نموذج أيناستو

نموذج أيناستو (بالإنجليزية: Einasto profile) هو دالة رياضية تصف كيف للكثافة ρ الخاصة بنظم النجوم الكروية أن تختلف مع المسافة r عن المركز. قدم جان إيناستو هذا النموذج في مؤتمر عام 1963 في ألماتي في كازاخستان.[1]

يمتلك نموذج إيناستو مقياسًا لوغارتميًّا لقانون الرفع إلى أس في شكل:

والتي يمكن إعادة ترتيبها لتظهر بالشكل الآتي:

الكمية α تتحكم في درجة الانحناء الخاص بالنموذج. يمكن رؤية ذلك بحساب الميل على الرسم البياني اللوغارتمي-اللوغارتمي:

كلما زادت α كلما زادت سرعة اختلاف الميل مع القطر. يمكن أن يوصف قانون إيناستو كتعميم لقانون الرفع، ρ∝r-N والذي له ميل ثابت على الرسم البياني اللوغارتمي-اللوغارتمي.

لنموذج إيناستو نفس الشكل الرياضي لقانون سيرسيك، والذي يستخدم لوصف سطوع السطح (الكثافة البارزة) للمجرات.[2] استُخدم نموذج إيناستو لوصف العديد من أنواع الأنظمة، منها المجرات وهالة المادة المظلمة.[3]

المراجع

  1. ^ J. Einasto (1965), Kinematics and dynamics of stellar systems, Trudy Inst. Astrofiz. Alma-Ata 5, 87
  2. ^ J. Einasto and U. Haud (1989), Galactic models with massive corona. I - Method. II - Galaxy Astron. Astrophys. 223, 89 نسخة محفوظة 17 يونيو 2019 على موقع واي باك مشين.
  3. ^ Merritt، David؛ Graham، Alister؛ وآخرون (2006). "Empirical Models for Dark Matter Halos". The Astronomical Journal. ج. 132 ع. 6: 2685–2700. arXiv:astro-ph/0509417. Bibcode:2006AJ....132.2685M. DOI:10.1086/508988.
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