# Has stellar evolution ever been modeled analytically?

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I'll still remember the handout my astronomy professor gave us more than several decades ago; Our Friends the Polytropes. We spent a lot of time learning how polytropes, simple analytical power-law models could reproduce some basic thermodynamic properties of stars, and how those properties would tend to vary with mass (and perhaps other parameters, I don't remember now).

Have polytrope models of stars (or other simple analytical models of stars) ever been "evolved" analytically in time? In other words, in addition to variations on radius, have a set of equations ever been written which also included a $$frac{partial}{partial t}$$ in such a way that they were amenable to an analytic solution?

Well yes, it is still a useful tool because it can give much more insight than the output from a black box computer code. However, you have to pick your problems or the complexity of the analysis can lose this advantage.

A particular case is the evolution of low mass pre main sequence stars along the Hayashi track. Since these stars are fully convective they can be treated as single polytrope a (to first order). Myself and a colleague have used such analytical calculations to study the effects of spots and magnetic fields on the evolution of PMS stars and on the rate at which they "burn" lithium in their cores (e.g. Jackson & Jeffries 2014a; Jackson & Jeffries 2014b).

In turn, this work was inspired by a much earlier analytical treatment of the Li depletion problem by Bildsten et al. (1997).

Analytic models have been applied to various phases of the evolution, though it would be impossible to apply a single model to all phases because the physics changes so much. Also, a star will often have very different physics going on in various different parts of the star, so analytic models sometimes have to treat different parts separately and then unify the results across boundaries (just as numerical simulations do). For example, I've seen different polytrope indices used in the convection, radiative, and core regions of the Sun.

I realize that your interest is when there is not a steady-state assumption, but rather time is a dynamical variable. But it is not always necessary to use time as a dynamical variable to do evolution. You can simply do a steady-state analytical model (like a polytrope, perhaps supported by a numerical piece that solves for some parameter like core pressure), and allow the parameters in your solution to be time varying in some simple analytical way. For example, you could study how mass loss affects a star by doing steady-state analytical models and just let the mass change with time according to some analytical mass-loss prescription (such as "Reimers' Law", something simple). So steady-state analytical models can be elevated into evolutionary models if you simply have an analytical way to change the parameters with time.

Another simple example is the evolution of a fully convective protostar. You simply fix the mass and initial radius, and you solve the interior by assuming it's all at the same entropy (a reasonable approximation for fully convective stars). Then you fix the surface temperature to lie on the Hayashi track, which for a very simple model could mean just pegging the surface T to 3000 K. That and the initial radius determines the luminosity, and the constant entropy assumption fixes the internal structure, so then you simply let it lose energy at the rate of the luminosity, and use the internal energy as the variable that changes with time, always updating the radius to be consistent with the new internal energy (a la the virial theorem), and that gives the new luminosity and so forth. A simple fully analytic model until the star is no longer fully convective (and we then might call it a pre-main-sequence star).

I've also seen white dwarf cooling done analytically. It's a similar idea-- take the surface temperature as an initial condition and just let it lose heat via its luminosity. The radius doesn't really change, so all you need is to keep updating the surface temperature as a function of the internal energy, which can be handled via some analytic internal heat transport treatment. If you are willing to make approximations that address the key physics, you can do almost anything analytically.

## Stellar population

During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations.

In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926:

[. ] The two types of stellar populations had been recognized among the stars of our own galaxy by Oort as early as 1926. [1]

Baade noticed that bluer stars were strongly associated with the spiral arms and yellow stars dominated near the central galactic bulge and within globular star clusters. [2] Two main divisions were defined as

they are often simply abbreviated as Pop. I, Pop. II, and Pop. III .

Between the population types, significant differences were found with their individual observed stellar spectra. These were later shown to be very important, and were possibly related to star formation, observed kinematics, [3] stellar age, and even galaxy evolution in both spiral or elliptical galaxies. These three simple population classes usefully divided stars by their chemical composition or metallicity. [4] [3]

By definition, each population group shows the trend where decreasing metal content indicates increasing age of stars. Hence, the first stars in the universe (very low metal content) were deemed Population III, old stars (low metallicity) as Population II, and recent stars (high metallicity) as Population I. [5] The Sun is considered Population I, a recent star with a relatively high 1.4 percent metallicity. Note that astrophysics nomenclature considers any element heavier than helium to be a "metal", including chemical non-metals such as oxygen.

## Contents

### Protostar Edit

Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years (9.5 × 10 14 km) across and contain up to 6,000,000 solar masses (1.2 × 10 37 kg). As it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat. As its temperature and pressure increase, a fragment condenses into a rotating ball of superhot gas known as a protostar. [3] Filamentary structures are truly ubiquitous in the molecular cloud. Dense molecular filaments will fragment into gravitationally bound cores, which are the precursors of stars. Continuous accretion of gas, geometrical bending, and magnetic fields may control the detailed fragmentation manner of the filaments. In supercritical filaments, observations have revealed quasi-periodic chains of dense cores with spacing comparable to the filament inner width, and embedded two protostars with gas outflows. [4]

A protostar continues to grow by accretion of gas and dust from the molecular cloud, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. Mass is typically compared to the mass of the Sun: 1.0 M (2.0 × 10 30 kg) means 1 solar mass.

Protostars are encompassed in dust, and are thus more readily visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer (WISE) have been especially important for unveiling numerous galactic protostars and their parent star clusters. [5] [6]

### Brown dwarfs and sub-stellar objects Edit

Protostars with masses less than roughly 0.08 M (1.6 × 10 29 kg) never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses ( M J), 2.5 × 10 28 kg, or 0.0125 M ). Objects smaller than 13 M J are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets). [7] Both types, deuterium-burning and not, shine dimly and fade away slowly, cooling gradually over hundreds of millions of years.

### Stellar mass objects Edit

For a more-massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, first to deuterium and then to helium. In stars of slightly over 1 M (2.0 × 10 30 kg), the carbon–nitrogen–oxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core maintains a high gas pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution.

A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small, relatively cold, low-mass red dwarfs fuse hydrogen slowly and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years. A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan.

Eventually the star's core exhausts its supply of hydrogen and the star begins to evolve off the main sequence. Without the outward radiation pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass.

### Low-mass stars Edit

What happens after a low-mass star ceases to produce energy through fusion has not been directly observed the universe is around 13.8 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for fusion to cease in such stars.

Recent astrophysical models suggest that red dwarfs of 0.1 M may stay on the main sequence for some six to twelve trillion years, gradually increasing in both temperature and luminosity, and take several hundred billion years more to collapse, slowly, into a white dwarf. [9] [10] Such stars will not become red giants as the whole star is a convection zone and it will not develop a degenerate helium core with a shell burning hydrogen. Instead, hydrogen fusion will proceed until almost the whole star is helium.

Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch. When hydrogen shell burning finishes, these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star, but at lower luminosity, to become a white dwarf. [2] A star with an initial mass about 0.6 M will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red-giant branch. [11]

### Mid-sized stars Edit

Stars of roughly 0.6–10 M become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lie along the right edge of the Hertzsprung–Russell diagram due to their red color and large luminosity. Examples include Aldebaran in the constellation Taurus and Arcturus in the constellation of Boötes.

Mid-sized stars are red giants during two different phases of their post-main-sequence evolution: red-giant-branch stars, with inert cores made of helium and hydrogen-burning shells, and asymptotic-giant-branch stars, with inert cores made of carbon and helium-burning shells inside the hydrogen-burning shells. [12] Between these two phases, stars spend a period on the horizontal branch with a helium-fusing core. Many of these helium-fusing stars cluster towards the cool end of the horizontal branch as K-type giants and are referred to as red clump giants.

#### Subgiant phase Edit

When a star exhausts the hydrogen in its core, it leaves the main sequence and begins to fuse hydrogen in a shell outside the core. The core increases in mass as the shell produces more helium. Depending on the mass of the helium core, this continues for several million to one or two billion years, with the star expanding and cooling at a similar or slightly lower luminosity to its main sequence state. Eventually either the core becomes degenerate, in stars around the mass of the sun, or the outer layers cool sufficiently to become opaque, in more massive stars. Either of these changes cause the hydrogen shell to increase in temperature and the luminosity of the star to increase, at which point the star expands onto the red-giant branch. [13]

#### Red-giant-branch phase Edit

The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface during the first dredge-up, with lower 12 C/ 13 C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for many evolved stars.

The helium core continues to grow on the red-giant branch. It is no longer in thermal equilibrium, either degenerate or above the Schönberg–Chandrasekhar limit, so it increases in temperature which causes the rate of fusion in the hydrogen shell to increase. The star increases in luminosity towards the tip of the red-giant branch. Red-giant-branch stars with a degenerate helium core all reach the tip with very similar core masses and very similar luminosities, although the more massive of the red giants become hot enough to ignite helium fusion before that point.

#### Horizontal branch Edit

In the helium cores of stars in the 0.6 to 2.0 solar mass range, which are largely supported by electron degeneracy pressure, helium fusion will ignite on a timescale of days in a helium flash. In the nondegenerate cores of more massive stars, the ignition of helium fusion occurs relatively slowly with no flash. [14] The nuclear power released during the helium flash is very large, on the order of 10 8 times the luminosity of the Sun for a few days [13] and 10 11 times the luminosity of the Sun (roughly the luminosity of the Milky Way Galaxy) for a few seconds. [15] However, the energy is consumed by the thermal expansion of the initially degenerate core and thus cannot be seen from outside the star. [13] [15] [16] Due to the expansion of the core, the hydrogen fusion in the overlying layers slows and total energy generation decreases. The star contracts, although not all the way to the main sequence, and it migrates to the horizontal branch on the Hertzsprung–Russell diagram, gradually shrinking in radius and increasing its surface temperature.

Core helium flash stars evolve to the red end of the horizontal branch but do not migrate to higher temperatures before they gain a degenerate carbon-oxygen core and start helium shell burning. These stars are often observed as a red clump of stars in the colour-magnitude diagram of a cluster, hotter and less luminous than the red giants. Higher-mass stars with larger helium cores move along the horizontal branch to higher temperatures, some becoming unstable pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a blue tail or blue hook to the horizontal branch. The morphology of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are still being modelled. [17]

#### Asymptotic-giant-branch phase Edit

After a star has consumed the helium at the core, hydrogen and helium fusion continues in shells around a hot core of carbon and oxygen. The star follows the asymptotic giant branch on the Hertzsprung–Russell diagram, paralleling the original red-giant evolution, but with even faster energy generation (which lasts for a shorter time). [18] Although helium is being burnt in a shell, the majority of the energy is produced by hydrogen burning in a shell further from the core of the star. Helium from these hydrogen burning shells drops towards the center of the star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes even into the post-asymptotic-giant-branch phase. Depending on mass and composition, there may be several to hundreds of thermal pulses.

There is a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from the core to the surface. This is known as the second dredge up, and in some stars there may even be a third dredge up. In this way a carbon star is formed, very cool and strongly reddened stars showing strong carbon lines in their spectra. A process known as hot bottom burning may convert carbon into oxygen and nitrogen before it can be dredged to the surface, and the interaction between these processes determines the observed luminosities and spectra of carbon stars in particular clusters. [19]

Another well known class of asymptotic-giant-branch stars is the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes up to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more-massive stars the stars become more luminous and the pulsation period is longer, leading to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infrared and showing OH maser activity. These stars are clearly oxygen rich, in contrast to the carbon stars, but both must be produced by dredge ups.

#### Post-AGB Edit

These mid-range stars ultimately reach the tip of the asymptotic-giant-branch and run out of fuel for shell burning. They are not sufficiently massive to start full-scale carbon fusion, so they contract again, going through a period of post-asymptotic-giant-branch superwind to produce a planetary nebula with an extremely hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in heavy elements created within the star and may be particularly oxygen or carbon enriched, depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star, ideal conditions are formed in these circumstellar envelopes for maser excitation.

It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and poorly understood stars known as born-again asymptotic-giant-branch stars. [20] These may result in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables.

### Massive stars Edit

In massive stars, the core is already large enough at the onset of the hydrogen burning shell that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as dramatically as lower-mass stars however, they were more luminous on the main sequence and they evolve to highly luminous supergiants. Their cores become massive enough that they cannot support themselves by electron degeneracy and will eventually collapse to produce a neutron star or black hole. [ citation needed ]

#### Supergiant evolution Edit

Extremely massive stars (more than approximately 40 M ), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation are about 100-150 M because the outer layers would be expelled by the extreme radiation. Although lower-mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing. [21]

The core of a massive star, defined as the region depleted of hydrogen, grows hotter and more dense as it accretes material from the fusion of hydrogen outside the core. In sufficiently massive stars, the core reaches temperatures and densities high enough to fuse carbon and heavier elements via the alpha process. At the end of helium fusion, the core of a star consists primarily of carbon and oxygen. In stars heavier than about 8 M , the carbon ignites and fuses to form neon, sodium, and magnesium. Stars somewhat less massive may partially ignite carbon, but are unable to fully fuse the carbon before electron degeneracy sets in, and these stars will eventually leave an oxygen-neon-magnesium white dwarf. [22] [23]

The exact mass limit for full carbon burning depends on several factors such as metallicity and the detailed mass lost on the asymptotic giant branch, but is approximately 8-9 M . [22] After carbon burning is complete, the core of these stars reaches about 2.5 M and becomes hot enough for heavier elements to fuse. Before oxygen starts to fuse, neon begins to capture electrons which triggers neon burning. For a range of stars of approximately 8-12 M , this process is unstable and creates runaway fusion resulting in an electron capture supernova. [24] [23]

