Gravity / Quantum Physics / Quantum Physics

19
Jan

The Chandrasekhar Limit: The Threshold That Makes Life Possible

There is a thin line between a bang and a whimper.

For stars, this line is called the Chandrasekhar Limit, and it is the difference between dying in a blaze of glory and going out in a slow fade to black. For our universe, this line means much more: Only by exceeding it can stars sow the seeds of life throughout the cosmos.

The Chandrasekhar Limit is named for Subrahmanyan Chandrasekhar, one of the great child prodigies. Chandrasekhar graduated with a degree in physics before reaching his twentieth birthday. He was awarded a Government of India scholarship to study at Cambridge, and in the fall of 1930 boarded a ship to travel to England. While aboard the ship—still before reaching his twentieth birthday—he did the bulk of the work for which he would later be awarded a Nobel Prize.

By the 1920s—a decade before Chandrasekhar began his journey to England—astronomers had realized that Sirius B, the white dwarf companion to the bright star Sirius, had an astoundingly high density—more than a million times the density of the sun. An object of this density could only exist if the atoms comprising the star were so tightly compressed that they were no longer individual atoms. Gravitational pressure would compress atoms so much that the star would consist of positively-charged ions surrounded by a sea of electrons.

Prior to the discovery of quantum mechanics, physicists knew of no force capable of supporting any star against such gravitational pressure. Quantum mechanics, though, suggested a new way for a star to hold itself up against the force of gravity. According to the rules of quantum mechanics, no two electrons can be in the exact same state. Inside an extremely dense star like Sirius B, this means that some electrons are forced out of low energy states into higher ones, generating a pressure called electron degeneracy pressure that resists the gravitational force. This makes it possible for a star like Sirius B to achieve such extreme density without collapsing in on itself.

This discovery was made by Ralph Fowler, who would later become Chandrasekhar’s graduate supervisor. But Chandrasekhar realized what Fowler had missed: The high-energy electrons inside the white dwarf would have to be traveling at velocities near the speed of light, invoking a set of bizarre relativistic effects. When Chandrasekhar took these relativistic effects into account, something spectacular happened. He found a firm upper limit for the mass of any body which could be supported by electron degeneracy pressure. Once this limit—the Chandraskehar limit—was exceeded, the object could no longer resist the force of gravity, and it would begin to collapse.

When Chandrasekhar published these results in 1931, he set off a battle with one of the greatest astrophysicists of the era, Sir Arthur Eddington, who believed that the white dwarf state was the eventual fate of every star. At a conference in 1935, Eddington told his audience that Chandrasehkar’s work “was almost a reduction ad absurdum of the relativistic degeneracy formula. Various accidents may intervene to save a star, but I want more protection than that. I think there should be a law of Nature to prevent a star from behaving in this absurd way!”

Chandrasekhar was deeply hurt by Eddington’s reaction, but colleagues can disagree profoundly and still remain friends. Chandrasekhar and Eddington remained friends, went to the Wimbledon tennis tournament together and went for bicycle rides in the English countryside. When Eddington passed away in 1944, Chandrasekhar spoke at his funeral, saying “I believe that anyone who has known Eddington will agree that he was a man of the highest integrity and character. I do not believe, for example, that he ever thought harshly of anyone. That was why it was so easy to disagree with him on scientific matters. You can always be certain he would never misjudge you or think ill of you on that account.”

Vindication would eventually come to Chandrasekhar when he was awarded the Nobel Prize in 1983 for his work. The Chandrasekhar Limit is now accepted to be approximately 1.4 times the mass of the sun; any white dwarf with less than this mass will stay a white dwarf forever, while a star that exceeds this mass is destined to end its life in that most violent of explosions: a supernova. In so doing, the star itself dies but furthers the growth process of the universe—it both generates and distributes the elements on which life depends.

The life of a star is characterized by thermonuclear fusion; hydrogen fuses to helium, helium to carbon, and so on, creating heavier and heavier elements. However, thermonuclear fusion cannot create elements heavier than iron. Only a supernova explosion can create copper, silver, gold, and the “trace elements” that are important for the processes of life.

Lighter elements like carbon, oxygen, and nitrogen are also essential to life, but without supernova explosions, they would remain forever locked up in stars. Being heavier than the hydrogen and helium that comprise most of the initial mass of the stars, they sink to form the central core of the star—just as most of the iron on Earth is locked up in its core. If stars are, as Eddington believed, destined to become white dwarfs, those elements would remain confined to the stellar interior, or at best be delivered in relatively minute quantities to the universe as a whole via stellar winds. Life as we know it requires rocky planets to form, and there simply is no way to get enough rocky material out into the universe unless stars can deliver that material in wholesale quantities. And supernovae do just that.

