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class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../823/astrophysics.html">Astrophysics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Stellar characteristics</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../astro/3-stars-1.jpg" style="float: left; width: 250px; height: 118px;">Stars can be displayed on a diagram and categorized in a number of ways.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p>A Hertzsprung-Russell (HR) diagram plots stars according to their luminosity (<strong>vertical</strong> axis) and surface temperature (<strong>horizontal</strong> axis). Unlike most graphs in Physics, the HR diagram is not used to obtain a perfect correlation but is instead used to explore the evolution of stars.</p> <p style="text-align: center;"><img alt="" height="317" src="../../astro/screenshot-2019-08-03-at-12.21.07.png" width="307"></p> <div class="box"> <p>There are a few points to note about the diagram:</p> <ul> <li>The temperature axis is absolute (K), decreasing from left to right and has a non-linear scale.</li> <li>The luminosity axis is logarithmic.</li> <li>The diagonal lines represent radius.</li> </ul> </div> <p>While unlikely to be reproduced on an exam script, this <a href="http://www.eso.org/public/unitedkingdom/images/eso0728c/">ESO</a> HR diagram also indicates the colour of stars according to their temperature and, hence, spectral class.</p> <p style="text-align: center"><img alt="" src="../../astro/eso-hr.jpg" style="width: 600px; height: 598px;"></p> <p>The <em>regions</em> of the HR diagram reveal some groupings of stars with similar surface temperature and luminosity. We now know that each of these represents a portion of a star's evolution. These are the main sequence, red giants, super giants and white dwarfs. Note that there are other stages in the evolution of a star, but these cannot be accommodated within the axes of the diagram.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/358639836"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <h4>Main sequence</h4> <p><img alt="" src="../../astro/sun-1.jpg" style="float: left; width: 150px; height: 150px;">Stars in the <em>main sequence</em> have balanced forces between inward gravitation and outward radiation pressure. This is the longest stage in a star's evolution and continues until all hydrogen in the star has fused to become helium. The duration of the main sequence decreases as the mass of the star increases due to the higher temperatures in the core.</p> <p>Main sequence stars can be of any spectral class due to the possible luminosities and temperatures. The Sun is an example of a main sequence star with surface temperature 6000 K. This makes it spectral class G.</p> <p>The luminosity of a main sequence star increases with its mass according to the mass-luminosity relation:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(L\propto M^{3.5}\)</span></p> <ul> <li><span class="math-tex">\(L\)</span> is the luminosity of the star (W, or any consistent unit of power due to the proportional relationship)</li> <li><span class="math-tex">\(M\)</span> is the mass of the star (kg, or any consistent unit of mass due to the proportional relationship)</li> <li><span class="math-tex">\(3.5\)</span> is the exponent for main sequence stars</li> </ul> <p>Alternatively the relationship could be expressed as:</p> <p style="text-align: center;"><span class="math-tex">\({L_1 \over L_2}=({M_1\over M_2})^{3.5}\)</span></p> </div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/358639940"></iframe></div> <hr class="hidden-separator"> <h4>Red giants</h4> <p><img alt="" src="../../astro/sun_red_giant.svg" style="float: right; width: 282px; height: 250px;">When no hydrogen remains in the core, the outer layers of the star collapse under gravity, increasing the temperature of the core. Depending on the mass of the star, the temperature rise may be sufficient to recommence fusion of hydrogren from the outer layers or to commence fusion of helium. This process will repeat for as long as the temperature will allow, with the star contracting and expanding as each new type of nucleus, including carbon, is born. The expanded star is a <em>red giant</em>.</p> <p>With their large radius (the diagram shows the scale that the Sun will reach as a red giant), the surface temperature of a red giant is lower than in the main sequence. The appearance of the red giant is from yellow-orange to red, including the spectral types K and M.</p> <p>The contractions under gravity retain a radius sufficient to keep the electrons from entering the same quantum mechanical state. This <em>electron degeneracy </em>creates an outward pressure that prevents total collapse.</p> <hr class="hidden-separator"> <h4>White dwarfs</h4> <p><img alt="" src="../../astro/white-dwarf-sirius.png" style="float: left; height: 250px; width: 229px;"><em>White dwarf </em>stars can form in one of two ways:</p> <div class="box"> <ul> <li>Directly from the main sequence, for stars of mass under 0.3 times that of the Sun.</li> <li>From red giants with mass under 10 times that of the Sun, having cast off a <em>planetary nebula</em> of dust and gas due to the weaker gravitational field at the outer layers of the star.</li> </ul> </div> <p>White dwarfs are hot and small, on a similar scale to the Earth, but with no fusion taking place to produce light. This places white dwarf stars to the bottom right of the HR diagram, in spectral classes O, B and A.