In more massive stars, the fusion of neon proceeds without a runaway deflagration. This is followed in turn by complete oxygen burning and silicon burning, producing a core consisting largely of iron-peak elements. Surrounding the core are shells of lighter elements still undergoing fusion. The timescale for complete fusion of a carbon core to an iron core is so short, just a few hundred years, that the outer layers of the star are unable to react and the appearance of the star is largely unchanged. The iron core grows until it reaches an effective Chandrasekhar mass, higher than the formal Chandrasekhar mass due to various corrections for the relativistic effects, entropy, charge, and the surrounding envelope. The effective Chandrasekhar mass for an iron core varies from about 1.34 M in the least massive red supergiants to more than 1.8 M in more massive stars. Once this mass is reached, electrons begin to be captured into the iron-peak nuclei and the core becomes unable to support itself. The core collapses and the star is destroyed, either in a supernova or direct collapse to a black hole. [23]

#### Supernova Edit

When the core of a massive star collapses, it will form a neutron star, or in the case of cores that exceed the Tolman–Oppenheimer–Volkoff limit, a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. Because some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium. [25] Although non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in the Solar System, so both supernovae and ejection of elements from red giants are required to explain the observed abundance of heavy elements and isotopes thereof.

The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Current understanding of this energy transfer is still not satisfactory although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material. [26] However, neutrino oscillations may play an important role in the energy transfer problem as they not only affect the energy available in a particular flavour of neutrinos but also through other general-relativistic effects on neutrinos. [27] [28]

Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core. [29]

The most massive stars that exist today may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding energy. This rare event, caused by pair-instability, leaves behind no black hole remnant. [30] In the past history of the universe, some stars were even larger than the largest that exists today, and they would immediately collapse into a black hole at the end of their lives, due to photodisintegration.

After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.

### White and black dwarfs Edit

For a star of 1 M , the resulting white dwarf is of about 0.6 M , compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons, a consequence of the Pauli exclusion principle. Electron degeneracy pressure provides a rather soft limit against further compression therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.

A white dwarf is very hot when it first forms, more than 100,000 K at the surface and even hotter in its interior. It is so hot that a lot of its energy is lost in the form of neutrinos for the first 10 million years of its existence, but will have lost most of its energy after a billion years. [31]

The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow the star apart in a supernova. [32] A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.

In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarfs to exist yet.

If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 M for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will lead either to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova. [33] These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 M can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.

If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction at its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.

### Neutron stars Edit

Ordinarily, atoms are mostly electron clouds by volume, with very compact nuclei at the center (proportionally, if atoms were the size of a football stadium, their nuclei would be the size of dust mites). When a stellar core collapses, the pressure causes electrons and protons to fuse by electron capture. Without electrons, which keep nuclei apart, the neutrons collapse into a dense ball (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli exclusion principle, in a way analogous to electron degeneracy pressure, but stronger.

These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the size of a large city—and are phenomenally dense. Their period of rotation shortens dramatically as the stars shrink (due to conservation of angular momentum) observed rotational periods of neutron stars range from about 1.5 milliseconds (over 600 revolutions per second) to several seconds. [34] When these rapidly rotating stars' magnetic poles are aligned with the Earth, we detect a pulse of radiation each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic radiation detected from pulsars is most often in the form of radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths. [35]

### Black holes Edit

If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 M .

Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.

Because the core-collapse mechanism of a supernova is, at present, only partially understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.

A stellar evolutionary model is a mathematical model that can be used to compute the evolutionary phases of a star from its formation until it becomes a remnant. The mass and chemical composition of the star are used as the inputs, and the luminosity and surface temperature are the only constraints. The model formulae are based upon the physical understanding of the star, usually under the assumption of hydrostatic equilibrium. Extensive computer calculations are then run to determine the changing state of the star over time, yielding a table of data that can be used to determine the evolutionary track of the star across the Hertzsprung–Russell diagram, along with other evolving properties. [36] Accurate models can be used to estimate the current age of a star by comparing its physical properties with those of stars along a matching evolutionary track. [37]

## Stellar Evolution, Distant Starlight and Biblical Authority

Does the size of the universe prove that it must be billions of years old?

I am currently studying astronomy and stellar evolution (quite different from macro evolution ) and have come to the conclusion that the Earth and the universe is not only 6000 years old. There are stars and galaxies that are billions of light years away that we can see. If the light traveling from the star travels one light year a year (the definition of a light year) and takes that much time to reach us, the universe has to be at least that old, if not more.

We also know that stars that begin as gas and are then compacted into protostars and then become full fledged stars on the mainsequence for millions of years. They then go supernova and spread all of their elements throughout space.

The proton-proton cycle turns hydrogen to helium in a star and then the triple alpha process turns helium into carbon-the same carbon that makes up human beings. The carbon is then sent through space along with oxygen and iron and numerous other elements made in a star. That is why hydrogen is the most abundent element, stars use it to make everything else.

What was God supposed to tell Moses? That he blew up millions of stars billions of years ago and fused their elements to make the Earth in an interstellar vacuum? It would be much easier for Moses to explain it in a parable that Moses could actually understand. The geneologies we have are true, but incomplete, as many generations were left out. Honestly, how were they supposed to remember that many names? They simply remembered the important figures. Adam, the first man, walked this Earth around 50,000 years ago, not 6,000.

What is a day to God ? We created the 24 hour system based on the earth’s rotation. What is a day on Mars or Neptune or deep space where there is no sun. God is the God of the universe, not exclusively Earth, even though it is important. God created first and then came the definition of a day, not the other way around.

How can anyone say for certain that the universe is only a couple of thousand of years old when what is actually in the universe is not even known. Using high powered telescopes, we can see about 18 billion light years away, and then everything stops. What’s wrong? Is the telescope broken? Do we need to build a bigger one? No. The biggest telescope in the universe could not see what is 19 billion light years away. There’s stuff out there, but the universe is only 18 billion years old. The light has not had enough time to even reach us yet!!

I agree with you that we did not come from monkies (DNA science proves this) and that evolution is false, but to reject avaiable evidence that the universe is older than we want it to be is bad science.

S.D.
USA

I am currently studying astronomy and stellar evolution (quite different from macro evolution ) and have come to the conclusion that the Earth and the universe is not only 6000 years old. There are stars and galaxies that are billions of light years away that we can see.

This just means that the universe is very big. It doesn’t indicate that it is old unless you make secular assumptions (as will be shown). I want to encourage and challenge you to really think about what your professor is teaching learn to separate facts from interpretations. Learn to recognize the assumptions (especially anti-biblical assumptions) that go into various theories, and not just blindly accept everything you are taught in your astronomy class.

If the light traveling from the star travels one light year a year (the definition of a light year) and takes that much time to reach us, the universe has to be at least that old, if not more.

i am a teacher working in a christian school. today march of the penguins was screened for the teachers. i enjoyed the film. but aig site told me much more about penguins in the right perspectve. i used the search option in aig website. you are doing a great job. god bless you.

