# Hayashi track

The Hayashi track is a luminosity–temperature relationship obeyed by infant stars of less than 3 M in the pre-main-sequence phase (PMS phase) of stellar evolution. It is named after Japanese astrophysicist Chushiro Hayashi. On the Hertzsprung–Russell diagram, which plots luminosity against temperature, the track is a nearly vertical curve. After a protostar ends its phase of rapid contraction and becomes a T Tauri star, it is extremely luminous. The star continues to contract, but much more slowly. While slowly contracting, the star follows the Hayashi track downwards, becoming several times less luminous but staying at roughly the same surface temperature, until either a radiative zone develops, at which point the star starts following the Henyey track, or nuclear fusion begins, marking its entry onto the main sequence.

The shape and position of the Hayashi track on the Hertzsprung–Russell diagram depends on the star's mass and chemical composition. For solar-mass stars, the track lies at a temperature of roughly 4000 K. Stars on the track are nearly fully convective and have their opacity dominated by hydrogen ions. Stars less than 0.5 M are fully convective even on the main sequence, but their opacity begins to be dominated by Kramers' opacity law after nuclear fusion begins, thus moving them off the Hayashi track. Stars between 0.5 and 3 M develop a radiative zone prior to reaching the main sequence. Stars between 3 and 10 M are fully radiative at the beginning of the pre-main-sequence. Even heavier stars are born onto the main sequence, with no PMS evolution.[1]

At an end of a low- or intermediate-mass star's life, the star follows an analogue of the Hayashi track, but in reverse—it increases in luminosity, expands, and stays at roughly the same temperature, eventually becoming a red giant.

Stellar evolution tracks (blue lines) for the pre-main-sequence. The nearly vertical curves are Hayashi tracks.
Low-mass stars have nearly vertical evolution tracks until they arrive on the main sequence. For more-massive stars, the Hayashi track bends to the left into the Henyey track. Even more-massive stars are born directly onto the Henyey track.
The end (leftmost point) of every track is labeled with the star's mass in solar masses (M), and represents its position on the main sequence. The red curves labeled in years are isochrones at the given ages. In other words, stars ${\displaystyle 10^{5}}$ years old lie along the curve labeled ${\displaystyle 10^{5}}$, and similarly for the other 3 isochrones.

## History

In 1961, Professor Chushiro Hayashi published two papers[2][3] that led to the concept of the pre-main-sequence and form the basis of the modern understanding of early stellar evolution. Hayashi realized that the existing model, in which stars are assumed to be in radiative equilibrium with no substantial convection zone, cannot explain the shape of the red giant branch.[4] He therefore replaced the model by including the effects of thick convection zones on a star's interior.

A few years prior, Osterbrock proposed deep convection zones with efficient convection, analyzing them using the opacity of H- ions (the dominant opacity source in cool atmospheres) in temperatures below 5000K. However, the earliest numerical models of Sun-like stars did not follow up on this work and continued to assume radiative equilibrium.[1]

In his 1961 papers, Hayashi showed that the convective envelope of a star is determined by:

${\displaystyle E=4\pi G^{3/2}(\mu H/k)^{5/2}M^{1/2}R^{3/2}P/T^{5/2}}$

where E is unitless, and not the energy. Modelling stars as polytropes with index 3/2—in other words, assuming they follow a pressure-density relationship of ${\displaystyle P=K\rho ^{5/3}}$—he found that E=45 is the maximum for a quasistatic star. If a star is not contracting rapidly, E=45 defines a curve on the HR diagram, to the right of which the star cannot exist. He then computed the evolutionary tracks and isochrones (luminosity-temperature distributions of stars at a given age) for a variety of stellar masses and noted that NGC2264, a very young star cluster, fits the isochrones well. In particular, he calculated much lower ages for solar-type stars in NGC2264 and predicted that these stars were rapidly contracting T Tauri stars.

In 1962, Hayashi published a 183-page review of stellar evolution. Here, he discussed the evolution of stars born in the forbidden region. These stars rapidly contract due to gravity before settling to a quasistatic, fully convective state on the Hayashi tracks.

In 1965, numerical models by Iben and Ezer & Cameron realistically simulated pre-main-sequence evolution, including the Henyey track that stars follow after leaving the Hayashi track. These standard PMS tracks can still be found in textbooks on stellar evolution.

