Distant Supernovae Evince Accelerating Expansion of our Universe

In 1998, it was discovered by two independent research teams through the study of distant Type Ia supernovae that our expanding universe has an expansion rate that is accelerating.  This was a completely unexpected result.

A Type Ia supernova occurs in a close binary star system where mass from one star accretes onto a white dwarf until it reaches a critical mass and a supernova explosion ensues.  Many of these events, chosen carefully, can be used as “standard candles” for distance determination.  The intrinsic peak luminosity of a typical Type Ia supernova is a function of the light curve decay time.  Type Ia supernovae whose luminosity curves rise and fall more rapidly are less intrinsically luminous at maximum brightness.  Type Ia supernovae whose luminosity curves rise and fall more slowly are more intrinsically luminous at maximum brightness.

If we know the intrinsic luminosity of an object (the absolute magnitude) and can measure the apparent luminosity of that object (the apparent magnitude), we can calculate its distance.  Type Ia supernovae are on the order of a million times brighter than Cepheid variables, and are in fact the brightest of all “normal” supernovae.  They can thus be used to measure the distance to extremely distant objects.

The evidence for an accelerating universe is that these distant supernovae appear fainter than they should be at their measured cosmological redshift, indicating that they are farther away than expected.  A number of possible explanations for the faint supernova phenomenon had to be eliminated before the conclusion that the universe’s expansion is accelerating could be arrived at, including

(1) Do distant supernovae (and therefore supernovae that occurred many billions of years ago) have the same intrinsic brightness as comparable nearby supernovae that occurred in the recent past?

(2) Are the distant supernovae being dimmed by galactic and intergalactic extinction due to dust and gas along our line of sight to the supernova?

As described above, the shape of the supernova light curve indicates the supernova’s intrinsic brightness, analogous in a way to the period of a Cepheid indicating its intrinsic brightness.  Though there is evidence that ancient supernovae may have been a little different than those today because of lower metallicity, the effect is small and doesn’t change the overall conclusion of an accelerating universe.  However, properly characterizing the influence of metallicity will result in less uncertainly in distance and therefore less uncertainty in the acceleration rate of the universe.

Extinction is worse at bluer wavelengths, but how the apparent magnitude changes as a function of distance is independent of wavelength, so the two effects can be disentangled.  2011 Nobel physics laureate Adam Riess in his award-winning 1996 Ph.D. thesis developed a “Multicolor Light Curve Shape Method” to analyze the light curves of a large ensemble of type Ia supernovae, both near and far, allowing him to determine their distances more accurately by removing the effects of extinction.

Separating Observer from Observed

One of the most difficult things to do in observational science is to separate the observer from the observed.  For example, in CCD astronomy, we apply bias, dark, and flat-field corrections as well as utilize median combines of shifted images to yield an image that is, ideally, free of any CCD chip defects including differences in pixel sensitivity and zero-point.

We as observers are constrained by other limitations.  For example, when we look at a particular galaxy, we observe it from a single vantage point in space and time, a vantage point we cannot change due to our great distance from the object and our existence within an exceedingly short interval of time.

Yet another limitation is a phenomenon that astronomers often call “observational selection”.  Put simply, we are most likely to see what is easiest to see.  For example, many of the exoplanets we have discovered thus far are “hot Jupiters”.  Is this because massive planets that orbit very close to a star are common?  Not necessarily.  The radial velocity technique we use to detect many exoplanets is biased towards finding massive planets with short-period orbits because such planets cause the biggest radial velocity fluctuations in their parent star over the shortest period of time.  Planets like the Earth with its relatively small mass and long orbital period (1 year) are much more difficult to detect using the radial velocity technique.  The same holds true for the transit method.  Planets orbiting close to a star will transit more often—and are more likely to transit—than comparable planets further out.  Larger planets will exhibit a larger Δm than smaller planets, regardless of their location.  It may be that Earthlike planets are much more prevalent than hot Jupiters, but we can’t really conclude that looking at the data collected so far (though Kepler has helped recently to make a stronger case for abundant terrestrial planets).

Here’s another important observational selection effect to consider in astronomy: the farther away a celestial object is the brighter that object must be for us to even see it.  In other words, many far-away objects cannot be observed because they are too dim.  This means that when we look at a given volume of space, intrinsically bright objects are over-represented.  The average luminosity of objects seems to increase with increasing distance.  This is called the Malmquist bias, named after the Swedish astronomer Gunnar Malmquist (1893-1982).

