Circling the color wheel

 kw: color studies, spectroscopy, colorimetry, spectra, photo essays

Recently I was cleaning out an area in the garage and came across an old lamp for illuminating display cases. The glass bulb is about a quarter meter (~10") long. It's been hiding in a box for decades, ever since I stopped trying to keep an aquarium. It has a long, straight filament, which makes it a great source of incandescent light for occasional spectroscopic studies I like to do.

(The metal bar seen here is the filament support. The filament itself is practically invisible in this photo.)

This prompted me to rethink the way I've been setting up spectroscopy. Before, I had a rather clumsy source-and-slit arrangement. I decided to try a reflective "slit", that is, a thick, polished wire. As a conceptual test I set up a long-bladed screwdriver with a shaft having a diameter of 4.75mm. It isn't as badly beat up as most of my tools, and the shaft, some 200 mm long, is fresh and shiny. Based on these tests, I can use a thinner wire, in the 1-2 mm range, for a sharper slit. Later I may set up a lens to focus light on the wire for a brighter image.

I threw together a desk lamp and baffle arrangement, put the camera on a tripod with a Rainbow Symphony grating (500 lines/mm) mounted in a plastic disk that fits inside the lens hood, and produced these spectra. I also made a test shot with my Samsung phone and the grating, to see if I had sufficient brightness. Then I put various bulbs in the desk lamp and shot away. Here are the results. Each of the photos with my main camera shows the "slit" (screwdriver) along with the spectrum, to facilitate calibration and alignment of the spectra. Not so the cell phone image, which I fudged into place for this montage. The montage was built in PowerPoint.

The first item I note is the difference in color response between my main camera and the cell phone. The camera's color sensor cells have very little overlap between the three primary color responses, red, green and blue, so the yellow part of the spectrum is nearly skipped. The rapid fading in blue is a consequence of the very small amount of blue light an incandescent lamp produces. The cell phone sensor has more color overlap, more similar to the eye.

The two spectra in the middle of the sequence are both of mercury-vapor compact fluorescent bulbs. The white light bulb takes advantage of a few bright mercury emission lines, and adds extra blue, yellow, and orange colors with phosphors, which are excited by the ultraviolet (filtered out and not seen) and by the deep blue mercury emission line that shows as a sharp blue line. In the UV lamp, a "party light", the ultraviolet line at 365 nm is the point, and visible light is mostly filtered out; just enough is allowed out so that you know the lamp is on. There is also a phosphor inside that converts shortwave UV from mercury's strongest emission line as 254 nm to a band in the vicinity of the 365 nm and 405 nm lines; it shows as a blue "fuzz" here. The camera sensor has a UV-blocking filter, which doesn't quite eliminate the 365 nm line, so you can see a faint violet line where I marked it with an arrow. The emission lines visible in this spectrum are:

• 365 nm, near UV
• 405 nm, deep blue
• 436 nm, mid-blue (barely visible, directly below the mid-blue line shown in the Compact Fluorescent spectrum)
• 546 nm, green
• 577 & 579 nm, yellow, a nice doublet, and I'm glad the system could show them both
• 615 nm, red-orange, quite faint

I was curious to see if my "bug light" was really filtering out all the blue and UV light, and it seems that it is. There are still insects that get attracted to it, probably because they see the green colors. The "warm white" spectrum shows that the blue LED excitation wavelength is at about 415 nm, with a width of about 20 nm. Modern phosphors used in LED bulbs are quite wide band, as we see here, which makes them much better for showing true colors than the CFL bulbs we used for several years.

With a bit of careful looking, we can see that the LED bulbs don't have red emission quite as deep as the incandescent lamp does. That is the reason that for some purposes specialty lamps such as the CREE branded bulbs have a special phosphor formula with a longer-wavelength red end.

I also got to thinking about the way most of us see colors these days, on the screen of a computer or phone. The digital color space contains exactly 16,777,216 colors. Each primary color, R, G, and B, are represented as a number between 0 and 255, although they are very frequently represented as hexadecimal numbers from #00 to #FF, where "F" represents 15 and "FF" represents 255. The fully saturated spectral colors, also called pure colors, for which at least one of the three primaries is always #00 and at least one is always #FF, are then comprised of six sets of 255 colors, for a total of 1,520 virtual spectral colors…except that 2/3 of them are red-blue mixes that are not spectral colors. They are the purples. Note that violet is the bluest blue and is not considered a purple color, at least in color theory. The rest of the sixteen million colors have values "inside" the numerical space defined by the "corners" of the RGB space.

I prepared a chart of the pure colors, a dozen sections of the full "color wheel", which we will see is actually a color triangle. The RGB values for the end points of each strip are shown at their ends. "7F" equals 127, halfway from 00 to FF. They are separated as to spectral colors and purples.

To name the twelve colors at the ends of these sections, in order, with full primary colors in CAPS and the halfway points in lower case:

RED - orange - YELLOW - chartreuse - GREEN - aqua - CYAN - sky blue - BLUE - purple - MAGENTA - maroon - and back to RED.

To see why I spoke of "color triangle" let us refer to the CIE Colorimetry chart, based on publications in 1931 that are still the definitive work on human color vision. I obtained the following illustration from Wikipedia, but it was low resolution, so I used Upscayl with the Remacri model to double the scale.

There is a lot on this multipurpose chart. Careful work was put into the color representations. Though they are approximate, they show in principle how the spectrum "wraps around" a perceptual horseshoe, with the purples linking the bottom corners. The corners of the white triangle are the locations in CIE color space of the three color phosphors in old cathode-ray-tube TV sets. The screens of phones or computers or modern television sets use various methods to produce colors, but all their R's cluster near the Red corner of the diagram, all the B's cluster near the Blue corner, and all the G's are in the region between the top tip of the white triangle and the tight loop at the top of the horseshoe. Getting a phosphor or emitter that produces a green color higher up in that loop is expensive, and so it is rare.