Let’s think through some of the many hidden assumptions in this line of reasoning. First, you have assumed that light has always traveled at the same speed. (Most creationists think this is probably a reasonable assumption—but it is an assumption, not an observable fact.) Second, you have assumed that the effects of gravitational time dilation are insignificant. Einstein tells us that time can flow at different rates under different circumstances. Under the right conditions, light from the most distant galaxies could have arrived at Earth in very short amounts of time. Yet you seem to have totally ignored this important principle of physics.

Third, you have assumed (without justification) a particular synchrony convention. The terrestrial equivalent of this fallacy would be assuming that noon in England is the same as noon in Cincinnati. Fourth, and perhaps most importantly, you have assumed that the light arrived entirely by natural means. However, God created the stars supernaturally during Creation Week ( Genesis 1:14–19 ) and made them to give light upon Earth. Since this happened during Creation Week, God may have used different means to get distant starlight here than the “natural” means by which He upholds the universe today. Such reasoning is no different than those who reject the resurrection of Christ because it cannot be explained by natural forces.

We would also point out that the big bang (the most popular secular alternative to biblical creation) has a light travel-time problem of its own (the horizon problem).

We also know that stars that begin as gas and are then compacted into protostars and then become full fledged stars on the mainsequence for millions of years.

This is not known it is blindly assumed by those who reject biblical creation. Have you or anyone else ever observed a star form? It supposedly takes millions of years (in the secular model), so no one could actually observe it even in principle. Those who believe in the big bang and secular models of star formation have no observational evidence that these things have occurred nor is there any sort of recorded eyewitness account. However, Christians have a perfect eyewitness and His recorded account. God was there and He told us how and when He did it: Genesis 1:14 .

They then go supernova and spread all of their elements throughout space.

We have observed supernova and so we would agree on that part. But whether or not supernova spread all of their elements throughout space is questionable. In the secular view, the central portion of the star (the “core”) has the heavier elements that it has produced from fusion. But the core is not blasted away in the supernova rather it collapses to form either a neutron star, or black hole.

The proton-proton cycle turns hydrogen to helium in a star

Although this is not directly observed, we do directly observe the neutrinos that are produced in the process. So we have good scientific reasons to accept this theory. However, much of the rest of what you have written is not well established by observation it is instead assumed to be true based merely on secular beliefs.

and then the triple alpha process turns helium into carbon-the same carbon that makes up human beings. The carbon is then sent through space along with oxygen and iron and numerous other elements made in a star. That is why hydrogen is the most abundent element, stars use it to make everything else.

That’s the secular story. It is the atheistic/secular attempt to explain the abundance of the elements. We would like to point out that God tells us that the earth was created first and that Adam was created from the dust of the earth not the stars. Since the earth was created first then we are made from the carbon of the earth not of the stars. Also, all of the above statements are assumed without any evidence. Big bang supporters themselves acknowledge that the big bang could not have produced anything heavier than lithium, so the only way to explain the heavier elements, like carbon, is to say that the stars did it. Notice there is no observational evidence or recorded eyewitness accounts to support this, just man’s fallible opinions about the past.

The real issue is this: Do you place your faith in ideas about the past by men who weren’t there and are imperfect, or do you place your faith in God ’s perfect Word, who eyewitnessed the past? Who are you going to trust first?

What was God supposed to tell Moses? That he blew up millions of stars billions of years ago and fused their elements to make the Earth in an interstellar vacuum? It would be much easier for Moses to explain it in a parable that Moses could actually understand.

The idea that Moses was not intelligent enough to understand how God really created (thereby forcing God to use a parable) is an example of what C.S. Lewis called “chronological snobbery”. Genesis is not written as a parable, but as historic narrative. The frequent use of the Hebrew waw-consecutive, the specific names and places, even the Hebrew verb forms1 used, all confirm that Genesis is literal history. If God had used the big bang and billions of years, He certainly could have stated so in Hebrew in a way that Moses would have understood (see Genesis according to evolution).

The geneologies we have are true, but incomplete, as many generations were left out. Honestly, how were they supposed to remember that many names? They simply remembered the important figures. Adam, the first man, walked this Earth around 50,000 years ago, not 6,000.

How do you know that many generations were left out? Jude points out that Enoch was the seventh from Adam, giving clear testimony that the genealogies were accurate. The idea that there are gaps in the genealogies is refuted in the article Are There Gaps in the Genesis Genealogies?.

What is a day to God ? We created the 24 hour system based on the earth’s rotation. What is a day on Mars or Neptune or deep space where there is no sun. God is the God of the universe, not exclusively Earth, even though it is important. God created first and then came the definition of a day, not the other way around.

You’re right about one thing: God is the God of the universe, not just the earth. But God did create the day in Genesis 1 and defined what it was: God called the light day, and the darkness He called night. And there was evening and there was morning, one day ( Genesis 1:5 ). Notice that day is defined two ways here: the daylight portion or one rotation of Earth with respect to a light source. It cannot be a day on any other planet, because the sun, stars and other planets were not created until the fourth day.

It would be very presumptuous of us as fallible, sinful human beings to tell a perfect God how He really created everything.

We should be learning from God , not rewriting what He said He did.

How can anyone say for certain that the universe is only a couple of thousand of years old when what is actually in the universe is not even known.

God fully knows everything about the universe. He was there when it was created, so He knows exactly how old it is. And He has given us some of that knowledge through His Word. It would be folly to reject what He has told us, and instead rely on human speculations about the past when “the universe is not even known” (fully) by humans.

Using high powered telescopes, we can see about 18 billion light years away, and then everything stops. What’s wrong? Is the telescope broken? Do we need to build a bigger one? No. The biggest telescope in the universe could not see what is 19 billion light years away. There’s stuff out there, but the universe is only 18 billion years old. The light has not had enough time to even reach us yet!!

Actually, secular astronomers claim the universe is about 13.7 billion years old. They assume without any evidence at all that the galaxies go on forever, but that we can’t see them beyond a certain distance for whatever reason—perhaps because the light hasn’t reached us yet. But what if the reason we don’t see galaxies beyond a certain distance is because there are none beyond that distance. That’s at least as reasonable as any other explanation. And if true, it would mean that our portion of the galaxy is in a gravitational well—which causes time-dilation. This potentially would make starlight from the most distant regions of the universe arrive on Earth in only thousands of years Earth-time. See How can we see distant stars in a young universe?

I agree with you that we did not come from monkies (DNA science proves this) and that evolution is false, but to reject avaiable evidence that the universe is older than we want it to be is bad science.

S.D.
USA

But then evolutionists would say that rejecting their interpretation of a high level of human-chimp DNA similarity is bad science. The real issue is whether or not you are going to trust a perfect God ’s Word about the past or fallible man’s ideas. S.D., I want to encourage you to trust God ’s Word and not reinterpret it based on man’s ideas.

