The physics and evolution of small molecular clouds in nebulæ: globulettes as seeds for planets?

MASTER’S THESIS

2010:058 CIV

Universitetstryckeriet, Luleå

Karsten Dittrich

The Physics and Evolution of Small Molecular Clouds in Nebulæ

- Globulettes as Seeds for Planets?

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

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

per cent. According to this simulation, about 3.35 · 10

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

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

cm = 10

µm.

• Astronomical unit (AU) - the average earth-sun distance: 1 AU = 1.496 · 10

cm.

• Parsec (pc) - the distance from which the radius of the Earth’s orbit around the sun takes up an angle of 1

: 1 pc = 206, 265 AU = 3.086 · 10

cm. Thus, an angle of 1

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 · 10

cm.

Definitions of other units used to describe mass:

• The atomic mass unit (u): 1u = 1.6605 · 10

g

• The mass of the Earth (M♁): 1M♁ = 5.974·10

g.

• The mass of the planet Jupiter (M

): 1M

= 1.899 · 10

g.

• The solar mass (M): 1M = 1048M

= 1.989 · 10

g.

Contents

1 Introduction 1

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 Observations 9 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

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

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

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

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 accretion to the

central star. So a disk-like structure, of 1 − 2 per cent of the star’s mass, is formed around the

star. Planets are believed to evolve from such “protoplanetary” disks. These disks are assumed to

be the birthplace of planets, asteroids and comets, but the exact formation process is still poorly

understood. The Hubble Space Telescope (HST) imaged numerous protoplanetary disks in the Milky Way. This indicates that solar systems such as ours are rather common in our galaxy.

The basic theory for the formation of planets, as described in Lissauer (1993), is as follows:

Dust particles and primitive meteorites in the protoplanetary disks, with sizes of 0.05 − 100 µm, stick together, collide pairwise and thus form larger bodies, so-called planetesimals. The larger a body is, the faster its surface grows. That results in more headwind, i.e., it is slowed down due to friction. So those larger bodies spiral inwards, and find their orbits closer to the star. The largest objects grow rapidly, and become by far the most massive bodies for each accretion zone. Giant gas planets are formed around icy solid cores. These are the most massive bodies in such a state of the development of a solar system. They catch most of the gas from the surrounding discs.

Due to this gas drag, the gaseous planets nowadays consist to 90 per cent (Jupiter) or 77 per cent (Saturn) of hydrogen and helium. Terrestrial planets have a higher proportion of heavier elements and hence are rocky.

Free-floating planetary objects were recently discovered (Lucas & Roche 2000) in star-rich regions, such as the Orion Nebula. Their detection raises the question of their origin. Fogg (1990) gave some ideas on how these free-floating objects may originate. He suggested that they were either formed like the stars, just out of smaller clouds, or they were formed around stars in protoplanetary discs and were later ejected by a destructive event. Such an event could be, for instance, a supernova explosion or a close stellar encounter.

If the new star has a mass lower than 0.08M, no hydrogen fusion can start. This means the star appears very dark, which is why it was called a “black” dwarf in Kumar (1962). Later Tarter named these objects brown dwarfs in her Ph.D. thesis. Actually brown dwarfs are red, but the term red dwarf was already used, when Nakajima et al. (1995) first observed a brown dwarf.

Today we know of the existence of many brown dwarfs, e.g., in the Pleiades Cluster (Martín et al. 2000).

1.2 Extrasolar planets

“Just fourteen years ago the Solar System represented the only known planetary system in the Galaxy, . . . Since then, 320 planets have been discovered orbiting 276 individual stars.” (John- son 2009). Extrasolar planets (or shorter, exoplanets) were mostly discovered using Doppler techniques or photometric transit surveys. Some more have been detected by gravitational mi- crolensing, and a few were directly imaged. These techniques are described in various articles and textbooks, e.g., in Lunine et al. (2009). Today, the “planet count” is at 429 planets around 362 stars (NASA Planet Quest 2010). At this web address, a list of all exoplanets can be found.

According to Johnson et al. (2007), stars of different masses have different possibilities of being host for a planet. Johnson et al. plotted the percentage of stars with planets against the stellar mass. The main quantities from this plot are summarized in Table 1.1. This table shows that most stars with planets are sun-like, while the relative number is highest for larger stars.

This table includes neither the biggest, nor the smallest stars. The reason, put simply, is that no exoplanets have been found around those stars yet.

In our solar system we find the heavy gas planets in the outer parts, whereas the terrestrial,

1.3 Contraction of a cloud lighter planets are in the inner parts. However, there are observations also of massive planets very close to some stars. They form a distinct class of exoplanets, called “hot Jupiters”. These planets have masses of around 1M

and orbit very close to their stars. They have some remarkable properties, such as their low density. Due to the latter, they would “float on water.” Also, they have to be migrated in this low orbit, as they cannot have been formed that close to a star. “Hot Jupiters” are easier to observe as they transit the star more frequently. Also, those planets are very big, due to their mass and low density. Although most “hot Jupiters” have a mass of around 1M

, some with the mass of 21M♁ were detected (Léger et al. 2009). However, there is no evidence that there is a lower mass limit for those planets.