I added bubbles and boxes to the chart to show where the boundaries of the colored bars are in the upper illustration:

 

I think this makes it clear that the "color wheel" we all conceptualize turns into a "color triangle" when it is implemented on our screens. All the colors our screens can produce are found inside the triangle anchored by the R, G, and B color emitters.

How real is dark energy?

kw: cosmological musings, dark energy, spectroscopy, universe evolution

I approach cosmology from a recreational perspective. I was introduced to extremely basic astronomy and cosmology during early primary education at a private school that followed the Classical model. But for a third-grader, a basic introduction to the Big Bang—early enough that Fred Hoyle's contention on behalf of a Steady State universe was still well regarded by many—was about as far as that instruction got. It piqued my interest, and I have enjoyed amateur astronomy, and also followed cosmology, sporadically and from a distance, ever since.

The apparent discovery of cosmological acceleration and "dark energy" just over twenty years ago got my attention. Over the past two decades I have pondered numerous aspects of cosmology, and while I still have my wits about me, it is time to record a few ideas. Allow me to state my bias at the outset: I think the analyses so far performed are incomplete, and that eventually the Cosmological Constant will be returned to zero, from the present hypothesis that it is either -1 or -0.3, depending on the units chosen by various authors.

I collected my thoughts on the matter and wrote this list of discussion topics. I don't plan to discuss each topic in detail, and not in this order. But the first item on the list is a good place to begin.

Photon "Experience"

Albert Einstein began by imagining he could follow a beam of light in a rail car. From the speculations that followed, he applied appropriate mathematical treatments to derive the theory of Special Relativity.

With a much more modest goal, I began by considering what it would be like to "be" a photon. What does a photon experience? From our point of view, a photon is emitted, typically by an accelerating charged particle (I include quantum transitions as "acceleration"), it then travels some distance before being absorbed, either by being converted to heat energy or by causing a quantum transition in an electron orbital. I will take advantage of my experience as a spectroscopist, primarily of near-to-medium infrared (NIR and MIR), but also plenty of visible and near-ultraviolet (V and NUV) spectra, and even some time spent working with vacuum UV or far UV (FUV).

What is the photon's point of view? If we imagine a photon as having sufficient awareness to "experience" anything, what does it experience? Let us first consider emission by a quantum transition, such as an electron of a hydrogen atom in the first excited state, dropping to the ground state. The energy of the photon is 10.2 eV, and it has a nominal wavelength in FUV of 121.6 nm. This is the Lyman-alpha (Lyα) transition. As a spectroscopist I primarily worked with cesium. Considering its ground state of five filled shells plus one s-electron as a lower-energy "virtual hydrogen atom", the first-level-to-ground transition energy is 1.39 eV, with a NIR wavelength of 895 nm. The higher-energy transitions of cesium's outer electron to ground have wavelengths in the visible spectrum, with the strongest being a bright green 540 nm.

I'll analyze the "experience" of a 540 nm photon. Although we tend to think of photon emission as instantaneous, it is more reasonable to consider that it occurs in a tiny slice of time. How tiny? The travel time at c across one wavelength at 540 nm is 1.8x10^-15 s, or 1.8 femtoseconds (fs). If the photon is to "experience" its creation, it must think very fast because it has only a fs or two of "assembly time" before it begins its journey.

Skipping over the journey for the moment, it is reasonable to assume that "disassembly" occurs on a similar time scale of 1-2 fs. Now, as to the journey itself, what might the photon experience? Special relativity dictates that time dilation at velocity c is infinite; from the photon's point of view, the duration of the journey is precisely zero, and it experiences nothing!

Thus we can say that the "life experience" of a photon consists of at most 1-2 fs of assembly (birth?) followed immediately by at most 1-2 fs of disassembly (dissolution). Whether it is consumed in pushing an electron into a higher orbital, or exciting vibrational states in a molecule, which then turn into phonons and heat things up a tad, the photon itself experiences nothing whatever on its journey, whether the distance is a micron or a gigaparsec.

This in itself is quite tangential to cosmology. However, as a concept, wherever it might prove useful, I'll refer back to it.

Cosmological Red Shift

Note: For calculations of the age of the universe at different red shift I used calculators provided by NED at CalTech. NED is the NASA/IPAC Extragalactic Database.

The first date of interest to a visual observer is the formation of the first stars, which ionized the hydrogen and helium filling the young universe so that light could travel with little absorption. This date is widely considered to be about 400 My (0.4 Gyr, or 2.9% of current age) after the Big Bang, and if any light from this era is observable, its red shift ought to be about z=11.3

The second date of interest is at the completion of ionization by the first stars, now being formed into galaxies, at about 1Gy (7.3%), at a red shift of z=5.7.

The studies of supernovae used to winkle out the Cosmological Constant, and thus Dark Energy, have typically been undertaken between 0.1<z<1.0 (as compared to supernovae closer than z=0.1). This corresponds to ages between 5.87 Gyr (43%) and 12.4 Gyr (90%).

Mechanism of a Type Ia Supernova

This is relevant at this point, because so much hinges on the peak brightness of these phenomena.

The two principal mechanisms that produce supernovae are core collapse and thermal runaway. Core collapse supernovae may have spectra that contain hydrogen lines, meaning the star exploded before running out of hydrogen; these are Type II. There are several subtypes, but they don't pertain to this discussion, and there is a wide variation in their peak luminosity. If a core collapse occurs after the hydrogen is exhausted, no hydrogen spectral lines will be seen; such supernovae are Type I. These also have a few subtypes, which don't concern us.

A supernova that contains no hydrogen lines in its spectrum, and also has a strong line of singly ionized silicon (615 nm), is interpreted as a thermal runaway supernova of Type Ia. What is thermal runaway?

The basic mechanism starts with a white dwarf. This is what remains after a main sequence star with an initial mass less than 8 times that of the Sun (M*<8M☉) has used up all its fuel. The time this takes varies depending on the mass of the star. The initial mass is called its "Zero-age mass", setting zero at the point hydrogen fusion begins. 

