Question

Discuss the similarities and differences of the HR diagrams in terms of the physics occurring in the 10-solar-mass star. In order to interpret what is happening, use a selection of appropriate plots

Answer 1

The time scales of stellar evolution depend on the mass of the star. The rule governing stellar evolution is the more mass present, the faster the evolution for the star through the fuel consumption stages. Another property directly linked to the mass and evolution of a star is its luminosity.

The mass-luminosity relation demonstrates that the main sequence on an H-R diagram (a chart plotting the the luminosities of stars against their surface temperatures) is a progression in mass as well as in luminosity and surface temperature (Kaufmann,1991, pg. 356). The Hertzsprung- Russell diagram is two possible plots of spectral types dependent on absolute magnitude when compared to temperature and luminosity.

These H-R diagrams allow astronomers to conceptualize visually the mass-luminosity relationship as it pertains to the fuel consumption evolution of stars. The H-R diagram allows astronomers to plot visually the different stages in the evolving life cycle of stars.

A H-R diagram (the red line represents the Main Sequence Stars).

Stages in the Life of an Evolving Star

Welcome to the life of a new born star. Main sequence stars are a range of stars based on size and surface temperature starting from the hot, bright, bluish stars in the upper left corner of a H-R diagram to the cool , dim, reddish stars in teh lower right corner of the diagram. Life for new stars begins in the Main Sequence. These mature stars undergo a remarkable transformation after they consume all the hydrogen in their core. With the hydrogen consumed, stars leave the main sequence and expand to form red giants. With this new stage, the fusion of helium begins to form heavier elements like Oxygen and Carbon. This process of expansion- collapse-expansion of stars forms the light elements present in the universe (up to Fe).

Life in the Suburbs : a Main Sequence Star. Main sequence stars are stars who�s luminosity and surface temperature place it in the �main sequence� of a Hertzsprung- Russell diagram.

A fundamental property of all main sequence stars is thermal equilibrium. Thermal equilibrium is the liberation of energy from the interior of the star balanced by the energy released at the surface of the star. The energy released by a main sequence star is produced by hydrogen burning in its core (the fusion of 4H into 4He).

Another fundamental property of a main sequence star evolution is hydrostatic equilibrium. Hydrostatic equilibrium reflects the required pressure in the core of a star to support the weight of the outer plasma layers. The heat produced from hydrogen in the core burning supports this outward pressure upon the outer plasma layers.

As a main sequence star depletes the supply of hydrogen in the core, thermal equilibrium unbalances and the pressure in the star�s core lessens. Thermal equilibrium unbalances because the fusion of four hydrogen atoms into one helium atom decreases the number of particles present in the star�s core. The star beings to collapse inward because the fewer particles cannot maintain the pressure needed to support the star�s outer layers.

Without the necessary pressure, the star�s core contracts slightly under the weight of its outer layers. This collapse increases the pressure and temperature of the core causing the luminosity of the star's surface to increase. This increase in pressure on the layers just outside the core raises their temperature to the necessary point in which the outer layers of hydrogen begin fusion.

This occurrence of hydrogen fusion in the outer layers of a collapsing star is called shell hydrogen burning. Shell hydrogen burning allows the star to remain in the main sequence for another few million years. Despite this struggle to remain on the main sequence, the supply of hydrogen for fusion into helium in a star�s inner most layers depletes, which takes the star from the main sequence and to the next step of solar fuel consumption.

The next stage of solar fuel consumption starts when hydrogen burning in the core ceases and ignites hydrogen burning in the star's outer layers. When hydrogen burning ceases in the star�s core, it begins to collapse again. At this point, the star converts gravitational energy into thermal energy because it must maintain thermal equilibrium.

Stars sustain thermal equilibrium within their interiors through the ignition of helium burning. The collapse of the outer hydrogen burning shell upon the core raises the temperature and pressure in the core and begins helium burning. Because the temperature and energy needed to ignite helium fusion is greater than that of hydrogen, the energy released by helium fusion in the star�s core is greater than needed to support the weight of the outer layer.

This excess energy expands the star�s outer layers beyond its previous radius and star�s volume increases. A star going through this stage of fuel consumption (collapse and expansion) is a Red Giant. The following diagram shows the dramatic expansion of a main sequence star as it begins helium fusion.

Our Sun today compared to its future Red Giant self

1 AU is approximately 150 million kilometers or the distance from the sun to the Earth's orbit

The Life of a Red Giant : A Star in Old Age. In the final states of hydrogen fusion the hydrogen burning shell adds to the mass of the star�s helium core. This added mass and pressure increases the star�s temperature. Temperature within the core of stars greater than three solar masses soon exceeds the 100 million Kelvin degrees barrier, at which it reaches the temperature needed for the onset of helium fusion.

Core helium burning reestablishes the thermal equilibrium needed to support the star�s outer layers preventing further gravitational contraction. With gravitational contraction halted, the heat and energy from the core helium burning again begins the expansion of the star's outer layers. The method by which a star begins core helium burning depends upon the mass of the star.

