2010:058 CIV MASTER’S THESIS The Physics and Evolution of Small Molecular Clouds in Nebulæ - Globulettes as Seeds for Planets? Karsten Dittrich MASTER OF SCIENCE PROGRAMME Mechanical Engineering Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Physics 2010:058 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 10/058 - - SE Universitetstryckeriet, Luleå Hier ist wahrhaftig ein Loch im Himmel! Sir William Herschel, 1834 (English: Here is truly a hole in the sky!) Abstract Globulettes have recently been found in the Rosette Nebula, the Carina Nebula and other nebulæ. They are expected to be seeds of brown dwarfs and free-floating planetary-mass objects. The size distribution in the Carina Nebula was found to follow a power-law, and the same power-function resulted in 880 ± 250 globulettes in total in the Rosette Nebula. Compared to the 145 observed objects in this nebula, many globulettes are beneath the resolution limit of the Nordic Optical Telescope, which was used to explore the Rosette Nebula. A simulation that arranged all these globulettes randomly in the nebula determined that some globulettes are captured by stars. They are believed to form into one or more planets, orbiting the star thereafter. The possibility that globulettes result into the formation of planets, orbiting a star, is some 4:75·10−2 per cent. According to this simulation, about 3:35·10−3 per cent of the stars with spectral type A to M host one or more planets that once have been globulettes. Keywords: free-floating planets - H II regions - ISM: individual: Carina Nebula, Rosette Nebula - ISM: globules, globulettes - planet capturing i Acronyms B68 Barnard 68 (object 68 in Barnard’s catalogue) CN Carina Nebula CTIO Cerro Tololo Inter-American Observatory ESO European Southern Observatory FWHM Full Width at Half Maximum GMC Giant Molecular Cloud HST Hubble Space Telescope IR InfraRed NIR Near InfraRed NOT Norther Optical Telescope NTT New Technology Telescope RN Rosette Nebula SPH Smoothed Particle Hydrodynamics SST Spitzer Space Telescope UV UltraViolet VLT Very Large Telescope Units and symbols In this thesis, cgs units are used. That is, centimeter for length, gram for weight and second for time. Definitions of other units used to describe distance: • Angström (Å): 1 Å = 10−8 cm = 10−4 µm. • Astronomical unit (AU) - the average earth-sun distance: 1 AU = 1:496·1013 cm. • Parsec (pc) - the distance from which the radius of the Earth’s orbit around the sun takes up an angle of 100: 1 pc = 206;265 AU = 3:086·1018 cm. Thus, an angle of 100 in the Rosette Nebula (at a distance of ≈ 1400 pc), corresponds to a distance of ≈ 1400 AU. • Light-year (ly) - the distance that light travels in one year: 1 ly = 63;240 AU = 0:3066 pc = 9:461·1017 cm. Definitions of other units used to describe mass: • The atomic mass unit (u): 1u = 1:6605·10−24 g • The mass of the Earth (M ): 1M = 5:974·1027 g. 30 • The mass of the planet Jupiter& (M&J): 1MJ = 1:899·10 g. 33 • The solar mass (M ): 1M = 1048MJ = 1:989·10 g. iii Contents 1 Introduction1 1.1 Formation of stars and planets...........................1 1.2 Extrasolar planets..................................2 1.3 Contraction of a cloud...............................3 1.4 Fragmentation of a molecular cloud........................4 1.5 H II regions and emission nebulæ..........................5 1.6 Stellar wind and the motion of the clouds.....................7 1.7 Aim and outline of the work............................8 2 Observations9 2.1 Observations with the Nordic Optical Telescope..................9 2.2 Observations with the Hubble Space Telescope..................9 3 Globulettes 11 3.1 Interstellar cloud structures............................. 11 3.2 What is a globulette?................................ 14 3.3 Physical properties of a globulette......................... 16 3.4 Mass estimation and density distribution...................... 16 3.5 The virial theorem.................................. 18 3.6 Size and mass distributions............................. 19 3.7 Extrapolation fit functions............................. 21 4 Evolution of globulettes 23 4.1 Possible evolution scenarios............................ 23 4.2 Possibility of a capture as a free-floating planet-like object............ 26 4.3 Possibility of a capture as a cloud.......................... 26 4.4 Computing the possibility of a star capturing a globulette............. 27 5 Results 29 5.1 Fitting the Carina Nebula size distribution..................... 29 5.2 Extrapolating the Rosette Nebula size distribution................. 31 5.3 Comparison of the two nebulæ........................... 31 5.4 Probability of globulettes being captured by stars................. 34 6 Discussion 39 6.1 Size distributions.................................. 