Table 1.1 – The percentage of stars with detectable planets as a function of stellar mass, from Johnson et al. (2007, Fig. 6). The number of hosts (N

), i.e., stars with planets, and the number of studied stars (N

) can be found in the same figure. The spectral classification of the stars was taken from Johnson (2009). The uncertainty limits are from Poisson statistics.

Spectral type Stellar mass M N

N

% stars with planets

M4 - K7 0.1 - 0.7 169 3 1.8 ± 1.2

K5 - F8 0.7 - 1.3 803 34 4.13 ± 0.67

F5 - A5 1.3 - 1.9 101 9 8.80 ± 2.27

1.3 Contraction of a cloud

Every massive object affects its surroundings by gravity. So molecular clouds, which consist of tiny particles such as molecules of hydrogen and helium, and dust particles can contract due to gravity. But for such diffuse objects, one has to take the movement of the particles into consideration.

The virial theorem (derived in Appendix A) applicable for clouds is 2 (K

− K

) +W + E

= 1

2 d

dt

I, (1.1)

where the total kinetic energy inside the cloud can be described by K

=

Z

V

 3

2 P

+ 1 2 ρ v



dV ≡ 3

2 PV ¯ . (1.2)

Here P

is the local thermal pressure, v the local turbulent velocity, V the volume of the cloud and ¯ P is expressed by the pressure of the ideal gas equation:

P ¯ = Nk

T

V = M

µ uV

k

T . (1.3)

The symbols have the same meanings as explained above.

The external energy K

is a term concerning, for example, the outer pressure from the sur- rounding environment. For a spherical cloud of uniform density, mass M and radius R, the gravitational energy W becomes

W

= −3GM

5R . (1.4)

The magnetic energy E

can be described by the magnetic field B. The total magnetic energy for a sphere of radius R can be expressed by the magnetic energy density B

/8π times the volume of the sphere:

E

= B

8π · 4π

3 R

= B

R

6 . (1.5)

On the right-hand side of Equation (1.1), one finds the second derivative of the moment of inertia I. Generally, the moment of inertia can be written as

I = Z

r

dm. (1.6)

The rate of change of the size and shape of the gas system is described by ¨ I in the virial theorem.

If one neglects the magnetic energy and the outer pressure, then for static clouds, i.e., ¨ I ∼ = 0, Equation (1.1) simplifies to

2K

+W = 0. (1.7)

When the kinetic energy is balanced by the gravitational energy, the cloud is referred to be in virial equilibrium. Thus, if a cloud changes in shape and size, Equation (1.7) becomes an inequality. If ¨ I < 0, the ratio

< 1 and the cloud becomes smaller, i.e., contracts. For the opposing case ¨ I > 0, the ratio

> 1, and the cloud dissipates into space.

1.4 Fragmentation of a molecular cloud

Usually GMCs and globules have masses of several hundred M (compare Section 3.1). But there are no stars that are so massive. Thus these clouds have to fragment before they collapse to a star. The size distribution of such fragments is important for this analysis.

The clouds split up into smaller structures with a mass distribution that follows a power law.

This power law was determined with the help of smoothed particle hydrodynamic (SPH) sim- ulations. They lead to a mass distribution following dN/dM ∝ M

with ν . −2 for turbulent models (Klessen 2001). Without turbulence, the exponent becomes rather ν ≈ −1.5 (Klessen 2001; Klessen et al. 1998).

If asteroids collide with each other, they form many small objects and a relatively small number

of larger objects. The size distribution of such objects follows a power law (Capaccioni et al.

1.5 H II regions and emission nebulæ 1986). The size distribution of molecular clouds shall also follow a power law. There are some values for the exponent in Ormel et al. (2009), yet they are for microscopic grains. Hence the size distribution also of the globulettes is assumed to follow a power law.

1.5 H II regions and emission nebulæ

H II regions are regions with ionized hydrogen. For all elements, the following description is valid: Elements marked with “I” are neutral, those marked with “II” are ionized once, and so on.

There are a lot of H II regions in the Milky Way, and some of these bright nebulæ are visible to the naked eye. Nevertheless, they were first noticed in the 17

century, after the advent of the telescope.

H II regions can be very large - one single O-type star may ionize a region of up to 100 pc, while a B type star still ionizes a few parsecs. However, most H II regions are ionized by a group of O- and B-type stars - the brightest members of a stellar cluster. O- and B-type stars are very massive and luminescent, with very strong stellar winds (a few times 1000 km s

), as well as with powerful and energetic radiation. Due to their high loss of mass, their lifetime is very limited, so O-type stars leave the main sequence after 3 − 6 million years. The radiation pressure and the stellar wind condense the surrounding gas, creating a thin, but dense, shell in the inner part of the local cloud. The cloud expands outwards with accelerated speed. The region near the cluster is filled with warm plasma and appears as a “bubble” in the cloud. Typically H II regions have a particle number density of 10 − 100 cm

, consisting mainly of hydrogen (73 per cent) and helium (35 per cent). Heavier elements are much rarer, and make up the remaining 2 per cent.

H II regions usually appear reddish. It is easily explained why they have this appearance.

The high-energetic photons from the UV radiation from the O- and B-type stars knock out the electrons of hydrogen. In the region of the warm plasma, the protons and electrons are too fast to recombine. In the bright regions, it is cold enough for them to recombine, so the electrons cascade down to the lowest energy level. During this they emit light at fixed wavelengths. This gives an emission line-spectrum, wherefrom we know the constituents of the nebulæ. In the visible spectrum, by far the strongest emission line is the H

-line with λ = 6563 Å (= 0.6563 µm).