In stars below three solar masses (low-mass stars), helium fusion begins in a more spectacular manner. Helium burning begins explosively and abruptly. This process of quick ignition of helium fusion is a helium flash. The universe does not limit helium flash to low-mass stars; Helium is present in red giants and red supergiants as well.

Red supergiants and red giants share the same physical characteristics and properties, with size and luminosity the only major difference between them. To understand this size difference we use our sun as a reference point. Red giants have solar radii up to 10 to 100 times larger than our sun, while supergiants boast a solar radii 1000 times larger than that of our sun.

A Low-Mass Stars� last gasp. Stellar evolution can end in several ways. After a long life, an aging star completes its red supergiant stage of evolution and shell helium burning begins. Since this shell of helium burning is thin, the star becomes unstable. This instability in the aging star increases the temperature and energy within the star, which thickens the shell of burning helium surrounding the helium-depleted core.

The shell of burning helium thickens until it can support the pressures of the star�s outer layers. As the shell helium burning increases the temperature and energy of the surrounding outer layers of the star, it ignites the outer hydrogen shell into fusion through thermonuclear reactions. This process of outer hydrogen shell fusion is a thermal pulse.

During thermal pulses, the star�s luminosity increases by a factor of ten. This final expansion and ignition of outer layers is the star�s final moments before death overcomes the star. In its final moments, a star ejects its outer layers emitting ultraviolet radiation. This emission of ultraviolet radiation ionizes the ejected gases, giving them a glow known as a planetary nebula.

A planetary nebula, the death of a low mass star

The ejection of stellar remnants is the low-mass star�s supernova. On Earth, we measure the effects of this supernova in the increased luminosity. After a low-mass star�s death (supernova), it often leaves behind material that forms new stellar bodies.

This is the end of stars with low masses (less than four solar masses) because they cannot reach the appropriate t temperature levels to begin the fusion of carbon (C) into oxygen (O). These stars burn off or eject their remaining outer layers leaving only the stellar core behind.

Stellar remnants, a star�s afterlife: white dwarfs, neutron stars and pulsars. Due to the enormous mass of this remaining stellar core, the core begins to collapse and fuse. As the stellar core collapses, it electrons become degenerate (a phenomenon, due to the quantum mechanical effects, whereby the pressure exerted by a gas does not depend on its temperature) and stop the gravitation collapse. This contracted stellar core is a white dwarf.

White dwarf stars are approximately the size of our planet, but their mass and density is much greater. White dwarfs are so dense, when compared to the Earth, that a teaspoon of matter from a white dwarf would weigh 5.5 metric tons on the Earth�s surface! The universe places limits on the life of a white dwarf, familiar to the main sequence star from which it originates.

The white dwarf glows for billions of year from the energy released from cooling thermal radiation. Eventually all the radioactive matter of a white dwarf cools until it reaches the temperature of surrounding space which is a few degrees above absolute zero.

A Neutron Star

Neutron Stars and Pulsars : Sometimes the core remnant of a low-mass star is too dense to form a white dwarf. In these cases, the core�s stellar collapse forms a neutron star.

Neutron stars are incredibly dense spheres of degenerate neutrons (a gas in which all the allowed states for particles, electrons or neutrons, have been filled, thereby causing the gas to behave differently from ordinary gases). Some neutron stars have massive magnetic fields that sweep out beams of radiation into space, much like light beams from a lighthouse. Such �pulsating� neutron stars are called pulsars. This measurable �pulse� of radiation is where this type of neutron star derives its name.

Astronomical models suggest that the properties of superconductivity and superfluity dominate the cores of neutrons stars. These models also suggest there is an upper l limit in the mass of neutron stars. These upper limits are in the range of the mass of the largest possible white dwarfs.

The Little Bang : The death of high-mass stars. This death of a low mass star into a white dwarf contrast with the final stages of high-mass, main sequence stars (i.e., greater than four solar masses). Unlike low mass stars, high mass stars can extend their lives through the fusion of elements heavier than carbon.

After the fusion of helium ends, high mass stars begin burning carbon as their next fuel consumption stage. Carbon burning begins when the star's core reaches temperatures greater than 600 million degrees Kelvin. The greater the mass of the original main sequence star the longer the star continues to burn heavier elements. Incredibly massive stars continue fusion from helium until they create iron (Fe) in their core.

In this fusion process, these massive stars create neon (Ne), magnesium (Mg), oxygen (O), sulfur (S), silicon (Si) and finally iron (Fe). Each stage of fuel consumption parallels a raise in the star�s core temperature. Neon fusion begins when the star�s core temperature reaches one billion degrees Kelvin followed by oxygen at 1.5 billion degrees Kelvin. Silicon fusion does not begin until the star�s core temperature reaches an amazing 3 billion degrees Kelvin.

