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Most stars are observed to be members of binary star systems , and the properties of those binaries are the result of the conditions in which they formed . A gas cloud must lose its angular momentum in order to collapse and form a star . The fragmentation of the cloud into multiple stars distribute some of that angular momentum . The primordial binaries transfer some angular momentum by gravitational interactions during close encounters with other stars in young stellar clusters . These interactions tend to split apart more widely separated ( soft ) binaries while causing hard binaries to become more tightly bound . This produce the separation of binaries into their two observed populations distributions .

Every star generate a stellar wind of particles that cause a continual outflow of gas into space . For most stars , the mass lost is negligible . The Sun lose 10 − 14 M ☉ every year , or about 0 @.@ 01 % of its total mass over its entire lifespan . However , very massive stars can lose 10 − 7 to 10 − 5 M ☉ each year , significantly affecting their evolution . Stars that begin with more than 50 M ☉ can lose over half their total mass while on the main sequence .

The time a star spend on the main sequence depend primarily on the amount of fuel it have and the rate at which it fuse it . The Sun 's is expected to live 10 billion ( 1010 ) years . Massive stars consume their fuel very rapidly and are short @-@ lived . Low mass stars consume their fuel very slowly . Stars less massive than 0 @.@ 25 M ☉ , called red dwarfs , are able to fuse nearly all of their mass while stars of about 1 M ☉ can only fuse about 10 % of their mass . The combination of their slow fuel @-@ consumption and relatively large usable fuel supply allow low mass stars to last about one trillion ( 1012 ) years ; the most extreme of 0 @.@ 08 M ☉ ) will last for about 12 trillion years . Red dwarfs became hotter and more luminous as they accumulate helium . When they eventually run out of hydrogen , they contract into a white dwarf and decline in temperature . However , since the lifespan of such stars is greater than the current age of the universe ( 13 @.@ 8 billion years ) , no stars under about 0 @.@ 85 M ☉ are expected to have moved off the main sequence .

Besides mass , the elements heavier than helium can play a significant role in the evolution of stars . Astronomers label all elements heavier than helium " metals " , and call the chemical concentration of these elements in a star , its metallicity . A star 's metallicity can influence the time the star take to burn its fuel , and control the formation of its magnetic fields , which affect the strength of its stellar wind . Older , population II stars have substantially less metallicity than the younger , population I star due to the composition of the molecular clouds from which they formed . Over time , such clouds become increasingly enriched in heavier elements as older stars die and shed portions of their atmospheres .

As stars of at least 0 @.@ 4 M ☉ exhaust their supply of hydrogen at their core , they start to fuse hydrogen in a shell outside the helium core . Their outer layers expand and cool greatly as they form a red giant . In about 5 billion years , when the Sun enter the helium burning phase , it will expand to a maximum radius of roughly 1 astronomical unit ( 150 million kilometres ) , 250 times its present size , and lose 30 % of its current mass .

As the hydrogen shell burning produce more helium , the core increases in mass and temperature . In a red giant of up to 2 @.@ 25 M ☉ , the mass of the helium core become degenerate prior to helium fusion . Finally , when the temperature increase sufficiently , helium fusion begin explosively in what is called a helium flash , and the star rapidly shrink in radius , increase its surface temperature , and moves to the horizontal branch of the HR diagram . For more massive stars , helium core fusion start before the core become degenerate , and the star spend some time in the red clump , slowly burning helium , before the outer convective envelope collapses and the star then move to the horizontal branch .

After the star have fused the helium of its core , the carbon product fuses producing a hot core with an outer shell of fusing helium . The star then follow an evolutionary path called the asymptotic giant branch ( AGB ) that parallel the other described red giant phase , but with a higher luminosity . The more massive AGB stars may undergo a brief period of carbon fusion before the core become degenerate .

The core contracts and the temperature and pressure rise enough to fuse carbon ( see Carbon burning process ) . This process continue , with the successive stages being fueled by neon ( see neon burning process ) , oxygen ( see oxygen burning process ) , and silicon ( see silicon burning process ) . Near the end of the star 's life , fusion continue along a series of onion @-@ layer shell within a massive star . Each shell fuse a different element , with the outermost shell fusing hydrogen ; the next shell fusing helium , and so forth .

The final stage occur when a massive star begin producing iron . Since iron nuclei are more tightly bound than any heavier nuclei , any fusion beyond iron do not produce a net release of energy . To a very limited degree such a process proceed , but it consume energy . Likewise , since they are more tightly bound than all lighter nuclei , such energy cannot be released by fission . In relatively old , very massive stars , a large core of inert iron will accumulate in the center of the star . The heavier elements in these stars can work their way to the surface , forming evolved objects known as Wolf @-@ Rayet stars that have a dense stellar wind which shed the outer atmosphere .

As a star 's core shrinks , the intensity of radiation from that surface increases , creating such radiation pressure on the outer shell of gas that it will push those layers away , forming a planetary nebula . If what remain after the outer atmosphere have been shed is less than 1 @.@ 4 M ☉ , it shrink to a relatively tiny object about the size of Earth , known as a white dwarf . White dwarfs lack the mass for further gravitational compression to take place . The electron @-@ degenerate matter inside a white dwarf is no longer a plasma , even though stars are generally referred to as being spheres of plasma . Eventually , white dwarfs fade into black dwarfs over a very long period of time .

In larger stars , fusion continue until the iron core have grown so large ( more than 1 @.@ 4 M ☉ ) that it can no longer support its own mass . This core will suddenly collapse as its electrons are driven into its protons , forming neutrons , neutrinos , and gamma rays in a burst of electron capture and inverse beta decay . The shockwave formed by this sudden collapse cause the rest of the star to explode in a supernova . Supernovae become so bright that they may briefly outshine the star 's entire home galaxy . When they occur within the Milky Way , supernovae have historically been observed by naked @-@ eye observers as " new stars " where none seemingly existed before .

A supernova explosion blow away the star 's outer layers , leaving a remnant such as the Crab Nebula . The core is compressed into a neutron star , which sometimes manifest itself as a pulsar or X @-@ ray burster . In the case of the largest stars , the remnant is a black hole greater than 4 M ☉ ) s . In a neutron star the matter is in a state known as neutron @-@ degenerate matter , with a more exotic form of degenerate matter , QCD matter , possibly present in the core . Within a black hole , the matter is in a state that is not currently understood .

The post – main @-@ sequence evolution of binary stars may be significantly different from the evolution of single stars of the same mass . If stars in a binary system are sufficiently close , when one of the stars expand to become a red giant it may overflow its Roche lobe , the region around a star where material is gravitationally bound to that star , leading to transfer of material to the other . When the Roche lobe is violated , a variety of phenomena can result , including contact binaries , common @-@ envelope binaries , cataclysmic variables , and type Ia supernovae .