This chart shows the time, in billions of years, that a star spends on the Main Sequence, fusing hydrogen exclusively, until it begins to fuse helium in its core, at which time it "leaves the Main Sequence" and grows to be a Red Giant. The data for this chart came from one of many reports about computer modeling of stellar evolution.

Depending on the star's mass, it takes between a few million years and half a billion years for a red giant to complete helium fusion, at which point it will erupt in a gentler way than a supernova, "whooshing" away up to half its mass or even more (which often becomes a planetary nebula), and then it shrinks into a white dwarf. A new-born white dwarf is actually rather blue, with a temperature of around 100,000K.

The blue line tracks stars of similar composition to the Sun, but a little less initial helium (parameter "y"). The green line tracks stars with very low amounts of "metals", by which an astronomer means all elements heavier than helium. The symbol for metallicity is "z" (don't confuse this with z, for redshift), and for the Sun it is about 1%, called "hi" in this chart. The green and violet lines are for z=0.00001, or 0.001%, which would represent the second generation of stars in the early universe. The first generation had a metallicity of zero, and behaved very differently from stars with even a few parts per million of "metals"; for one thing, they couldn't really get fusion going until their mass exceeded 50-100 solar masses, and they then burned very brightly and used up all their fuel in just a few million years. At that point they exploded as a supernova (I don't know what type). That explosion synthesized elements of the entire periodic table in a very short time, so the first generation of stars seeded the universe with elements that let all succeeding generations of stars "work" the way stars now operate. Over time, supernovae of types I, II and III added more and more metals, so that five billion years ago when our Sun was formed, that part of the galaxy had a metallicity of about 1%.

I am interested in the formation of the earliest white dwarfs. These would have been produced from middleweight stars, with mass between 4 and 8 solar masses (M☉). Their main sequence "dwell time" would be about 100 million years for those near 4 M☉, and just 10-20 million years for the heaviest stars. Just as the main sequence dwell time is much shorter for more massive stars, so is the period of helium burning. While the red giant that the Sun becomes will spend perhaps half a billion years burning helium, a star 6-8 times as massive will burn through all its helium in a million years or so, and become a white dwarf soon thereafter ("soon" meaning probably less than a million years). When we're looking back to a time before the universe's age was about 6 billion years, a few million one way or another is negligible.

What is the composition of such a white dwarf (WD hereafter)? Their basic composition is carbon and oxygen, formed by helium fusion. In the heaviest "middleweights", a little fusion of the C and O can occur, yielding magnesium (C+C→Mg) and silicon (C+O→Si). In the earliest WD's we would not expect other elements in more than trace amounts, but in later ones, minor element abundance will be similar to that of the original star.

Now we are ready to talk mechanisms. When the Sun becomes a WD, it will have a mass of about 60% of its present mass. In the late stages of being a red giant it will expel the rest of the mass in a big "whoosh". Heavier stars expel a larger proportion, and no WD gets formed with more than about 1.4 M☉. This is because the only thing keeping a WD from collapsing into a neutron star or black hole is electron degeneracy, a quantum-mechanical effect. The 1.4 M☉ limit, first calculated by Chandrasekhar, and named for him, is the limit of the strength of degeneracy. This is the key to the fixed value of the luminosity of a Type Ia supernova.

Once a WD forms, if it is isolated, it remains forever, slowly cooling to a black dwarf (which takes a few trillion years). But many stars are members of a doublet. The companion star of the WD can do several things to add mass to it, and once its mass exceeds the Chandrasekhar Limit, it will collapse, from the core first: Beginning at the core, rapid deflagration occurs and soon consumes the entire star. The detonation outshines a typical galaxy and can be seen across the visible universe. That is a Type Ia supernova.

There are two principal ways a companion star might add mass to a WD.

1. The companion will itself eventually become a red giant. If the orbit with the WD is small enough, material from the giant will be swept onto the WD. This can go on until the WD detonates, incidentally giving the companion a "kick" that sends it careening away at a good fraction of the speed of light.
2. The companion may not push enough mass to the WD to make it detonate. Instead, when it begins its late stage "whoosh", some of the cloud thus released can stay behind, and friction will result, such that the WD and the fading red giant, on the way to becoming a WD itself, spiral toward one another. In time they will merge, combining their masses into one larger WD. It is very likely that this combined WD will have a mass greater than 1.4 M☉, and it may even approach 2.8 M☉ if both stars' initial mass exceeded 6 M☉. The new WD doesn't even settle down, but detonates right away. 

Interestingly, all the literature I have read indicates that the second mechanism is apparently much more common than the first. Perhaps only 5% of Type Ia supernovae occur by the first mechanism. That presents a problem, because we now have a 2:1 range of "mass detonated", which ought to have a big influence on the peak luminosity of the supernova.

If that were all there is to it, I could say with confidence that the spread in luminosity is too great for these supernovae to be a useful "standard candle." However, the studies that led to the discovery of apparent cosmological acceleration, and later researchers seeking to confirm it, have another ace up their sleeve. They use spectroscopic criteria to distinguish different subtypes of Type Ia. If they aren't fooling themselves with circular reasoning (and I do not claim they are), the selected supernovae do seem to exhibit extra dimming with distance, consistent with the acceleration hypothesis.

For example, this figure from a short publication by the Dark Energy Survey shows the effect. The authors used spectroscopy to identify more than 250 supernovae with redshift between 0.1 and 1.0 (1.4 Gyr ago to 7.9 Gyr ago), shown by the red symbols. They used the same criteria to gather a sample of similar size of more recent supernovae, shown by the yellow symbols.

They normalized the data to the hypothetical model with acceleration, so their hypothesis follows the horizontal line in the lower diagram. The lower, dashed blue line shows where they would expect these data to fall if there were no acceleration and the universe were flat.