As the star begins each new fuel consumption stage, its lifetime in each stage becomes shorter. The following table illustrates the amount of time an aging star spends in each fuel consumption stage.

A H-R diagram (The red line represents the Main Sequence stars and their evolution toward the top right hand corner of the diagram).

These massive stars continue to exist by burning the heavier nuclides (magnesium, silicon, phosphorous et al) until they reach the heaviest nuclide that fusion can produce, iron. The iron rich cores of these massive stars can reach sizes equivalent to the Earth. The size of the surrounding shells burning the various lighter elements (H, He, C, O) dwarf this iron core, as they reach sizes that would extend to the orbit of Jupiter.

When the core of a high-mass star consists completely of iron, fusion can no longer take place. At this point, the mass of the daughter (one iron nuclide) is heavier than the total mass of the parent nuclides used to produce iron. With this difference in mass, the process begins to absorb energy instead of releasing it back into the star, whichunbalances thethermal equilibrium of the star.

With fusion ceased and the thermal equilibrium unbalanced, a star�s only source of energy is from the contraction of the star�s outer layers. This contraction raises the star�s core temperature to 5 billion Kelvin and increases the pressure to the point that the iron core collapses upon itself.

The incredible pressures that the collapse of the star�s iron core force many of the existing (but not all) protons and electrons to combine into neutrons. For a moment the star releases this abundance of neutrons as neutrinos. In this brief escape, many neutrinos bombard the iron core and combine with iron nuclides to form the elements heavier than iron. These escaping neutrinos and the electromagnetic forces that repel protons and neutrons force the star into a final expansion.

A Star�s Eulogy, a Supernova. This final expansion sends a shock wave through the star�s outer layers until it reaches the star�s surface creating a supernova. This shock wave ejects all the material of the star, including the core into the cosmos leaving behind only a nebula of cooling gasses.

A section of space before the supernova

The same section of space after the supernova

Stars too big for their britches : Black Holes. Sometimes high-mass stars are too massive to become white dwarfs or neutron stars. A high-mass star this massive also has the gravitational forces to prevent the escape of stellar matter through a supernova. Stars with this great of mass become black holes at the end of their stellar evolution.

Black holes are the result of the overpowering weight of the star�s massive outer layers pressing inward from all sides on the core causing the rapid contraction of the dying star. With this great mass pressing inward, the star�s core can no longer support the star�s outer layer structure.

The matter within a high-mass star in this process is so condensed that the gravity produced is strong enough to prevent the escape of light energy from the cooling radioactive material. Light cannot escape because the escape velocity at the star�s surface is greater than that of the speed of light.

Gravity of this magnitude has profound effects upon the star�s shape and on the structure of the surrounding space. With the star collapsing in upon itself, the star changes from a spherical shape to a broader plane in space. The gravity from the center of this plane curves its surrounding space to create a whirlpool-like drain that absorbs the star itself and all surrounding matter.

An Artist rendition of a black hole event horizon (notice the whirlpool like shape that leads to the blackhole's singularity).

This plane at the mouth of the whirlpool-like drain is called an event horizon. The immense gravitational forces of the black hole compacts all the matter within the star after it moves past the event horizon of the newly formed black hole. The gravity of the black hole compresses the star�s matter, as well as any other matter captured by the black hole�s gravitational forces through its existence, to infinite density. This infinitely dense matter within the black hole is called a singularity. The gravitational pull of a singularity is so great that it pulls matter from all surrounding areas into the event horizon of the black hole.

If light cannot escape black holes, how do we find them? Until recently black holes were only theoretical speculations, but with today�s technology we are now finding black holes by measuring x-ray emissions in space.

As the black holes immense gravity captures surrounding matter, this matter accelerates toward the event horizon and singularity and releases high amounts of x-rays. These x-rays leave a trail through space as the black hole absorbs the matter into its singularity. X-ray trails leave �halos� around the black hole called accretion disks.

Another method of detecting black holes in space is their effects on binary star systems. When a black hole occurs close to two stars, its gravity impacts their spatial relationships. Each star�s gravity has a calculable effect upon the other�s orbit, however the invisible black hole affects these orbits.

An Artist rendition of a blackhole syphoning plasma gas from a nearby star (this acceleration of matter emits x-rays that form a accretion disk and make the blackhole detectable [x-ray emissions represented by the arrows]).

To contrast the idea of black holes being places in the universe with infinite lifetimes where no matter (including light) ever escapes, the universe holds a few exceptions. The British physicist Stephen W. Hawking has proven that black holes do in fact have definite lifetimes.

As black holes reach the end of their life, they begin to evaporate. In the final stages of this evaporation, the black hole reverses itself and pours matter back out into the universe. When a black hole begins to eject its matter, it is a white hole. With this transformation in the life of a black hole, the universe appears to maintain the fundamental universal energy-matter law with this process. While the black hole, to physics' laws, is an unbalancing factor in universal laws, the white hole exists to restore this matter and balance.