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The Webfooted Astronomer - March 2001

 

Minutes: Double Your Pleasure, Double Your Sun

By Greg Donohue

MARY Ingersoll opened the meeting, asking if there were any first time attendees. Two or three people raised their hands. Mary reminded the group that Astronomy Day is April 28, and the Pacific Science Center would like us to set up for solar viewing. Loren Bush (of Captain's Nautical Supply) has bulk material for making solar filters. Randy Johnson will coordinate purchasing a quantity of this material and dividing it among the 8 or 9 people who expressed interest in making their own solar filters.

Randy gave an update on Poo Poo Point on Tiger Mountain. SAS has been negotiating with the Department of Natural Resources (DNR) to gain limited access to the site, which is gated. DNR will provide SAS with a single key. The DNR's requirements for insurance coverage and community service have now been met. We will have up to 12 viewing nights per year. Beginning in a couple of months, SAS will be doing monthly events at Poo Poo Point (maybe during third quarter or new Moon). Those interested will need to rendezvous at the gate and caravan up as a group, because the gate must remain locked. The road up to the site is well maintained, so four-wheel drive is not needed. The turnoff to Highway 18 from I-90 is at milepost 25. The entrance gate to Poo Poo Point is on Highway 18, about 4 miles from the I-90/Highway 18 turn off.

Greg Donohue met with Skip Murray to pursue an agreement with the Cedar Falls Watershed that would allow SAS to use the west side of Rattlesnake Lake. We now have locks installed on both gates and expect to have a written agreement with the Watershed in a few weeks. We should have access to the site in the next few months. More information to follow.

Brian Allen had the new membership brochures, public star party flyers, and general meeting flyers available. These brochures look terrific, and can be used in many different venues as a great vehicle for getting information out to the public.

Evolution of Binary Stars

George Best introduced the evening's guest speaker, Dr. Albert Linnell. Now a visiting scholar at UW, Dr. Linnell has been Professor Emeritus at Michigan State since 1991, where he taught from 1966 to 1991, and was chairman of the Astronomy Department from 1966 to 1976. Dr. Linnell received his Ph.D. from Harvard in 1950, and taught at Amherst College from 1949 to 1966. His subject for the evening was "The Evolution of Binary Stars." Binary star systems display many interesting phenomena not found in solitary stars. Some 50%-60% of stars in the Sun's vicinity are binary stars. To understand binary stars, we must first have a good understanding of how solitary stars evolve.

The Main Sequence on the HR diagram represents a sorting of stars by mass. Those stars above (giants) and below (white dwarfs) the main sequence represent evolved stars.

One of the triumphs of modern astronomy is our understanding of how single stars work and how they evolve with time. We know that thermonuclear reactions (namely the fusion of 4 hydrogen nuclei to form one helium nucleus) in a star's core is what enables it to produce such prodigious amounts of energy over enormous periods of time. The outward pressure thus produced counters the inward pull of gravity, supporting the star's outer layers, and keeping the star in a state of equilibrium throughout most of its life span. Through radiation and convection, the energy produced in the core works its way to the surface, over the course of perhaps a million years, where it is liberated as the light.

Over time, more and more hydrogen is converted into helium in the stellar core. The lighter hydrogen nuclei move more rapidly than the heavier helium nuclei. The net effect is a gradual reduction in the ability to hold up the outer layers, shrinking the core slightly. As it shrinks, the core liberates potential energy, which in turn raises the core's temperature. The thermonuclear processes in a star are very sensitive to temperature; a slight temperature increase results in a large increase in energy output. So, while the core shrinks, the outer layers expand due to the increased energy output and resultant increase in outward pressure.

It is believed that star clusters form from the collapse of interstellar gas clouds. Since they were birthed by the same cloud, stars within a cluster, such as the Pleiades, should all have formed at about the same time and had the same initial chemical composition. Stars of similar chemical composition but differing masses follow different evolutionary tracks on the HR diagram. Our own Sun's temperature/luminosity has increased by 40% since its birth, and it will eventually evolve into the "giant branch" on the HR diagram. In general, more massive stars evolve more quickly, reaching the main sequence (of stable hydrogen burning) sooner than their less massive cousins. The more massive stars also evolve off the main sequence much sooner than less massive ones.

Isochrones (meaning "same time") are curves on the HR diagram occupied by stars of different masses but the same age. For stars of similar initial chemical composition, we can use the standard stellar model to plot them at various ages, resulting in a series of isochrones. Stars in a given cluster, while differing in mass, are all still of the same age and initial composition, so plotting a single cluster's stars on the diagram should also result in an isochrone. This real data can be compared against the various theoretical isochrones to give us an indication of the cluster's age.