Dodgeville is Not Bicycle Friendly

Quite a few people living in Dodgeville work at Lands’ End, but there really isn’t a safe bicycle route connecting Lands’ End with most of Dodgeville.  Right now, we basically have two choices—neither of them are very safe.  You can ride down Lehner Rd. to US 18 and then ride along the south shoulder of the highway until you get up to King St., then cross the highway there (no traffic lights and a 55 mph speed limit).  Or, alternatively, you can ride on the busiest street in town, N. Bequette St. (Wisconsin Hwy 23) and then follow rubblized W. Leffler St. up to King St.

There’s a large piece of farm land for sale between W. North St. and US 18, and though most of us would prefer that it remain farm land, chances are that it will someday be developed into Dodgeville’s newest residential subdivision.  If and when that happens, we should put in an asphalt bike path adjacent to the new road that will almost certainly get built to connect W. Chapel St. to King St.  Of course, the W. Chapel / US 18 / King St. intersection will need to have traffic signals.  What a wonderful addition this bike path would be for our community!

In the meantime, it would help if Lands’ End constructed a short connector bike path from the north shoulder of US 18 just east of the Lehner Rd. intersection to Lands’ End Lane as shown below.  Wisconsin DOT would need to review and approve the project, but it is likely they would be supportive of such a project given the unsafe conditions that exist today.

Another option would be to make use of the City of Dodgeville utility access road already in place on the north side of US 18, just a little west of the Lehner Rd. intersection.  A connector bike path could be built to Lands’ End Lane as shown below.

While we’re on the topic of bicycles, has anyone else noticed how much worse condition the streets are in—not just in Dodgeville but everywhere—than they were, say, 40 or 50 years ago?  The transverse cracking and alligator cracking on our city streets is as bad as I have ever seen, and certainly must be a major factor in why there are so few bicycle riders in our town.

The Language We Use

Much has been said about how television, movies, video games, and the internet contributes to the culture of violence in our uncivilization, and this extends to even the language we use to describe events, activities, and phenomena.  Even astronomy is not immune from pervasive, perverse imagery.  Little things add up.  For example, why do we call THE event 13.8 billion years ago the Big Bang instead of something like the Great Flaring Forth?  And, instead of telling a group of eager young stargazers, “Our next target will be M13” why not say something like “Our next destination will be M13”?  And why do we call a smaller galaxy merging with a larger one “galactic cannibalism”?  You get the idea.

Fred Rogers (1928-2003) had it right: “Of course, I get angry.  Of course, I get sad.  I have a full range of emotions.  I also have a whole smorgasbord of ways of dealing with my feelings.  That is what we should give children.  Give them ways to express their rage without hurting themselves or somebody else.  That’s what the world needs.”

Think about it.  Then do something about it.

Cosmologically Distant Objects Appear Magnified

George F. R. Ellis writes in section 2.3.3 of his outstanding survey paper, Issues in the Philosophy of Cosmology:

…there is a minimum apparent size for objects of fixed physical size at some redshift zc = z depending on the density parameter and the cosmological constant.  The past light cone of the observer attains a maximum area at z; the entire universe acts as a gravitational lens for further off objects, magnifying their apparent size so that very distant objects can appear to have the same angular size as nearby ones.  For the Einstein-de Sitter universe, the minimum angular diameter is at z = 1.25; in low density universes, it occurs at higher redshifts.

Electromagnetic radiation such as visible light that we observe from a source that is in motion relative to us (the observer) experiences a change in wavelength that is given by

This is called redshift and is positive for a source that is moving away from us and negative for a source that is moving towards us.  The higher the relative speed toward or away from us, the greater the magnitude of the redshift.  Superimposed upon the kinematic velocities of individual galaxies relative to our Milky Way galaxy, since 1929 we have known that there is a cosmological redshift (called the Hubble flow) that is always positive and increasing in magnitude with increasing distance between any two galaxies.  In the nearby universe, the redshift (or blueshift) from kinematic velocities (often referred to as “peculiar velocities”) swamp the contribution from the Hubble flow, so some galaxies are actually approaching each other.  A good example of this is M31 and the Milky Way galaxy.  For more distant galaxies, however, the cosmological redshift swamps any contribution from the kinematic velocities.  Thus, redshift becomes a useful proxy for distance at cosmological distances.