Light with this wavelength is emitted by the electrons going from the third to the second excited level of hydrogen.

The closest of such nebulæ is the Orion Nebula, at a distance of 414 pc (Menten et al. 2007).

This nebula has been the object of numerous studies, due to its closeness. There is an over- whelming amount of evidence that this nebula is a star-birth region (Hillenbrand 1997). O‘dell et al. (1993) have found protoplanetary discs (proplyds) in the Orion Nebula. Another very fa- mous H II region is the Rosette Nebula (Figure 1.1), which is one of the two main areas of this work. It is situated around the cluster NGC 2244, with several O- and B-type stars within. The most accurate distance to NGC 2244 is derived to be 1.39 ± 0.10 kpc (Hensberge et al. 2000).

It spans some 30.6 pc in diameter and has an age of a few Myr (Viner et al. 1979). It is, as the

Orion Nebula, a good region to study star formation and the interaction between the H II region

and the surrounding molecular cloud. The Rosette Nebula (RN) shows many interesting struc-

tures, such as the rotating elephant trunks (Schneps et al. 1980; Gahm et al. 2006) and many

globulettes (Grenman 2006; Gahm et al. 2007). The elephant trunks have an estimated age of (2.6 − 5.8) · 10

yr (Schneps et al. 1980).

Figure 1.1 – The Rosette Nebula, a large emission nebula some 1400 pc away. The hole in the middle was blown free by the strong stellar winds of the open cluster NGC 2244, seen greenish in this representation. In the bright region, several filamentary structures and other dark markings can be spotted. This false-colour image uses three emission lines: H

for red, [O III] for green and [S II] for blue. Image source: http://www.noao.edu/image_gallery/images/d2/ngc2237.

jpg.

1.6 Stellar wind and the motion of the clouds Probably the most impressive H II region is the Carina Nebula (Figure 1.2). It hosts also the biggest star found in our galaxy so far. The star (η Carinae) has a mass of 100 solar masses (Davidson & Humphreys 1997) and is 5 · 10

times as bright as our sun. This star is currently classified as a luminous blue variable binary star that has brightness variations. For instance, it appeared as the second brightest star at the night sky in 1843. Compared to the large distance of approximately 2.3 kpc (Smith et al. 2003), this shows the amazing power of this star. The Carina Nebula hosts several clusters and spans about 80 pc across, that is about seven times the size of the Orion Nebula. In this nebula, several objects were found that might be proplyds (Smith et al. 2003) or globulettes (Grenman & Gahm 2009/10). In this analysis it is assumed that these objects are globulettes.

Figure 1.2 – The Carina Nebula here as a mosaic of images collected with the 1.5-m Danish telescope at ESO’s La Silla Observatory. The nebula, 7500 ly away, spans some 260 ly across and is as big as seven Orion Nebulæ. The brightest star in this image is what can be the heaviest star in our Milky Way galaxy, called η Carinae. Image source: http://www.eso.org/public/archives/

images/large/etamosaicnm2.jpg.

1.6 Stellar wind and the motion of the clouds

All stars lose mass over time. The mass loss ˙ M is measured in M/yr. It can be so severe that

a star throws out 10

solar masses per year. Our sun loses 10

M/yr, so its mass loss does

not affect its development. Stars of the spectral type O and B have very strong stellar winds, with velocities up to 2000 km s

(Weaver et al. 1977). These stars have a mass loss ˙ M = 10

M/yr (Snow & Morton 1976).

For the RN, the velocity of the stellar wind is ∼ 2000 km s

(Conti 1978). However, the stellar winds from the central cluster of the RN are stopped at the shock front. But, due to this stop, the warm gas outside the inner bubble expands. This expansion moves the molecular clouds against the stars, of which the latter are many orders of magnitude smaller than the globulettes in surface area.

The globules (and with them the globulettes) in the RN move outwards with the velocity of 23 km s

(Schneps et al. 1980). However, Schneps et al. used 1600 pc as the distance to the RN, so this value has to be corrected to ∼ 20 km s

.

1.7 Aim and outline of the work

In this work, the statistics of the globulettes in the Rosette Nebula (RN) (Grenman 2006) and the Carina Nebula (CN) (Grenman & Gahm 2009/10) will be compared in order to estimate the total number of globulettes in the RN.

Therefore, the size distribution of the globulettes in the CN, which goes to much smaller sizes, will be fitted to a power-function. This curve will be used to fit and extrapolate the size distribution of the globulettes in the RN.

Thereafter, a simulation is used to estimate how many of these globulettes may be captured by a star. This program also distinguishes between the spectral types of the stars.

The outline of this work is as follows:

• Chapter 2 gives an overview of the observations of the studied nebulæ.

• Chapter 3 describes interstellar cloud structures, gives details about the physical parame- ters of the globulettes and how they are computed, along with some statistical calculations.

• Chapter 4 examines the evolution of the globulettes and gives an outline of how they may evolve further on.

• Chapter 5 presents the results.

• Chapter 6 contains a discussion about the fate of the globulettes, and age discrepancy between the CN and the RN. Also some suggestions for future work are given.

• Chapter 7 gives the conclusions.

• Appendix A shows the derivation of the virial theorem.

