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In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. The relationship is represented by the equation: where L⊙ and M⊙ are the luminosity and mass of the Sun and 1 < a < 6. The value a = 3.5 is commonly used for main-sequence stars. This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M⊙ < M < 55M⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1.

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  • علاقة الكتلة والضياء (ar)
  • Masse-Leuchtkraft-Beziehung (de)
  • Relazione massa-luminosità (it)
  • Mass–luminosity relation (en)
  • 質量光度関係 (ja)
  • 질량-광도 관계 (ko)
  • Massa-lichtkrachtrelatie (nl)
  • Зависимость масса — светимость (ru)
  • 質光關係 (zh)
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  • علاقة الكتلة والضياء (بالإنجليزية: mass–luminosity relation)‏ هي معادلة رياضية في الفيزياء الفلكية تصف علاقة كتلة النجم بضيائه، أول من أشار إليها هو ، وتعطى العلاقة بالشكل التالي: حيث أن هو الضياء الشمسي، و هي كتلة الشمس، والأس يأخذ قيم بين تبعاً لنوع النجم، ولكن أكثر قيمة إستخداماً له هي لنجوم التتابع الرئيسي التي تملك كتلة بين، لكن لا يمكن استخدام هذه القيمة على العمالقة الحمر والأقزام البيضاء. تكون قيمة الأس تساوي إذا إقترب النجم من ضياء إدينغتون. (ar)
  • Eine Masse-Leuchtkraft-Beziehung stellt einen Zusammenhang dar zwischen der Masse eines Objektes, beispielsweise eines Sterns, und seiner Leuchtkraft. Dieser Zusammenhang kann verwendet werden zur Abschätzung der Masse eines Sterns allein aus der Beobachtung seiner Leuchtkraft. Alternativ zur Leuchtkraft kann auch die Effektivtemperatur oder der Spektraltyp eines Sterns verwendet werden, die meist einfacher zu bestimmen sind. (de)
  • In astrofisica la relazione massa-luminosità è un'equazione che illustra il rapporto esistente fra la massa di una stella e la sua luminosità. (it)
  • 質量光度関係 (英: mass–luminosity relation) は、恒星の質量と光度を結び付ける式である。Jakob Karl Ernst Halm によって初めて記述された。恒星の質量を、光度を とすると、質量光度関係は以下の式で表される。 ここで、 と はそれぞれ太陽光度と太陽質量であり、a は 1〜6 の値を取る。主系列星に対しては一般的に a = 3.5 が用いられる。この関係式と一般的な a = 3.5 という値は 2〜55太陽質量を持つ主系列星には当てはまるが、赤色巨星や白色矮星には当てはまらない。また恒星の光度がエディントン光度に近づくにつれ、a = 1 に近づく。 (ja)
  • 질량-광도 관계(mass–luminosity relation)란 천체물리학에서 별의 질량과 광도 사이의 관계에서 주어지는 방정식이다. 관계는 다음 식으로 표현된다. 이때 L⊙과 M⊙은 각각 태양의 광도 및 질량이고 1 < a < 6이다. 주계열성의 경우 a값은 a=3.5이다. 별이 에딩턴 광도에 가까워지면 a=1이 된다. 요약하면 다음과 같다. (ko)
  • De massa-lichtkrachtrelatie is een vergelijking uit de astrofysica die een verband geeft tussen de massa van een hoofdreeksster en haar lichtkracht. De relatie is gebaseerd op waarnemingen maar kan ook theoretisch worden verklaard. (nl)
  • In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. The relationship is represented by the equation: where L⊙ and M⊙ are the luminosity and mass of the Sun and 1 < a < 6. The value a = 3.5 is commonly used for main-sequence stars. This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M⊙ < M < 55M⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1. (en)
  • Зависимость масса — светимость — в астрофизике уравнение, показывающее связь между массой звезды и её светимостью. Данное уравнение имеет вид где L⊙ и M⊙ — светимость и масса Солнца, 1 < a < 6. Значение a = 3.5 обычно используется для звезд главной последовательности с массами 2M⊙ < M < 20M⊙ и не применимо к красным гигантам или белым карликам. В случае достижения звездойпредела Эддингтона значение a = 1. Для различных диапазонов масс звезд зависимость масса-светимость выглядит следующим образом: (ru)
  • 質光關係是天文物理中顯示恆星光度與質量之間關係的方程式。以公式表示的關係是: 此處的L⊙和M⊙是太陽的光度和質量,並且1 < a < 6。在主序帶上的恆星,通常 a = 3.5。 這個方程式使用a = 3.5 的值只適用於主序帶上質量在2M⊙ < M < 20M⊙,並且不適用於紅巨星和白矮星。 總之,不同質量範圍的恆星使用下面的關係式會得到更好的近似值: 對質量低於 .43M⊙的恆星,對流是唯一的能量傳輸程序,這使得關係發生重大的改變。對質量M > 20M⊙的恆星,這關係變得平坦的L ∝ M。這可以顯示這樣的變化是因為大質量恆星輻射壓力的增加。這些關係是憑藉著觀測距離經由標準的視差或其他方法正確測量出的聯星所得到的經驗方程式。在繪製出足夠的恆星之後,恆星會呈現對數函數圖,有著一定斜率的線對應於特定的a值。 (zh)
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  • علاقة الكتلة والضياء (بالإنجليزية: mass–luminosity relation)‏ هي معادلة رياضية في الفيزياء الفلكية تصف علاقة كتلة النجم بضيائه، أول من أشار إليها هو ، وتعطى العلاقة بالشكل التالي: حيث أن هو الضياء الشمسي، و هي كتلة الشمس، والأس يأخذ قيم بين تبعاً لنوع النجم، ولكن أكثر قيمة إستخداماً له هي لنجوم التتابع الرئيسي التي تملك كتلة بين، لكن لا يمكن استخدام هذه القيمة على العمالقة الحمر والأقزام البيضاء. تكون قيمة الأس تساوي إذا إقترب النجم من ضياء إدينغتون. (ar)