In His name and for His glory,
Dr. Jason Lisle and David Wright
AiG–USA

## Planets are Evolving Stars, Stellar Evolution is actually planet formation, they are the same things

Exactly. The title implies that planets are actually in the process of becoming massive enough to become a star someday. They aren't.

Any other Redditors read those PDFs this guy posted? Of course this person has a Youtube channel discussing this stuff.

This very much falls in line with, "The universe is this way, all the mainstream scientists are wrong and think Im crazy! It's very hard for me to accept that everyone in society has been lied to, here's the real truth!"

Reading these "findings", has given me the slight sensation that this "scientist", is very close to what some people refer to as "insane". There are some clear symptoms here:

Said individual has huge theory about the universe.

Theory is being suppressed by large, strategic conspiracy.

Said individual uses scientific buzzwords and phrases instead of actual scientific data.

That's all I have to add at this point, no need to bash the guy. Please comment on this fellow Redditors.

"Young boys and girls are taught in early schooling that a star is something different than a planet. It has been culturally accepted for centuries, thus very few people questioned whether the two were the same. Even if they were to question it, most of those questioners did nothing about it, because it is a belief that is rooted in culture and persists even in the year 2017. Think about it. Young boys and girls long before they learn the scientific method are told, by their teachers who are most likely not scientists, that planets and stars are different. The Sun is a star and the Earth is a planet along with the other 8. It is an enormously unfortunate event in the life of a child. A very deep, and powerful history of the Earth and the stars can be presented to them from the very start, but they are first conditioned into a culturally accepted idea that is officially completely false. It is like teaching children the Earth is flat. Even though I'm one of the principle discoverers of this understanding, because of the cultural conditioning I was subjected to in school from a very early age, it is still hard for me to accept mentally and emotionally. It also puts me in a separate group of people socially, I cannot discuss this new fact, not even with physics teachers! They just get upset! It is unlike anything I've ever understood before, as well, to understand it takes a mind that is actually, genuinely open to new ideas. Once children reach a certain age, say, young adulthood, their minds are mostly completely made up. Their worldview was presented and given to them, and was accepted by them long before they even got to college and began studying the stars. Thus, their culturally defined meaning of planet/star remains and they look through their telescopes absolutely sure of what they are seeing, long before they started questioning what they are looking at. The transcendence of astronomy was murdered, by a large overwhelming majority of people who do not possess the capacity to question themselves. An echo chamber of cultural proportions was thrust upon them long before they learned what an echo really is."

It is not a conspiracy. The fact is that they have accepted culturally that stars and planets are mutually exclusive objects well before any theory of stellar evolution or planet formation was drawn up. Thus all theories of planet formation and stellar evolution accept that they are different objects.

The fact is that they are not different objects. They are the same things. Stellar evolution is planet formation. The young hot plasmatic/gaseous planets lose mass and cool down, becoming old, cold, solid planets.

It is on par with the realization that Earth is not the center of the solar system. Only with this understanding the Earth is not related to the other objects in the solar system, it is completely independent of the other objects in the solar system except for its current orbit.

There are multiple assumptions that became dogma.

Astronomical assumptions Visible spectrums A main astronomical assumption is that all stars have visible spectrums. This assumption has lead to scientists neglecting the vast majority of stars that do not have visible spectrums. Calling them planets/exoplanets does not resolve the issue. It is only until scientists realize that the majority of stars no longer shine will they understand how stellar evolution works.

Massive stars It is assumed that all stars are massive like the Sun. This directly contradicts a fact of astrophysics called the conservation of mass and energy. All stars lose mass and energy in great amounts as they evolve. They can start out big and hot like the Sun, but will eventually cool, and lose the majority of their mass to solar wind, CME's, solar flares, photoevaporation, impacts, etc. This also means that as it shrinks, it also loses the angular momentum (mass loss), which means its rotational velocity will remain constant.

Sun reliance It is assumed that the evolution of all the solar system objects relies on the fate of the Sun alone and that they are not independent objects. This directly contradicts the principle of multiple nebulas and the principle of stellar adoption in stellar metamorphosis. The solar system is an adopted family, with mini solar systems inside of it. It is much more reasonable to actually look at the objects and notice they are all different in size, look different and are in different random orbits, meaning the Sun plays a minor and temporary role in their evolutionary sequences, until it loses them and they wander the galaxy as rogue objects, taking up orbit around another bigger, less evolved star or group of stars.

The whole volume of a star evolves, therefore their evolution is mostly independent of the relatively small surface area impacted by a hotter host. This means they are definitely mostly independent of the Sun, except for their current orbits. Rocky/metal surfaces are not subject to photoevaporation as are younger more gaseous stars, so they are even more independent of the Sun's features except for their thin (if existent) atmospheres such as the Earth.

Mutual exclusiveness The main astronomical assumption accepted which has prevented understanding is of assuming a star to be big, hot and bright and planet as small, cold and dim, which was rooted in appearances. It is pointed out that the appearances of there being two distinct classes of objects has always been a deception. The two are not mutually exclusive. The big, hot and bright star shrinks, cools and dims, becoming the planet. This assumption has allowed for entire models and theories to be designed to fit in stars as being similar in age to planets, regardless if the former is actually the younger by many magnitudes. It also applies to objects that are both classified as planets. Venus is roughly the same size as Earth, is composed of rocks like the Earth, and no longer has a magnetic field. How do two very similar objects form at the same time and one have volcanic activity and the other is a lifeless world without any activity. Clearly Venus is vastly older than the Earth and has almost completely solidified and hid all evidence for having be composed of multiple plates in the lithosphere well in its past. Simply put, all the lava has already escaped.[54]

By-product reinterpretation Another root assumption of astrophysics is that planets are by-products of star formation, which could be misleading. In this theory planets are by-products of stellar evolution, meaning the planet is not the remains of stellar birth, but the remains of an evolving/evolved star itself. This reversing of assumption simplifies all astrophysical interpretations regarding stellar evolution and planet formation models. The majority of accepted models for both stellar evolution and planet formation could probably be using an assumption that does not work, according to Anthony J. Abruzzo.[55]

Disk nebula A reinterpretation of the apparent evidence of planets being formed in disks is provided. It is stated, "They (protoplanetary disks) are evidence for planet destruction and collision events. The disks radiate strongly in the infrared, meaning the material is liquid hot like magma. In essence they are shrapnel fields, and this shrapnel can re-enter the atmospheres of other stars as meteors and can be found on the ground as meteorites, and even leaves rings around other evolved stars and asteroid fields and in meteor showers.

Disk age interpretation In the accepted sciences, the presence of a disk of material around a big hot star means the star is young. In stellar metamorphosis the determination of a star’s age based on the presence of disks can be ignored as unnecessary. It is simply an assumption based off the nebular hypothesis, which originally was beat out by the island universe hypothesis. The nebulas that were disk shaped spotted by early astronomers were not young solar systems forming planets inside of the Milky Way, they were entire galaxies. Somehow this tidbit of scientific history has escaped the theorists.