From our everyday experience, we know that the further away an object is, the smaller is its angular size.  However, there comes a point where the angular size of an object reaches a minimum, and at even greater distances, its angular size increases!  As George Ellis states above, the entire universe acts as a gravitational lens to magnify distant objects.

Michael Richmond presents an equation for angular size as a function of redshift (based on some classical assumptions about the structure of the universe).  In his equation, the angular size of an object also depends upon the value we choose for H0, the Hubble constant, the matter density parameter, ΩM, and, of course, the physical size of the object of interest.

Let’s work through an example using this equation.  The visible part of the Andromeda Galaxy is estimated to be about 220,000 light years across.  In megaparsecs, that is 0.0675.  This is the value we will use for S.

For the Hubble constant, H0, let use a recent result: 71.9 km/s/Mpc.

And, for the matter density parameter, ΩM, let’s use 1.0.  This indicates that we live in a universe that has just enough matter for the universe to eventually recollapse, were it not for dark energy.  Though Richmond’s equation above only applies to a matter-dominated universe where the dark energy density parameter ΩΛ is zero, as George Ellis indicates above, a minimum angular diameter is still reached in a universe with dark-energy (i.e. low density universe), only this occurs at a higher redshift than that presented here.

I have not been able to find or derive a more general equation for angular size as a function of redshift that will work for a dark-energy-dominated universe (perhaps a knowledgeable reader will post a comment here providing some insight into this issue), but it will be a useful exercise to continue with the calculation assuming the matter-dominated Einstein-de Sitter universe.

Casting Michael Richmond’s equation into the following SAS program, I was able to find that the Andromeda galaxy would reach a minimum angular size of 11.3 arcseconds at z = 1.25, as shown below.

In principle, measuring the angular size of a “standard” object at various redshifts could allow us to determine what kind of universe we live in.  But there’s a problem.  As we look further out into space we are also looking further back in time, so there is no guarantee that a “standard” object in today’s universe (say, a spiral galaxy such as M31) would have looked the same or even existed billions of years ago.

Ellis, G. F. R. 2006, 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.

Richmond, Michael, Two classic cosmological tests

M31, M33, and the Milky Way

We live within a small cluster of at least 54 galaxies (most of them small), given the unassuming name “The Local Group” by Edwin Hubble (1889-1953) in 1936. The largest of these, M31 (the Andromeda Galaxy) is a barred spiral galaxy 2.5 million light years from Earth.  The second largest galaxy in the Local Group is our Milky Way, a barred spiral galaxy whose center lies about 26,000 light years away in Sagittarius.  The third largest galaxy in the Local Group is M33 (the Triangulum Galaxy), a spiral galaxy (possibly barred) located 3.0 million light years from Earth.  There are no other spiral galaxies in the Local Group.

M31 and our Milky Way are moving towards each other, and will pass through one another (or at least graze: shall we call it star grazing?) in about 4 billion years.

M33, however, is only about 860,000 light years from M31.  Isn’t M33 in even greater danger of colliding with M31?  The answer is no, we don’t think so, because M33 appears to be orbiting M31.  M33’s eventual role in the Battle of the Titans remains to be determined.

Gentle Giant?

Pollux (Beta Geminorum) is the nearest giant star to Earth, between 33.7 and 33.9 light years away.  Its spectral type, K0III, indicates its photosphere is cooler than the Sun’s.  Relative to our Sun, Pollux is 8.8 times wider, 2.0 times more massive, and 43 times more luminous.  Many giant stars are larger than Pollux.

Beginning its life as an A-type main sequence star, but now evolved to a K-type giant, Pollux is only about 724 Myr old.

Pollux has the current distinction of being the brightest star in the night sky known to harbor at least one planet: a super-Jupiter 2.9 times as massive as Jupiter, and orbiting Pollux every 590 days at a distance of 1.7 AU.  The planet’s name is Thestias.

If you have trouble remembering which star is Castor and which star is Pollux in Gemini, here’s an easy way to remember: Castor sides with Capella, and Pollux sides with Procyon.  Another way to tell: Pollux is half a magnitude brighter than Castor.

Aldebaran Crossing

On the evening of March 4, 2017 (5 Mar 2017 UT), the Moon passed in front of the 0.9-magnitude star Aldebaran (α Tau).  Currently, this is the brightest star the Moon ever crosses (excepting the Sun, of course).  The favorable first quarter moon (with the nearside 45.9% illuminated) was at a respectable altitude of 31° in the western sky at the time of the dark-limb disappearance.  It is not an instantaneous event.  The effects of diffraction plus the non-zero angular size of the star ensure that the star disappears over several frames of a high-speed camera, as shown in my video recording of the event below.

