What forces are in mechanical balance for a star to be on the main sequence

Details in Chapters 19 and also 20 should be self-studied

Mass Dictates the Life of a Star after the Key Sequence Phase

The life of stars of all masses in the time of the primary sequencephase is exceptionally comparable. The major distinction is that the greater the mass, themore luminous the star and the shorter the primary sequence life time. What happens after
the primary sequence phase counts on the mass of the star. Define the adhering to mass ranges: Very Low Mass Stars: M Sun Low Mass Stars: 0.4 MSun Sun Medium Mass Stars: 4 MSun Sun High Mass Stars: M > 8 MSun Most essential processes for succeeding development are Burning of heavier and heavier aspects that require better and also highertemperatures at the facility of stars. New sources of pressure - degenerate (quantum mechanical!) behaviour of matter at high densities Also convection plays function, given that it mixes facets. Low mass stars are convective in the outer layers, high mass stars - in the core. Mass loss in the time of advancement - final masses are not the exact same as massesthe stars had on while on main sequence. Must save in mind Evolution is regularly disbalance, at least thermal, however occasionally during violentstperiods, dynamical Must distinguish main and also surconfront (oboffered in HR) temperature. Centraltemperature parctically constantly increases, surchallenge - experiences complcated changes. In this lecture we will emphasis on low and mediummass stars. The early stperiods of advancement for the mediumand also high mass stars are incredibly equivalent to the low massstars, but they happen much faster.

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The End of the Key Sequence Phase

The major sequence, hydrogen burning, phase for a star with the exact same mass as the Sun lasts for around 1010 years. Key sequence phase is finished when supply of Hydrogen inthe inner 10% of the Sun runs out. At the finish of this phase we have an inner core of Heliumsurrounded by Hydrogen. The temperature at the core is just around 15 million Kelvin,which is warm sufficient for Hydrogen fusion to happen, but also coolfor Helium fusion. The temperature external of the core is cooler and also is notwarm sufficient for Hydrogen fusion. Not feasible for any nuclear reactions to occur!! No source of energy to produce outward push to balancegravity. The core of the star will start to progressively collapse. The collapse of the core will cause it to warmth up.

The Red Giant Stage

As the contracting core heats up, a shell of hydrogen about the inert Heliumcore will certainly warmth approximately 15 million K and start to fuse. This starts the phase of shell-Hydrogen burning. The burning of Hydrogen in the shell actually produces morepower than in the major sequence phase (because of the better T). However before, the inert Hydrogen outside of the shell hindersthe movement of the photons. When photons have trouble relocating with a tool, theyfinish up pushing outwards on the issue. This is calledradiation pressure. The additional pholoads produced in the shell of hydrogen press outwards on the outer layers of the star. The growth of the outer layers reasons them to cooldvery own. General Picture in this phase: Helium core contracts and heats up. Hydrogen shell around the core contracts, heats up and ignites. Outer Hydrogen expands and also cools off. Due to the fact that the star"s surface temperature is lower, itwill look redder than during the main sequence phase. The radius of the star boosts by a large factorand becomes a giant. Final radius is 10 to 100 times the original size of the star. Final surface temperature is about 1/2 the original surchallenge temperature. Luminosity provided by blackbody equation increases. This stage is dubbed the Red Giant Stage of a star"s life. This phase lasts for about 2 billion years for a Sun-choose star.

Degeneprice Matter

As the helium core contracts it becomes denser. When matter becomes very thick, a starray quantum mechanicalresult deserve to take location. The helium core is a mixture of helium nuclei and electrons. The electrons obey the Pauli Exclusion Principle whichcomes from quantum mechanics. Pauli Exclusion Principle: No 2 electrons are allowedto have actually precisely the very same properties. One important property is position: If you attempt to squeezetogether as well many type of electrons right into a little room they will certainly repeleach other. This repulsion is dubbed Electron Degeneracy Pressure
. This repulsion is much more powerful (and also different) thanthe usual repulsion which exists between charged pshort articles. When degeneracy press is stronger than thermal press,we speak to the gas degeneprice. In the situation of the Sun"s core, it becomes degeneprice once thickness islarger than 106 kg/m3 (thousand timesthe thickness of water) temperature is near 20 million K. The Sun"s helium core becomes degenerate early duringthe red large phase of its life. In all the low mass stars, the helium core becomesdegeneprice in the time of the red large phase. Medium and also High mass stars are not degenerate while red giants.

Properties of Degenerate Gases

A degenerate gas is incredibly different from an ideal gas. An appropriate gas"s pressure relies on the density and the temperature. An degenerate gas"s press only counts on density. As lengthy as the temperature is cool sufficient that the gas is degenerateit doesn"t matter just how T transforms, the push just counts on density.

