Tag: Cepheid

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.

Constant as the Northern Star

There are frequent astronomical references in the plays of William Shakespeare (1564?-1616).  One famous example is in the tragedy Julius Caesar, written around 1599, where Julius Caesar states,

“I am constant as the northern star,
Of whose true-fix’d and resting quality
There is no fellow in the firmament.”

Little did Shakespeare know that Ejnar Hertzsprung (1873-1967) would discover some 312 years later in 1911 that Polaris, the North Star, actually varies in brightness.  Of course, Shakespeare was referring to Polaris’ proximity to the north celestial pole, but there are multiple ironies in that Polaris varies in brightness—albeit a tiny amount—and it will not always be the “pole star”, thanks to the precession of the Earth’s axis.

Polaris is a classical Cepheid pulsating variable star, with a visual magnitude that has historically ranged as much as 1.9 – 2.1 over a period of about 4 days.

At a distance between 426 and 439 ly, Polaris is the nearest and brightest Cepheid variable star in our night sky. Polaris is a supergiant star (F7Ib) weighing in at about 5.4 solar masses. Polaris and its nearest companion star (F6V, 1.3 solar masses) enjoy a complete orbital pas de deux every 30 years.

Currently, Polaris lies only 40 arcminutes from the north celestial pole (declination +89° 20′).  As with all stars, the Earth’s rotation causes the stars to wheel around the celestial poles, although in the case of Polaris the angular speed is exceedingly slow, making it a great target for a telescope without a clock drive.

Let’s figure out how fast glacial Polaris moves. It traverses a tiny circle around the north celestial pole every sidereal day (23h56m04s), so what is its angular speed?  We need only divide the path length (the circumference of a circle of radius 40′) in arcseconds by the number of seconds in a sidereal day to get the angular speed in arcseconds per second of time. The circumference of a circle is 2πr, so plugging and chugging we get [(2)(3.141592654)(40*60)] / 86164 = 0.18 arcsecond per second of time. Sound like a lot, or a little?  This angular speed means that Polaris moves an arcsecond every 5.7 seconds, or 11 arcseconds every minute, or 11 arcminutes every hour. That’s just 4.2° per day.

Not quite a perfect pole star, but it will certainly deux.