Astronomy

Alfven Radius of mainsequence stars

Alfven Radius of mainsequence stars


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Is there any average value for the Alfven radius of main-sequence stars? if there are no such values, then how may I calculate it??


There is no average value. The large scale magnetic fields of main sequence stars are both a function of spectral type and rotation. In turn, rotation is age-dependent. In addition, the gas pressure at a distance from the star depends on conditions in the stellar wind and this too will depend on spectral type, rotation and age.

There are no universally agreed models for the behaviour of these quantities.


Alfven Radius of mainsequence stars - Astronomy

The detection of solid grains with temperatures of 50 to 125 K and fractional bolometric luminosities in the range 10 exp -5 to 10 exp -3 early in the IRAS mission around three nearby A main-sequence stars, Alpha Lyrae (Vega), Alpha Piscis Austrinus (Fomalhaut), and Beta Pictoris, is discussed. Spatial resolution of the emission indicates that: the grains are larger than interstellar grains, the material probably lies in disks in the stellar equatorial planes, the disks extend to distances of 100 to 1000 AU from the stars, and zones a few tens of AU in radius around the central stars are relatively empty. Subsequent surveys of IRAS data reveal more than 100 main-sequence stars of all spectral classes having unresolved excesses with similar temperatures and fractional luminosities to the three prototypes. Some stars with excesses have estimated ages of 1 to 5 Gyr. Thus, main-sequence FIR excesses appear to be widespread and are present in systems old enough to be probably past the stage of active planet formation.


Alfven Radius of mainsequence stars - Astronomy

What kind of stars are found here?

Try to read the values of L, T, and R for yourself from the diagram. Do you estimate values for the luminosity, temperature, and size of the star similar to those listed above?

The basic properties of the stars which lie along the Main Sequence differ from each other in predictable ways. They are all clustered tightly around a central line which runs down the middle of the Hertzsprung-Russell diagram. Because of this, for any one luminosity the range of possible radii and temperatures for Main Sequence stars is extremely small. Similarly, for any one temperature the range of possible radii and luminosities for Main Sequence stars is also fairly small. (Only at temperatures below 4,000 K does the distribution of stars along the Main Sequence begin to broaden, with many star of different luminosities and radii being found with the same temperature).

    A horizontal line running across the diagram represents all of the locations where stars are found that have the same luminosity. Any star which lies along the horizontal green line drawn above has a luminosity of 600 L. (This includes a number of red giants, as well as a narrow band along the Main Sequence.)

How can we use this narrow distribution to estimate the radii of a Main Sequence star from the temperature T alone?

Consider the case of a Main Sequence star, with a temperature T of 15,400 K. We will use the Hertzsprung-Russell diagram to estimate its radius R. Following the vertical green line draw up from 15,400 K on the x-axis, we see that quite a few yellow-coloured Main Sequence stars lie along it (we include all of the yellow-coloured stars which lie just above and just below the green cross). These are all the Main Sequence stars which have a temperature of 15,400 K. These stars are all related to one another in physical size. As stated above, diagonal lines drawn on the diagram represent the locations of stars all of the same size. Main Sequence stars with a temperature of 15,400 K thus extend over only a small range in radius.

Examine the Hertzsprung-Russell yourself, to estimate which two diagonal lines would best bound the location of these Main Sequence stars. These stars all lie above the line showing the location of all stars with the same radius as the Sun, and they lie below the the line showing the location of all stars with a radius ten times larger than that of the Sun. It is easy to see that all Main Sequence stars with a temperature of 15,400 K have a radius between one to ten times larger than the Sun &ndash but we can do better!

To keep the diagram easy to read, we have drawn lines of constant radius at the radius of the Sun, at ten times the radius of the Sun, at one hundred times the radius of the Sun, and such, marking only powers of ten. However, we could as easily draw a line of constant radius at twice the radius of the Sun, or two-hundred times the radius of the Sun, or at any other size scale.

With your mind, fill in the region between the diagonal line at one solar radius and the diagonal line at ten solar radii with additional lines, all parallel to the two found on the diagram. These lines will mark the location of stars which are twice as large as the Sun, three times as large as the Sun, four times as large as the Sun, and such, up to nine times as large as the Sun. You can use your powers of observation to see that the Main Sequence stars with a temperature of 15,400 K will all lie above the line where stars are twice as large as the Sun, and below the line where stars are six times as large as the Sun.