Faced with a chart like this, I have to accept the hypothesis, don't I? Not necessarily. The article has a comprehensive, but exceedingly compressed, discussion of the computational methods used to correct for intergalactic extinction (dimming of the light by gas and dust 'way out there'), for example. They may have corrected for the effect I am soon to discuss, but I could not determine if this were so. I also have a point to discuss relating to the composition of WD's.

I am quite impressed by the tightness of the error bars, a result of the selection criteria, considering that the pre-selection luminosity data must have had a scatter exceeding 2:1, for reasons noted a few paragraphs above.

White Dwarf Composition

The initial counter-idea I had, nearly 20 years ago, was, "Does the metallicity of the star that formed the WD have any effect on the actual value of the Chandrasekhar Limit for that particular WD?" Secondarily, does the composition modify the rate of deflagration, and thus the peak luminosity?

I don't have the mathematical or computation tools to delve into this directly. Perhaps someone will do so, or maybe someone has and I haven't seen the literature. However, I'll ask the questions in another way, and leave it as something for future resolution: "For a white dwarf with a mass just below the nominal Chandrasekhar Limit, and a metallicity very near zero, perhaps no more than a few ppm, will its diameter differ from that of a WD of the same mass but metallicity near 1%?" Similarly, "Will the exact value of the Chandrasekhar Limit differ between the two WD's?"

Either effect introduces systematic error. However, metallicity ought to affect the spectroscopy, so perhaps it has been accounted for, wittingly or not.

Density of Earlier Universe

In the second section above, I wrote that the lookback time represented by a redshift z=1 is 7.9 Gyr, when the universe's age was 5.87 Gyr, about 43% of its current age, here considered to be 13.77 Gyr. A simplistic understanding of the distances represented by redshift, based on neither acceleration nor deceleration, is that the light reaching us from the early universe has traveled one billion light years per gigayear, so the radius the observable universe would have been 43% of the present value at z=1. The cube of (5.87/13.77) is 0.077. Inverting this, the density of the intergalactic medium at z=1 then would be 12.9 times as great as it is now.

Things aren't that simple. The cosmological calculators I've been using for these figurations use the Friedmann equations to factor in the effects of the cosmological constant and general relativity, such that the "distance" light has traveled since the big bang isn't 13.77 billion light years (GLy), but about 46.1 GLy. The "extra" 33 GLy is from cosmological expansion of space, which carried the light along with it. According to the Friedmann equations, the lookback distance to z=1 is 11.05 GLy, which means the distance light came to reach that point was 35.05 GLy, or 76% of the full distance. The cube of (35.05/46.1) is 0.440; inverting this yields 2.275. If these are the right figures, the universe was only a little more than twice as dense then, compared to now.

So, which is it? The Friedmann equations are used in the calculation of 13.77 Gyr as the "age" of the big bang, and they have built into them the cosmological constant and are thus are based on the existence of dark energy. Here the reasoning does seem circular. Again, I'll put that notion on hold until I learn more.

The fact remains that the density of the universe about 8 billion years ago was between about 2.3 and 13 times the present value.

That is not all. While the Milky Way is thought to have formed within 100 million years after the big bang, and many other large galaxies also, other galaxies are of more recent vintage, some as recent as half a billion years. What proportion of the primordial gas that now makes up the stars—and the supernova-processed material of the interstellar medium and intergalactic medium—had been gathered into galaxies in the first 6 billion years after the big bang? Half of it? 80%? . . . 20%? I have not seen any well-supported estimates. Galaxy formation is written about as a continuous process. If the most recent "new" galaxy has an age of 500 million years, there are others, not yet discerned, of a wide span of ages.

The universe of between 4 and 8 billion years ago contained intergalactic material that has since been swept into galaxies and used to form newer stars. Our Sun, of age about 5 Gyrs, was probably formed mainly from material that had been in the Milky Way almost from the beginning, but was more recently-gained material also included? It it likely.

Interstellar Extinction and Intergalactic Extinction

In astronomical terms, "extinction" is nothing like biological extinction. It refers to the dimming of the light by absorption as it passes through gas and dust between the stars and, for anything outside the Milky Way, between the galaxies. When measuring the brightnesses of stars we actually have to correct for atmospheric extinction also, for telescopes on Earth. Space telescopes, of course, are above the atmosphere, which removes this complication. But the effect of the atmosphere is a familiar starting point toward understanding how gas and dust in space affects starlight.

The clean air of a cloudless day scatters more than ¼ of sunlight before it reaches the surface near the Equator, and even more at other latitudes. The scattered light is the blue sky we see, because the scattering is more efficient for bluer light. Thus, at the equator direct sunlight, which began at the top of the atmosphere with an intensity represented by the Solar Constant of about 1,370 W/m², has an intensity of about 1,000 W/m² when it hits a beach in western Ecuador. The other 370 Watts has been scattered such that half goes up and half goes down, which means the sky brightness has an intensity of 185 W/m². At the latitude where I live, near 40° north, photovoltaic solar panel systems are designed for peak insolation of about 700 W/m².

If there is any dust in the air, it absorbs more of the light, sometimes nearly all of it. Scattering by dust is also more efficient for bluer light, but the spectral function is not as steep as it is for clear-gas scattering (Rayleigh scattering). We have all seen a sunset on a windy day with very dramatic colors because of dust in the air; we can look right at the deep red Sun without harm.

There is a lot of dust in the interstellar medium within the Milky Way. That is why galactic surveys are undertaken far from the trace of the Milky Way on the sky. Most of the intergalactic medium is thought to be gas, with much less dust.