</p> <p>Approximately 97% of stars in the Milky Way will become a white dwarf at the end of their lives. They cool with time. </p> <hr class="hidden-separator"> <h4>Super giants </h4> <p><img alt="" src="../../astro/binding-energy.png" style="width: 300px; height: 200px; float: left;"><em>Super giant</em> stars are large enough to fuse nuclei to produce elements as large as iron, the nucleus of highest stability according to binding energy. They come from main sequence stars of spectral class O and B with masses over 8 times that of the sun.</p> <p>Super giant stars are both massive and luminous, placing them at the top of the HR diagram. The temperature range of supergiant stars spans 3000 K to over 20 000 K with any spectral class possible.</p> <hr class="hidden-separator"> <p><img alt="" src="../../astro/blue_supergiant_scale-small.jpg" style="float: right; width: 324px; height: 200px;">The Sun will never become a super giant, because of its limted mass. However, the image shows the scale of a blue supergiant in comparison to Jupiter's orbit in the Solar System.</p> <p>When fusion of iron ceases in a super giant, the star collapses once and then explodes in a <em>supernova</em>, releasing mass outwards. A supernova's luminosity is too great to be displayed on the HR diagram. A supernova is the only cosmological event that is sufficiently energetic for the fusion of elements heavier than iron.</p> <p>The outcome of a supernova depends, once again, on the mass of the material remaining. A <em>neutron star </em>or <em>black hole</em> will form. These vary from white dwarfs because their mass exceeds the <em>Chandrasekhar limit</em>, above which the electron degeneracy pressure in the star's core is insufficient to balance the inward force of gravity. The Chandrasekhar limit is 1.4 solar masses.</p> <hr class="hidden-separator"> <h4>Neutron stars</h4> <p><img alt="" src="../../astro/neutron.jpg" style="float: left; width: 151px; height: 150px;"></p> <p>Neutron stars (after a supernova of 10 to 29 solar masses) have a mass up to two or three times that of the Sun and a radius in the order of 10 km (roughly a city!). This gives neutron stars a density of approximately 10<sup>17</sup> kgm<sup>-3</sup>.</p> <p>An example of a neutron star is a <em>pulsar</em> with a periodically rotating magentic field. These can be detected using radio telescopes on Earth, provided that the plane of the magnetic field intersects with that of the detector.</p> <p>The incredibly high temperatures of a neutron star means that they are not visible on the HR diagram. The radius of a neutron star is upheld by <em>neutron degeneracy</em>, an outward pressure that prevents total collapse.</p> <hr class="hidden-separator"> <h4>Black holes</h4> <p><img alt="" src="../../astro/black-hole.jpg" style="float: right; width: 169px; height: 150px;"></p> <p>What happens to masses above three times that of the Sun after a supernova is unclear. So far mankind has not detected stars of between 3 to 5 solar masses. Beyond 10 solar masses, the gravitational field is so strong that the star collapses to produce a black hole, in spite of neutron degeneracy. </p> <p>The <em>Oppenheimer–Volkoff limit </em>is the maximum mass that a neutron star may have before further collapse into a black hole. This is estimated to be 3 solar masses.</p> <p>Black holes are given their title as their escape velocity exceeds the speed of light, which means that no electromagnetic radiation is observed from their core. The gravitational field is strong enough to distort the path of light passing nearby.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use flashcards to practise your recall.</i></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1" data-mode="Normal" data-topics="835" data-subject-id="6" data-n-flashcards="15" style="text-align:center">Show flashcards</a></div><hr> <p><i>Use quizzes to practise application of theory.</i> </p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#bef4f6d9"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="bef4f6d9"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Stellar characteristics <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-309-831" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>This image shows the stars in the constellation Orion.</p><p style="text-align: center;"><img alt="" height="289" src="../../astro/orionlabel.png" width="339"></p><p>From this photo we can deduce that compared to Rigel, Betlegeuse is...</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>the same radius</span></label> </p><p><label class="radio"> <input type="radio"> <span>more luminous</span></label> </p><p><label class="radio"> <input type="radio"> <span>further away</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>a lower temperature</span></label> </p></div><div class="q-explanation"><p>We cannot measure a star's radius, luminosity or distance from the Earth without knowing some of these other quantities.</p><p>The redder colour, however, indicates the lower temperature (NB: Hertzsprung-Russell).</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The ratio <span class="math-tex">\(L_\text{Z}\over L_\text{sun}\)</span> is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>2</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>100</span></label> </p><p><label class="radio"> <input type="radio"> <span>20</span></label> </p><p><label class="radio"> <input type="radio"> <span>10</span></label> </p></div><div class="q-explanation"><p>Z is positioned two divisions vertically above the sun. Knowing that the luminosity scale is logarithmic, one division is x10 and the second x100.