## Forbidden zone and Hayashi limit

The forbidden zone is the region on the HR diagram to the right of the Hayashi track where no star can be in hydrostatic equilibrium, even those that are partially or fully radiative. Newborn protostars start out in this zone, but are not in hydrostatic equilibrium and will rapidly move towards the Hayashi track.

Because stars emit light via blackbody radiation, the power per unit surface area they emit is given by the Stefan-Boltzmann law:

${\displaystyle j^{\star }=\sigma T^{4}}$

The star's luminosity is therefore given by:

${\displaystyle L=4\pi R^{2}\sigma T^{4}}$

For a given L, a lower temperature implies a larger radius, and vice versa. Thus, the Hayashi track separates the HR diagram into two regions: the allowed region to the left, with high temperatures and smaller radii for each luminosity, and the forbidden region to the right, with lower temperatures and correspondingly higher radii. The Hayashi limit can refer to either the lower bound in temperature or the upper bound on radius defined by the Hayashi track.

The region to the right is forbidden because it can be shown that a star in the region must have a temperature gradient of:

${\displaystyle {\frac {d\ln T}{d\ln P}}>0.4}$

where ${\displaystyle {\frac {d\ln T}{d\ln P}}=0.4}$ for a monatomic ideal gas undergoing adiabatic expansion or contraction. A temperature gradient greater than 0.4 is therefore called superadiabatic.

Consider a star with a superadiabatic gradient. Imagine a parcel of gas that starts at radial position r, but moves upwards to r+dr in a sufficiently short time that it exchanges negligible heat with its surroundings—in other words, the process is adiabatic. The pressure of the surroundings, as well as that of the parcel, decreases by some amount dP. The parcel's temperature changes by ${\displaystyle dT=0.4{\frac {T}{P}}dP}$. The temperature of the surroundings also decreases, but by some amount dT' that is greater than dT. The parcel therefore ends up being hotter than its surroundings. Since the ideal gas law can be written ${\displaystyle P={\frac {\rho RT}{\mu }}}$, a higher temperature implies a lower density at the same pressure. The parcel is therefore also less dense than its surroundings. This will cause it to rise even more, and the parcel will become even less dense than its new surroundings.

Clearly, this situation is not stable. In fact, a superadiabatic gradient causes convection. Convection tends to lower the temperature gradient because the rising parcel of gas will eventually be dispersed, dumping its excess thermal and kinetic energy into its surroundings and heating up said surroundings. In stars, the convection process is known to be highly efficient, with a typical ${\displaystyle {\frac {d\ln T}{d\ln P}}}$ that only exceeds the adiabatic gradient by 1 part in 10 million.[5]

If a star is placed in the forbidden zone, with a temperature gradient much greater than 0.4, it will experience rapid convection that brings the gradient down. Since this convection will drastically change the star's pressure and temperature distribution, the star is not in hydrostatic equilibrium, and will contract until it is.

A star far to the left of the Hayashi track has a temperature gradient smaller than adiabatic. This means that if a parcel of gas rises a tiny bit, it will be more dense than its surroundings and sink back to where it came from. Convection therefore does not occur, and almost all energy output is carried radiatively.

## Star formation

Stars form when small regions of a giant molecular cloud collapse under their own gravity, becoming protostars. The collapse releases gravitational energy, which heats up the protostar. This process occurs on the free-fall timescale, which is roughly 100,000 years for solar-mass protostars, and ends when the protostar reaches approximately 4000 K. This is known as the Hayashi boundary, and at this point, the protostar is on the Hayashi track. At this point, they are known as T Tauri stars and continue to contract, but much more slowly. As they contract, they decrease in luminosity because less surface area becomes available for emitting light. The Hayashi track gives the resulting change in temperature, which will be minimal compared to the change in luminosity because the Hayashi track is nearly vertical. In other words, on the HR diagram, a T Tauri star starts out on the Hayashi track with a high luminosity and moves downward along the track as time passes.