If the air in the sky above that beach in Ecuador didn't decrease in pressure with altitude, the depth of the atmosphere would be about 7.8 km (4.8 miles). That is sufficient to scatter away 27% of the sunlight by Rayleigh scattering. However, the primary gas in space is molecular hydrogen, not nitrogen. The Rayleigh scattering cross section of nitrogen is reported as about five times that of hydrogen. We may thus determine that, to absorb 27% of incoming sunlight, normalized across the visible spectrum, a thickness of 39 km of hydrogen, at a pressure of 760 Torr, is required. One-third of this depth of gas will absorb 10%, so a base thickness of 13 km is a good starting point for what follows. Even then, the calculations will be pretty rough because I don't want to enter into the complexities of integrating across the spectrum.

The gas "pressure" in interstellar space is quite variable but over long distances it averages out to between 10^-10 and 10^-11 Torr. That is less than a trillionth of the gas density of the atmosphere. Fifty years ago, working as a high-vacuum technician and spectroscopist, I regularly achieved pressures in this range in a stainless steel chamber (with various sorts of viewports) that had a volume of a couple of cubic feet.

The ratio 760 T/10^-11 T is 7.6x10¹³, and this times 13 km is 9.88x10¹⁴ km. That is about 104 light years. This is convenient: interstellar extinction by hydrogen is about 10% per hundred light years, within the Milky Way at least. In areas with pressure closer to 10^-10 T, it is 10% per ten light years.

In intergalactic space the gas density is about a million times less, with a "pressure" of about 10^-17 T. When we look out away from the play of the Milky Way, the thickness of nearby gas may come to several hundred light years, and absorb perhaps half the light. Beyond that, each hundred million light years, intergalactic extinction would be about 10%.

Here I have to step back to say, "Is this reasonable? At redshift distance of z=1, or about 8 GLy (uncorrected by Friedmann equations), is the remaining light really 0.9⁸⁰, or 0.00022?" That is nine magnitudes! I suspect the material I read that compared Rayleigh scattering in hydrogen with other gases had a value too high for hydrogen. If it is even half the value I've used, the base depth of 13 km would instead be 26 km, and intergalactic extinction would be 10% per 200 million light years, leading to extinction of 0.9⁴⁰, or 0.015, which is 4.5 magnitudes, a much more likely value.

This emphasizes that the observed luminosity of distant objects must be properly corrected by a correct model of intergalactic absorption.

This is the final concern I have with the measured luminosities of distant supernovae. If the volume of the universe at z=1 was less than half what it is now, or perhaps much less than that, the density of the intergalactic medium was at least twice as great, and perhaps much more, depending on how much was already sequestered into galaxies.

The reports from the Dark Energy Survey state a scatter in corrected luminosity of their supernovae of about 20%, which is small enough that the effect can be seen. Yet, if the extinction calculations are not taking proper account of the change in density of the intervening gas (and dust) over time, a rather small error in the extinction coefficient, drawn out over billions of light years, makes a large difference.

Conclusion

It takes a long chain of reasoning to draw the conclusion that the Hubble expansion of the universe is accelerating. Is it possible that the cosmologists have thought of absolutely everything that could systematically bias the measurements on which they rely? Everything? Possibly, but it is unlikely.

Here are the factors that may be confusing the matter:

• The peak luminosity of a Type Ia supernova may depend on the metallicity of the original stars, which would have been very low in the early universe.
• Intergalactic extinction is based on the total gas column between the source and the observer. The gas density has changed through time, firstly because of thinning in an expanding universe.
• The gas density has also changed through time as gas was gathered into galaxies, and in particular how rapidly that gas was taken up and thus removed from most sight lines.
• The Friedmann equations used to determine lookback distance depend on the cosmological model, including values of Ω_o, Ω_M, and Ω_vacuum. Unless used with care, calculating distances to use for extinction calculations becomes circular reasoning.

With these in mind, I think it is very, very premature to conclude that cosmological acceleration is real.

Tea light of another color

kw: analytical projects, lamps, spectroscopy

Recently a friend gave us a goblet she made that she calls Tree of Life. Perhaps there are 12 colors on it to match the 12 fruits mentioned in the book of Revelation (I didn't count). She also gave us a candle to put in it, but the candle was in a large jar and didn't illuminate all of the goblet. So we tried a tea light candle, which worked nicely. However, we don't usually burn candles, and we wanted something safer (the cat might knock it over). So we tried an amber-colored LED tea light. That was a poor choice! We had a different kind of LED candle, with a whitish-yellow colored light, so we tried that, with mixed results. Here is the goblet with the three lights inside in order: flame, whitish LED, and amber LED.

These are the lights in the order shown above. The flame is clearly the best all around. The whitish-yellow LED candle is too tall to illuminate the whole goblet, but it show the colors well. It also uses a moving reflector to make a flame effect, but that blocks most of the light that would go out the back. The amber LED tea light, while it illuminates the whole goblet, has no range of color! (There are blue reflections in the second and third photo from a nearby computer monitor.)

It is clear that the amber LED has a narrow spectrum. How narrow? I determined to find out. Here are the results of spectroscopy of the three lamps, and also an incandescent lantern bulb.

While the flame (second spectrum) is whiter than the whitish-yellow LED, it has a broader color spectrum, though not as broad as the incandescent lamp shown first. The bright peak at the blue end of the third spectrum is normal for an LED using phosphors to add the red through green and light blue colors. LED lamps for home use use the same principle.

The amber LED (fourth spectrum) does not use phosphors. It is a low-voltage LED that has a color peak in the orange-yellow area (near 590 nm). Its bandwidth is similar to that of the blue excitation band of the other LED that does use phosphors. There is just a trace of red and a bit of green, but they are overwhelmed by the yellow-orange peak. So all the colored blobs on the goblet just look yellowish.

The lantern bulb has a full-width spectrum, from below 400 nm to beyond 700 nm; the visible portion is 300 nm wide. The candle and the whitish LED have bandwidths nearly as broad. But the amber LED's bandwidth is a mere 75 nm, and the brightest portion is no wider than half that. It mostly just makes amber-colored light and nothing else.

I plan to carry a hand spectroscope with me the next time I go to buy LED tea lights, to find a brand with a broad spectrum that'll illuminate this goblet properly!

