Sains Malaysiana 44(3)(2015): 457–462

The Nonlinear Least Square Fitting for Rotation Curve of Orion Dwarf Spiral

(Penyuaian Kuasa Dua Terkecil Tak Linear bagi Putaran Lengkung Orion Kerdil Berpilin)

N. HASHIM¹*, Z.Z. ABIDIN², U.F.S.U. IBRAHIM¹, M.S.R. HASSAN², Z.S. HAMIDI², R. UMAR⁴ & Z.A. IBRAHIM³

¹Centre for Foundation Studies in Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

²Radio Cosmology Research Lab, Physics Department, Faculty of Science, Universiti Malaya

50603 Kuala Lumpur, Malaysia

³Faculty of Applied Sciences, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor Darul Ehsan, Malaysia

⁴Astronomy Unit, Universiti Sultan Zainal Abidin, 21300 Kuala Terengganu,

Terengganu Darul Iman, Malaysia

Received: 15 January 2014/Accepted: 21 August 2014

ABSTRACT

The basis of the nonlinear least square fitting is to fit the nonlinear rotation curve model with the observed rotation curve of the Orion dwarf galaxy. It has been the most powerful tool to study the distribution of dark matter in galaxies where it is used to obtain the proper mass model of a galaxy. In this paper, we present the rotation curve fit of Orion dwarf galaxy, corrected for asymmetric drift by using the gradient method of nonlinear least square. Our results showed an excellent agreement between the mass models of cored halo profile with the observed rotation curve. Thus, we can estimate the value of disk mass, MD; the core radius, r0 and core density, roof the galaxy with 1-s of uncertainty. We finally indicated the dark matter halo distribution as cored dark matter halo with density, 3.9 × 106MŸ kpc-3.

Keywords: Dwarf spiral - rotation curve - dark matter; fitting; galaxies; gradient method

ABSTRAK

Asas kepada penyuaian kuasa dua terkecil tak linear adalah menyuaikan model putaran lengkung dengan cerapan putaran lengkung galaksi Orion kerdil. Ia telah menjadi kaedah yang paling berkuasa dalam kajian taburan jirim gelap di dalam galaksi dan ia digunakan untuk mendapatkan model jisim yang bersesuaian untuk suatu galaksi. Di dalam artikel ini, kami mempersembahkan suaian putaran lengkung bagi galaksi Orion kerdil yang telah dibetulkan pecutan asimetri dengan menggunakan kaedah kecerunan daripada kuasa dua terkecil tak linear. Keputusan yang kami peroleh menunjukkan keselarian yang cemerlang antara model jisim profil halo teras dengan cerapan putaran lengkung. Justeru, kami boleh menganggarkan nilai jisim cakera, MD; jejari teras, r0 dan ketumpatan teras, ro bagi suatu galaksi di bawah 1-s ketidakpastian. Kami juga akhirnya menunjukkan bahawa taburan halo jirim gelap adalah halo jirim gelap berteras dengan ketumpatan, 3.9 × 106MŸ kpc-3.

Kata kunci: Galaksi; kaedah kecerunan; kerdil berpilin - putaran lengkung - jirim gelap; penyuaian

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*Corresponding author; email: norsiahashim@um.edu.my