The Chandrasekhar Limit is therefore not just as upper limit to the maximum mass of an ideal white dwarf, but also a threshold. A star surpassing this threshold no longer hoards its precious cargo of heavy elements. Instead, it delivers them to the universe at large in a supernova that marks its own death but makes it possible for living beings to exist.

Go Deeper
Editor’s picks for further reading

BBC: Test Tubes and Tantrums: Arthur Stanley Eddington and Subrahmanyan Chandrasekhar
In this radio program, discover the history of one of the nastiest disagreements in astrophysics.

FQXi: Exploding the Supernova Paradigm
In this blog post, Zeeya Merali investigates gaps in our understanding of supernova explosions.

Nobelprize.org: Subramanyan Chandrasekhar – Autobiobraphy

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jstein-big

James Stein

    James D. Stein is a past member of the Institute of Advanced Studies and is currently a professor of Mathematics at California State University (Long Beach). His list of publications includes: How to Shoot from the Hip Without Getting Shot in the Foot (with Herbert L. Stone and Charles V. Harlow); How Math Explains the World (a Scientific American Book Club selection); The Right Decision (also a Scientific American Book Club selection); and How Math Can Save Your Life. He has been a guest blogger for Psychology Today and his work has been featured in the Los Angeles Times. His latest book is Cosmic Numbers: The Numbers That Define Our Universe. He lives in Redondo Beach, California.

    • http://www.facebook.com/profile.php?id=100002673633498 Tom Klecker

      When stars fuse hydrogen and helium nuclei to create the nuclei of elements up to and including iron there is a release of energy that ‘powers’ the star. This is a release of potential energy that had been bound in the nuclear forces of hydrogen and helium since the ‘big bang’.

      But it is the gravitational force that ‘ignites’ the fusion process by compressing and heating the hydrogen and helium. The potential energy being released by the gravitational compression also has the ‘big bang’ as it’s original source.

      Gravitational potential energy is also the source of the compression force that builds the heavier elements during a supernova.

      The ‘big bang’ is the ultimate source of the energy of nuclear fusion, fission and decay. These nuclear processes are the producers of the energy that powers the stars and ultimately warms the Earth, illuminates the day, drives weather and powers life.

      • Desp50

        This is a very interesting subject for sure. However, I don’t know that we should be crediting the ‘big bang’ with so much, as it has never been proven ‘beyond a doubt’ to have existed… Microwave background radiation, which is a typical so called ‘proof”, can be explained in other ways… I for one believe that we are mistaken about that ‘proof’, altogether, and can think of other reasons for that radiation being there. In particular, afer 40 years working in the engineering sciences, I’ve had plenty of time to read, learn and question the prevailing theories. I once simply accepted that the ‘big bang’ was a given but now have serious doubts. We ought not elicit the ‘big bang’ in subject above… its too far fetched and uncertain. I cannot see any rational way to interpret the ‘Whole’ of the known universe as having once being compressed into essentially ‘nothing’, only to produce all the matter that we now see in the universe. The Chandrasekhar Limit: The Threshold article is exciting and really helps clarify the need to be open to new ideas and not simple always accept the ‘main stream prevailing theories’. I found the article informative and really see a place for all those child protegies that keep popping up every now and again, at convenient times in human history, to help us experience the ‘reality checkups’ that are essential for us to advance in our knowlege of life and purpose.
        Cheers

        • pepe

          So, how would yo explain the microwave background without the BigBang? How would you explain the perfect fit of a black-body function to the microwave background? How would you explain the baryonic acoustic oscillations? How would you explain the perfect match of temperature oscillations between regions of the Universe which are today causal-disconnected? I don’t think you have any idea what you are talking about.

          • vijay

            To an un-initiated person, shall Big Bang be cause of what we see, the universe can not be omni-directional. This is seen as weekness of Bing-Bang. The explainations can be built, argued, understood and accepted by a section of community. The fact of CBR is in conflict with Big-Bang, and new theories and arguments are required/formed to explain it away.

    • Jack Kessler

      There is a misleading mis-statement in this article. The writer suggests that heavy elements (all elements heavier than helium, loosely “metals”) sink to the cores of a star the way iron sank to the core of the newly-formed earth, by a combination of their weight and by convection.

      They do not.

      Heavy elements collect at the cores of stars because they are formed there, not because they have sunk there. Judging by the sun, there is little transfer of material by convection between the core and the outer layers of a star. Necessarily there is little transfer in the opposite direction as well. Heavy elements (all elements heavier than helium, loosely “metals”) collect at the cores of stars not on account of convection but on account of the lack of it.

    • Ujjalgoraya

      I agree 100% with Prof. Stein’s accessment of this article. It was an explosion of a Supernova long time ago that on Earth we are blessed with metals like copper, silver and Gold!