It have been a long @-@ held assumption that the majority of stars occur in gravitationally bound , multiple @-@ star systems . This is particularly true for very massive O and B class stars , where 80 % of the stars are believed to be part of multiple @-@ star systems . The proportion of single star systems increases with decreasing star mass , so that only 25 % of red dwarfs are known to have stellar companions . As 85 % of all stars are red dwarfs , most stars in the Milky Way are likely single from birth .

Stars are not spread uniformly across the universe , but are normally grouped into galaxies along with interstellar gas and dust . A typical galaxy contain hundreds of billions of stars , and there are more than 100 billion ( 1011 ) galaxies in the observable universe . In 2010 , one estimate of the number of stars in the observable universe was 300 sextillion ( 3 × 1023 ) . While it is often believed that stars only exist within galaxies , intergalactic stars have been discovered .

Due to the relatively vast distances between stars outside the galactic nucleus , collisions between stars are thought to be rare . In denser regions such as the core of globular clusters or the galactic center , collisions can be more common . Such collisions can produce what are known as blue stragglers . These abnormal stars have a higher surface temperature than the other main sequence stars with the same luminosity of the cluster to which it belong .

Most stars are between 1 billion and 10 billion years old . Some stars may even be close to 13 @.@ 8 billion years old — the observed age of the universe . The oldest star yet discovered , HD 140283 , nicknamed Methuselah star , is an estimated 14 @.@ 46 ± 0 @.@ 8 billion years old . ( Due to the uncertainty in the value , this age for the star do not conflict with the age of the Universe , determined by the Planck satellite as 13 @.@ 799 ± 0 @.@ 021 ) .

When stars form in the present Milky Way galaxy they are composed of about 71 % hydrogen and 27 % helium , as measured by mass , with a small fraction of heavier elements . Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere , as iron is a common element and its absorption lines are relatively easy to measure . The portion of heavier elements may be an indicator of the likelihood that the star have a planetary system .

The star with the lowest iron content ever measured is the dwarf HE1327 @-@ 2326 , with only 1 / 200,000th the iron content of the Sun . By contrast , the super @-@ metal @-@ rich star μ Leonis have nearly double the abundance of iron as the Sun , while the planet @-@ bearing star 14 Herculis have nearly triple the iron . There also exist chemically peculiar stars that show unusual abundances of certain elements in their spectrum ; especially chromium and rare earth elements . Stars with cooler outer atmospheres , including the Sun , can form various diatomic and polyatomic molecules .

The disks of most stars are much too small in angular size to be observed with current ground @-@ based optical telescopes , and so interferometer telescopes are required to produce images of these objects . Another technique for measuring the angular size of stars is through occultation . By precisely measuring the drop in brightness of a star as it is occulted by the Moon ( or the rise in brightness when it reappear ) , the star 's angular diameter can be computed .

Stars range in size from neutron stars , which vary anywhere from 20 to 40 km ( 25 mi ) in diameter , to supergiants like Betelgeuse in the Orion constellation , which have a diameter approximately 1 @,@ 070 times that of the Sun — about 1 @,@ 490 @,@ 171 @,@ 880 km ( 925 @,@ 949 @,@ 878 mi ) . Betelgeuse , however , have a much lower density than the Sun .

When both rates of movement are known , the space velocity of the star relative to the Sun or the galaxy can be computed . Among nearby stars , it have been found that younger population I star have generally lower velocities than older , population II stars . The latter have elliptical orbits that are inclined to the plane of the galaxy . A comparison of the kinematics of nearby stars have allowed astronomers to trace their origin to common points in giant molecular clouds , and are referred to as stellar associations .

The magnetic field of a star is generated within regions of the interior where convective circulation occur . This movement of conductive plasma functions like a dynamo , wherein the movement of elecrical charges induce magnetic fields , as do a mechanical dynamo . Those magnetic fields have a great range that extend throughout and beyond the star . The strength of the magnetic field vary with the mass and composition of the star , and the amount of magnetic surface activity depend upon the star 's rate of rotation . This surface activity produce starspots , which are regions of strong magnetic fields and lower than normal surface temperatures . Coronal loops are arching magnetic field flux lines that rise from a star 's surface into the star 's outer atmosphere , its corona . The coronal loops can be seen due to the plasma they conduct along their length . Stellar flares are bursts of high @-@ energy particles that are emitted due to the same magnetic activity .

One of the most massive stars known is Eta Carinae , which , with 100 – 150 times as much mass as the Sun , will have a lifespan of only several million years . Studies of the most massive open clusters suggest 150 M ☉ as an upper limit for stars in the current era of the universe . This represent an empirical value for the theoretical limit on the mass of forming stars due to increasing radiation pressure on the accreting gas cloud . Several stars in the R136 cluster in the Large Magellanic Cloud have been measured with larger masses , but it have been determined that they could have been created through the collision and merger of massive stars in close binary systems , sidestepping the 150 M ☉ limit on massive star formation .

With a mass only 80 times that of Jupiter ( MJ ) , 2MASS J0523 @-@ 1403 is the smallest known star undergoing nuclear fusion in its core . For stars with metallicity similar to the Sun , the theoretical minimum mass the star can have and still undergo fusion at the core , is estimated to be about 75 MJ . When the metallicity is very low , however , the minimum star size seem to be about 8 @.@ 3 % of the solar mass , or about 87 MJ . Smaller bodies called brown dwarfs , occupy a poorly defined grey area between stars and gas giants .

The combination of the radius and the mass of a star determine its surface gravity . Giant stars have a much lower surface gravity than do main sequence stars , while the opposite is the case for degenerate , compact stars such as white dwarfs . The surface gravity can influence the appearance of a star 's spectrum , with higher gravity causing a broadening of the absorption lines .

The rotation rate of stars can be determined through spectroscopic measurement , or more exactly determined by tracking their starspots . Young stars can have a rotation greater than 100 km / s at the equator . The B @-@ class star Achernar , for example , have an equatorial velocity of about 225 km / s or greater , causing its equator to be slung outward and giving it an equatorial diameter that is more than 50 % greater than between the poles . This rate of rotation is just below the critical velocity of 300 km / s at which speed the star would break apart . By contrast , the Sun rotate once every 25 – 35 days , with an equatorial velocity of 1 @.@ 994 km / s . A main sequence star 's magnetic field and the stellar wind serve to slow its rotation by a significant amount as it evolve on the main sequence .

Degenerate stars have contracted into a compact mass , resulting in a rapid rate of rotation . However they have relatively low rates of rotation compared to what would be expected by conservation of angular momentum — the tendency of a rotating body to compensate for a contraction in size by increasing its rate of spin . A large portion of the star 's angular momentum is dissipated as a result of mass loss through the stellar wind . In spite of this , the rate of rotation for a pulsar can be very rapid . The pulsar at the heart of the Crab nebula , for example , rotate 30 times per second . The rotation rate of the pulsar will gradually slow due to the emission of radiation .