The Hayashi track describes a fully convective star. This is a good approximation for very young pre-main-sequence stars they are still cool and highly opaque, so that radiative transport is insufficient to carry away the generated energy and convection must occur. Stars less massive than 0.5 M remain fully convective, and therefore remain on the Hayashi track, throughout their pre-main-sequence stage, joining the main sequence at the bottom of the Hayashi track. Stars heavier than 0.5 M have higher interior temperatures, which decreases their central opacity and allows radiation to carry away large amounts of energy. This allows a radiative zone to develop around the star's core. The star is then no longer on the Hayashi track, and experiences a period of rapidly increasing temperature at nearly constant luminosity. This is called the Henyey track, and ends when temperatures are high enough to ignite hydrogen fusion in the core. The star is then on the main sequence.

Lower-mass stars follow the Hayashi track until the track intersects with the main sequence, at which point hydrogen fusion begins and the star follows the main sequence. Even lower-mass 'stars' never achieve the conditions necessary to fuse hydrogen and become brown dwarfs.

## Derivation

The exact shape and position of the Hayashi track can only be computed numerically using computer models. Nevertheless, we can make an extremely crude analytical argument that captures most of the track's properties. The following derivation loosely follows that of Kippenhahn, Weigert, and Weiss in Stellar Structure and Evolution.[5]

In our simple model, a star is assumed to consist of a fully convective interior inside of a fully radiative atmosphere.

The convective interior is assumed to be an ideal monatomic gas with a perfectly adiabatic temperature gradient:

${\displaystyle {\frac {d\ln {T}}{d\ln {P}}}=0.4}$

This quantity is sometimes labelled ${\displaystyle \nabla }$. The following adiabatic equation therefore holds true for the entire interior:

${\displaystyle P^{1-\gamma }T^{\gamma }=C}$

where ${\displaystyle \gamma }$ is the adiabatic gamma, which is 5/3 for an ideal monatomic gas. The ideal gas law says:

${\displaystyle P=NkT/V}$
${\displaystyle ={\frac {\rho kT}{\mu H}}}$
${\displaystyle =({\frac {k\rho C}{\mu H}})^{\gamma }}$

where ${\displaystyle \mu }$ is the molecular weight per particle and H is (to a very good approximation) the mass of a hydrogen atom. This equation represents a polytrope of index 1.5, since a polytrope is defined by ${\displaystyle P=K\rho ^{1+1/n}}$, where n=1.5 is the polytropic index. Applying the equation to the center of the star gives: ${\displaystyle P_{c}=({\frac {k\rho _{c}C}{\mu H}})^{\gamma }}$ We can solve for C:

${\displaystyle C={\frac {\mu HP_{c}^{1/\gamma }}{\rho _{c}k}}}$

But for any polytrope, ${\displaystyle P_{c}=W_{n}{\frac {GM^{2}}{R^{4}}}}$, ${\displaystyle \rho _{c}=K_{n}\rho _{avg}}$, and ${\displaystyle R^{\frac {3-n}{n}}M^{\frac {n-1}{n}}={\frac {K}{GN_{n}}}}$. ${\displaystyle W_{n},K_{n},N_{n},}$ and K are all constants independent of pressure and density, and the average density is defined as ${\displaystyle \rho _{avg}\equiv {\frac {M}{4/3\pi R^{3}}}}$. Plugging all 3 equations into the equation for C, we have:

${\displaystyle C\sim M^{2-\gamma }R^{3\gamma -4}}$

where all multiplicative constants have been ignored. Recall that our original definition of C was:

${\displaystyle P^{1-\gamma }T^{\gamma }=C}$

We therefore have, for any star of mass M and radius R:

${\displaystyle P^{1-\gamma }T^{\gamma }\sim M^{2-\gamma }R^{3\gamma -4}}$

${\displaystyle \ln P={\frac {2-\gamma }{1-\gamma }}\ln M+{\frac {3\gamma -4}{1-\gamma }}\ln R-\gamma \ln T}$

(1)

We need another relationship between P, T, M, and R, in order to eliminate P. This relationship will come from the atmosphere model.