After a star has evolved through the giant branch, subsequent evolution throws off its outer layers to form a planetary nebula. In the center of these nebulae is an extremely hot, white star. This is the exposed core of the evolved star. With the outer layers gone, the downward pressure on the core is relieved, and the thermonuclear processes in the core cease. These stars are still nearly as massive as the sun, but are comparable in size to the Earth, having very high densities and surface gravities. The core is kept from further collapse not by fusion, but by electron degeneracy (a quantum mechanical effect preventing electrons from being squeezed closer together). As time goes on, the core of a planetary nebula cools, resulting in a dead white dwarf star. This is the final stage of evolution for a single star. Interestingly, as a white dwarf carbon core continues to cool, the atoms arrange into a regular crystalline structure, effectively becoming one huge diamond!

Binary star formation also results from the collapse of an interstellar gas cloud. The binary components must form together at the same time. Creation of a binary star system through gravitational capture is a virtual impossibility, and could only happen under the most exotic circumstances. If the orbital plane of a binary system intersects our line of sight, then these stars will eclipse one another as they revolve around their common center of mass. Total eclipses produce light curves similar to "square waves." The brightness drops quickly, the bottom of the curve is fairly flat, and the brightness then increases just as quickly. Partial eclipses produce different light curves, which are more saw-toothed in nature. Dr. Linnell has helped develop a computer program to model stellar eclipses. The center of stars are brighter than the edges (known as limb darkening), so more light is blocked off when the eclipsing star is near the center, which results in a light curve with more of a rounded bottom.

The brightest star in the night sky, Sirius, is a binary system. Sirius A is on the main sequence. Since it is also appreciably more massive than the Sun, it must also be younger than the Sun (more massive stars evolve more quickly). But the second component, Sirius B, is a white dwarf—it is at the end of its evolution. But both had to be born together, so what's the deal? It has to do with binary star evolution.

Around each member of a close binary system is a 3-dimensional teardrop-shaped sphere of influence known as a Roche lobe. Any material within a star's Roche lobe will stay within that star's gravitational influence. The narrow ends of the two Roche lobes in a binary system are connected, producing a dumb-bell-like shape. The connection point is the L1 Lagrange point, where the gravitational fields of the stars are in balance. Mass can only be transferred between binary stars through this L1 point. The center of mass of the system, about which the stars orbit each other, is closer to the more massive of the pair, placing it inside that star's Roche lobe.

The more massive star of the pair (which we'll call A) will evolve more quickly, eventually swelling until it expands to the very boundary of its own Roche lobe. Until this point, A had maintained a constant mass but ever increasing radius. A star cannot grow larger than its Roche lobe, so once A reaches this limit, mass is forced through the L1 point into the Roche lobe of the smaller star (B), with the incoming gas traveling at speeds in the 100s of km/sec. This increases the size of B's Roche lobe, while decreasing that of A. That forces even more material into B's lobe, resulting in a sort of siphoning action that strips material from A and transfers it to B. Eventually B becomes the more massive star, and the center of mass moves through the L1 point into B's Roche lobe. Since stars can't outgrow their Roche lobes, the two stars begin to separate, the system's orbital period increases, and the Roche lobes of both stars increase in size. A, still the more evolved star, continues to fill its ever-enlarging Roche lobe. Eventually its thermonuclear processes cease, and the expanded gas collapses back onto the core.

Once an interstellar gas cloud collapses, binary star formation can take place in a timeframe on the order of 100,000 years. Subsequent evolution of the stars can take billions of years, depending on their sizes. But once a component star starts to expand, it can fill its Roche lobe very quickly. For stars in radiative equilibrium, this can occur in 1,000s to 10,000s of years. For stars in convective equilibrium, this time can be as short as centuries or even decades!

What happens to the gas transferred through the L1 point to B? Gas dynamics models show that the gas falls toward B in a curving orbit. If B were a point-mass, then the gas would continue to orbit around the star in a pattern like the simple daisy flower figures made by a Spirograph. The star is not a point mass, so the gas collides with the star, but not directly. The incoming gas can form an accretion disk around a star. Due to viscosity in the disk (probably due to magnetic affects in the disk itself), gas at the outer edge eventually works its way through the disk to be deposited onto the star.

A cataclysmic variable is composed of a white dwarf, and a fairly low mass star that has expanded to fill its Roche lobe, feeding mass back onto the white dwarf. As further gas spirals in, it collides with the accretion disk around the white dwarf, creating a hot, bright spot, which may be brighter than the white dwarf. Eclipses of such systems now involve the low-mass companion, the white dwarf, the accretion disk, and the hot spot. Analyses of these complex light curves help us understand accretion disks and their associated hot spots.

We now know that dwarf novae, novae, polars, intermediate polars, X-ray binaries, pulsars, and type Ia supernovae all result from Roche lobe transfers.

With our knowledge of binary star evolution, we return to Sirius. Sirius B was originally the more massive component of the system, and became a white dwarf thanks to its faster evolution, which resulted in Roche lobe mass transfer to its originally smaller companion, Sirius A. Sirius A, now the more massive, will eventually evolve and expand, and start feeding material back onto its white dwarf companion, thus completing a game of give and take of truly stellar proportions!

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