The surface temperature of a main sequence star is determined by the rate of energy production of its core and by its radius , and is often estimated from the star 's color index . The temperature is normally given in terms of an effective temperature , which is the temperature of an idealized black body that radiate its energy at the same luminosity per surface area as the star . Note that the effective temperature is only a representative of the surface , as the temperature increase toward the core . The temperature in the core region of a star is several million kelvins .

The energy produced by stars , a product of nuclear fusion , radiate to space as both electromagnetic radiation and particle radiation . The particle radiation emitted by a star is manifested as the stellar wind , which stream from the outer layers as electrically charged protons and alpha and beta particles . Although almost massless , there also exist a steady stream of neutrinos emanating from the star 's core .

The production of energy at the core is the reason stars shine so brightly : every time two or more atomic nuclei fuse together to form a single atomic nucleus of a new heavier element , gamma ray photons are released from the nuclear fusion product . This energy is converted to other forms of electromagnetic energy of lower frequency , such as visible light , by the time it reach the star 's outer layers .

The color of a star , as determined by the most intense frequency of the visible light , depend on the temperature of the star 's outer layers , including its photosphere . Besides visible light , stars also emit forms of electromagnetic radiation that are invisible to the human eye . In fact , stellar electromagnetic radiation span the entire electromagnetic spectrum , from the longest wavelengths of radio waves through infrared , visible light , ultraviolet , to the shortest of X @-@ rays , and gamma rays . From the standpoint of total energy emitted by a star , not all components of stellar electromagnetic radiation are significant , but all frequencies provide insight into the star 's physics .

Using the stellar spectrum , astronomers can also determine the surface temperature , surface gravity , metallicity and rotational velocity of a star . If the distance of the star is found , such as by measuring the parallax , then the luminosity of the star can be derived . The mass , radius , surface gravity , and rotation period can then be estimated based on stellar models . ( Mass can be calculated for stars in binary systems by measuring their orbital velocities and distances . Gravitational microlensing have been used to measure the mass of a single star . ) With these parameters , astronomers can also estimate the age of the star .

The luminosity of a star is the amount of light and other forms of radiant energy it radiate per unit of time . It have units of power . The luminosity of a star is determined by its radius and surface temperature . Many stars do not radiate uniformly across their entire surface . The rapidly rotating star Vega , for example , have a higher energy flux ( power per unit area ) at its poles than along its equator .

Patches of the star 's surface with a lower temperature and luminosity than average are known as starspots . Small , dwarf stars such as our Sun generally have essentially featureless disks with only small starspots . Giant stars have much larger , more obvious starspots , and they also exhibit strong stellar limb darkening . That is , the brightness decrease towards the edge of the stellar disk . Red dwarf flare stars such as UV Ceti may also possess prominent starspot features .

The apparent brightness of a star is expressed in terms of its apparent magnitude . It is a function of the star 's luminosity , its distance from Earth , and the altering of the star 's light as it pass through Earth 's atmosphere . Intrinsic or absolute magnitude is directly related to a star 's luminosity , and is what the apparent magnitude a star would be if the distance between the Earth and the star was 10 parsecs ( 32 @.@ 6 light @-@ years ) .

Both the apparent and absolute magnitude scales are logarithmic units : one whole number difference in magnitude is equal to a brightness variation of about 2 @.@ 5 times ( the 5th root of 100 or approximately 2 @.@ 512 ) . This mean that a first magnitude star ( + 1 @.@ 00 ) is about 2 @.@ 5 times brighter than a second magnitude ( + 2 @.@ 00 ) star , and about 100 times brighter than a sixth magnitude star ( + 6 @.@ 00 ) . The faintest stars visible to the naked eye under good seeing conditions are about magnitude + 6 .

Relative to both luminosity and distance from Earth , a star 's absolute magnitude ( M ) and apparent magnitude ( m ) are not equivalent ; for example , the bright star Sirius have an apparent magnitude of − 1 @.@ 44 , but it have an absolute magnitude of + 1 @.@ 41 .

The Sun have an apparent magnitude of − 26 @.@ 7 , but its absolute magnitude is only + 4 @.@ 83 . Sirius , the brightest star in the night sky as seen from Earth , is approximately 23 times more luminous than the Sun , while Canopus , the second brightest star in the night sky with an absolute magnitude of − 5 @.@ 53 , is approximately 14 @,@ 000 times more luminous than the Sun . Despite Canopus being vastly more luminous than Sirius , however , Sirius appear brighter than Canopus . This is because Sirius is merely 8 @.@ 6 light @-@ years from the Earth , while Canopus is much farther away at a distance of 310 light @-@ years .

As of 2006 , the star with the highest known absolute magnitude is LBV 1806 @-@ 20 , with a magnitude of − 14 @.@ 2 . This star is at least 5 @,@ 000 @,@ 000 times more luminous than the Sun . The least luminous stars that are currently known are located in the NGC 6397 cluster . The faintest red dwarfs in the cluster was magnitude 26 , while a 28th magnitude white dwarf was also discovered . These faint stars are so dim that their light is as bright as a birthday candle on the Moon when viewed from the Earth .

The current stellar classification system originated in the early 20th century , when stars was classified from A to Q based on the strength of the hydrogen line . It thought that the hydrogen line strength was a simple linear function of temperature . Rather , it was more complicated ; it strengthened with increasing temperature , it peaked near 9000 K , and then declined at greater temperatures . When the classifications was reordered by temperature , it more closely resembled the modern scheme .

Stars are given a single @-@ letter classification according to their spectra , ranging from type O , which are very hot , to M , which are so cool that molecules may form in their atmospheres . The main classifications in order of decreasing surface temperature are : O , B , A , F , G , K , and M. A variety of rare spectral types are given special classifications . The most common of these are types L and T , which classify the coldest low @-@ mass stars and brown dwarfs . Each letter have 10 sub @-@ divisions , numbered from 0 to 9 , in order of decreasing temperature . However , this system break down at extreme high temperatures as classes O0 and O1 may not exist .

In addition , stars may be classified by the luminosity effects found in their spectral lines , which correspond to their spatial size and is determined by their surface gravity . These range from 0 ( hypergiants ) through III ( giants ) to V ( main sequence dwarfs ) ; some authors add VII ( white dwarfs ) . Most stars belong to the main sequence , which consist of ordinary hydrogen @-@ burning stars . These fall along a narrow , diagonal band when graphed according to their absolute magnitude and spectral type . The Sun is a main sequence G2V yellow dwarf of intermediate temperature and ordinary size .

Additional nomenclature , in the form of lower @-@ case letters added to the end of the spectral type to indicate peculiar features of the spectrum . For example , an " e " can indicate the presence of emission lines ; " m " represent unusually strong levels of metals , and " var " can mean variations in the spectral type .