Nuclear Reactions in a Degeneprice Gas

Nuclear reactions in a degenerate gas tend to be explosive. Imagine you rotate on a nuclear reactivity. The power output heats up the gas. If the gas is right, its press rises and also itbroadens and cools dvery own. If the gas is degenerate, a rise in temperature doesn"tincrease the pressure, so it does not expand or cool down. Increasing the temperature provides it much easier for nuclear reactions to take place, so the cycle is repeated and also the reactions occur swiftly. This can proceed till the temperature gets so highthat the core is no much longer degenerate.

The Helium Flash

The red huge stage via an inert Helium core continues until the helium is hot sufficient for ignition with the triple-alpha procedure
3 4He &rarr 8Be* + He &rarr 12CSince the Helium core is degeneprice (in low-mass stars), the Helium-burningreactivity is explosive: a large amount of the Helium fusesto Carbon in a few seconds. This is dubbed the Helium Flash, however it is notobservable, since the pholoads produced in the explosion aretrapped in the Hydrogen layers. The flash does not last lengthy, considering that it easily gets hot sufficient the gas returns to the right gas state. After the flash, the helium burning reactions occurin a warm right gas, and also the reactions take place at a slow-moving,steady rate. (Difference in between a nuclear reactor and also a bomb.) After the flash, the luminosity decreases, and theexternal layers of the star shrink. The period of secure helium fusion in the core is called the Horizontal Branch.

Final Steras of Life of a Low-Mass Star

Burning Helium leaves behind Carbon "ashes". In time the core is depleted of Heliumand the Carbon collects at the centre of the star. The Helium forms a shell roughly the Carbon and theHydrogen forms a shell roughly the Helium. Carbon ignition calls for hotter temperatures than areavailable in the core. But Oxygen is commonly developed in some quantitiesby 12C + 4He &rarr 16O As in the formation of a red huge, the star beginsto contract and also warmth up. Helium in the shell starts to fuse to Carbon. Hydrogen fsupplies in a shell around the Helium. The burning in the shell causes the star to expand again, becoming redder. This is the start of a second red large stage.(Also dubbed an asymptotic gigantic branch, AGB.) This phase doesn"t last very lengthy, only one million years for the Sun.
The core during the last phase never gain hot enough for the Carbon to ignite. However before, the once the Helium shell ignites, it oftendoes so in a collection of flashes which tfinish to push the outer layers outwards. The star at this phase is giant, so the accelerationbecause of gravity at the surchallenge of the star is extremely low. g = GM/R2 = acceleration as a result of gravity It is basic to launch the outer gas of the star so thatit escapes from the star! The final stage of the Sun"s life will be the ejectionof the outer Helium and also Hydrogen layers. These external layers are hot and also glow. The glowinghot ejected gas is called a planetary nebula. (Note: nothing to perform via planets!)

Left over main core

The Carbon (+Oxygen) core left behind is degeneprice and also supportedby degeneracy press. No nuclear fusion necessary to save the left-over corefrom collapsing. Quantum mechanics will not permit the core to gain toothick. The left-over Carbon core is called a White Dwarf
. The White Dwarf"s initial surconfront temperature could be as highas actually 200,000 K so it will certainly glow blue-white. In time, the White Dwarf cools, becoming redder andless luminous. Common mass of a white dwarf is similar to the Sun, butits radius is similar in dimension to the Earth! Very dense!

The Ring Nebula

This photo of the Ring Nebula reflects the glowing ejected outerlayers of the Sun-favor star. The dot in the centre isthe White Dwarf. Ring Nebula is around 1 light-year in diameter.(Compare via existing size of Sun!) Ultraviolet photons from the hot main White Dwarfionize the gas in the nebula, which glows once theelectrons recombine with the nuclei. Blue = emission from Helium (hottest region) Environment-friendly = emission from Oxygen Red = emission from Nitrogen (coolest region) The Sun might look choose this one day. We can observe the Ring Nebula from our rooftop observatoryin the Fall Semester.

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Different Planetary Nebulae

Planetary Nebulae aren"t always spherical in form. These photos were all taken by the Hubble SpaceTelescope.

Differences between Low and Medium Mass stars

Low mass stars end up as White Dwarfs composed of largely Carbon and Oxygen. Medium mass stars have better temperatures in their cores. The better T allows fusion reactions creatingOxygen, Neon, Sodium and Magnesium. Medium mass stars finish up as White Dwarfs created ofthe higher mass aspects.

