Madagascar and only officially recognized as a distinct mineral in 2003. Its formula is Cs(Be2Li)Al2Si6O18
What’s the ultimate source of oxygen? Big or small, stars spend the bulk of their time on the main sequence, a hydrogen-fusing stage that actually lasts longer for smaller stars. This is because a star’s lifetime is proportional to its mass but inversely proportional to the fourth power of its core temperature. Although small stars have less hydrogen, the smallest of the chemical elements, they also fuse it at a lower temperature from the lower force acting on its core. The product of the sequence of reactions involved in the fusion of hydrogen is helium. While helium grows as an onion-like outer-layer during its residence as a main sequence star, the temperature isn’t high enough to fuse the helium into bigger elements. But when the hydrogen fuel runs out, the star is for a while no longer in equilibrium. The outward radiative pressure isn’t there to balance out gravity, so the large force towards the star’s center “ignites” the fusion of helium and the star becomes a red giant.
When the star’s core temperature reaches 108 K, from the diagram we see a pair of helium nuclei fusing to form an unstable beryllium nucleus, which then fuses to give us the life-essential carbon. This in turn fuses with another helium to produce oxygen. Oxygen can continue to fuse, but there are enough nuclei that remain as such. When stars, in a later stage of their evolution, either shed their outer layers either as a planetary nebula or supernova, stellar dust receives these oxygen atoms, some of which ended up in our water , skin and in our pezzottaite.
To get silicon we need a more massive star capable of generating a red-giant-temperature and density of 500 million K and 5 million g/cm3. Under these conditions two oxygens (atomic number 8) will combine to create a silicon nucleus(atomic number 16). Fittingly some of this product and progenitor are eventually reunited on planets as sand, sandstone, quartz, clay and a wide variety of minerals that contain either silica or some form of silicate— including that of pezzottaite.
Lithium and Beryllium
A neat thing about pezzottaite is that it has two(lithium and beryllium) of three light elements that are relatively rare in the universe. The presence of each of lithium, beryllium and boron is only one billionth that of hydrogen and about a millionth of that of carbon, nitrogen and oxygen. The reason for this is that the bulk of Li, Be and B do not survive any of the stages of stellar evolution. Their fragile nature suggested they were synthesized in low-density, low-temperature environments.
One area where a high concentration of these light elements occurred was in galactic cosmic rays. This suggested that perhaps they are not being carried from elsewhere but being synthesized on the spot by the nuclear reaction between alpha particles(helium nuclei) or protons of the cosmic rays and larger elements like carbon, nitrogen and oxygen. This process is now called spallation. While other genesis-models failed to predict the exact concentrations of the isotopes, the spallation hypothesis came closest to account for the relative ratios.
In the 1980s Viola and Mattheson used a cyclotron to accelerate protons and helium nuclei to the energies of cosmic rays and aimed them at targets of He, N, C and O to generate new nuclei. When the particles’ energies and speeds were analyzed, their calculated masses allowed them to identify the isotopes. Their abundance was similar to that found in galactic cosmic rays. The three reactions that created a fair amount of the lithium and beryllium in our pezzottaite are:
4He + 12C → 7Li + 2 4He + 1H (main isotope of lithium, 92.5% of what’s found on Earth)
2 4He → 6Li + 1H + 10n
1H+ 14 N →9Be + 4He + 2 1H
One anomaly, however, was that the amount of 7Li ( the heavier isotope) made in the cyclotron was a little lower than what’s actually found in space, suggesting that a minority of 7Li was not made in the cosmic rays but originated elsewhere. Some of the discrepancy is partly accounted for by the small amount made in the Big Bang, but in 2013, analyses of the Subaru Telescope High Dispersion Spectrograph revealed that a more significant contribution comes from novae. Smaller stars eventually become white dwarfs after passing through the red giant stage. But these remnants, if part of a binary system, could suddenly brighten from explosive nuclear reactions when material from its partner-star is pulled onto the dwarf’s surface. The nuclear reactions create a different series of elements compared to those produced in stellar interiors or during supernova explosions. One of these atypical reactions is the conversion of beryllium-7 to lithium-7 by electron capture, which lowers the atomic number without affecting the atomic mass.
To explain the origin of the final two elemental components of pezzottaite, Al and Cs we need to examine supernovae. The next avenue of evolution of large stars is a type II supernova, which briefly outshines its entire galaxy. When all fuel is spent in large stars iron is left at the stellar core and a gravitational collapse ensues. In a rapid process-set of reactions ( r-process), neutrons are initially generated by the gravitational collapse during photodisintegration, a process where gamma causes the fission of heavier nuclei. For example here’s a sequence of reactions generating a total of 7 neutrons from a single iron nucleus:
56Fe + ϒ → 13 4He + 4 10n 4He + ϒ → 2 ‘H + 2 10n
‘H + e- → 10n + ν
Then in the actual r-process neutrons are captured to form unstable neutron-rich isotopes which then undergo beta decay and turn into elements of higher atomic number.How does this happen? A little background info: Being electrically neutral, neutrons can penetrate the positively charged nucleus, especially at low temperatures. But free-roaming neutrons are short-lived lasting only about ten minutes as one of their down-quarks becomes an upquark, a process that generates a proton, a beta particle and an antineutrino. This raises the atomic number by 1. To generate sufficient numbers of neutrons and provide a constant supply of these ephemeral neutral particles, the high-energy environment of something like a supernova is needed. For example with the provided energy, gamma will break down enough iron to generate enough neutrons, which in turn can convert other iron atoms (atomic number 26) into heavier iron isotopes, one of which will beta-decay into cobalt (number 27). That isotope of cobalt can then absorb more neutrons and eventually undergo beta decay to create an even higher-numbered element, Ni. The isotopes created by the r-process are not the stable ones of the heavier elements. But they can later become stable ones by undergoing fission and beta decay.
Once the stellar material has been enriched with the ejection of these new atoms, subsequent generations of stars can generate other isotopes in the slow process (s -process), which also involves absorption of neutrons but at a slower rate. In a less violent environment such as that of a red giant, the absorbed neutron has time to decay into a proton so it tends to produce isotopes of medium to lower atomic numbers. For example some of pezzottaite’s cesium 133 (atomic number 55) could have been directly produced by the breakdown of an isotope created by the r-process or it could have formed later in another generation of stars by the beta-decay of xenon 133:
13354 Xe →13355 Cs +0-1 β
As shown in the diagram below, the unstable xenon 133 isotope was in itself generated by s-process. A 5-step sequence of neutron-absorption beginning with xenon-128 took place. In an r-process environment, more neutrons would have been absorbed before beta decay would have been possible.
Finally we get to aluminum. Before becoming a type II supernova, there is an important set of reactions that occurs in the core of a star exceeding 8-11 solar masses. Silicon burning -reactions mainly begin with silicon(atomic number 14) and add on a helium nucleus, creating sulfur(16), argon(18), and so on until iron is formed. But above a critical temperature explosive silicon burning photodisintegrates all nuclei and rebuilds them up during the expansion. In one of these reactions magnesium-26 captures a proton to form aluminum 27.
William Blake was right. There is indeed a world in a grain of sand—and, we may add, a universe in a mineral.
Formation of the Chemical Elements and the Evolution & of Our Universe, V. E. Viola Journal of Chemical Education, 1990, 67 (9)
Scientific American Grant J. Mathews, Victor E. Viola May, 1987