White dwarf stars have their own class that begin with the letter D. This is further sub @-@ divided into the classes DA , DB , DC , DO , DZ , and DQ , depending on the types of prominent lines found in the spectrum . This is followed by a numerical value that indicate the temperature .

During their stellar evolution , some stars pass through phases where they can become pulsating variables . Pulsating variable stars vary in radius and luminosity over time , expanding and contracting with periods ranging from minutes to years , depending on the size of the star . This category include Cepheid and Cepheid @-@ like stars , and long @-@ period variables such as Mira .

Eruptive variables are stars that experience sudden increases in luminosity because of flares or mass ejection events . This group include protostars , Wolf @-@ Rayet stars , and flare stars , as well as giant and supergiant stars .

Cataclysmic or explosive variable stars are those that undergo a dramatic change in their properties . This group include novae and supernovae . A binary star system that include a nearby white dwarf can produce certain types of these spectacular stellar explosions , including the nova and a Type 1a supernova . The explosion is created when the white dwarf accretes hydrogen from the companion star , building up mass until the hydrogen undergoes fusion . Some novae are also recurrent , having periodic outbursts of moderate amplitude .

Stars can also vary in luminosity because of extrinsic factors , such as eclipsing binaries , as well as rotating stars that produce extreme starspots . A notable example of an eclipsing binary is Algol , which regularly vary in magnitude from 2 @.@ 3 to 3 @.@ 5 over a period of 2 @.@ 87 days .

As atomic nuclei are fused in the core , they emit energy in the form of gamma rays . These photons interact with the surrounding plasma , adding to the thermal energy at the core . Stars on the main sequence convert hydrogen into helium , creating a slowly but steadily increasing proportion of helium in the core . Eventually the helium content become predominant , and energy production ceases at the core . Instead , for stars of more than 0 @.@ 4 M ☉ , fusion occur in a slowly expanding shell around the degenerate helium core .

In addition to hydrostatic equilibrium , the interior of a stable star will also maintain an energy balance of thermal equilibrium . There is a radial temperature gradient throughout the interior that result in a flux of energy flowing toward the exterior . The outgoing flux of energy leaving any layer within the star will exactly match the incoming flux from below .

The radiation zone is the region of the stellar interior where the flux of energy outward is dependent on radiative heat transfer , since convective heat transfer is inefficient in that zone . In this region the plasma will not be perturbed , and any mass motions will die out . If this is not the case , however , then the plasma become unstable and convection will occur , forming a convection zone . This can occur , for example , in regions where very high energy fluxes occur , such as near the core or in areas with high opacity ( making radiatative heat transfer inefficient ) as in the outer envelope .

The occurrence of convection in the outer envelope of a main sequence star depend on the star 's mass . Stars with several times the mass of the Sun have a convection zone deep within the interior and a radiative zone in the outer layers . Smaller stars such as the Sun are just the opposite , with the convective zone located in the outer layers . Red dwarf star with less than 0 @.@ 4 M ☉ are convective throughout , which prevent the accumulation of a helium core . For most stars the convective zones will also vary over time as the star ages and the constitution of the interior is modified .

The photosphere is that portion of a star that is visible to an observer . This is the layer at which the plasma of the star become transparent to photons of light . From here , the energy generated at the core become free to propagate into space . It is within the photosphere that sun spot , regions of lower than average temperature , appear .

Above the level of the photosphere is the stellar atmosphere . In a main sequence star such as the Sun , the lowest level of the atmosphere , just above the photosphere , is the thin chromosphere region , where spicules appear and stellar flares begin . Above this is the transition region , where the temperature rapidly increase within a distance of only 100 km ( 62 mi ) . Beyond this is the corona , a volume of super @-@ heated plasma that can extend outward to several million kilometres . The existence of a corona appear to be dependent on a convective zone in the outer layers of the star . Despite its high temperature , and the corona emit very little light , due to its low gas density . The corona region of the Sun is normally only visible during a solar eclipse .

From the corona , a stellar wind of plasma particles expand outward from the star , until it interact with the interstellar medium . For the Sun , the influence of its solar wind extend throughout a bubble @-@ shaped region called the heliosphere .

The hydrogen fusion process is temperature @-@ sensitive , so a moderate increase in the core temperature will result in a significant increase in the fusion rate . As a result , the core temperature of main sequence stars only vary from 4 million kelvin for a small M @-@ class star to 40 million kelvin for a massive O @-@ class star .

Where e + is a positron , γ is a gamma ray photon , νed is a neutrino , and H and He are isotopes of hydrogen and helium , respectively . The energy released by this reaction is in millions of electron volts , which is actually only a tiny amount of energy . However enormous numbers of these reactions occur constantly , producing all the energy necessary to sustain the star 's radiation output . In comparison , the combustion of two hydrogen gas molecules with one oxygen gas molecule release only 5 @.@ 7 eV .

In evolved stars with cores at 100 million kelvin and masses between 0 @.@ 5 and 10 M ☉ , helium can be transformed into carbon in the triple @-@ alpha process that use the intermediate element beryllium :

In massive stars , heavier elements can also be burned in a contracting core through the neon burning process and oxygen burning process . The final stage in the stellar nucleosynthesis process is the silicon burning process that result in the production of the stable isotope iron @-@ 56 , an endothermic process that consume energy , and so further energy can only be produced through gravitational collapse .

The example below show the amount of time required for a star of 20 M ☉ to consume all of its nuclear fuel . As an O @-@ class main sequence star , it would be 8 times the solar radius and 62 @,@ 000 times the Sun 's luminosity .

Perry the Platypus , also known as Agent P or simply Perry , is an anthropomorphic platypus from the animated series Phineas and Ferb . Perry was created by the series ' coed @-@ founders , Dan Povenmire and Jeff " Swampy " Marsh . He first appeared along with the majority of the main cast in the pilot episode " Rollercoaster . " Perry is featured as the star of the B @-@ plot for every episode of the series , alongside his nemesis Dr. Heinz Doofenshmirtz . A mostly silent character , his lone vocal characteristic ( a rattling of Perry 's beak ) was provided by Dee Bradley Baker .

Perry is the pet platypus of the Flynn @-@ Fletcher family , and is perceived as mindless and domesticated . In secret , however , he live a double life as a member of an all @-@ animal espionage organization referred to as O.W.C.A. ( The Organization Without a Cool Acronym ) . Many secret entrances to his underground lair exist all around the house ; such as the side of the house , most notably the tree that his owners sit under in the backyard , and several other everyday objects that seem to elude the family 's attention . He engage in daily battles with Dr. Heinz Doofenshmirtz , an evil scientist who desire to take over the Tri @-@ state area with obscure contraptions that work perfectly according to his intended function but fail in his application of them every time .