The atmosphere is assumed to be thin, with average opacity k. Opacity is defined to be optical depth divided by density. Thus, by definition, the optical depth of the stellar surface, also called the photosphere, is:

${\displaystyle {\frac {d\tau }{dr}}=k\rho }$
${\displaystyle \tau =\int _{R}^{\infty }k\rho dr}$
${\displaystyle =k\int _{R}^{\infty }\rho dr}$

where R is the stellar radius, also known as the position of the photosphere. The pressure at the surface is:

${\displaystyle P_{0}=\int _{R}^{\infty }g\rho dr}$
${\displaystyle ={\frac {GM}{R^{2}}}\int _{R}^{\infty }\rho dr}$
${\displaystyle ={\frac {GM\tau }{kR^{2}}}}$

The optical depth at the photosphere turns out to be ${\displaystyle \tau =2/3}$. By definition, the temperature of the photosphere is ${\displaystyle T=T_{eff}}$ where effective temperature is given by ${\displaystyle L=4\pi R^{2}T_{eff}^{4}}$. Therefore, the pressure is:

${\displaystyle P_{0}={\frac {GM}{R^{2}}}{\frac {2}{3k}}}$

We can approximate the opacity to be:

${\displaystyle k=k_{0}P^{a}T^{b}}$

where a=1, b=3. Plugging this into the pressure equation, we get:

${\displaystyle P_{0}=const({\frac {M}{R^{2}T_{eff}^{b}}})^{\frac {1}{a+1}}}$

${\displaystyle \ln P_{0}=\ln {const}+{\frac {1}{a+1}}(\ln {M}-2\ln {R}-b\ln {T_{eff}})}$

(2)

Finally, we need to eliminate R and introduce L, the luminosity. This can be done with the equation:

${\displaystyle L=4\pi R^{2}\sigma T_{eff}^{4}}$

${\displaystyle \ln {R}=0.5\ln {L}-2\ln {T_{eff}}+const}$

(3)

Equation 1 and 2 can now be combined by setting ${\displaystyle T=T_{eff}}$ and ${\displaystyle P=P_{0}}$ in Equation 1, then eliminating ${\displaystyle P_{0}}$. R can be eliminated using Equation 3. After some algebra, and after setting ${\displaystyle \gamma =5/3}$, we get:

${\displaystyle \ln {T_{eff}}=A\ln {L}+B\ln {M}+const}$

where

${\displaystyle A={\frac {0.75a-0.25}{5.5a+b+1.5}}}$
${\displaystyle B={\frac {0.5a+1.5}{5.5a+b+1.5}}}$

In cool stellar atmospheres (T < 5000 K) like those of newborn stars, the dominant source of opacity is the H- ion, for which ${\displaystyle a\approx 1}$ and ${\displaystyle b\approx 3}$, we get ${\displaystyle A=0.05}$ and ${\displaystyle B=0.2}$.

Since A is much smaller than 1, the Hayashi track is extremely steep: if the luminosity changes by a factor of 2, the temperature only changes by 4 percent. The fact that B is positive indicates that the Hayashi track shifts left on the HR diagram, towards higher temperatures, as mass increases. Although this model is extremely crude, these qualitative observations are fully supported by numerical simulations.

At high temperatures, the atmosphere's opacity begins to be dominated by Kramers' opacity law instead of the H- ion, with a=1 and b=-4.5 In that case, A=0.2 in our crude model, far higher than 0.05, and the star is no longer on the Hayashi track.

In Stellar Interiors, Hansen, Kawaler, and Trimble go through a similar derivation without neglecting multiplicative constants,[6] and arrived at:

${\displaystyle T_{eff}=(2600K)\mu ^{13/51}({\frac {M}{M_{\odot }}})^{7/51}({\frac {L}{L_{\odot }}})^{1/102}}$

where ${\displaystyle \mu }$ is the molecular weight per particle. The authors note that the coefficient of 2600K is too low—it should be around 4000K—but this equation nevertheless shows that temperature is nearly independent of luminosity.

## Numerical results

Hayashi tracks of a 0.8 M star with helium mass fraction 0.245, for 3 different metallicities

The diagram at the top of this article shows numerically computed stellar evolution tracks for various masses. The vertical portions of each track is the Hayashi track. The endpoints of each track lie on the main sequence. The horizontal segments for higher-mass stars show the Henyey track.

It is approximately true that:

${\displaystyle {\frac {\partial \ln {T_{eff}}}{\partial \ln {M}}}\approx 0.1}$.