39 v Contents 6.2 Evolution of globulettes............................... 39 6.3 Future research................................... 42 7 Conclusions 45 Acknowledgments 47 Bibliography 51 A Derivation of the virial theorem 53 B Linear fitting with singular value decomposition 55 C The capture mechanism with SPH computation 57 Statutory Declaration 59 vi List of Figures 1.1 The Rosette Nebula.................................6 1.2 The Carina Nebula.................................7 2.1 Inner Carina Nebula with the HST......................... 10 3.1 B68 without star background............................ 12 3.2 B68 with star background.............................. 13 3.3 Different appearances of the globulettes...................... 15 3.4 Observed size distribution in RN and CN..................... 20 3.5 Observed mass distribution in RN and CN..................... 21 4.1 Fragmentation of a globule............................. 24 4.2 The Wrench trunk and fragmentation of a globulette................ 25 5.1 Carina Nebula fit.................................. 30 5.2 Rosette Nebula fit.................................. 32 5.3 Evolved and fitted size distribution in RN and CN................. 33 5.4 Start arrangement of stars and globulettes..................... 35 5.5 End arrangement of stars and globulettes...................... 36 5.6 Captured globulettes by spectral type of the capturing star............. 37 5.7 Percentage of capturing stars for each spectral type................ 38 6.1 Twice the capture range............................... 40 6.2 Double amount of stars............................... 41 6.3 Time dependence of the captures.......................... 42 C.1 SPH simulation plots of captured condensations.................. 58 vii List of Tables 1.1 Percentage of planets around stars of different spectral types...........3 4.1 Average stellar density in the Milky Way...................... 28 5.1 Percentage of star hosts for each spectral type................... 38 6.1 Comparison of host spectral types......................... 40 ix 1 Introduction Earth is “an utterly insignificant little blue-green planet far out in the uncharted backwaters of the unfashionable end of the western spiral arm of the galaxy” (Adams 1979). That is how Douglas Adams described the position of our planet in his novel The hitchhiker’s guide to the galaxy. The Milky Way galaxy is a spiral galaxy with around 100 billion stars. It is composed of spiral arms, which rotate around the galactic center. If the rotation speed of the stars in a galaxy against the distance to the center of the galaxy is measured, there is a big discrepancy with the theoretical value from the law of gravity (Zwicky 1933). The stars in the outer parts are much faster than expected. This can be explained, if one assumes that there is more mass in our galaxy than the luminescent one. According to some calculations (Turner 1999b), this would give rise to the idea that almost 90 per cent of the mass of our galaxy is invisible to us, in short: dark. This dark matter is mainly composed of nonbaryonic matter. There are many theories for it, but as of yet, all efforts to measure the form of it have failed. Dark objects, as, for instance, “dark stars” (black dwarfs, neutron stars, black holes or objects of mass around or below the hydrogen-burning limit) and interstellar cloud structures (Turner 1999a), were, for a long time, suggested as the missing dark matter. But even all “dark stars” and clouds together amount to only a small fraction of the measured discrepancy. Nevertheless, those “dark” objects are very interesting, and, due to some lucky circumstances, one can see interstellar cloud structures in some parts of the galaxy. 1.1 Formation of stars and planets In order to describe the formation of stars, one should distinguish between low-mass (< 2M ) stars, and high-mass stars. The mechanism for high-mass stars is poorly understood. Low-mass stars are mostly formed in giant molecular clouds (GMCs) or globules (see Sec- tion 3.1). According to the standard theory, star formation takes place in the core of dense and cold (10 − 20 K) molecular clouds, due to their gravitational energy. During star formation, the cloud decreases in size by several orders of magnitude from a pc- to a 100 AU-scale. Big clouds, of several hundred or thousand solar masses, fragment into smaller clouds until the remaining clouds have approximately solar masses. All such clouds have some initial angular momentum, due to some inhomogeneity in the cloud. Angular momentum is conserved during the contraction process, so the inner parts start to spin relatively fast. At some point, the infalling matter has enough transversal velocity to prevent direct