Perry is the docile pet platypus of the blended Flynn @-@ Fletcher family , who adopted him because his unfocused gaze made it seem as if he was looking at both Phineas and Ferb at the same time , as shown in the 2011 movie , Phineas and Ferb the Movie : Across the 2nd Dimension . Unbeknownst to them , Perry live a double life as a crime @-@ fighting spy working for the " Organization Without a Cool Acronym " / The OWCA , going by the codename " Agent P. " He report to his superior , Major Monogram , via telecast in his large , high @-@ tech , underground hideout . Every day , he engage in battles with the evil scientist Dr. Heinz Doofenshmirtz , who try using inventions to take over the tri @-@ state area . Perry is always able to foil Doofenshmirtz 's plans and in doing so accidentally lead to the destruction of whatever form of contraption his owners , Phineas Flynn and Ferb Fletcher , are building in order to make summer better . Phineas and Ferb are aware that something happen to get rid of their scheme for the day , but do not know that Perry is the cause behind it and are largely dismissive of it . Their sister , Candace , also do not know that Perry is behind the destruction and is driven to near insanity trying to figure it out . Throughout the series , Perry is aware of Phineas and Ferb 's inventions , but is largely uninterested in them , save whenever he notice that their latest invention may help him thwart Doofenshmirtz .

Perry and Doofenshmirtz at first seem to loathe each other in the beginning of the series , and have been arch @-@ nemeses since the day they met . However , they are often cordial and friendly towards one another and it is said by Doofenshmirtz that Perry is his best friend , and Perry will often act to save Doofenshmirtz 's life when his plot inevitably blow up in his face . Habitually , their daily brawls involve Doofenshmirtz devising a scheme , which Perry go to stop after being briefed by Major Monogram . He is trapped by Doofenshmirtz while trying to do so and is told of the doctor 's scheme , usually pertaining to some backstory or pet peeve . He then escape and the two fight , Perry coming out victorious . The two rely on this daily structure , Doofenshmirtz even specifically mentioning it in " Journey to the Center of Candace " and in episodes such as " It 's About Time ! " in which Doofenshmirtz temporarily replace Perry with secret agent Peter The Panda and they become depressed about not having each other to fight . Perry realize he miss Doof too . When Perry do not arrive on the scene of Doofenshmirtz 's evil plan , the doctor hesitate to execute his plans and fears for where Perry have gone , though he note that he " hope something terrible have happened to him . " . Sometimes , they decided not to fight and have fun , as shown in " Happy New Year ! " and " Candace Disconnected " . On other occasions , depending on whatever situation Doofenshmirtz is facing , Perry would often help Doofenshmirtz with his non @-@ evil plans , such as helping him overcome evil scientist 's block , helping him put on a birthday party for his 16 @-@ year @-@ old daughter Vanessa , impressing a square dancing girl with programmable square dancing boots that Doofenshmritz created , working together to stop a raging platypus hunter from hunting them down , or helping him convince his rich ex @-@ wife to help pay off his mortgage debt . Also , Perry tend to use Doofenshmirtz 's inventions to erase evidence of whatever contraptions Phineas and Ferb had made , leaving Candace unable to bust them . Examples include when Perry asked to borrow Doofenshmirtz 's robot Norm to pick up footage from the city surveillance cameras in order to preserve his job as an agent , as well as using Doofenshmirtz 's Pick @-@ Him @-@ Up @-@ inator to rescue a lost Candace and bring her home .

In Phineas and Ferb the Movie : Across the 2nd Dimension , an alternate reality ( yet more evil and ruthless ) version of Perry ( known as Platyborg ) appear as the secondary antagonist , with the regular Perry serving as a supporting protagonist . Platyborg would later return in the episode sequel , Tales from the Resistance : Back to the 2nd Dimension , this time , as a supporting protagonist .

While working on the animated television series Rocko 's Modern Life , Phineas and Ferb coed @-@ founder Dan Povenmire and Jeff " Swampy " Marsh utilized several recurring elements in the episodes that they wrote . Among these was actions sequences and chase scenes . Povenmire and Marsh wanted to reuse these elements in their series and chose Perry to execute it . The pair gave him a consistent and continuous nemesis in the form of Doofenshmirtz as a means of allowing viewers to get to know him .

While choosing a species for Perry , Povenmire and Marsh wanted to keep in mind selecting one that was uncommon , an animal that kids could not " pick out at a pet store and beg [ their parents ] for . " They chose a platypus because of the animal 's obscure and striking appearance . The animal was scarcely used in American animated programs , so the pair opined that Perry " would not have to compete with preconceived notions that viewers might bring to a more conventional critter . " The blank storyboard they was given allowed them to " make stuff up " since " no one know very much about [ them ] . "

Perry have a theme song tentatively entitled " Perry , " performed by Randy Crenshaw and Laura Dickinson , and written by Povenmire and Marsh , who write the majority of songs in the series . The song , along with the number " Gitchee Gitchee Goo " from the episode " Flop Starz , " was the first musical composition Povenmire and Marsh pitched to The Walt Disney Company . They was nervous doing so , because , as Povenmire explained , " Disney have a big history of music -- what if they hate it ? " Their reaction , however , was considerably positive and the pair was asked to write a song for each episode , which they vehemently agreed to . The opening lyrics for the song describe Perry as a standard textbook definition of a platypus : " He 's a semi @-@ aquatic egg @-@ laying mammal of action . "

Like the other characters of the series , Perry was structured in a simple style to allow young viewers to easily draw him . In keeping with the show 's general design scheme , Perry is constructed of geometric shapes in a style reminiscent of deceased Looney Tunes animator Tex Avery . Povenmire use different design styles for drawing Perry depending on how he is portrayed . When Perry is portrayed as a domesticated and mindless pet , Povenmire begin with a square shaped like a loaf of bread . He then draw his front legs and feet before drawing his bill , which is set at a certain angle . Povenmire then draw his eyeballs , which are never focused and look in opposing directions in a daze . He conclude the figure by adding his hind legs , tail , hair , and finally color .

When portrayed as a secret agent , Povenmire start with a similar bread loaf square design , but draw it standing up vertically and place a fedora on the top of his head , which is combined with the square torso . In contrast to his mindless and wild @-@ eyed expression as a pet , the secret agent version of Perry is detailed with eyes " full of steely blue resolve . " Povenmire proceed by drawing his arms , which bear hands that are open and prepared for fighting or any danger . His legs are bent , as well prepared for an act of danger or action needed . Povenmire finish the design by adding his beaver tail and color .

Perry 's undercover identity as a pet lead to characters throughout the series to deem him as a " mindless domestic pet " that " doesn 't do much " . This definition of the character led to Phineas and Ferb spearheading production of a new toyline based on Perry called " Perry the Inaction Figure , " whose tagline revolved around it not doing anything but allowing the customer to make it whatever they desire it to be . In all actuality , Perry is a skilled fighter who is able to perform several implausible judo fighting moves and escapes . He have access to several different types of technology and inventions provided to him by The O.W.C.A. , including a hover craft dubbed the " Platypusmobile , " a jet ski , and a whistle set that allow him to summon different types of animals .