• Appendix B explains how one can fit linear graphs with singular value decomposition.

• Appendix C summarizes the capture mechanism from Oxley & Woolfson (2000).

2 Observations

2.1 Observations with the Nordic Optical Telescope

Ten H II regions were observed during 5 nights in December 1999 and 5 nights in November and December in 2000. The observations were carried out on behalf of Gahm and Kristen with the Nordic Optical Telescope (NOT) on the island of La Palma, Spain. NOT’s main mirror has a diameter of 2.56 meter.

The Rosette Nebula was observed during one night in 2000 with the ALFOSC camera. This camera has a field of view of 6.4

× 6.4

. The used filters were centered at 6563 Å, the wave- length of the H

radiation. The exposure time was typically 1800 s, while the resolution under best conditions was about 0.4

. The CCD detector has a resolution of 0.188

per pixel. In the observation in 2000, a 180 Å FWHM filter was used. This filter allowed the inclusion of the wavelengths of the [N II]-emission lines at 6548.1 and 6583.6 Å. From the stars in the field, angular resolution was measured to be in the range of 0.7 − 1.3

. Hence, the smallest objects resolved by the NOT in the Rosette Nebula span 980 − 1820 AU across, depending on the field where the objects are found. It has to be noted, that not the whole nebula was covered by the observation and thus some smaller objects in other areas can have escaped detection.

The images were corrected for instrumental effects and cosmic ray excitations. Bias, dark current and flat field correction were applied, as well as corrections for the sky background as extracted from sky field exposures. The night during the observations was dark, except for some moonlight in parts of the nights of December 2 and 3.

2.2 Observations with the Hubble Space Telescope

The Carina Nebula was observed with the Wide-Field Channel of the Hubble Space Telescope’s (HST’s) Advanced Camera for Surveys. “Because of the large area of the Carina Nebula, it was impractical to make a single contiguous map of the entire region with HST . . . ” (Smith et al.

2010). Thus, the nebula was mapped with two joint programs (GO-10241 and GO-10475) in Cycles 13 and 14 of the HST. During Cycle 13, a large (13.5

× 27

) mosaic image was made.

In this first survey, the brightest inner parts (the clusters Tr14 and Tr16, the Keyhole Nebula and η Carinae) were given priority. An HST image of the inner Carina Nebula can be seen in Figure 2.1.

In all observations of this survey, the F658N filter was used. This filter transmits H

and [N

II] at λ = 6583.6 Å. The total exposure time was 1000 s at each position (500 s per individual

exposure). The pixel resolution of the Wide-Field Channel in the HST is 0.05

per pixel, which

is also the angular resolution, as there are no atmospheric turbulences. Thus the smallest objects in the Carina Nebula that are resolved by the HST span ∼ 115 AU across.

All images were reduced and combined using the PYRAF routine MULTIDRIZZLE, with manually determined pixel shifts using the pipeline-calibrated, flat-fielded individual exposures.

This routine not only combines the exposures, it also generates static bad-pixel masks, corrects for image distortions and removes cosmic rays using the

-

pairs. During this investiga- tion, 98 per cent of the Carina Nebula was imaged with the HST. The remaining gaps were filled with images obtained with the MOSAC camera on the 4 m Blanco telescope at Cerro Tololo Inter-American observatory (CTIO).

Figure 2.1 – This image of the inner Carina Nebula was made from a large H

mosaic for the intensity scale using the Advanced Camera for Surveys at the Hubble Space Tele- scope (HST). The ground-based narrow-band images obtained with the MOSAIC camera on the 4 m Blanco telescope at CTIO was used for color coding. Blue is [O III], green is H

and red is [S II]. North is to the upper right. This image can be found in full res- olution (24, 000 × 12, 000 pixel) at http://hubblesite.org/gallery/wall_murals/

download/2-carina-color/full/carina_80x40full.jpg.

3 Globulettes

Globulettes were first investigated in Grenman (2006). In her licentiate thesis all observed prop- erties of the globulettes were determined. The size of the globulettes was measured, while fitting an ellipse in the dark pattern of each globulette. For non-spherical globulettes the orientation was determined. The mass was calculated due to their extinction values. Assuming ellipsoidic bodies, their volume, mass density and particle density were evaluated. Also, their tendency to collapse or dissipate into space was computed with the help of the virial theorem.

There are several evidences (Grenman 2006; Gahm et al. 2007) that globulettes are not smaller globules, or a “tail” of normal globules. They form a separated group in mass and size distribu- tions. They also have a much higher particle density than “tails” of globules usually have. Finally, they have another appearance than globules. Globulettes form more roundish or teardrop shapes rather than complex structures.

Grenman included two H II regions in her investigation (2006), and in Gahm et al. (2007) all 10 regions of the observation with the NOT (see Section 2.1) were included. A total of 173 clouds were found in these surveys, and 145 of them lie in the Rosette Nebula (RN). In order to make the statistics more reliable, only the number of objects from the RN are used in this work.

3.1 Interstellar cloud structures

What Herschel in 1834 has described as “holes in the sky” (Houghton 1942) is nowadays well known as dark nebulæ. The Barnard Catalogue (Barnard 1919) was a first list of “182 dark markings”. One very distinct cloud from Barnard’s catalogue is Barnard 68, seen in Figure 3.1.