The diagram to the right shows how Hayashi tracks change with changes in chemical composition. Z is the star's metallicity, the mass fraction not accounted for by hydrogen or helium. For any given hydrogen mass fraction, increasing Z leads to increasing molecular weight. The dependence of temperature on molecular weight is extremely steep—it is approximately

${\displaystyle {\frac {\partial \ln {T_{eff}}}{\partial \ln {\mu }}}\approx -26}$.

Decreasing Z by a factor of 10 shifts the track right, changing ${\displaystyle \ln {T_{eff}}}$ by about 0.05.

Chemical composition affects the Hayashi track in a few ways. The track depends strongly on the atmosphere's opacity, and this opacity is dominated by the H- ion. The abundance of the H- ion is proportional to the density of free electrons, which, in turn, is higher if there are more metals because metals are easier to ionize than hydrogen or helium.

## Observational status

The young star cluster NGC 2264, with a large number of T Tauri stars contracting towards the main sequence. The solid line represents the main sequence, while the two lines above that are the ${\displaystyle 10^{6.5}}$ yr (upper) and ${\displaystyle 10^{6.7}}$ yr (lower) isochrones.

Observational evidence of the Hayashi track comes from color-magnitude plots—the observational equivalent of HR diagrams—of young star clusters.[1] For Hayashi, NGC 2264 provided the first evidence of a population of contracting stars. In 2012, data from NGC 2264 was re-analyzed to account for dust reddening and extinction. The resulting color-magnitude plot is shown at right.

In the upper diagram, the isochrones are curves along which stars of a certain age are expected to lie, assuming that all stars evolve along the Hayashi track. An isochrone is created by taking stars of every conceivable mass, evolving them forwards to the same age, and plotting all of them on the color-magnitude diagram. Most of the stars in NGC 2264 are already on the main sequence (black line), but a substantial population lies between the isochrones for 3.2 million and 5 million years, indicating that the cluster is 3.2-5 million years old and a large population of T Tauri stars is still on their respective Hayashi tracks. Similar results have been obtained for NGC 6530, IC 5146, and NGC 6611.[1]

The numbered curves show the Hayashi tracks of stars of that mass (in solar masses). The small circles represent observational data of T Tauri stars. The bold curve to the right is the birthline, above which few stars exist.

The lower diagram shows Hayashi tracks for various masses, along with T Tauri observations collected from a variety of sources. Note the bold curve to the right, representing a stellar birthline. Even though some Hayashi tracks theoretically extend above the birthline, few stars are above it. In effect, stars are 'born' onto the birthline before evolving downwards along their respective Hayashi tracks.

The birthline exists because stars formed from overdense cores of giant molecular clouds in an inside-out manner.[4] That is, a small central region first collapses in on itself while the outer shell is still nearly static. The outer envelope then accretes onto the central protostar. Before the accretion is over, the protostar is hidden from view, and therefore not plotted on the color-magnitude diagram. When the envelope finishes accreting, the star is revealed and appears on the birthline.

## References

1. ^ a b c d Palla, Francesco (2012). "1961–2011: Fifty years of Hayashi tracks": 22–29. doi:10.1063/1.4754323. ISSN 0094-243X.
2. ^ Hayashi, C. (1961). "Stellar evolution in early phases of gravitational contraction". Publ. Astron. Soc. Jpn. 13: 450–452. Bibcode:1961PASJ...13..450H.
3. ^ Hayashi, C. (1961). "The Outer Envelope of Giant Stars with Surface Convection Zone". Publ. Astron. Soc. Jpn. 13: 442–449. Bibcode:1961PASJ...13..450H.
4. ^ a b Stahler, Steven W. (1988). "Understanding young stars - A history". Publications of the Astronomical Society of the Pacific. 100: 1474. Bibcode:1988PASP..100.1474S. doi:10.1086/132352. ISSN 0004-6280.
5. ^ a b Stellar structure and evolution. New York: Springer. 2012. pp. 271–282. ISBN 978-3-642-30255-8.
6. ^ Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia. (2004). Stellar interiors : physical principles, structure, and evolution. New York: Springer. pp. 367–374. ISBN 978-0-387-20089-7.
Bright giant

The luminosity class II in the Yerkes spectral classification is given to bright giants. These are stars which straddle the boundary between ordinary giants and supergiants, based on the appearance of their spectra.