Although his appearance as a domestic pet is mostly a cover , Perry have nonetheless expressed care and devotion for the Flynn @-@ Fletcher family . In the episode " The Ballad of Bad Beard " , Perry managed to drag Candace out of the Dark Cave before it caved in because of Dr. Doofenshmirthz 's " self destruction button " that which Candace had accidentally pressed while under the orange moss hallucination , thinking it was a vending machine . He did this even though he knew that Candace saw that Perry was a secret agent talking to Agent E ( Eagle ) and to Major Monogram in a cracked egg . Candace thought she was just hallucinating because of the orange moss she accidentally touched earlier in the episode . Also , when an invention of Doofenshmirtz 's in the episode " Journey to the Center of Candace " might cause severe harm to Phineas and Ferb , Perry thoroughly beat up Doofenshmirtz and quickly handcuff him . He then tie him to a pipe and , instead of just leaving him like he usually do in the series , call for special forces from the O.W.C.A. to come and arrest the doctor , though they never show up . In " Oh , There You Are , Perry , " Doofenshmirtz is downgraded to a low threat level and Perry is reassigned to a new nemesis . This cause him to have to leave his home with the Flynn @-@ Fletchers , which make him sad and he do not enjoy his new villain . Phineas and Ferb are fearful about where Perry could have gone to and put up several flyers around town for people to find him . They decide to throw a concert on the roof of a building , singing a song about how much they love Perry and want him to come home . Concurrently , Perry is reassigned to Doofenshmirtz again and return to the brothers once more .

Though Perry is anthropomorphic , he do not speak , only communicating through an " aggravated purr " type of noise made by flapping his bill . This noise is provided by actor Dee Bradley Baker ; to this day , Povenmire and Marsh do not understand how Baker produce the noise . Thomas Sangster , who play Ferb , is notoriously good at making the noise and is considered second only to Baker himself . When in his " Agent P " persona , Perry is almost completely silent .

As a character , Perry have been well received by both fans and critics . As Cynthia Littleton of Variety magazine wrote , " Perry the platypus is a breakout star from the Disney Channel toon ' Phineas and Ferb . ' " The New York Times writer Susan Stewart called him " intrepid . " Jean Yoo , a press member for Disney Channel , said that Perry is " suave " and " make James Bond look like a rank amateur . " Aaron H. Bynum of Animator Insider opined that he is " indubitably confident . " Carly H. of Scholastic , Inc. declared Perry " pretty darn awesome . " Josh Jackson , editor of Paste , described Perry and Doofenshmirtz 's relationship as " pitch @-@ perfect . "

Certain reviewers have also commented negatively about Perry and his subplot , which Sherry Robinson of the St. Petersburg Times consider " pretty trippy . " Kevin McDonough of Sun Coast Today described it as " complicated " and " loosely connected " to the rest of the series , writing that he is " not sure what this accomplish except to add the noise of explosions to the already constant din of singing and screaming . " Ed Liu of Toon Zone feel it is " truly puzzling what Perry the secret agent is doing in this show in the first place . " Liu consider his subplot to be a type of " throw everything against the wall and see what sticks " element and write that " many of the earlier episodes of the show don 't manage to do a very good job of balancing the subplot and the main one . "

In addition to the main television series , Perry have appeared in several pieces of Phineas and Ferb merchandise . To date , he have appeared in all Phineas and Ferb novelizations , published by Disney Press . The character have been adapted into a 20 inch plush toy , released by The Walt Disney Company . The plush have a button on its hand that allow it to emit Perry 's signature chattering noise . Certain t @-@ shirts based on the series released by both Disney and the online retail website Zazzle also display Perry and the phrase " Hey , where 's Perry ? " which most characters like Phineas , Isabella , Stacy , Irving , Ferb , and Lawrence utter when Perry go to Major Monogram in his secret lair in almost every episode . There also is a T @-@ Shirt with Perry 's face . Perry appear in the Nintendo DS video game based on the series , simply titled Phineas and Ferb , where a mini @-@ game involve Perry stopping Doofenshmirtz 's latest evil scheme . As of 1 April 2014 , Perry is also a playable character in the video game Disney Infinity .

Amylostereum is the single genus in the fungal family Amylostereaceae . The genus currently comprise four saprotrophic and parasitic species , which live off living or dead wood . The Amylostereaceae cause white rot in the wood by disintegrating the tissue component lignin . They produce crust @-@ like , partially wavy fruit bodies on the surface of infested trees , which are similar to those produced by Stereum species .

There are four described species in the Amylostereaceae : A. chailletii ( the type ) , A. areolatum , A. ferreum and A. laevigatum . The species was initially considered part of Stereum until mycologist Jacques Boidin found atypical microscopic differences between them . Forty years after his extensive researches from 1958 , Boidin reclassified Amylostereum into its own family .

Three Amylostereum species are symbionts of wood wasps in the genera Sirex , Urocerus , and Xoanon , which infest conifers . The female wood wasps deposit their eggs together with fungal spores and mucus in trees , and the fungus is eaten by the wasp 's larva as food . The fungus propagate vegetatively through the formation of asexual spores in newly emerged females that are stored in special structures adapted for the transport of symbiotic fungi . The A. areolatum – Sirex woodwasp ( S. noctilio ) symbiont complex have been studied extensively because of its potential to cause substantial economic losses in the forestry industry , particularly in non @-@ native regions .

Amylostereaceae species was for a long time classified in the genus Stereum , based primary on the layered structure of the fruit body and the similar physiological activity . Mycologist Jacques Boidin separated Amylosterum from Stereum in 1958 , justifying this decision by explaining that microscopic differences such as amyloid spores and encrusted cystidia was sufficiently distinct to warrant recognition as a new genus . Although the type species of the genus ( today called A. chailletii ) was initially named Trichocarpus ambiguus , the name Trichocarpus had already been used for a genus in the flowering plant family Malvaceae . Boidin thus chose the genus name Amylostereum , referring to the amyloid spores .

The similarities between A. chailletii and A. areolatum have caused some confusion regarding their placement in the genus . As only the size of their fruit bodies differ from each other in appearance , researcher German Josef Krieglsteiner assumed that both are the same species in different age stages . Experiments with pure cultures of the fungi , however , showed that the mycelia of A. chailletii , A. laevigatum and A. ferreum was partially compatible to each other , but the mycelium of A. areolatum was incompatible to other species . Boidin believe that the common ancestor of all Amylostereum fungi used yellowwoods as a host . This genus of conifers was native in Europe until the Paleogene and Neogene Periods ( 66 million to 2 @.@ 6 million years ago ) , but became extinct there , so the Amylostereum fungi specialized on other conifers and differentiated into several species . Only A. ferreum specialized on yellowwoods in South America .