“Disks cannot be used to determine the age of a star, they are independent structures.” Disks do not signal youth nor do they signal planet formation, as planets are simply more evolved stars that orbit younger ones forming systems.

Solar system wall It is assumed that nothing can enter the solar system from another star system entirely, yet it is very clear that there are no walls preventing objects from entering the solar system. The heliosphere is not a physical wall, it is a concept. If any galactic objects have enough mass and momentum they will enter freely. This means the Oort cloud is probably an unnecessary concept, as well means that objects found as meteorites probably came from outside the solar system entirely and have origins from some other place in the galaxy, or another galaxy entirely. With this realization it becomes obvious that our own system of objects was subject to capture by the Sun, including the Earth, Jupiter, Saturn, Neptune, Uranus and all their moons.

Fusion powered stars It is assumed that stars are fusion powered, they cannot be hot for any other reason. This ignores a fact of thermodynamics that plasma recombines into gas, releasing heat. This is known as plasma recombination and is a basic thermodynamic phase transition. Plasma recombination/re-ionization fueled via gravitational collapse keeps young stars hot and luminous. As the gravitational field diminishes to mass loss, via the conservation of mass, the feedback loop becomes interrupted and the plasma recombines into superheated gaseous matter which then transforms into much more complex molecules to dissipate the left over heat for many more billions of years. This means stars are hot and can remain hot as they evolve with mechanisms completely absent the concept of fusion, and can almost ignore radioactive material heating any matter.

Chemistry assumption It is assumed that chemistry is not important to explain the behavior of stellar events, yet stars are giant celestial chemistry demonstrations involving all naturally occurring chemical reactions. This is evidenced by the presence of all naturally occurring chemical compounds being found on the Earth, an evolved star.

## Abstract

In the present manuscript, we have constructed an anisotropic solution for spherically symmetric space-time that satisfies Karmarkar’s condition in the context of f ( R , T ) theory of gravity where R and T represent the Ricci scalar and the trace of Energy-momentum tensor, respectively. In order to achieve our goal, we chose a one of the gravitational potentials having regular behavior and obtained a closed form of the solution. This expression of the gravitational potential enables the embedding equation to be solved and the field equations to be integrated. The resulting current anisotropic solution is well-behaved and can be used to build realistic static fluid spheres. Our anisotropic solution represents compact structures like V e l a X − 1 and 4 U 1608 − 52 to a very high degree of precision. It has also been presented that our stellar model is physically accepted and satisfies all the physical criteria required to meet for a stable hydrostatic equilibrium configuration.

## Thought Questions

What can we learn about the formation of our solar system by studying other stars? Explain.

Earlier in this chapter, we modeled the solar system with Earth at a distance of about one city block from the Sun. If you were to make a model of the distances in the solar system to match your height, with the Sun at the top of your head and Pluto at your feet, which planet would be near your waist? How far down would the zone of the terrestrial planets reach?

Seasons are a result of the inclination of a planet’s axial tilt being inclined from the normal of the planet’s orbital plane. For example, Earth has an axis tilt of 23.4° (Appendix F). Using information about just the inclination alone, which planets might you expect to have seasonal cycles similar to Earth, although different in duration because orbital periods around the Sun are different?

Again using Appendix F, which planet(s) might you expect not to have significant seasonal activity? Why?

Again using Appendix F, which planets might you expect to have extreme seasons? Why?

Using some of the astronomical resources in your college library or the Internet, find five names of features on each of three other worlds that are named after real people. In a sentence or two, describe each of these people and what contributions they made to the progress of science or human thought.

Explain why the planet Venus is differentiated, but asteroid Fraknoi, a very boring and small member of the asteroid belt, is not.

Would you expect as many impact craters per unit area on the surface of Venus as on the surface of Mars? Why or why not?

Interview a sample of 20 people who are not taking an astronomy class and ask them if they can name a living astronomer. What percentage of those interviewed were able to name one? Typically, the two living astronomers the public knows these days are Stephen Hawking and Neil deGrasse Tyson. Why are they better known than most astronomers? How would your result have differed if you had asked the same people to name a movie star or a professional basketball player?

Using Appendix G, complete the following table that describes the characteristics of the Galilean moons of Jupiter, starting from Jupiter and moving outward in distance.

#### Table A

This system has often been described as a mini solar system. Why might this be so? If Jupiter were to represent the Sun and the Galilean moons represented planets, which moons could be considered more terrestrial in nature and which ones more like gas/ice giants? Why? (Hint: Use the values in your table to help explain your categorization.)