    • GL

      You are such a bigger bag of mostly water, is the way humans were described in one Star Trek episode. Please refrain from misleading humanity into your delusional fantasy.

      GL

    • varghese jidhi jacob

      My one question about the Chandrasekhar limit is that ” Does the limit remain constant in relation to the mass of the sun..? As we are all aware that the mass of sun is decreasing constantly, the C limit should increase proportionally as such. else the size of the star which can enter into a supernova decreases with time….” Please clarify…just curious to know..:)

    • http://www.hawking.org.uk Sankaravelyudhan nandakumar

      superabsorption of light beyond the limits of classical physics possible
      during the end of white dwarf as Black dwarf

      Sir Arthur Edington was for a peaceful end of a star ,inspite of it the end of the white dwarf was enigmatic leading to a binary system as well
      as for a black dwarf.

      Magneticfields are produced as the result of dynamo
      processes at work in the stars’ interiors; the dynamo mechanism will differ
      with the internal structure of the star, i.e. thin outer convectionzone or
      fully convective star, and this affects the geometry of the large-scale fields
      produced.The magnetic fields in late-type stars are dynamic, producing changes
      in observed coronal structures and their effects over a wide range of
      timescales: minutes during large magnetic reconnection flares; fractions of the
      rotational or orbital period; years or decades of activity cycles; and
      evolutionary timescales, as non-uniform magnetic flux distributions affect the
      rate at which angular momentum loss occurs

      Along with magnetic fields, stellar rotation is required to
      understand stellar evolution, mass loss, and shaping of the circumstellar
      medium. The connection between magnetism, rotation, angular momentum, and mass
      loss is important but largely unexplored partly due to inadequate effective area
      to observe

      Magnetic reconnection is the
      breaking and rejoining of magnetic field lines in a highly conducting plasma The
      first task is to generalize the magnetic switch theory to include rotation as a
      triggering parameter, in addition to magnetic field strength and plasma density
      The basic process of reconnection has been understood from the late 1950s. If
      two parcels of magnetized plasma have oppositely directed magnetic fields and
      there is a region of weaker or zero field between them, then under the right
      circumstances the parcels can approach each other. The oppositely directed
      magnetic flux can cancel out (annihilate), and the plasma can jet outward along
      the weaker field directions at a characteristic speed called the Alfvén spee Magnetic
      field lines break and reconnect, plasma jets are formed, heat is released, and
      energy can be transferred from one region to another. In reconnection,
      large-scale dynamics and small-scale plasma physics come face to face: This is
      an essential feature of multiscale, nonlinear space plasma physics. Magnetism
      is also responsible for the formation of sunspots.
      Sunspots are small areas on the Sun that appear dark because of their relative
      low temperature. This low temperature is thought to be caused by magnetic
      fields. The magnetic field inhibits convection, or the distribution of heat,
      resulting in a cool sunspot

      In
      a properly-known quantum effect referred to as superradiance, atoms can emit
      light at an enhanced rate compared to what is possible in classical situations.
      This high emission price arises from the way that the atoms interact with the
      surrounding electromagnetic field. Logically, structures that superradiate will
      have to also absorb light at a larger price than standard, but so far the
      superabsorption of light has not been observed. This really happens in the end
      life of white dwarf ending in a dark dwarf..

      As the physicists explain,
      superabsorption is the reciprocal of superradiance. Superradiance was first
      introduced 60 years ago by the physicist Robert Dicke, and since then has found
      a variety of applications, including a new class of laser. Physically,
      superradiance occurs when a system of excited atoms decays and moves down a
      ladder of states called the “Dicke” or “bright” states. As
      a result, light can be emitted at an enhanced rate that is proportional to the
      square of the number of atoms.

      The physicists say that super
      absorption could be experimentally demonstrated in the future in a few
      different ways, with possibilities including an array of quantum dots or a
      Bose-Einstein condensate. In the future, they plan to investigate new methods
      for achieving extreme light absorption

      “We are working on an alternative scheme for quantum enhanced
      light absorption, which
      uses what’s called a ‘dark state of white dwarf ‘ as an efficient means of
      extracting energy from light, and is similar to what happens in photosynthesis,
      which is in contrast to super absorption, which is very different to how
      natural White dwarfs are very dense stars near the
      ends of
      their lives. The
      researchers studied the light absorbed by nickel and iron ions in the … light harvesters work,

      hubblesite.org support: ISSUE=8040 PROJ=13

      White dwarf sprewing water particles of sea over the neighboring planet as happened to our earth
      during its formation.

      Thank you for contacting Nature Publishing Group. We have
      received your query and will reply as soon as possible.

      This email has been automatically generated and does not require a reply.