White Dwarf Stars

White dwarfs are the exposed cores of Red Giant stars. The cores are frequently written of greatly Carbon,although Helium, Oxygen, Neon have the right to additionally exist. The Carbon is ionized, so the complace of thestar is a plasma of Carbon ions and also electrons. The Carbon behaves as a perfect gas, so the gas pressuredue to the Carbon decreases as the Carbon cools dvery own. Theelectrons obey the Heisenberg Suspicion principlewhich keeps the electrons from collapsing to the centre ofthe star. The electrons are negatively charged while theC ions are positively charged, so they are attracted toeach various other. The attractive electric forces between electrons andpositive ions keep the C ions from collapsing to the centreof the the star. The force of electron degeneracy pressure
balances the force of gravity in a White dwarf. Electron degeneracy press is independent oftemperature, so as the star cools, the internalpush remains constant, and also the framework of thestar remains consistent. White Dwarfs cannot exist if the mass exceeds the Chandrasekhar limiting mass of M = 1.4 MSun

Life History of a White Dwarf Star

When the external layers of the Red Giant areexpelled by the dying star, the inner White Dwarfcore has actually a surface temperature over 100,000 K. Wein"s legislation for a hot body via this temperatureprovides a height wavesize of 2.9 x 10-8m,corresponding to ultraviolet light. The pholots emitted from the surconfront of a hotwhite dwarf will be incredibly energetic and willconveniently have actually sufficient energy to ionize the gassurrounding the white dwarf. When the electrons reincorporate with the surroundingions, they often enter an excited state and then jumpdown to the ground state emitting visible photons.This process is known as fluorescence. We contact the glowing gas surrounding a hotwhite dwarf a planetary nebula. Planetary nebulae always have a warm white dwarfat their centre.

Cooling of the White Dwarf

Nuclear reactions perform not occur inside a white dwarf,so tright here is no resource of energy. With time the white dwarf cools. Because electron degeneracy pressure is independentof temperature, the star does not collapse andits radius stays consistent. From the Stefan-Boltzguy legislation, a star whose radius is contant, but has a surface temperature which changes via time has a luminosity which is proportional to T4. As the star cools, its luminosity will decrease. White dwarf stars slowly fade amethod. If they are bornwith a luminosity of 1/10 LSun, after about5 billion years, their luminosity will be about10-4 LSun. As the star cools, the pholots it emits have lessenergy and it is harder for the pholoads to ionize or excitethe planetary nebula, so the nebula will fade via time.As well, the gas in the nebula will be moving outwards,so it will slowly mix via the neighboring interstellarmedium. When the star becomes cool enough that the thermalkinetic power of the Carbon ions is less than theelectrostatic potential power of the ions, the Carbonions can "freeze" (i.e. develop bonds) right into a crystallattice framework. After this freezing, the whitedwarf is a solid.
On the H-R diagram, white dwarfs are born hot and luminous,and also over time cool and also become less luminous. With time,the white dwarfs relocate downwards and to the best alongan imaginary curve joining all of the white dwarfs.

Sirius B: a sample white dwarf

The Sirius star system is a binary system consistingof Sirius A and B. Sirius A is a main sequence starand Sirus B is a white dwarf. When we look at the star system withouta telescope, we only check out the incredibly bbest Sirius A. With a good telescope, you can see the muchfainter Sirius B.
With an X-ray telescope, Sirius B is exceptionally bbest,however Sirius A is very dim.
By comparing the brightness at miscellaneous wavelengths,we can find that the surface temperature of Sirius Bis T = 27,000 K. Due to the fact that we deserve to meacertain a parallax angle for Sirius,we have the right to uncover the distance to the star mechanism. We have the right to meacertain the intensity of light from Sirius B,so the luminosity deserve to be calculated. By assuming that the luminosity is offered bythe Stefan-Boltzman equation, we deserve to solve for theradius of Sirius B. The radius of Sirius B is calculated to beexceptionally close to the radius of the Earth!
The orbital period of the Sirius binary mechanism iscshed to 50 years. We deserve to usage Kepler"s orbital law and the centre of mass equation to find the masses of the stars. Sirius B has actually a mass almostthe same as the Sun"s mass. The average density of a star is its mass dividedby its volume. The volume of a spright here is V = 4/3 pi R3. The volume of Sirius B is V = 4/3 pi ( 7 x 106 m)3 = 1.4 x 1021 m3. The density of Sirius B is density = 2 x 1030 kg/V. = 1 x 109 kg/m3. Remember: thickness of water is 1000 kg/m3.The escape velocity from the surface of a star isvesc = (2GM/R)1/2 . For Sirius B, this coincides to a velocityof 6 x 106 m/s, around 2/100 c.

Mass-Volume relation for White Dwarf Stars

For normal matter, if you double the mass of anobject, its volume will certainly also double. For example in primary sequence stars, the highermass stars likewise have larger sizes. For degenerate matter, if you boost themass of a star, its radius and also volume decreases.Why? For degeneprice matter, the resource of push is thickness. So it preserve higher mass, one has to increase the thickness inside. But thickness = mass/volume, however, mass rise alone does not carry out enough density (and pressure) boost so the volume has to decrease as well in order to balance gravity. For white dwarfs, the masses and volumesare related by Mass x Volume = constant
. This is only approximate, given that at the Chandrasekhar limiting mass ofM = 1.4 MSun, the electronswould certainly need to move at the speed of light,so the mass-volume relationship does not holddown to zero volume. The Chandrasekhar mass is the largest massthat a white dwarf can perhaps have.
Next off lecture: Evolution of High Mass Stars