We have accomplished a great deal with a small amount of information! Using only the temperature of a star and the fact that it lies on the Main Sequence, we have limited its radius to between two and six times that of the Sun.


Red Supergiants

The Orion region showing the red supergiant Betelgeuse
By Rogelio Bernal Andreo CC BY-SA 3.0

Red supergiants have the largest radius of all known stars. They have low surface temperatures (for stars!) of below 4,100 K. This causes them to shine with a red colour. The star Betelgeuse in the constellation of Orion is a red supergiant.

Red supergiants evolve from large main sequence stars that contain more than 8 times the mass of our Sun. Some stars are born with more than 200 times the mass of the Sun! Like all stars, massive stars create energy through nuclear fusion, but these stars use up all of their supply of hydrogen after 5 - 20 million years. Their core then becomes made of helium, which starts to burn instead. A shell of hydrogen around the core also starts to fuse together. This creates lots of energy which causes the star to expand. As the star gets bigger it cools down becoming a red colour. These enormous, cool stars are known as supergiants.

Supergiants will burn all of the helium in their cores within a few million years. They will then start to burn carbon. This continues with heavier and heavier elements until the star contains a core of iron. At this stage the star can no longer fuse elements to produce energy so the star collapses under gravity and produces a supernova.


Parallax only works for the closest stars

  • The Sun is G2V, V being the stellar luminosity class for the main-sequence.
  • Betelgeuse is M2Ia
  • Visual Binary - See Orbiting Stars - double star Kruger 60
  • Spectroscopic Binary - Spectrum reveals binary nature thru Doppler Effect
  • Eclipsing Binary - Light curve shape
    a = semimajor axis = radius for circular orbit
    p = period of orbit
  • Note: I don't expect you to know this formula, just that there is a relationship between the mass, the period, and the size (semimajor axis) of the orbit
  • bright Sirius A and faint companion Sirius B
  • orbital period = 50 years
  • semi-major axis = 20 AU
  • MA + MB = 3.2 Msun
  • further study reveals:
    • MA = 2.1 Msun
    • MB = 1.1 Msun
    • variation of mass along the main sequence

    Main sequence stars range in mass from 0.1 to 20 times the mass of the Sun (with a few exceptions)

    Most main-sequence stars are low-mass stars, and only a small fraction are much more massive than the Sun

    • mass-radius relation for main sequence stars
    • mass-luminosity relation for main sequence stars
      • luminosity


      Alfven Radius of mainsequence stars - Astronomy

      1. Stars shine because they're hot and dense: emit a thermal (blackbody) radiation spectrum modified by absorption lines this absorption line spectrum is produced at its surface (called a photosphere).

      • the result of the gravitational collapse of a gas cloud
      • pressure - gravity balance
        • given their mass relative to their size, this means stars must be and remain hot
        • sets up structure within star: pressure (P), temperature (T), number density of particles (n) - in order for the star to support itself against its own weight, all three of these must reach their highest values within the star's core, and then diminish in value toward the star's surface. Recall that gas pressure P is proportional to the product of the number density of particles n and temperature T.
        • energy generated by the star's core is transported through it, to & through the star's envelope (the portion of the star outside of its core), and then to the surface by radiation (photons) or by convection. Photons stream out of the star's photosphere into dark, cold space - that which we call star light.
        • energy balance & energy transport: energy lost at surface in the form of light (luminosity L*) is replaced precisely by energy released via fusion (Lfusion) within star's core, i.e., L*= Lfusion. In this case, the star need not contract to remain hot enough to generate sufficient pressure to avoid collapsing under its own weight.
        • pressure-temperature thermostat regulates fusion within core (keeps star from exploding like a thermonuclear bomb), & together with energy transport regulate the energy balance of star
        • require higher T at every layer within for sufficient pressure support against gravity
          • T at the star's surface (Ts) dictates star's spectrum (thermal radiation spectrum modifed by absorption lines)
          • T within core sets energy released by fusion - higher central T means greater Lfusion, thus balancing a more massive star's greater surface luminosity L*

          M/R 3 ), then the size of the star would be larger for a larger mass, scaling like R

          M 1/3 . However, a star that is supported against its weight by pressure that depends on temperature (such as gas pressure) cannot have both more mass and an equal or higher density . Therefore, higher mass MS stars must be less dense than lower mass ones. In fact the sizes of main sequence stars scale more rapidly with mass, as R

          Remember, you can compare the structures of only those stars that have the same energy source in their cores. For main sequence stars, this is the fusion of hydrogen into helium in their central most regions. Can you see how the many known observed facts of main sequence stars are logically and causally linked together by the laws of nature?