      Kind regards,

      Nature Publishing Group Customer Services.

      ref:_00D20M75Y._500D0hTrVy:ref

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    • http://www.hawking.org.uk Sankaravelyudhan nandakumar

      Chandrasekhar limit has increased to 2.4 as observed now and land still a white dwarf can prevail as super limit of Chandrasekhar.
      .

      Citation:Magnetic
      field reversal and jet speed variation
      contributing a reversiable magnetic field call for an acceleration and
      deceleration in Blackholes:

      Galaxies are thought to have
      formed from matter and energy that originated in the Big Bang, the theoretical
      explosion that started the expansion of the universe. How supermassive black
      holes formed at the center of active galaxies is under lively debate. The
      dominant school of thought is that matter clumped together to form stars during
      the initial phases of the first galaxies, and some stars were so large and
      dense that they could not withstand their own gravity and imploded to create
      black holes. Another school of thought, to which Vestergaard’s research has
      contributed, is that black holes came into being first and stars formed around
      them to create galaxies.

      Sankaravelayudhan
      Nandakumar,Oford astrophysicist says that temperature difference in condensed
      matter physics of space may call for a spring type reaction calling for
      magneticfield reversal under extreme temperature variations in understanding
      blackhole dynamics as energy rewinding and future radiation of evolution. in
      galaxies forming a blackhole. BH from a low-mass galaxy but is below the escape
      velocity from the Milky Way (MW) galaxy. If central BHs were common in the
      galactic building blocks that merged to make the MW, then numerous BHs that
      were kicked out of low-mass galaxies should be freely floating in the MW halo
      today. We use a large statistical sample of possible merger tree histories for
      the MW to estimate the expected number of recoiled BH remnants present in the
      MW halo today. We find that hundreds of BHs should remain bound to the MW halo
      after leaving their parent low-mass galaxies.

      The galaxies around these early
      supermassive black holes were very young, with intense star formation. Other
      astronomers have established that the mass of a black hole and the mass of its
      galaxy are strictly correlated. These data support the theory that early black
      holes formed first and galaxies formed around them. “But we need a lot more
      data on this to know for sure if this hypothesis is correct,” says Vestergaard

      Understanding this connection
      between stars in a galaxy and the growth of a black hole, and vice-versa, is the
      key to understanding how galaxies form throughout cosmic time”If a black
      hole is spinning it drags space and time with it and that drags the accretion
      disc, containing the black hole’s food, closer towards it. This makes the black
      hole spin faster, a bit like an ice skater doing a pirouette. A
      new way to measure supermassive black hole spin in accretion disc-dominated
      active galaxies Astronomers report the exciting discovery of a new way
      to measure the mass of super massive black holes in galaxies. By measuring
      the speed with which carbon monoxide molecules orbit around such black holes,
      this new research opens the possibility of making these measurements in many
      more galaxies than ever before. Supermassive black holes are now known to
      reside at the centres of all galaxies. In the most massive galaxies in the
      Universe, they are predicted to grow through violent collisions with other
      galaxies, which trigger the formation of stars and provides food for the black
      holes to devour. These violent collisions also produce dust within the galaxies
      therefore embedding the black hole in a dusty envelope for a short period of
      time as it is being fed. Galaxies with hidden supermassive black holes tend to
      clump together in space more than the galaxies with exposed, or unobscured,
      black holes. The Herschel Space Observatory has shown galaxies with the most
      powerful, active black holes at their cores produce fewer stars than galaxies
      with less active black holes. The results are the first to demonstrate black
      holes suppressed galactic star formation when the universe was less than half
      its current age. Galaxies with massive black holes were found to have high
      rates of star formation, with some forming stars at a thousand times the rate
      of our own Milky Way galaxy today. But intriguingly, the Herschel results show
      that the fastest-growing black holes are in galaxies with very little star
      formation – once the radiation coming from close to the black hole exceeds a
      certain power, it tends to “switch off” star formation in its galaxy.

      Gas falling toward a black hole spirals inward and piles up into an accretion
      disk, where it becomes compressed and heated. Near the inner edge of the disk,
      on the threshold of the black hole’s event horizon — the point of no return –
      some of the material becomes accelerated and races outward as a pair of jets
      flowing in opposite directions along the black hole’s spin axis. These jets
      contain particles moving at nearly the speed of light, which produce gamma rays
      – the most extreme form of light — when they interact.

      The idea is that low-mass proto-galaxies with
      black holes at their center would have merged, creating a gravitational kick
      that would send the now larger black hole outward fast enough to escape the
      host dwarf galaxy, but not fast enough to leave the overall galactic halo. Hubblesite.org
      support: ISSUE=7909 PROJ=13

      A new type of combinational hydrodynamics over Bermuda
      triangle – 00132046

      hubblesite.org support: ISSUE=7955 PROJ=13

      hubblesite.org support: ISSUE=7972 PROJ=13