Compatibility tests as well as molecular analysis indicated that A. areolatum separated very early from other Amylostereum fungi . The other three species separated later from each other and are thus partially compatible to each other . A. ferreum and A. laevigatum produced in 59 % of all cases a common mycelium , A. ferreum and A. chailletii only in 44 % . There is an undescribed species in Amylostereum ; according to DNA analysis , it stand between A. laevigatum and A. ferreum . This is remarkable , as these fungi originated from Mycetangae ( storing organs of Platypodinae ) of a North American wood wasp , while A. laevigatum have never been seen as symbiont of wood wasps , neither in North American nor in Europe . The fungus possibly represent a separated species or a subtaxon of A. laevigatum . As A. areolatum and A. chailletii mainly reproduce asexually through the symbiosis of wood wasps , the genetic variability within these species is relatively low .

The Amylostereaceae produce crust @-@ like , dry and leathery @-@ corky fruit bodies on the bark of infested trees . The fruit bodies are 0 @.@ 5 – 1 @.@ 5 mm ( 0 @.@ 02 – 0 @.@ 06 in ) thick , irregularly shaped and are able to cover a large surface on the bark or otherwise can appear as small spots . They lie directly on the bark . The ochrous , grey or brownish fruit body ( hymenium ) have a smooth to warty surface texture and is turned outwards . It is bordered by a highly bent and wavy ( effuso @-@ reflex ) edge on all species except A. laevigatum , which have a churlish surface ( a tomentum ) and is usually dirty @-@ brown coloured . In some species , the tomentum stand clearly above and form a kind of roof above the fruit body ; if it completely surround this roof , there might appear cuplike shapes .

With the exception of A. laevigatum , all species have a thin separating layer , the cortex , between the hymenium and the tomentum . A cortex is also present on many Stereum fungi ( on a broader front ) and serve to bend up the fruit body . As this cortex is missing on A. laevigatum , its fruit body lie flat on the bark .

The basidia are 15 – 25 × 3 @.@ 5 – 5 @.@ 5 µm and have a slim , club @-@ like shape . Each basidium feature four sterigmata , each of which bear one spore . The spores ' shape is slimly ellipsoidal or cylindrical . Their surface is smooth and their walls are thin . Although they are colourless and hyaline , the spores are amyloid , meaning they will turn bluish or purple when stained with Melzer 's reagent . This characteristic differs from other very similar species , and this gave the genus its name .

Amylostereaceae usually infest only dead or cut down conifer wood . Three species – A. areolatum , A. laevigatum and A. chailletii – may also establish a symbiosis with wood wasps ( Siricidae ) , which beside freshly logged trees also infest living trees and infect them with fungi . Symbioses have been recorded with several species : Sirex noctilio , S. juvencus , S. nitobei , S. cyaneus , S. edwarsii , S. nitidus , and , in Japan , Urocerus antennatus and Xoanon matsumurae . Wasps of the genera Sirex and Urocerus store oidia ( the hypha of fungi split up to spores ) in special abdominal organs . The wood wasps infect trees by splashing a phytotoxic secretion below the bark and at the same time injecting fungal spores into the hole . The secretion weaken the tree and temporarily diminish its immune system , whereby the fungus can spread along the xylem . The infection with Amylostereaceae fulfill two functions for the wasps : it provide the larvae food , because the white rot soften the wood ; at the same time , the mycelia of the fungi serve as food for the larvae . After the larvae pupate , it absorb the mycelia of the Amylostereaceae into its body to oviposit together with its eggs . The fungus benefits from the symbiosis as it spread faster and more effectively than through airborne spores and furthermore do not need to develop fruit bodies . A. ferreum is the only Amylosterum species that have not been associated with any woodwasps .

The host spectrum of the Amylostereaceae comprise several , partially very different genera of Coniferae . A. chailletii usually infest Pinaceae such as firs ( Abies ) and spruce ( Picea ) , but also cedars ( Cedrus ) and Douglas firs ( Pseudotsuga ) . A. areolatum have a similar host spectrum , which use mainly firs , Japanese cedars ( Cryptomeria ) , larches ( Larix ) , spruces , pines ( Pinus ) and Douglas firs as hosts . While spruces dominate as hosts in the native habitat , this species is more common in pines on other locations . The host spectrum of A. laevigatum comprise Cupressaceae such as junipers ( Juniperus ) or cypresses ( Cupressus ) and the English yew ( Taxus baccata ) . A. ferreum is , however , only common on neotropic yellowwoods ( Podocarpus ) .

The Amylostereaceae are white rot pathogens . They disintegrate the lignin of the host wood , whereby the infested wood parts become less stable and take a fibrous structure . The wood bleach as fungal enzymes break down and remove the brown @-@ pigmented lignin . The distribution in wood take place mainly along the transport channels in the xylem . If the wood is crosscut , the red rot is vertically positioned , on which bleached , infested areas contrast with intact wood . Symptoms of infestion by the symbiotic partner — wood wasps — include circular exit holes in the crust and acute stress through dryness , common in hanging , falling or tanning needles .

In their native habitat , all Amylostereum species have a minor importance as forest pests . The infestation through wood wasps do not assume greater dimensions and is , compared with other pests , almost insignificant . The infection rates are even lower during sexual reproduction via fruit bodies , as the wasps do not play a part in the process . Furthermore , the Amylostereum fungi are alone often incapable of infesting healthy trees . They thus mostly act as saprobiontics . Pine monocultures in Australia , New Zealand , Africa and South America was shown to be susceptible to the Sirex woodwasp ( Sirex noctilio ) , which was introduced there and which is associated with A. areolatum . The wasp 's phytotoxic secretion , its larvae and the fungus combine very effectively with each other and contribute to forest decline rates of up to 80 % . This is mainly owing to the poor water and nutrient supply of the trees , which can poorly reconcile the drought stress caused by infestation . S. noctilio was detected in North America in the 2000s ( decade ) ; in Canada alone , the total economic loss to the forestry industry caused by the Sirex – Amylostereum symbiosis could be as high as $ 254 million per year for the next 20 years .

As a countermeasure , cultures of the nematode Deladenus siricidicola have been used as biological control to protect trees since the 1980s . This parasite feed on the mycelia of A. areolatum and is therefore a food competitor of wood wasp larvae . Where S. noctilio larvae are present , the parasite infect and sterilize the eggs of female wasps , causing them to be infertile . These infertile females lay infected eggs into new trees and thus spread the nematode . This control method have proven to be relatively successful to combat the Sirex – Amylostereum complex . In the Southern Hemisphere , where the technique have been widely employed , reductions of parasitism levels of 70 % – 100 % have been achieved .