At my location, the middle of Aldebaran’s disappearance occurred at 3:56:00.570 ± 0.001s UT.  Thin clouds and wind interfered with a pristine recording of the event, but even so you can see in the trace below that the star took about nine frames (~0.017s each) to completely disappear.

The bright limb reappearance was more difficult to time.  In my video recording below, you can see that Aldebaran first reappears at about 4:29:39.828 UT.  By that time, the Moon had descended to an altitude of 25° and was accompanied by a fair amount of atmospheric turbulence.

All in all, I felt very lucky to have observed both of these events.  Soon afterwards, it completely clouded up!

Wind in the Window

One very windy morning last week I lay in bed listening to the wind whistling in the window above me.  It was playing a pentatonic scale!  Albeit accompanied by some very complex and interesting overtones.  The pitches formed a major pentatonic scale: G♭4 – A♭4 – B♭4 – D♭5 – E♭5.

This led me to reflect on the origins of human music.  Even though there were no windows in prehistoric times, there has always been the sound of the wind amongst the rocks and the trees, and a myriad of other sounds in the natural world.  These sounds of nature must have provided the initial impetus for human music making, both vocal and instrumental.

The Nearest Stars

Within 5 light years (ly) of the Earth, there are 4 stars known (just the Sun and the Alpha Centauri system).  Within 10 ly, there are 14.  Within 15 ly, there are 60 stars.  The number goes up—rapidly!  Undoubtedly, more stars will be discovered within 15 light years of the Sun.

And, cool is the rule when it comes to nearby stars.  Of the 60 known stars within 15 ly of Earth, an amazing 40 (two-thirds) are class M stars.  The remaining one-third include one A star, one F star, three G stars, six K stars, one L infrared dwarf, five very cool T infrared dwarfs, and three white dwarfs.

The hottest (and bluest) star within 15 light years of the Sun is none other than Sirius (α Canis Majoris)—the brightest star in the night sky—just 8.58 light years distant.  Sirius A is an A1V (main-sequence) star, twice as massive as our Sun, 71% wider, 25 times more luminous, and only 225 to 250 million years old—just a single orbit around the galactic center.  Sirius rotates much faster than the Sun, too, spinning around once on its axis every 5.4 days.  Think about all these things the next time you look up and see Sirius chasing Orion across the meridian these late-winter eves.  And that Sirius has a white dwarf companion that orbits it once every 50 years, too.

All but two of the nearest 57 stars that are not white dwarfs have a luminosity class of V, meaning they are dwarf or main-sequence stars.  The first exception is Procyon (α CMi A).  Its luminosity class of IV-V indicates it is bright for its temperature and spectral type (F5) and beginning to evolve into a subgiant star on its way towards becoming a giant star.  The other exception is Kapteyn’s Star, a red subdwarf star of spectral type and luminosity class M2VI.  A subdwarf star is underluminous for its temperature and spectral type.  This is caused by low metallicity.  The scarcity of elements other than hydrogen and helium in the star results in a more transparent stellar photosphere and thus a star that is a little smaller than it normally would be.  Incidentally, the fact that we have three white dwarf stars within just 15 light years of us suggests that white dwarfs are copious throughout our galaxy.

You might be wondering how many planets have been discovered orbiting these 60 nearest stars.  Beyond the eight planets orbiting our Sun we find another eleven confirmed planets, plus several more unconfirmed planets.  This is a rapidly advancing field and no doubt many more planets will be added to the list in the coming decade.

The masses of the confirmed planets include one a little over three times the mass of Jupiter, one a little more massive than Neptune, one a little less massive than Uranus, six super-Earths, and two just a third more massive than Earth.  Their orbital periods range from 4.7 up to 121.5 terrestrial days, and then one planet (the super-Jupiter) orbiting once every 6.9 years.  Orbital eccentricities range from circular (0.00) to 0.32, with the super-Jupiter in a very elliptical orbit having an eccentricity of 0.702.  The super-Jupiter is orbiting Epsilon Eridani (K2V, 10.48 ly), with all the rest of the confirmed exoplanets orbiting M-dwarf stars.

“The Nearest Stars” by Todd J. Henry, Observer’s Handbook 2017, RASC, pp. 286-290.