          1 Strictly speaking, this is true when averaged over the characteristic time required to transport the energy through the star. If for any reason the star isn't in energy balance, you can bet that it is adjusting its structure (expanding/cooling or contracting/heating) until it is.
          2 By this time these objects' densities have become so high that a weird quantum mechanical pressure known as "electron degeneracy pressure" becomes important. Since this kind of pressure does not depend on temperature, it can balance against the force of gravity even though the object continues to radiate energy away as light from its surface. As a consequence the object does not contract, and without contraction no more gravitational potential energy can be released to raise the temperature, and so the temperature slowly falls over the eons of time.
          Kirk Korista
          Professor of Astronomy
          Department of Physics
          Western Michigan University


          Alfven Radius of mainsequence stars - Astronomy

          Magellanic Clouds Two nearby small irregular galaxies about 160,000 light years (Large Magellanic Cloud), and 200,000 light years (Small Magellanic Cloud) distant, visible to the naked eye from the southern hemisphere

          magnetic field Field which accompanies any electric current or changing electric field, and governs the influence of magnetized objects on one another.

          magnetosphere The region of space surrounding a rotating, magnetized object in which the motions of charged particles are controlled by the object's magnetic field..

          magnitude The method we use today to compare the apparent brightness (magnitude) of stars began with Hipparchus, a Greek astronomer who lived in the second century BC. Hipparchus called the brightest star in each constellation "first magnitude." Ptolemy, in 140 A.D., refined Hipparchus' system and used a 1 to 6 scale to compare star brightness, with 1 being the brightest and 6 the faintest. [More Info]

          main sequence A well-defined band on an H-R diagram on which most stars tend to be found, running from the top left of the diagram to the bottom right.

          main-sequence turnoff Special point on an H-R diagram for a cluster. If all the stars in a particular cluster are plotted, the lower mass stars will trace out the main sequence up to the point where stars begin to evolve off the main sequence toward the red giant branch. The point where stars are just beginning to evolve off is the main-sequence turnoff.

          mass A measure of the total amount of matter contained within an object.

          mass-luminosity relation The dependence of the luminosity of a main-sequence star on its mass. The luminosity increases roughly as the mass raised to the third power.

          mass-radius relation The dependence of the radius of a main-sequence star on its mass. The radius rises roughly in proportion to the mass.

          matter-dominated universe A universe in which the density of matter exceeds the density of radiation. The present-day universe is matter-dominated.

          matter-antimatter annihilation A highly efficient process in which equal amounts of matter and anti-matter collide and destroy each other, producing a burst of energy, primarily in the form of gamma rays.

          micro-quasar: A stellar-mass black hole that launches powerful jets of particles and radiation.

          microwave radiation Radiation between radio and infrared wavelengths, having a wavelength between about 0.1 and 10 cm. [More Info]

          microwave background radiation See cosmic microwave background radiation.

          Milky Way Galaxy The specific galaxy to which the Sun belongs, so named because most of its visible stars appear overhead on a clear, dark night as a milky band of light extending across the sky. [More Info: Field Guide]

          millisecond pulsar A pulsar whose period indicates that the neutron star is rotating nearly 1000 times each second.

          molecular cloud A cold, dense interstellar cloud which contains a high fraction of molecules. It is widely believed that the relatively high density of dust particles in these clouds plays an important role in the formation and protection of the molecules.

          molecular cloud complex Collection of molecular clouds that spans as much as 150 light years and may contain enough material to make millions of Sun-sized stars.

          molecule A tightly bound collection of atoms held together by the electromagnetic fields of the atoms. Molecules, like atoms, emit and absorb photons at specific wavelengths.

          momentum A measure of the state of motion of a body the momentum of a body is the product of its mass and velocity. In the absence of a force, momentum is conserved.


          If a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47. Figure 18.15 Schematic H−R Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram they are both hot and dim, and must be white dwarfs. Figure 18.14 H−R Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.

          If a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47.

          Figure 18.15 Schematic H−R Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram they are both hot and dim, and must be white dwarfs.

          Figure 18.14 H−R Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.


          Analyzing the Universe - Course Wiki: The Stellar Family Tree

          The astronomy department from the University of Nebraska-Lincoln hosts a great website with various educational resources, one of which is a very informative Interactive H-R Diagram. Let's take a closer look at this guide.