Alkan earned many awards at the Conservatoire de Paris , which he entered before he was six . His career in the salons and concert halls of Paris was marked by his occasional long withdrawals from public performance , for personal reasons . Although he had a wide circle of friends and acquaintances in the Parisian artistic world , including Eugène Delacroix and George Sand , from 1848 he began to adopt a reclusive life style , while continuing with his compositions – virtually all of which are for the keyboard . During this period he published , among other works , his collections of large @-@ scale studies in all the major keys ( Op. 35 ) and all the minor keys ( Op. 39 ) . The latter include his Symphony for Solo Piano ( Op. 39 , nos . 4 – 7 ) and Concerto for Solo Piano ( Op. 39 , nos . 8 – 10 ) , which are often considered among his masterpieces and are of great musical and technical complexity . Alkan emerged from self @-@ imposed retirement in the 1870s to give a series of recitals that was attended by a new generation of French musicians .

Alkan was born Charles @-@ Valentin Morhange on 30 November 1813 at 1 , Rue de Braque in Paris to Alkan Morhange ( 1780 – 1855 ) and Julie Morhange , née Abraham . Alkan Morhange was descended from a long @-@ established Jewish Ashkenazic community in the region of Metz ; the village of Morhange is located about 30 miles ( 48 km ) from the city of Metz . Charles @-@ Valentin was the second of six children – one elder sister and four younger brothers ; his birth certificate indicate that he was named after a neighbour who witnessed the birth .

Alkan Morhange supported the family as a musician and later as the proprietor of a private music school in le Marais , the Jewish quarter of Paris . At an early age , Charles @-@ Valentin and his siblings adopted their father 's first name as their last ( and was known by this during their studies at the Conservatoire de Paris and subsequent careers ) . His brother Napoléon ( 1826 – 1906 ) became professor of solfège at the Conservatoire , his brother Maxim ( 1818 – 1897 ) had a career writing light music for Parisian theatres , and his sister , Céleste ( 1812 – 1897 ) , was also a pianist . His brother Ernest ( 1816 – 1876 ) was a professional flautist , while the youngest brother Gustave ( 1827 – 1882 ) was to publish various dances for the piano .

Alkan was a child prodigy . He entered the Conservatoire de Paris at an unusually early age , and studied both piano and organ . The records of his auditions survive in the Archives Nationales in Paris . At his solfège audition on 3 July 1819 , when he was just over 5 years 7 months , the examiners noted Alkan ( who is referred to even at this early date as " Alkan ( Valentin ) " , and whose age is given incorrectly as six @-@ and @-@ a @-@ half ) as " having a pretty little voice " . The profession of Alkan Morhange is given as " music @-@ paper ruler " . At Charles @-@ Valentin 's piano audition on 6 October 1820 , when he was nearly seven ( and where he is named as " Alkan ( Morhange ) Valentin " ) , the examiners comment " This child have amazing abilities . "

Alkan became a favourite of his teacher at the Conservatoire , Joseph Zimmermann , who also taught Georges Bizet , César Franck , Charles Gounod , and Ambroise Thomas . At the age of seven , Alkan won a first prize for solfège and in later years prizes in piano ( 1824 ) , harmony ( 1827 ) , and organ ( 1834 ) . At the age of seven @-@ and @-@ a @-@ half he gave his first public performance , appearing as a violinist and playing an air and variations by Pierre Rode . Alkan 's Opus 1 , a set of variations for piano based on a theme by Daniel Steibelt , date from 1828 , when he was 14 years old . At about this time he also undertook teaching duties at his father 's school . Antoine Marmontel , one of Charles @-@ Valentin 's pupils there , who was later to become his bête noire , wrote of the school :

Young children , mostly Jewish , was given elementary musical instruction and also learned the first rudiments of French grammar ... [ There ] I received a few lessons from the young Alkan , four years my senior ... I see once more ... that really parochial environment where the talent of Valentin Alkan was formed and where his hard @-@ working youth blossomed ... It was like a preparatory school , a juvenile annexe of the Conservatoire .

Throughout the early years of the July Monarchy , Alkan continued to teach and play at public concerts and in eminent social circles . He became a friend of many who was active in the world of the arts in Paris , including Franz Liszt ( who had been based there since 1827 ) , George Sand , and Victor Hugo . It is not clear exactly when he first met Frédéric Chopin , who arrived in Paris in September 1831 . In 1832 Alkan took the solo role in his first Concerto da camera for piano and strings at the Conservatoire . In the same year , aged 19 , he was elected to the influential Société Académique des Enfants d 'Apollon ( Society of the Children of Apollo ) , whose members included Luigi Cherubini , Fromental Halévy , the conductor François Habeneck , and Liszt , who had been elected in 1824 at the age of twelve . Between 1833 and 1836 Alkan participated at many of the Society 's concerts . Alkan twice competed unsuccessfully for the Prix de Rome , in 1832 and again in 1834 ; the cantatas which he wrote for the competition , Hermann et Ketty and L 'Entrée en loge , have remained unpublished and unperformed .

In 1834 Alkan began his friendship with the Spanish musician Santiago Masarnau , which was to result in an extended and often intimate correspondence which only came to light in 2009 . Like virtually all of Alkan 's correspondence , this exchange is now one @-@ sided ; all of his papers ( including his manuscripts and his extensive library ) was either destroyed by Alkan himself , as is clear from his will , or became lost after his death . Later in 1834 Alkan made a visit to England , where he gave recitals and where the second Concerto da camera was performed in Bath by its dedicatee Henry Ibbot Field ; it was published in London together with some solo piano pieces . A letter to Masarnau and a notice in a French journal that Alkan played in London with Moscheles and Cramer , indicate that he returned to England in 1835 . Later that year , Alkan , having found a place of retreat at Piscop outside Paris , completed his first truly original works for solo piano , the Twelve Caprices , published in 1837 as Opp . 12 , 13 , 15 and 16 . Op. 16 , the Trois scherzi de bravoure , is dedicated to Masarnau . In January 1836 , Liszt recommended Alkan for the post of Professor at the Geneva Conservatoire , which Alkan declined , and in 1837 he wrote an enthusiastic review of Alkan 's Op. 15 Caprices in the Revue et gazette musicale .

From 1837 , Alkan lived in the Square d 'Orléans in Paris , which was inhabited by numerous celebrities of the time including Marie Taglioni , Alexandre Dumas , George Sand , and Chopin . Chopin and Alkan was personal friends and often discussed musical topics , including a work on musical theory that Chopin proposed to write . By 1838 , at 25 years old , Alkan had reached a peak of his career . He frequently gave recitals , his more mature works had begun to be published , and he often appeared in concerts with Liszt and Chopin . On 23 April 1837 Alkan took part in Liszt 's farewell concert in Paris , together with the 14 @-@ year @-@ old César Franck and the virtuoso Johann Peter Pixis . On 3 March 1838 , at a concert at the piano @-@ maker Pape , Alkan played with Chopin , Zimmerman , and Chopin 's pupil Adolphe Gutmann in a performance of Alkan 's transcription , now lost , of two movements of Beethoven 's Seventh Symphony for two pianos , eight hands .