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Buy a single issue of Science for just $15 USD. ### Science Vol 308, Issue 5719 08 April 2005 ### Article Tools Please log in to add an alert for this article. By Marcin Hajduk , Albert A. Zijlstra , Falk Herwig , Peter A. M. van Hoof , Florian Kerber , Stefan Kimeswenger , Don L. Pollacco , Aneurin Evans , José A. Lopéz , Myfanwy Bryce , Stewart P. S. Eyres , Mikako Matsuura Science 08 Apr 2005 : 231-233 An extinguished star was seen to reignite explosively, producing large amounts of new elements unexpectedly rapidly, perhaps because mixing in the star was suppressed. ASTR 1303: STELLAR ASTRONOMY CLASS LOCATION: (RGC1, room 328) COURSE NAME & SYNONYM: (43387PHYS 1312 Lec 005) CLASS TIME: (Tuesday/Thursday, Noon &ndash 1:20pm) OFFICE HOURS: TTh 10:50am &ndash 11:50am OFFICE LOCATION: RGC1 room 325 COURSE DESCRIPTION: Welcome! Stellar astronomy is a study of stars, galaxies, and the universe. It includes discussion of atomic spectra, nuclear energy, and astronomical tools (such as optical, radio, and other telescopes and image enhancers) as they provide knowledge about distant objects. Recent discoveries about quasars, black holes, and cosmology will be emphasized. The course prerequisites are MATD 0390 (Intermediate Algebra) or one year of high school algebra or the equivalent. One year of high school science is recommended, but not required. TEXT and Other Necessary Materials: Bring your course text Astronomy Today, 7 th Edition- Chaisson & McMillan and a calculator to each class session. INSTRUCTIONAL METHODOLOGY:This course is a lecture-based course which includes time for class discussions, demonstrations, student projects and/or activities guided by the instructor. COURSE RATIONALE: This course is an introduction to Stellar Astronomy, a college-level science course intended to help students fulfill degree requirements in science. Since our courses are intended for transfer to a four-year institution, they will be taught at the University level. COURSE GOALS and OBJECTIVES: Many students are attracted to astronomy because of its &ldquoshock and awe&rdquo power (i.e. vast distances and times, colorful events like supernovae and eclipses&hellip). Further, the daily media announces astounding new discoveries like exo-planets and traces of life forming elements aboard meteorites. Understanding the astrophysics behind these heady events will, I believe, enhance your appreciation of our Universe, and instill a lifelong interest in the subject area. At each lecture and throughout the formal course materials, explanations and insights to these topics will be evinced to aid your learning of this material. Further, the tests will ask probative questions to help us understand your successful learning of the &ldquoshock and awe of astronomy&rdquo. And lastly (but not the least) your participation in getting out under the wonderful Texas skies to actually participate in viewing the heavens will indelibly connect to you to our Universe. A more educationally oriented (less prosaic) set of objectives follows: Upon successful completion of this course, students will be able to: 1. Demonstrate knowledge of the basic laws of physics that pertain to the study of the stars and galaxies 2. Demonstrate knowledge of the basic properties of stars, and how those properties are determined 3. Demonstrate knowledge of the different stages in a star's development, including its birth, life, and death 4. Demonstrate knowledge of the nature of the expansion of the Universe, and what that expansion tells us about the past, present, and future of the Universe 5. Demonstrate knowledge of the scale of the Universe and how it is determined 1. Tests There will be three, non-comprehensive tests valued at 20% each covering a section of the course as outlined below. The exams will cover about four chapters each. There will be an optional comprehensive final given at the end of the semester. If you choose to take this final and then do better on it than on one of the previous exams, it will replace the lowest test grade. You must have taken all previous exams in order to take advantage of this option Let me iterate the optional comprehensive final may not be taken to replace a zero on anyone of the other scheduled tests. The tests will require you to analyze material emphasized in lecture and your textual readings. There will be mostly essay questions whose answers may bring into play: 1. Analyzing of diagrams, formulae, and some mathematical computations, 2. clearly written sentences which answer the question at hand will be necessary to score well, and 3. a cadre of facts germane to the question. These facts will be emphasized in the course lectures and will be of an appropriate number given the introductory nature of the course. 4. The same will be true for any synthesis type questions. The formal tools (mathematical computation, diagrams, formulae, etc.) will be from a limited set which have been explicated in the lectures and homework. The level of formalism required on tests is as per the requirements of the course, id est basic algebra. 2. Homework assignments There will be three homework assignments, one for each of the three sections of the course. Each assignment contributes 5% of the course grade. An assignment will be approximately five &lsquoproblems&rsquo in extent. Help for these assignments are available from the instructor during office hours and at tutoring labs located at all the major campuses of ACC. The problems will give you practice for the exams, extend and amplify the lecture material. They are due at the beginning of class on the day of the test for that section. 3. Observing activities These may include on and off campus telescopic and naked eye astronomical observing which are valued @ 15% of your course grade. You are required to attend one out of the half dozen or so scheduled. The schedule will be given in class. Note that it is best to attend the first available one that agrees with your schedule because each observation opportunity is weather dependent. A written report of your observations will be proffered for grading on the very next test day after the observing date. The first report will count toward the 15% above, and each additional one will count toward the extra credit part of your grade as discussed below. You will find these &lsquostar parties&rsquo essential in connecting to much of the material presented in the text and lecture. Having the warm eyeball on the subject matter will not only give you indelible insights into the physical universe but also will be very enjoyable. It has been my experience after teaching many years that most students consider this part of the course the real &ldquowow&rdquo of astronomy. 4. Class attendance / participation and extra credit possibilities Attendance will be taken at each lecture period. Your attendance and participation in class activities (exempli gratis, laboratory exercises, discussion projects, computational examples, etc) will account for 5% of your course grade. In my mind, your attendance in class is not only the most important marker for attaining the learning objectives of the course but also your participation in class is valuable for other students attaining those objectives through your questions and general discussion of the material which occurs during each class. Extra credit possibilities will be offered throughout the course and will make up 5% of your course grade. These &lsquoextra&rsquo assignments will give the student who wishes to dive more deeply into some particular areas (observing, internet research, mathematical problems, etc.). Students may pick from the &ldquosmorgasbord&rdquo of opportunities and need only complete &ldquo100 points&rdquo to obtain full credit in this category. This &ldquo100&rdquo point system (that is not overburdening) will be explained more fully as the course continues. It will be handed in with the other assignments, outlined above, at each test. A = 90-100, B = 80-89, C = 70-79, D = 60-69, F < 60 Grading Recap Three Exams (the last of which is not comprehensive) weighted @ 20 % each for a total of 60% toward your course grade Homework, which will include but is not limited to: short numerical problems, internet research activities and current event searches valued @ 15% of your course grade. Observing activities which may include on and off campus telescopic and naked eye astronomical observing @ 15% of your course grade Attendance & participation in class & extra credit assignments outside of class @ 10% of your course grade COURSE POLICIES: Withdrawals:-- Physical Sciences Department policy is that instructors will not withdraw students or grant incompletes except in the most extreme circumstances. If instructors institute an attendance requirement, they may withdraw students for excessive unexcused absences. In all circumstances, extensive documentation of reasons will be required. The instructor reserves the right to withdraw students who have more than four unexcused absences. The instructor may also withdraw students for failure to meet course objectives, but makes no commitment to do so. After the withdrawal date each semester, neither the student nor the instructor may initiate a withdrawal. The last day this semester for a student to withdraw from a 16 week course is Apr. 23 rd 2012. Students are responsible to initiate withdrawals by this date if they so choose. Incompletes: The grade of &ldquoI&rdquo (for incomplete) may be given by an instructor for a course in which a student was unable to complete all of the objectives for the passing grade. Incomplete grades will rarely be given, and only if the student has taken all exams, is passing, and has a personal tragedy occur after the last date to withdraw that prevents course completion. See the ACC catalog for more information on Incompletes. Attendanceis important, expected, and part of your grade as indicated above. The number one criterion for excellent, grade / learning outcomes in this course will be regular attendance during lectures. Attendance will be taken each day of class. The instructor reserves the right to withdraw students who have more than four unexcused absences. Scholastic Dishonesty:Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work. Academic work submitted by students shall be the result of their thought, research or self-expression. Academic work is defined as, but not limited to tests, quizzes, whether taken electronically or on paper projects, either individual or group classroom presentations, and homework. In my class no student should ever turn in work essentially identical to another. Academic Freedom: Institutions of higher education are conducted for the common good. The common good depends upon a search for truth and upon free expression. In this course the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions. 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In serious cases, disruptive behavior may lead to a student being withdrawn from the class. Matters of student disciple will be adjudicated by the instructor on a case-by-case basis, in conjunction with the Department Chair or Dean. Students may consult with the Office of Student Services or the Associate Dean at their campus on these matters. ACC's policy on student discipline can at http://www.austincc.edu/handbook/policies4.htm Students with Disabilities:Each ACC campus offers support services for students with documented physical or psychological disabilities. Students with disabilities must request reasonable accommodations through the Office for Students with Disabilities on the campus where they expect to take the majority of their classes. Students are encouraged to do these three weeks before the start of the semester. Safety:Health and safety are paramount values in science classrooms, laboratories and field activities. 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Contact me before the test (email or phone, if you can&rsquot find me in person) to avoid receiving a zero if there is an unavoidable emergency. The documentation requirement will still hold. The above policy holds for late homework as well. Course Calendar (May be modified but with proper notification to the students): The chapters below will be covered sequentially. For a fuller description of the content that will be emphasized in each chapter a required topics list is included after this calendar. In that list you will notice a significant dose of physics to be covered under &ldquoThe Fundamentals&rdquo. These topics will be folded into the lectures as they arise, and citations to the appropriate chapters in your text will be given during the lectures. ## Galaxies If you want to know the amount of time that has passed since a particular galaxy formed, you probably are not going to get a very precise answer. Just like globular clusters, galaxies are nearly as old as the universe. Unlike globular clusters, they may evolve in rather complicated ways via interactions with their environments. For example, we know there are streams of "pristine," primordial gas (i.e. gas that has not been enriched with heavy elements by stars) falling into galaxies. At the same time, material is being ejected due to everything from stellar winds to supernovae to jets from supermassive black holes in the galaxies' centers. Moreover, galaxies may indeed merge, so it becomes unclear what counts as the "birth" of a particular galaxy. You could instead ask about the average ages of stars in a galaxy, or even in subsections of the galaxy. If there was a recent burst of star formation, there will be enough massive, hot, blue stars, making the overall light rather blue (as is often the case in spiral galaxies). If new stars haven't formed in a while, the massive ones will have died out, leaving just redder stars to dominate the integrated light. This is essentially the same procedure as for globular clusters, except we are projecting the temperature-luminosity points onto the temperature axis (weighted by luminosity). The only other catches are that • Star formation might have occurred over time, rather than a single burst, so you have to assume some model for this, possibly with a few adjustable parameters • You have to assume an initial mass function - a distribution of masses for newly formed stars - which is often posited to be the same for all conditions (an assumption we hope is not too wrong). On the other hand, if you just want to know "how long after the Big Bang was this galaxy in the state in which I currently see it?" then you really are in luck. If the galaxy is nearby enough to get a good spectrum, one can identify narrow spectral features that correspond to known transitions. The redshift$z$is defined by$ 1 + z = frac>>. $Assuming the redshift is dominated by cosmological expansion rather than the peculiar motion of us or the other galaxy, then the age of the universe when the light was emitted is given by$ t_mathrm = t_0 - frac<1> int_0^z frac<1><(1+z')sqrt+Omega_,0>(1+z')^3>> mathrmz'. $The cosmological parameters$t_0$(the current age of the universe),$H_0$,$Omega_$, and$Omega_,0>$are known from various sources, such as the CMB, the clustering of galaxies, or supernova surveys. In cases of extremely distant or faint galaxies, spectra might not be an option. One can do a similar but rougher analysis using different photometric bands to try to reconstruct the redshift, but this depends on having some a priori knowledge of what the overall spectrum looks like. One can thus get "ages" for individual galaxies. Plotting distributions of galaxy properties as functions of age shows a complicated history of how galaxies have changed over billions of years. 1 See for instance MESA, the core files of which consist of roughly$100<,>000$lines of code. 2 There is easily a factor of$10^4\$ between the main sequence lifetimes of the smallest versus the largest stars.