Scoping out lamp spectra

kw: analytical projects, spectroscopy, photographs

Technical photography of biological subjects has its tricky aspects. An important one is the quality of the lights. This picture shows one setup I have used to avoid the use of the compact fluorescent lamps (CFL's) that were brought in to replace the incandescent flood lamps they had been using, but which burn out on a regular basis…and they are hot. CFL's have serious drawbacks for color photography, which we'll see later on.

The little blue lamps, wrapped in tissues, are "work lights" from Harbor Freight, with 18 small LED bulbs each. They have a pretty good spectrum (I'll point out a similar one below).

We have been considering a more quantitative approach, particular for photos of birds. Few mollusks have "interesting" colors, but nearly all birds do. Birds have an extra color sensor in their eyes and can see ultraviolet light, so it is also of interest to be able to photograph birds in UV light.

I decided to explore the various lamps available, not only for these reasons but a few extra ones. In recent years I used pieces cut from a page-size sample of diffraction grating, obtained from Edmund Scientific many years ago, to make two spectroscopes. One, about a foot long, is for handheld use, and another, about twice the size, is for use with a camera.

I originally made them to investigate which yellow lamp would be the best "bug light". Night-flying insects see UV even better than birds do, and many of them cannot see yellow or red light, and have low sensitivity even to green. The ideal bug light would have a cutoff in the yellow-green range, and would be rather orange. In order to keep people on your doorstep from looking too weird, all commercial bug lights include some green and look distinctly yellow.

This shows a test setup with the large spectroscope on my workbench, using a black light as the source. Not only does the camera "see" UV, it is also being overloaded by the bright blue and violet lines of mercury (Hg). That black light bulb is not nearly this bright to my eyes. The camera at the left is set back a little farther than usual; I usually use it with the front of the zoom lens about two inches from the grating, which is at the end of the white bell-shaped "front" of the spectroscope. The "slit" is currently a thin slot sawn into a PVC cap at the end where the lamp is.

Initial tests verified that the camera's sensor can record UV and that the lens passes it, and also that none of the lens elements is fluorescent (a problem with the lens of another camera I have!). I also learned that the "UV filter" I was sold with the camera does not block UV-A (longwave, or near-UV). It does block short-wave UV, that is UV-B and UV-C, pretty well. So I bought a better filter, a UV(0) filter from Hoya. Now to the recent batch of tests, summarized in this image, a screen shot from PowerPoint:

Depending on your monitor, this might be hard to read. To summarize, the top shows the spectrum of a "black light" CFL (a "party light"), at two exposures; the next 11 sets are at three exposures each. From the top, then, we have

• two sets for different hues of fluorescent tube, 
• two sets for incandescent bulbs, 
• two sets for different hues of CFL, 
• a yellow CFL "party light", 
• two commercial "bug light" bulbs, and 
• two sets for LED bulbs from different manufacturers; the spectrum of the work lights from Harbor Freight is a little bluer than the bottommost set.

Only the black light has a spectrum that includes a strong UV line at 365 nm. Most of the lamps have a cutoff near 420 nm, though a couple of the CFL's let through a little deeper blue and the UV line. The spectra of the CFL's show very strong lines with darkness in between, which is why these lamps have poor "color rendering", as it is called. LED's, as shown at the bottom, come the closest to mimicking the spectra of incandescent lamps.

My preliminary conclusions are (1) that for ordinary color photography, LED lamps are the best choice among the "non-incandescent" ones, and (2) to get good UV images we'll need to use black light CFL's, probably with a visible-blocking filter. It may also work to use UV LED flashlights like the ones used by TSA at airports, though they are a bit costly, because they don't produce any visible light.

Lamp spectra - first try

kw: analysis, spectroscopy, lighting

In the past few years we have tried several lower-wattage "bug lights" as an alternative to the yellow 40-watt incandescent bulbs we've used before in our porch light fixture. When the one we had 4 years ago burnt out we got a 13 watt, yellow compact fluorescent spiral lamp by Sylvania. Though it was not marketed as a bug light, it worked pretty well, though some insects came to it. The next year I saw a 6 watt LED bug light, marketed as such by Feit, so we got that. It worked about equally well. Then I went looking for something that might be a little bit better, and got a 3 watt amber bug light, also by Feit. It doesn't draw insects, but it is pretty dim.

I decided to find out whether a little blue light is getting out of these lamps, so I made a crude spectroscope from a piece of diffraction grating and a short length of PVC pipe plus some odds and ends. In this photo it is on a tripod aimed at a test lamp. I aim a camera with a telephoto lens at the black aperture at the left, where the spectrum emerges.

I cut the end of the PVC for the grating at an angle so the spectrum would exit at right angles to the grating. It has the added benefit that, for visual use, looking the "back way" yields a spectrum about twice as wide. But the focal plane is strongly tilted, making it a poor choice for photography (though I tried!). The instrument has a number of shortcomings, but I think I know how to produce a better next version. For one thing, I'll use a different exit angle, so the diffraction grating doesn't reflect the camera and photographer! (see below)

I photographed the spectrum of nine lamps, the three test bug lights and several others either for spectrum reference or to see the spectral coverage of both incandescent and non-incandescent lamps. Eight of the lamps are shown here, and their spectra are tagged in the next image, followed by some explanation.

These are in the order listed in the spectra image.

The first three spectra are for reference. The 4000K (cool white) CFL shows a combination of spectral lines for mercury (Hg) and for the phosphors used to "whiten" the harsh blue-green light of raw Hg lamps. Mercury has a strong green spectral line at 546 nm, as seen in both this lamp and the 13W yellow CFL (A nearby strong green line is from a phosphor) and a strong blue-violet line at 405 nm, which excites some of the fluorescence, but a stronger near-UV line at 365 nm does most of that. The strong red-orange line at or near 615 nm is from a phosphor, as are the yellow-orange-green and green-blue-violet bands. The 40W incandescent lamp shows the smooth spectrum characteristic of a thermal source. The near-lack of yellow in this spectrum is because a camera's sensor sees colors differently from our eyes, but this is only evident when photographing spectra! The 60W "Reveal" lamp has a filter that cuts out most of the yellow and yellow-orange, making the light appear bluer and closer to daylight.