CN star

A CN star is a star with strong cyanogen bands in its spectrum. Cyanogen is a simple molecule of one carbon atom and one nitrogen atom, with absorption bands around 388.9 and 421.6 nm. This group of stars was first noticed by Nancy G. Roman who called them 4150 stars.

Convection zone

A convection zone, convective zone or convective region of a star is a layer which is unstable to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation and conduction.

Stellar convection consists of mass movement of plasma within the star which usually forms a circular convection current with the heated plasma ascending and the cooled plasma descending.

The Schwarzschild criterion expresses the conditions under which a region of a star is unstable to convection. A parcel of gas that rises slightly will find itself in an environment of lower pressure than the one it came from. As a result, the parcel will expand and cool. If the rising parcel cools to a lower temperature than its new surroundings, so that it has a higher density than the surrounding gas, then its lack of buoyancy will cause it to sink back to where it came from. However, if the temperature gradient is steep enough (i. e. the temperature changes rapidly with distance from the center of the star), or if the gas has a very high heat capacity (i. e. its temperature changes relatively slowly as it expands) then the rising parcel of gas will remain warmer and less dense than its new surroundings even after expanding and cooling. Its buoyancy will then cause it to continue to rise. The region of the star in which this happens is the convection zone.

Henyey track

The Henyey track is a path taken by pre-main-sequence stars with masses >0.5 Solar mass in the Hertzsprung–Russell diagram after the end of Hayashi track. The astronomer Louis G. Henyey and his colleagues in the 1950s, showed that the pre-main-sequence star can remain in radiative equilibrium throughout some period of its contraction to the main sequence.

The Henyey track is characterized by a slow collapse in near hydrostatic equilibrium. They are approaching the main sequence almost horizontally in the Hertzsprung–Russell diagram (i.e. the luminosity remains almost constant).

Infrared dark cloud

An infrared dark cloud (IRDC) is a cold, dense region of a giant molecular cloud. They can be seen in silhouette against the bright diffuse mid-infrared emission from the galactic plane.

A lead star is a low-metallicity star with an overabundance of lead and bismuth as compared to other products of the S-process.

Photometric-standard star

Photometric-standard stars are a series of stars that have had their light output in various passbands of photometric system measured very carefully. Other objects can be observed using CCD cameras or photoelectric photometers connected to a telescope, and the flux, or amount of light received, can be compared to a photometric-standard star to determine the exact brightness, or stellar magnitude, of the object.A current set of photometric-standard stars for UBVRI photometry was published by Arlo U. Landolt in 1992 in the Astronomical Journal.

Photosphere

The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/phos, photos meaning "light" and σφαῖρα/sphaira meaning "sphere", in reference to it being a spherical surface that is perceived to emit light. It extends into a star's surface until the plasma becomes opaque, equivalent to an optical depth of approximately 2/3, or equivalently, a depth from which 50% of light will escape without being scattered.

In other words, a photosphere is the deepest region of a luminous object, usually a star, that is transparent to photons of certain wavelengths.

Pre-main-sequence star

A pre-main-sequence star (also known as a PMS star and PMS object) is a star in the stage when it has not yet reached the main sequence. Earlier in its life, the object is a protostar that grows by acquiring mass from its surrounding envelope of interstellar dust and gas. After the protostar blows away this envelope, it is optically visible, and appears on the stellar birthline in the Hertzsprung-Russell diagram. At this point, the star has acquired nearly all of its mass but has not yet started hydrogen burning (i.e. nuclear fusion of hydrogen). The star then contracts, its internal temperature rising until it begins hydrogen burning on the zero age main sequence. This period of contraction is the pre-main sequence stage. An observed PMS object can either be a T Tauri star, if it has fewer than 2 solar masses (M☉), or else a Herbig Ae/Be star, if it has 2 to 8 M☉. Yet more massive stars have no pre-main-sequence stage because they contract too quickly as protostars. By the time they become visible, the hydrogen in their centers is already fusing and they are main-sequence objects.