As its distance to the sun is just 500 light-years (ly), it is not surprising that not a single star is in our field of view to this dark nebula. This opaque cloud blocks the light of over 3700 Milky Way stars (Alves 2001), due to its short distance to us. They are visible at longer wavelengths, as the molecular clouds are transparent for infrared (IR) light. Images, like Figure 3.2, prove that these clouds are not real holes in the sky.

In optical wavelengths, the internal structure of the clouds is hard to study. For such investiga- tions, CO-emission lines are used. These studies show that the dark clouds consist of molecules, mainly hydrogen. After these observations, dark clouds were named molecular clouds.

Molecular clouds differ very much in size and mass, so they are classified accordingly. There

are tiny structures with masses in the range of a Jupiter mass (M

). But there are also huge clouds

with more than 100, 000 solar masses (M). Sizes range from some 100 astronomical units (AU)

to 100 parsecs (pc). Star formation takes place in gravitationally unstable and massive clouds (see

Section 1.1).

Figure 3.1 – B68 seen by the Very Large Telescope (VLT) of the European Southern Observatory (ESO) and reproduced from http://www.eso.org/public/archives/images/large/

eso0102a.jpg. This cloud appears very distinct against a star-rich background of the Milky Way.

The molecular gas absorbs almost all visible light from the background stars. B68 is 0.5 light-years

in diameter, and is composed of a gas of about two solar masses (M). This cloud might collapse due

to its own gravity, and form one or more stars, possibly with planets. See Figure 3.2 for background

stars.

3.1 Interstellar cloud structures

Figure 3.2 – This view of the dark cloud B68 is a false-color composite based on a visible (here rendered as blue), a near-infrared (green) and an infrared (red) image. Since the light from stars behind the cloud is only visible at the longest (infrared) wavelengths, they appear red. This image is composed by measurements from the Very Large Telescope (VLT) and New Technology Tele- scope (NTT), and is reproduced from http://www.eso.org/public/archives/images/

large/eso0102b.jpg. See Figure 3.1 for the VLT image.

The largest molecular clouds build the class of the Giant Molecular Clouds (GMCs). GMCs have material with the mass of 10

M. Their lifetime is calculated to be some 10

years, the density is about 10

cm

, and the temperature inside is 10 − 100 K.

There are some smaller molecular clouds, of which the smallest ones are called globules. They have a mass of a few solar masses up to 10

M. They are much denser, with some 10

particles per cubic centimeter, and also colder, with temperatures around 10 K. They are thought to be a site of star formation (Bok 1977). Yun & Clemens (1990) proved this assumption with the detection of dense cores in many clouds. The globules are divided into two classes, namely the cometary globules and the Bok globules. Cometary globules have a cometary shape. Small, isolated clouds with a dense core, called the “head”, and a long tail with various structures are some major characteristic features for them. Some have bright rims, usually at the head of the globule. The tails point away from the most luminescent nearby stars. This shows the interaction between the ultraviolet (UV) radiation, and the strong stellar winds of O- or B-type stars and the molecular clouds. They are located in emission nebulæ such as the Gum Nebula (Hawarden & Brand 1976; Sandqvist 1976) or the RN (Herbig 1974), and have sizes that range from 0.05 to 1 pc, densities of some 10

− 10

cm

, and temperatures around 10 K. Bok globules are named after Bart J. Bok, who first named them globules (Bok & Reilly 1947). They are relatively isolated, can be seen in optical spectral regions, and are sharply outlined against a background of stars. Bok globules can be larger than cometary globules (0.2 − 2 pc), have masses of 5 − 500M, and are shown (Yun & Clemens 1990) to be sites of star formation. Cores within the globules typically consist of material with 1 − 5M and have radii of 0.05 pc, giving a density of 10

cm

.

The smallest distinct class of molecular clouds are the globulettes. The mass distribution of the globulettes reach from the lightest objects to some with 0.1M (≈ 100M

). They were first discussed in Grenman (2006), and might be the site of planet or low-mass brown dwarf formation (Gahm et al. 2007). These objects are the focus of my project work, and will now be described in more detail.

3.2 What is a globulette?

A globulette is a “tiny” molecular cloud with a mass smaller than 0.1M. They can be distin- guished in massive globulettes within the mass range of 30 − 100M

≈ 0.1M
and low-mass globulettes with masses lower than 30M

. Usually, globulettes measure some kAU in size and as such they are much bigger than the solar system. But due to their distance they appear as tiny dark spots in the observational limits with nowadays telescopes. They occur in many different shapes, as shown in Figure 3.3.

To give a definition for the size of a globulette, Grenman (2006) described the contour as the line where the pixel intensity dropped to 85 per cent intensity of the interpolated background.

With this description the contour line is defined and, as the globulettes have an elliptic appeare-

ance, they are fitted to ellipses, giving semi-major and semi-minor axes. This is done because all

computations are performed much easier if one has an ellipse, rather than an undefined, almost

elliptic shape. Because we do not have any possibility to determine the real three-dimensional

3.2 What is a globulette?

Figure 3.3 – Illustration of the variety of the globulettes in the Rosette Nebula and the Heart Nebula

(IC 1805). All images are taken with the NOT in H

light. They are marked with numbers of the data

tables in Grenman (2006). Each panel is 16

× 16

, except the second-lowest row, which has the size

5.5

× 5.5

. North is up and east to the left. This image was reproduced from Grenman (2006) with

permission of the author.

shape yet, an ellipsoidic body with two semi-minor axes is assumed. This gives the potential of calculating the volume and the densities.