The next three spectra are for the bug lights. The 13W yellow CFL has the same spectrum as the white CFL from green through red, but with extra yellow and orange, and the green-blue-violet phosphor is left out. Also, a filter removes the blue and violet lines of Hg. The two LED's have nearly identical spectra. The blue-violet light from the fluorescence-exciting blue LED is filtered out, leaving only light from the broad band phosphors. The 3W lamp has a little more red-orange than the 6W lamp, and this is visible when they are lit side-by-side; the 3W lamp's color is amber. In the photo of the lamps above, the filter is inside the 3W lamp's envelope, which is white. For these three spectra, the brownish features seen below the green band are reflections of either me or the camera off the diffraction grating film.

The 8.5W LED is the kind of "warm white" bulb we have begun to use around the house. It has a spectrum very similar to incandescent; it just has a dip in the mid-blue range, and a bright band in the blue-violet range, which is from the fluorescence-exciting LED. The UV CFL is a "black light", very similar to old black light fluorescent tubes used at parties, but in spiral form. Most of the visible light is filtered out. The green and violet lines at 546 and 405 nm are a little visible anyway, and the camera is barely able to record the 365 nm line that does all the work of making fluorescent things glow. I am puzzled by the line in between, at about 385 nm. I don't know what it could be from. However, I know that these lamps use a phosphor that responds to a strong Hg line at 254 nm and converts it to longer-wave UV, to get more "black light". Perhaps it is the source of the 385 nm line and other faint features in that space, but I think it mainly adds more 365 nm light.

Finally, the 40W fluorescent tube is of the kind that has been in use for nearly my whole life (7 decades), now mostly supplanted by CFL's and LED's. The two lines of Hg in blue-violet and green come through, but broad-band phosphors fill out the light making these pretty good for most uses. They actually have better color rendering values than CFL's, at the cost of using nearly twice the power: a 40W "tube" and a 23W CFL both emit about 1,600 lumens, but strongly colored items may look a little odd with the CFL.

As crude as it is, this simple spectroscope helped me understand these lamps better. I think the reason that some insects still come to the three non-incandescent bug lights is that they can see the green light. I don't have an incandescent bug light, but I suspect it to have less green light than the CFL or the LED's. This has been an instructive exercise.

Pioneers of celestial measurement

kw: book reviews, nonfiction, science, scientists, astronomy, astrophotography, spectroscopy

Look carefully at the white line across the gray band, where the ink marks are in each section. The ink marks were made by Edward Pickering in 1889, when he noticed the doubling of the Calcium K line (λ=393 nm, near UV) in the upper photo of the spectrum of Mizar. Mizar, also known as Zeta Ursa Majoris, is the brighter of the Mizar-Alcor double star in the "corner" of the handle of the Big Dipper. One needs keen eyes to see that it is double.

Mizar itself was found to be double by comparison of these two spectra photographed a week apart in 1887. It is the first known "spectroscopic binary". Two stars of roughly equal brightness circle each other in about 20½ days. The splitting of the K line (and all the other lines shown if you look closely) is because of the Doppler effect: when one star is moving toward us, and the other is moving away, the wavelength of the light that reaches us is shifted, one toward the blue, the other toward the red end of the spectrum.

This discovery was made possible by the "glass universe" being compiled at Pickering's behest by pioneers of astrophotography and astrospectroscopy whom he had commissioned to photograph the whole sky, over and over, on glass/emulsion plates using telescopes owned by Harvard Observatory.

This immense photographic effort, and the numerous women—and a few men—who made literally hundreds of thousands of discoveries using the plates, are chronicled in The Glass Universe: How the Ladies of the Harvard Observatory Took the Measure of the Stars, by Dava Sobel. I believe I must declare this book the most fascinating I have read so far this year. I have known for many years of "Pickering's Harem", the female "computers" who carried out manual calculations for the Harvard Observatory, and I knew of a few astronomers, names now to conjure with!, such as Annie Cannon, Mina Fleming, Cecelia Payne, and Henrietta Leavitt, whose work in the late 1800's and early 1900's literally opened the heavens by classifying the stars, discerning nebulae, measuring stars' temperatures, and discovering the period-luminosity relationship that became the yardstick for measuring the size of the Universe. This book brings them all to life for us.

Please forgive me a sort of quibble at the outset (not about what the author wrote, however): I read the Large Print edition by Thorndike Press. On the copyright page the publisher put a standard disclaimer for a work of fiction. I contacted Ms Sobel, and she assured me that there is no fiction in this book. I am very glad of that!

There is a common notion that the Harvard computers were given mainly "grunt work" and had little else of value to contribute. Not so! When Edward C. Pickering assumed leadership of the Harvard Observatory in 1877 a number of computers already worked there, most of them female, and he added more and more, eventually hiring more than 80. He always looked for hidden talents and helped the computers develop as far as they could. Williamina ("Mina") Fleming was originally hired as a maid, but he soon found she was a capable computer, and she went on to co-develop the system for classifying stars that we still use, based on the mnemonic "O, Be A Fine Girl, Kiss Me", which sorts the spectral types by temperature from hottest to "coolest" (still hotter than the filament in a light bulb). In this picture, Mrs. Fleming is standing, and the computers of the day, including Annie Cannon just below her, are shown searching photographic plates and calling out their readings to a compatriot seated nearby.