          1. Open the Interactive H-R Diagram. Note that the red x appears initially at the position where the sun resides.

          2. Select "magnitude" for the y-axis. Note that this is absolute magnitude , which quantifies the brightness of a star by telling you how bright it would appear if it were placed at a distance of 10 parsecs (32.6 light-years) from an observer on Earth. This gives a true measure of the power output of a star.

          3. Next select "show luminosity classes" under options and leave the instability strip button unselected for now. Below these buttons are options for plotted stars. Select the "both the nearest and brightest stars" button so that your screen looks like mine below.

          4. Let's discuss some of the many features of the H-R diagram that are displayed. The x-axis of the plot represents the temperature of a star (please note that the temperatures go from high to low if we look from left to right on the axis). This temperature scale is in Kelvin, which is similar to the centigrade scale in that a difference of 1 degree Celsius is equal to a difference of 1 degree in the Kelvin scale of temperature. However, zero (0) Kelvin is equal to about -273 degrees Celsius. Zero Kelvin is known as Absolute Zero, the temperature at which a gas would have zero energy, other than its own quantum fluctuations.

          The green diagonal lines that run from top-left to bottom-right, are lines upon which stars have the same physical size (i.e. they represent lines of constant radius). If you look at the screen near the bottom left you will see the mathematical expression that relates a star's temperature and luminosity (magnitude) to its radius. The green band that also runs from top-left to bottom-right with a thin red line running through it is known as the "Main Sequence". These are stars in the prime of their life where they have achieved a stable balance between the gravitational force on the star that acts inward towards the fiery core, and the outward pressure changes resulting from the heat generated by fusion in the core. This balance is called Hydrostatic Equilibrium.

          The top right of the diagram is where the Blue Supergiants reside. The Red Giant stars are immediately down and to the right of the blue supergiants, while the White Dwarf stars are shown as the gray band at the bottom of the H-R diagram. All of these groups are intimately related to the evolution of the main sequence stars, which are best described by two different paths that differ as a function of stellar mass.

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          Department of Physics & Astronomy, 136 Frelinghuysen Rd, Piscataway, NJ 08854
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          Star Main Sequence

          [/caption]
          Most of the stars in the Universe are in the main sequence stage of their lives, a point in their stellar evolution where they’re converting hydrogen into helium in their cores and releasing a tremendous amount of energy. Let’s example the main sequence phase of a star’s life and see what role it plays in a star’s evolution.

          A star first forms out of a cold cloud of molecular hydrogen and helium. Mutual gravity pulls the stellar material together, and this gravitational energy heats it up. The star first goes through a protostar phase for about 100,000 years, and then a T Tauri phase, where it shines only with the energy released from its ongoing gravitational collapse. This second T Tauri phase lasts a further 100 million years or so.

          Eventually temperatures and pressures in the core of the star are sufficient that it can ignite nuclear fusion, converting hydrogen atoms into helium. When this process gets going, a star is said to be in the main sequence phase of its life.

          In a star like our Sun, the core accounts for about 20% of its radius. It’s inside this region where all the energy of the Sun is released. The energy released in the core must then travel slowly through a radiative zone, where photons of energy are absorbed and then re-emitted. Energy is then carried through a convective zone, where columns of hot plasma carry bubbles of heated gas to the surface of the Sun where it’s released. The material cools down and falls back down inside the Sun where it’s heated up again. This journey can take more than 100,000 years for a single photon to get from the core of a star out to its surface.

          Over time, a star slowly uses up the supply of hydrogen in its core, and leftover helium builds up. But the main sequence phase can last a long time. Our Sun has already been in its main sequence for 4.5 billion years, and will probably last another 7.5 billion years before it runs out of fuel.

          The smallest red dwarf stars can smolder in the main sequence phase for an estimated 10 trillion years! The largest supergiant stars might only last a few million. It all comes down to mass.

          And mass defines how a star comes out of the main sequence phase of its life. For the smallest red dwarf stars, astronomers think they’ll just shut off once they’ve used up all their hydrogen, becoming white dwarfs. More massive stars, with up to 10 solar masses, will go through a red giant phase where they expand many times their original size before collapsing down to the white dwarf. And the most massive stars will just explode as supernovae.

          We have written many articles about stars on Universe Today. Here’s an article about the entire life cycle of stars, and different types of stars.

          We have recorded several episodes of Astronomy Cast about stars. Here are two that you might find helpful: Episode 12: Where Do Baby Stars Come From, and Episode 13: Where Do Stars Go When they Die?