3.3 Physical properties of a globulette

The contour of a globulette is defined as the border, where the pixel intensity is 85 per cent of the interpolated background. The semi-minor axis β as well as the semi-major axis α are given by an ellipse that is fitted to this contour. The size of the globulette is then defined by

R = p

α β . (3.1)

This provides one comparable value for all globulettes. Assuming the whole globulette is an ellipsoid with two semi-minor axes, as in Gahm et al. (2007), the volume can be calculated as

V = 4π

3 α β

= 4π

3 R

β . (3.2)

This assumption leads rather to a lower bound on the volume for such a globulette. They might be more elongated in the line of sight. Also, if the ellipsoid is inclined, the measured axes are smaller than the real axes and thus the volume is estimated to be too small. In Schneps et al. (1980), an inclination of 45

is assumed for the calculations, and this can also be done for the observed globulettes, as they have some connections to the globules. However, there is no evidence that they cannot have any other inclination.

The orientation, given through the position angle, was calculated for good elliptic globulettes, where the relation between the axes is α/β > 1.5. Most globulettes point inward to the central cluster, showing a strong relation to the stellar wind and the extreme radiation of the latter.

3.4 Mass estimation and density distribution

The mass of each globulette is estimated through measurements of the extinction rate. The relation between the extinction rate and the column particle density of hydrogen is described by Bohlin et al. (1978). It is expressed as

N (H

) = 9.4 · 10

A

cm

mag

 , (3.3) where A

is the extinction (absorption plus scattering) for the photometric V-band, i.e. the visible band. The extinction A

for a wavelength λ is defined by

A

= −2.5 log  I I



, (3.4)

where I is the light-intensity measured in a certain area inside the globulette, and where I

refers

to the nebular background. However, the observations were carried out in the wavelength of

3.4 Mass estimation and density distribution 6563 Å (H

). Therefore the relationship between the extinction at λ = 6563 Å and the V-band (centered at λ = 5500 Å) is needed. It was found, with the help of some interpolation of the tabulated values in Savage & Mathis (1979), to be

A

= 1.2A

(see Grenman (2006) for further description). (3.5) In order to get the column mass density, the mass of the hydrogen molecule has to be taken into account. Furthermore, one has to take into consideration that hydrogen makes up only 73 per cent of the total mass. So, the relationship between the column particle density and the column mass density is

N = 2 · 1.67 · 10

· 1

0.73 N (H

) = 4.58 · 10

N (H

) h g cm

i

. (3.6)

Hence, inserting Equations (3.6) and (3.5) in Equation (3.3) gives a direct relationship between the measured extinction and the column mass density:

N = 5.2 · 10

A

 g

cm

mag



. (3.7)

With this relation, one can calculate the mass per pixel in each globulette. This pixel mass is then used to compute the total mass of the globulette by simply multiplying this mass with the number of pixels inside its contour. But, we do not know whether the measured extinction is altered by foreground emission in the H II region. Therefore Grenman (2006) considered two extreme cases. In the first case, she assumed that the globulette is in front of the nebula in the line of sight, and hence has no foreground emission at all. That leads to a minimal mass. The second case pretends that the globulette is in the background of the nebula. Thus in this case the light measured from the darkest pixel (i.e., the highest extinction) is caused by foreground H

emission by 95 per cent. The value of 95 per cent is chosen for “technical” reasons to avoid division through zero, which would lead to infinite mass. The latter gives a maximal mass. For calculation, the arithmetic mean of these cases is used, denoted in my work by M. Comparison with objects from Gonzalez-Alfonso & Cernicharo (1994) gave good agreement.

By computing the volume with Equation (3.2), the mass density can be derived, simply fol- lowing the relation ρ = M/V . The particle density then is computed as

n = ρ

µ u , (3.8)

where µ = 2.4 is the mean molecular weight for molecular clouds, and u is the atomic mass unit.

Density distribution evaluations in Grenman (2006) show that the globulettes in the Rosette

Nebula are likely to have uniform densities. The density seems to flatten with respect to distance

than expected from a uniform distribution in the very outmost parts of the globulettes. This might

be a sign of outgassing due to interaction with the plasma environment.

3.5 The virial theorem

In order to determine whether a globulette is about to dissipate into space, collapse due to its own gravity, or not change its appearance, one may apply the virial theorem (see Section 1.3).

For the sake of simplicity and calculability, a spherical cloud is assumed, with a homogeneous gas temperature and density without turbulence or rotational energy. For the first investigation the simple form of Equation (1.1),

2K

+W = 1 2

d

dt

I (3.9)

is used. Therefore, one uses Equation (1.3), inserting the derived values for the mass and the vol- ume. The temperature is assumed to be 10 K for round globulettes, whereas teardrop globulettes have T = 15 K (Gonzalez-Alfonso & Cernicharo 1994). With this, the kinetic energy as well as the gravitational energy can be calculated, using the mass and size for each globulette.

The ratio

2K

−W



 

 

< 1 the object will contract

= 1 the object will not change in size

> 1 the object will dissipate into space

(3.10)

checks the future of the globulettes. For all globulettes in Grenman (2006), the ratio lies between 5 and 120, indicating that all objects would expand and disrupt.