Ms Sobel presents the life stories of a dozen or so of the computers-turned-astronomers and their colleagues, and shows equal interest in the instruments and methods used to make their discoveries. And the entire narrative is wrapped around the philanthropy of two women whose fortunes underwrote much of the work. Firstly, Anna Draper, wife and collaborator of astronomer Henry Draper, came to Pickering after her husband's untimely death in 1883 and offered to support a continuation of the stellar spectroscopy and cataloging work that Henry had begun with her assistance. The support continued until her death in 1914, and her bequest to the Observatory allowed the rest of the Henry Draper Catalog (still in use) to be completed thereafter. Stars with labels such as HD217014 (AKA 51 Pegasi, the star around which the first exoplanet was discovered) are cataloged therein. Secondly, Catherine Bruce funded the production of the Bruce Telescope, a 24-inch-diameter refractor, which was used first at Cambridge, Massachusetts in 1893, then in Peru and finally in South Africa until 1950. This telescope and several of smaller size were used to take the photographs that make up the bulk of the Glass Universe, a four-dimensional archive of the sky from 1885 to 1993!

This is a small segment of one of the glass plates, showing the globular cluster 4 Tucanae. Astrophoto plates are negative images, and were read directly by researchers such as the Harvard computers, one of whom has inked directly on the plate a few arrows and lines to point out certain stars of interest, most likely variable stars.

A technical note: Very early on it was found that the best discernment of star images could be had by exposing a plate until the background skyglow produced a "density 1" gray, which passes 10% of the light when the plate is back lit. Depending on the darkness of the sky at the observing location, and the photographic speed of the plates used, this would usually take an exposure of between 30 and 90 minutes. In one night of observing at a very dark site with fast plates, one might take 20 or more exposures.

A very major part of the work at HAO was to discover variable stars and chart their variation over time. The stars marked in this plate were found by comparing plates taken over several days' or weeks' time. The long- and medium-period variables were typically the most consistent, and this was fortuitous, because Henrietta Leavitt later discovered that the greatest number of these are Cepheid variables whose period of variation is proportional to their brightness at its peak.

Cepheid variables are giant stars with masses 4 to 20 times that of our Sun, and are as much as 100,000 times as bright. This makes them visible over very great distances, up to tens of millions of light-years, using larger telescopes. The Leavitt Law, or Period-Luminosity Relationship, allows measurement of the distance to galaxies within that range of distance. Such measurements led to Edwin Hubble's discovery of the expansion of the Universe.

If you look at a group of bright stars such as the Orion constellation or the Hyades cluster (the horns of Taurus, the Bull), after a while you can notice that a few stars are yellowish or reddish compared to the rest. Orion, in particular, has the star Betelgeuse (and, yes, it is pronounced "beetle juice"), which is visibly rather orange, in one corner. Most of the rest of the stars in Orion are quite bluish.

For stars, blue means very hot, white means "sorta hot", yellow is not as hot, and orange-red is the coolest. To put numbers on it, Rigel, in the corner of Orion opposite Betelgeuse, is a blue-white giant star with a visible-surface temperature of 12,000 K (over 21,000°F), as compared to our Sun, a yellow-white star of temperature about 5,800 K (9,900°F). Betelgeuse, while not the coolest visible star, comes close at a temperature of 3,500 K (5,800°F). The tungsten filament in a (now nearly obsolete) halogen light bulb typically has a temperature of 3,300 K (just below 5,400 °F), so a "piece" of Betelgeuse brought into your living room would look slightly less yellow than a halogen lamp.

The observers and computers at Harvard took advantage of spectroscopy to do much better than just making visual color estimates. The gray and black streaks on this plate image are spectra of stars, photographed with the help of an objective prism. The objective prism for the Bruce Telescope was a thin wedge of glass more than 24 inches in diameter that turned the whole telescope into a multi-stellar spectrograph. It also incorporated a slight curvature in one direction to turn a stellar point of light into a thin streak, so that the spectra would have useful width.

These little streaks may not look like much but they record an amazing amount of information about a star. Much more than the proportion of blue to red light—which are hard to determine from such photos, though it is not impossible—, the spectra include Fraunhofer lines. These are absorption lines caused by elements in the gaseous upper atmosphere of the star. The kinds of lines that are present are a much more sensitive indication of both the composition and the temperature of the star.

If one were to look through a telescope set up in this way, it might look something like this, from a photo taken at the University of Virginia. This shows the Hyades cluster; if you concentrate on the position of the red end of each spectrum you can see the tilted "V" shape of the cluster.

This photo as shown here is too small for Fraunhofer lines to be seen, so I made this clip of just a few of the spectra:

The dark lines are the more prominent Fraunhofer lines. The K line mentioned above is barely visible in one of these spectra at the far right. Its wavelength of 393 nm is just beyond the traditional edge of Ultraviolet (400 nm), but that wavelength is actually visible to most people if the spectrum is bright enough. Each line is characteristic of a particular element. A dark line in the narrow yellow area would indicate Sodium, for example, just as the K line indicates ionized Calcium. The very strong lines for Hydrogen and Helium found in the spectra of the hotter stars of categories O and B led to the discovery that stars are primarily made up of Hydrogen, about ¼ Helium, and all the other elements add up to no more than about 1%.

Annie Cannon and others excelled in looking at the gray streaks, the hundreds to thousands of them that populated each plate, and categorizing each star by temperature and "spectral type" such as G2 (the spectral type of our Sun). Miss Cannon eventually categorized a third of a million stars.

I could go on and on, but this is long enough already. I love a book like this, that tells about the people and the work they did and why it is important. Without the "boring" work of the Harvard computers and astronomers, nearly all female, we would know only a tiny fraction of what we have learned about the Universe.

Follow-up: The Harvard plates are presently being digitized for Digital Access to a Sky Century @ Harvard, or DASCH ("Dash"). Have a look, but beware, there is a large learning curve. If you want to have a turn at stellar classification, check out Stellar Classification Online Public Exploration, or SCOPE., a Citizen Science project. While a few million stars have been classified, the great majority of the billions of stars, just in the Milky Way galaxy, have yet to be classified. Enjoy!