The energy source of PMS objects is gravitational contraction, as opposed to hydrogen burning in main-sequence stars. In the Hertzsprung–Russell diagram, pre-main-sequence stars with more than 0.5 M☉ first move vertically downward along Hayashi tracks, then leftward and horizontally along Henyey tracks, until they finally halt at the main sequence. Pre-main-sequence stars with less than 0.5 M☉ contract vertically along the Hayashi track for their entire evolution.

PMS stars can be differentiated empirically from main-sequence stars by using stellar spectra to measure their surface gravity. A PMS object has a larger radius than a main-sequence star with the same stellar mass and thus has a lower surface gravity. Although they are optically visible, PMS objects are rare relative to those on the main sequence, because their contraction lasts for only 1 percent of the time required for hydrogen fusion. During the early portion of the PMS stage, most stars have circumstellar disks, which are the sites of planet formation.

Q star

A Q-Star, also known as a grey hole, is a hypothetical type of a compact, heavy neutron star with an exotic state of matter. The Q stands for a conserved particle number. A Q-Star may be mistaken for a stellar black hole.

Star formation

Star formation is the process by which dense regions within molecular clouds in interstellar space, sometimes referred to as "stellar nurseries" or "star-forming regions", collapse and form stars. As a branch of astronomy, star formation includes the study of the interstellar medium (ISM) and giant molecular clouds (GMC) as precursors to the star formation process, and the study of protostars and young stellar objects as its immediate products. It is closely related to planet formation, another branch of astronomy. Star formation theory, as well as accounting for the formation of a single star, must also account for the statistics of binary stars and the initial mass function. Most stars do not form in isolation but as part of a group of stars referred as star clusters or stellar associations.

Starfield (astronomy)

A starfield refers to a set of stars visible in an arbitrarily-sized field of view, usually in the context of some region of interest within the celestial sphere. For example: the starfield surrounding the stars Betelgeuse and Rigel could be defined as encompassing some or all of the Orion constellation.

Stellar atmosphere

The stellar atmosphere is the outer region of the volume of a star, lying above the stellar core, radiation zone and convection zone.

Stellar isochrone

In stellar evolution, an isochrone is a curve on the Hertzsprung-Russell diagram, representing a population of stars of the same age.The Hertzsprung-Russell diagram plots a star's luminosity against its temperature, or equivalently, its color. Stars change their positions on the HR diagram throughout their life. Newborn stars of low or intermediate mass are born cold but extremely luminous. They contract and dim along the Hayashi track, decreasing in luminosity but staying at roughly the same temperature, until reaching the main sequence directly or by passing through the Henyey track. Stars evolve relatively slowly along the main sequence as they fuse hydrogen, and after the vast majority of their lifespan, all but the least massive stars become giants. They then evolve quickly towards their stellar endpoints: white dwarfs, neutron stars, or black holes.

Isochrones can be used to date open clusters because their members all have roughly the same age. If the initial mass function of the open cluster is known, isochrones can be calculated at any age by taking every star in the initial population, using numerical simulations to evolve it forwards to the desired age, and plotting the star's luminosity and magnitude on the HR diagram. The resulting curve is an isochrone, which can be compared against the observational color-magnitude diagram to determine how well they match. If they match well, the assumed age of the isochrone is close to the actual age of the cluster.

Stellar mass

Stellar mass is a phrase that is used by astronomers to describe the mass of a star. It is usually enumerated in terms of the Sun's mass as a proportion of a solar mass (M☉). Hence, the bright star Sirius has around 2.02 M☉. A star's mass will vary over its lifetime as additional mass becomes accreted, such as from a companion star, or mass is ejected with the stellar wind or pulsational behavior.

Supernova impostor

Supernova impostors are stellar explosions that appear at first to be a supernova but do not destroy their progenitor stars. As such, they are a class of extra-powerful novae. They are also known as Type V supernovae, Eta Carinae analogs, and giant eruptions of luminous blue variables (LBV).

T Tauri star

T Tauri stars (TTS) are a class of variable stars associated with youth. They are less than about ten million years old. This class is named after the prototype, T Tauri, a young star in the Taurus star-forming region. They are found near molecular clouds and identified by their optical variability and strong chromospheric lines. T Tauri stars are pre-main-sequence stars in the process of contracting to the main sequence along the Hayashi track, a luminosity–temperature relationship obeyed by infant stars of less than 3 solar masses (M☉) in the pre-main-sequence phase of stellar evolution. It ends when a star of 0.5 M☉ develops a radiative zone, or when a larger star commences nuclear fusion on the main sequence.