I'll add a few more options for getting the ages of stars, beyond the HR diagram technique mentioned in Chris White's answer.

If you can get a R=50,000 optical spectrum of a star with decent signal to noise ratio will quite easily give you the temperature (to 100K), surface gravity (to 0.1 dex) and metallicity (to 0.05 dex), plus a host of other elemental abundances (including Li) to precisions of about 0.1 dex.

Gravity: You can then plot the star in the log g (gravity) vs Teff plane and compare it with theoretical isochrones appropriate for the star's metallicity. This is the best way to estimate the age of a solar-type (or more massive) star, even if you don't have a distance and is the most-used method. How well this works and how unambiguously depends on the star's evolutionary stage. For stars like the Sun, you get an age precision of maybe 2 Gyr. For lower mass stars, well they hardly move whilst on the main sequence in 10Gyr, so you can't estimate the age like this unless you know the object is a pre-main sequence star. In young, pre-main sequence stars that are contracting towards the main sequence, then the gravity as measured from the spectrum is age-dependent.

Lithium Abundances: You can look at the Li abundance. Li abundance falls with age for solar-mass stars and below. This would work quite well for sun-like stars from ages of 0.3-2Gyr and for K-type stars from 0.1-0.5 Gyr and for M-dwarfs between 0.02-0.1 Gyr - i.e. in the range where Li starts to be depleted in the photosphere and where is is all gone. Typical precision might be a factor of two. A high Li abundance in K and M dwarfs usually indicates a pre main sequence status.

Rotation: If you can obtain a rotation rate from the broadening of the spectral lines or from rotational modulation, then you can use Gyrochronology, which works because the rotation rates of stars are time-dependent. Again, the applicability varies with mass, but in the opposite way to Li. M-dwarfs maintain fast rotation for longer than G-dwarfs. Of course you have the problem of uncertain inclination angle if all you have rotational broadening from a spectrum.

Magnetic Activity: That brings us to activity-age relations. You can measure the levels of chromospheric magnetic activity in the spectrum or coronal X-ray activity. Then combine this with empirical relationships between activity and age (e.g. Mamajek & Hillenbrand 2008). This can give you the age to a factor of two for stars older than a few hundred Myr. Its poorly calibrated for stars less massive than the Sun though. But in general a more active M-dwarf is likely to be younger than a less active M dwarf. It should certainly distinguish between a 2Gyr and 8Gyr M dwarf.

Kinematics: If you measure the line of sight velocity from your spectrum, this can give you at least a probabilistic idea of what stellar population the star belongs to. Higher velocities would tend to indicate an older star. This would work better if you had the proper motion (and preferably the distance too, roll on the Gaia results). If you have 3D kinematics for a young star you might be able to project its motion back in the Galactic potential and work out how long it has been travelling from it's birth-place. This has been done for a few objects (e.g. runaway OB stars) to work out how long they have been travelling 9which of course is a lower limit to their age).

Metallicity: In a probabilistic sense, low metallicity stars are older than high metallicity stars. If you were talking about stars as old as 8Gyr, these would be quite likely to have low metallicity.

Radioisotope dating: As an add-on I'll also mention radio-isotope dating. If you can measure the abundances of isotopes of U and Th with long half lives and then make some guess at their initial abundances using other r-process elements as a guide then you get an age estimate - "nucleocosmochronology". Currently, these are very inaccurate - factors of 2 differences for the same star depending on what methods you adopt.

In summary. If you are talking about G-dwarfs you can get ages to precisions of about 20% using log g and Teff from the spectrum. For M dwarfs, unless you are fortunate enough to be looking at a young PMS object with Li, then your precision is going to be a few Gyr at best for an individual object, though combining probabilistic estimates from activity, metallicity and kinematics simultaneously might narrow this a bit.