  • Eine Masse-Leuchtkraft-Beziehung stellt einen Zusammenhang dar zwischen der Masse eines Objektes, beispielsweise eines Sterns, und seiner Leuchtkraft. Dieser Zusammenhang kann verwendet werden zur Abschätzung der Masse eines Sterns allein aus der Beobachtung seiner Leuchtkraft. Alternativ zur Leuchtkraft kann auch die Effektivtemperatur oder der Spektraltyp eines Sterns verwendet werden, die meist einfacher zu bestimmen sind. (de)
  • In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. The relationship is represented by the equation: where L⊙ and M⊙ are the luminosity and mass of the Sun and 1 < a < 6. The value a = 3.5 is commonly used for main-sequence stars. This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M⊙ < M < 55M⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1. In summary, the relations for stars with different ranges of mass are, to a good approximation, as the following: For stars with masses less than 0.43M⊙, convection is the sole energy transport process, so the relation changes significantly. For stars with masses M > 55M⊙ the relationship flattens out and becomes L ∝ M but in fact those stars don't last because they are unstable and quickly lose matter by intense solar winds. It can be shown this change is due to an increase in radiation pressure in massive stars. These equations are determined empirically by determining the mass of stars in binary systems to which the distance is known via standard parallax measurements or other techniques. After enough stars are plotted, stars will form a line on a logarithmic plot and slope of the line gives the proper value of a. Another form, valid for K-type main-sequence stars, that avoids the discontinuity in the exponent has been given by Cuntz & Wang; it reads: with (M in M⊙). This relation is based on data by Mann and collaborators, who used moderate-resolution spectra of nearby late-K and M dwarfs with known parallaxes and interferometrically determined radii to refine their effective temperatures and luminosities. Those stars have also been used as a calibration sample for Kepler candidate objects. Besides avoiding the discontinuity in the exponent at M = 0.43M⊙, the relation also recovers a = 4.0 for M ≃ 0.85M⊙. The mass/luminosity relation is important because it can be used to find the distance to binary systems which are too far for normal parallax measurements, using a technique called "dynamical parallax". In this technique, the masses of the two stars in a binary system are estimated, usually as being the mass of the Sun. Then, using Kepler's laws of celestial mechanics, the distance between the stars is calculated. Once this distance is found, the distance away can be found via the arc subtended in the sky, giving a preliminary distance measurement. From this measurement and the apparent magnitudes of both stars, the luminosities can be found, and by using the mass–luminosity relationship, the masses of each star. These masses are used to re-calculate the separation distance, and the process is repeated. The process is iterated many times, and accuracies as high as 5% can be achieved. The mass/luminosity relationship can also be used to determine the lifetime of stars by noting that lifetime is approximately proportional to M/L although one finds that more massive stars have shorter lifetimes than what the M/L relationship predicts. A more sophisticated calculation factors in a star's loss of mass over time. (en)
  • In astrofisica la relazione massa-luminosità è un'equazione che illustra il rapporto esistente fra la massa di una stella e la sua luminosità. (it)
  • 質量光度関係 (英: mass–luminosity relation) は、恒星の質量と光度を結び付ける式である。Jakob Karl Ernst Halm によって初めて記述された。恒星の質量を、光度を とすると、質量光度関係は以下の式で表される。 ここで、 と はそれぞれ太陽光度と太陽質量であり、a は 1〜6 の値を取る。主系列星に対しては一般的に a = 3.5 が用いられる。この関係式と一般的な a = 3.5 という値は 2〜55太陽質量を持つ主系列星には当てはまるが、赤色巨星や白色矮星には当てはまらない。また恒星の光度がエディントン光度に近づくにつれ、a = 1 に近づく。 (ja)
  • 질량-광도 관계(mass–luminosity relation)란 천체물리학에서 별의 질량과 광도 사이의 관계에서 주어지는 방정식이다. 관계는 다음 식으로 표현된다. 이때 L⊙과 M⊙은 각각 태양의 광도 및 질량이고 1 < a < 6이다. 주계열성의 경우 a값은 a=3.5이다. 별이 에딩턴 광도에 가까워지면 a=1이 된다. 요약하면 다음과 같다. (ko)
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