Timeline of stellar astronomy

Timeline of stellar astronomy

2300 BC — First great period of star naming in China.

134 BC — Hipparchus creates the magnitude scale of stellar apparent luminosities

185 AD — Chinese astronomers become the first to observe a supernova, the SN 185

964 — Abd al-Rahman al-Sufi (Azophi) writes the Book of Fixed Stars, in which he makes the first recorded observations of the Andromeda Galaxy and the Large Magellanic Cloud, and lists numerous stars with their positions, magnitudes, brightness, and colour, and gives drawings for each constellation

1000s (decade) — The Persian astronomer, Abū Rayhān al-Bīrūnī, describes the Milky Way galaxy as a collection of numerous nebulous stars

1006 — Ali ibn Ridwan and Chinese astronomers observe the SN 1006, the brightest stellar event ever recorded

1054 — Chinese and Arab astronomers observe the SN 1054, responsible for the creation of the Crab Nebula, the only nebula whose creation was observed

1181 — Chinese astronomers observe the SN 1181 supernova

1580 — Taqi al-Din measures the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using an "observational clock" he invented and which he described as "a mechanical clock with three dials which show the hours, the minutes, and the seconds"

1596 — David Fabricius notices that Mira's brightness varies

1672 — Geminiano Montanari notices that Algol's brightness varies

1686 — Gottfried Kirch notices that Chi Cygni's brightness varies

1718 — Edmund Halley discovers stellar proper motions by comparing his astrometric measurements with those of the Greeks

1782 — John Goodricke notices that the brightness variations of Algol are periodic and proposes that it is partially eclipsed by a body moving around it

1784 — Edward Pigott discovers the first Cepheid variable star

1838 — Thomas Henderson, Friedrich Struve, and Friedrich Bessel measure stellar parallaxes

1844 — Friedrich Bessel explains the wobbling motions of Sirius and Procyon by suggesting that these stars have dark companions

1906 — Arthur Eddington begins his statistical study of stellar motions

1908 — Henrietta Leavitt discovers the Cepheid period-luminosity relation

1910 — Ejnar Hertzsprung and Henry Norris Russell study the relation between magnitudes and spectral types of stars

1924 — Arthur Eddington develops the main sequence mass-luminosity relationship

1929 — George Gamow proposes hydrogen fusion as the energy source for stars

1938 — Hans Bethe and Carl von Weizsäcker detail the proton-proton chain and CNO cycle in stars

1939 — Rupert Wildt realizes the importance of the negative hydrogen ion for stellar opacity

1952 — Walter Baade distinguishes between Cepheid I and Cepheid II variable stars

1953 — Fred Hoyle predicts a carbon-12 resonance to allow stellar triple alpha reactions at reasonable stellar interior temperatures

1961 — Chūshirō Hayashi publishes his work on the Hayashi track of fully convective stars

1963 — Fred Hoyle and William A. Fowler conceive the idea of supermassive stars

1964 — Subrahmanyan Chandrasekhar and Richard Feynman develop a general relativistic theory of stellar pulsations and show that supermassive stars are subject to a general relativistic instability

1967 — Eric Becklin and Gerry Neugebauer discover the Becklin-Neugebauer Object at 10 micrometres

1977 — (May 25) The Star Wars film is released and became a worldwide phenomenon, boosting interests in stellar systems.

2012 — (May 2) First visual proof of existence of black-holes. Suvi Gezari's team in Johns Hopkins University, using the Hawaiian telescope Pan-STARRS 1, publish images of a supermassive black hole 2.7 million light-years away swallowing a red giant.

Yellow giant

A yellow giant is a luminous giant star of low or intermediate mass (roughly 0.5–11 solar masses (M)) in a late phase of its stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature as low as 5,200-7500 K. The appearance of the yellow giant is from white to yellow, including the spectral types F and G. About 10.6 percent of all giant stars are yellow giants.

Formation
Evolution
Luminosity class
Spectral
classification
Remnants
Hypothetical
stars
Nucleosynthesis
Structure
Properties
Star systems
Earth-centric
observations
Lists
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