However, Equation (3.9) is a much simplified version of the whole virial theorem (Equa- tion 1.1). Thus more terms have to be taken into consideration. Internal energy, like turbulence or magnetic fields, would make this situation even more pronounced. Turbulence inside the glob- ulettes is so far neglected, as there are no signs of any internal activity that would show some turbulence. Magnetic fields are assumed to be negligible, although there is no observational in- formation about that. Another disrupting force is photo-evaporation, and this was discussed in Kuutmann (2007). Due to his computations, the photo-evaporation of the globulettes is severe and dominates all other terms, reducing the lifetime to 5 · 10

years, compared to the calculated lifetime of (2 − 4) · 10

years in Gahm et al. (2007). However, Kuutmann states in the discussion that some values (e.g., the UV photon flux) might be overestimated. Additionally, no bow shock (i.e., the boundary between the stellar wind of the central cluster and the H II region) is included in his work, although it would stop the stellar wind. Thus, just the innermost globulettes of the nebula may experience severe disruption due to photo-evaporation.

Furthermore, the external pressure from the environment, i.e., the thermal (turbulent and gas pressure) and radiation pressures, is expected to be strong. The thermal pressure for a stable object is derived from the general virial theorem (Equation 1.1) to be

P

= 2K

+W

3V . (3.11)

The radiation pressure just affects the side of the cloud facing the central star cluster. As there

3.6 Size and mass distributions is no concrete information about the surface towards the central cluster this pressure was not included in the analysis. The calculated values for the globulettes, using Equation (3.11), are in good agreement with the estimations made by Gahm et al. (2006). Now a new ratio determines the future of the globulettes:

2K

−W + 3P

V , (3.12)

with the same cases as in Equation (3.10).

This new relation points out that most globulettes will either contract, or are close to virial equilibrium. For the ones that are about to contract, the free fall time can be calculated, using Equation (4.1) in the next Chapter.

3.6 Size and mass distributions

There is not an unrestricted resolution in our observation. In the Carina Nebula (CN) the res- olution limit is 115 AU. Yet the distribution falls off for objects smaller than ∼ 300 AU. This shows that not all objects at the resolution limit can be detected. It seems logical to choose the maximum in the bigger graph in Figure 3.4 for the minimum of the fit range, as the power- function is described best with these bins. As maximum it is sensible to chose the fifth bin, as all bins beyond this one do not follow the power-law very well. It has specific to be noted, that the observed globulettes in both nebulæ were extracted from some regions. Not the whole neb- ulæ were covered by the surveys. The CN was fully covered by the observations, but the data I got from Grenman & Gahm (2009/10) are just from selected regions. Hence, there can be some incompleteness in the distributions.

Objects in the Rosette Nebula (RN) with sizes beneath 980 AU are invisible, according to the minimal angular resolution mentioned in Section 2.1. In some areas the angular resolution is 1.3

, corresponding to 1820 AU as the smallest object that can be seen. Observations with the HST show that there can be much smaller globulettes found in the CN and, based on that fact, also smaller ones in the RN are expected. As explained above, it is reasonable to chose the maximum of the distribution. Hence the minimum of the fit range is chosen to be 2.25 kAU as the smallest reliable size.

The size distribution of the globulettes in both nebulæ can be described by a power-function:

f (R) ∝ R

. (3.13)

This behavior is expected according to the origin of the globulettes. As discussed in Section 1.4,

the size distribution of the fragments of a cloud follows a power-law. In Section 4.1 the glob-

ulettes’ origin is shown to be due to fragmentation.

Figure 3.4 – This size distribution shows the calculated sizes (see Equation (3.1)) in both the Rosette and the Carina Nebulæ versus the observed number of globulettes for each size bin with two different bin ranges. The height is normalized due to different numbers of globulettes in each nebula. The error bar (square-root of the number, as they are counted values) to the left corresponds to the Carina data, while the one to the right corresponds to the Rosette data. The histogram of the globulettes in the Carina Nebula has a slope (excluding the first bin) that can be described by a power-function.

The resolution limit for the Carina Nebula is 0.115 kAU. The histogram of the globulettes in the Rosette Nebula seems to have a similar power-law up to the bin for sizes between 2.25 kAU and 2.5 kAU, while it decreases for smaller sizes. The resolution limit is at 1.82 kAU in the worst case (see Section 2.1).

In Figure 3.5, the mass distributions of both nebulæ are mapped. As the mass is approximately proportional to the radius squared, this distribution is more spread for the Rosette Nebula. Also, for the Carina Nebula, the mass distribution is more spread (upper-right graph in Figure 3.5), but it still has a shape that can be explained with a power-function.

It follows that the CN distribution can be fitted with a power-law according to the fact that the

fragmentation of clouds, as discussed in Section 1.4, follows a power-law.

3.7 Extrapolation fit functions

Figure 3.5 – This mass distribution shows the calculated masses of the globulettes, in both the Rosette and the Carina Nebulæ versus the observed number of globulettes for each mass bin. Despite the fact that there are less globulettes in the Rosette Nebula, it is easily noticed that the observed globulettes in the Carina Nebula are much lighter than the ones in the Rosette Nebula. The smaller graph in the upper right shows that also in the Carina Nebula not all small globulettes could be observed. For both nebulæ the square-root of each bin height was taken for the error bar.