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The ratio <span class="math-tex">\(L_\text{Z}\over L_\text{Y}\)</span> is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>100</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1000</span></label> </p><p><label class="radio"> <input type="radio"> <span>10</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 000</span></label> </p></div><div class="q-explanation"><p>Z is positioned three divisions vertically above Y. Knowing that the luminosity scale is logarithmic, one division is x10, the second x100 and the third x1000.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The ratio <span class="math-tex">\(\text{radius}_\text{X}\over \text{radius}_\text{Y}\)</span> is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 000 000</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1000</span></label> </p><p><label class="radio"> <input type="radio"> <span>100</span></label> </p><p><label class="radio"> <input type="radio"> <span>3</span></label> </p></div><div class="q-explanation"><p>X is on the <span class="math-tex">\(10R_\text{sun}\)</span> diagonal line.</p><p>Y is on the <span class="math-tex">\(0.01R_\text{sun}\)</span> diagonal line.</p><p>The ratio required is <span class="math-tex">\({10\over0.01}=1000\)</span>.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The ratio <span class="math-tex">\(\text{radius}_\text{Z}\over \text{radius}_\text{sun}\)</span> is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>100</span></label> </p><p><label class="radio"> <input type="radio"> <span>10</span></label> </p><p><label class="radio"> <input type="radio"> <span>0</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1</span></label> </p></div><div class="q-explanation"><p>Z is on the <span class="math-tex">\(1\times R_\text{sun}\)</span> diagonal line.</p><p>Both stars have the same radius.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The temperature of Y is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>4000</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>20 000</span></label> </p><p><label class="radio"> <input type="radio"> <span>200 000</span></label> </p><p><label class="radio"> <input type="radio"> <span>7000</span></label> </p></div><div class="q-explanation"><p>The position of Y is to the left of the sun. This means it has a higher temperature than 6000 K. However, we know that it should not exceed tens of thousands of Kelvin in order to be displayed on the HR diagram.</p><p style="text-align: center;"> <img alt="" height="314" src="../../astro/screenshot-2019-08-03-at-12.21.07.png" width="305"></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>The ratio <span class="math-tex">\(\text{mass}_\text{Z}\over \text{mass}_\text{sun}\)</span>is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>4</span></label> </p><p><label class="radio"> <input type="radio"> <span>20</span></label> </p><p><label class="radio"> <input type="radio"> <span>2</span></label> </p><p><label class="radio"> <input type="radio"> <span>100</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(L\propto M^{3.5} \Rightarrow {M_Z\over M_\text{sun}} =\sqrt[3.5]{L_Z\over L_\text{sun}}\)</span></p><p>Using the two vertical divisions to deduce the relative luminosities:</p><p><span class="math-tex">\(L_Z =100L_\text{sun}\Rightarrow {M_Z\over M_\text{sun}} =\sqrt[3.5]{100}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>Which star is Betlegeuse?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Z</span></label> </p><p><label class="radio"> <input type="radio"> <span>X</span></label> </p><p><label class="radio"> <input type="radio"> <span>Y</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>W</span></label> </p></div><div class="q-explanation"><p>Betlegeuse is a red giant (high luminosity but low temperature) and so appears in the top-right of the HR diagram.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>Which stars are fusing Hydrogen to form helium?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>W and Y</span></label> </p><p><label class="radio"> <input type="radio"> <span>W, X , Y and Z</span></label> </p><p><label class="radio"> <input type="radio"> <span>X , W and Z </span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>X and Z</span></label> </p></div><div class="q-explanation"><p>Main sequence stars fuse hydrogren to form helium. X and Z are on the main sequence (the diagonal left to right strip).</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows an HR diagram with the values removed.</p><p style="text-align: center;"><img alt="" height="312" src="../../astro/hrblank.png" width="302"></p><p>What are the units of the y-axis?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Wm<sup>-1</sup></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>no units</span></label> </p><p><label class="radio"> <input type="radio"> <span>Wm<sup>-2</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>W</span></label> </p></div><div class="q-explanation"><p>Luminosity relative to the sun is a ratio of two dimensionally equivalent quantities. 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