3.7 Extrapolation fit functions

As M ∝ R

, it is reasonable to use the size distributions of the nebulæ for the extrapolations.

Since the CN distributions can be fitted by a power-function, a power-law fit like

f

(R) = A

· R

(3.14)

can be applied to the graph. Easier to fit is the logarithm of this function, which is

log f

(R) = log A

· R

= log A

+ B

· log R. (3.15)

This is a linear function, and hence it can be fitted by a singular value decomposition algorithm (see Appendix B). Thus the fit function for the CN is

y

(x) = log f

(R) = a

+ b

· x, (3.16) with a

= log A

, b

= B

and x = log R.

For the power-function in the RN, the function

f

(R) = A

· R

(3.17)

is assumed, as the globulettes in the RN have the same way of origination as the ones in the CN.

As the power-law in the RN is not that pronounced, the same slope for its fit function can be assumed. So the RN fit function is

y

(x) = log [ f

(R)] = a

+ b

· x, (3.18)

with a

= log A

and b

= B

.

4 Evolution of globulettes

Of major interest regarding the globulettes is their evolution. As these clouds have just a few Jupiter masses, they may evolve into free-floating planetary objects or low-mass brown dwarfs (Gahm et al. 2007). So it is necessary that the future fate of these objects be investigated. In this work, the possibility that a captured globulette will evolve into a planet around a star is estimated.

The origin of the globulettes was discussed (Grenman 2006; Gahm et al. 2007), and there seems to be no other explanation than the fragmentation of globules, or that a parent molecu- lar cloud disperses, leaving free cores that appear as globulettes. Filamentary connections (see Figure 4.1) and connected globulettes (Figure 4.2) are evidences for the fragmentation theory.

Since some free-floating planetary objects in the Orion Nebula were discovered recently (Lu- cas & Roche 2000), the question of their origin is raised. Earlier, Fogg (1990) gave some ideas as to how such planets could be formed. He suggested that they can either form like a star - out of smaller clouds of less mass - or that they are developed around stars in protoplanetary discs. The latter case would require a catastrophic event, such as a supernova explosion or a close stellar encounter, for the planet to become free-floating. The first explanation would fit very well with the observed globulettes in several H II regions, as discussed by Gahm et al. (2007).

On the other hand, it is also very interesting how the globulettes might evolve in the future.

Is it possible that the resulting free-floating planetary object will be captured by a star? May some parts of the cloud, once close enough to the gravitational field of a star, evolve into planets orbiting this star? These questions will be discussed in the following section.

4.1 Possible evolution scenarios

Depending on its virial ratio (Equation 3.12), the investitgated globulettes will collapse, remain stable (i.e., will not change in size) or dissipate into space. The latter is a rather boring case, as this would not result in anything we can observe or investigate. Clouds in virial equilibrium will neither collapse nor dissipate into space, according to the virial theorem (Equation 1.1).

These globulettes may remain stable for a long time and will just propagate through the space.

Collapsing globulettes close to virial equilibrium is very interesting, as they will be stable for a

long time. On the other hand, globulettes that collapse too fast may evolve into a free-floating

planetary object or brown dwarf without encountering any star before it collapses.

Figure 4.1 – A structure in the Rosette Nebula with connected globulettes marked by their numbers.

The dashed lines show possible “routes” of some of the globulettes. The globulettes 38 and 39 are close to the large globule, which suggests that they once broke off from it. Globulette 41 has still a tail that ends in the globule, while the globulettes 42 and 43 lost their tails, probably due to evaporation.

The image spans 118

× 121

and was reproduced from Grenman (2006) with permission of the

author. North is up and east to the left.

4.1 Possible evolution scenarios

Figure 4.2 – The globule, known as the “Wrench trunk” in the Rosette Nebula, is shown in the left panel in a color-coded image. It primarily consists of thin threads, which are twisted and connected to jaws at the massive head, seen at the bottom of that image. This image spans 140

× 306

. In the upper-right panel globulette 44 is shown, having an unusual shape. This image spans 18

× 18

. The intensity profile in the lower-right panel shows that this object contains three cores. They may form individual globulettes in the future. This is a very good example for the fragmentation of the globulettes out of bigger structures. All these images were reproduced from Grenman (2006) with permission of the author. North is up and east to the left.

A collapsing globulette will form an object with the mass of the former globulette, i.e., objects

with masses of some Jupiter masses. In order to start hydrogen fusion a star needs 0.075M,

which is equal to 80M

. Thus stars lighter than 0.075M form brown dwarfs. Brown dwarfs

also are sites of nuclear fusion, but there deuterium and lithium (for those with masses above

65M

) is fused. The mass limit to start deuterium-burning is 13M

. All objects lighter than 13M

have planetary masses. Thus most collapsing globulettes will evolve into planetary-like objects.

More information about the distinction between planets and brown dwarfs can be found in Cole (2000).

A question that arises is whether those objects can somehow support life. Of course most of them will be gas giants and as such not capable of supporting any known life form. But on the other hand, life on Earth would never have evolved as we know it, if there would not be the comet-magnet Jupiter. This gas giant attracts lots of debris that is flying around in our solar system, and Earth would much more often be the site of meteorite strikes without this shelter.

Also, a moon orbiting these exoplanets may support life (like Europa around Jupiter might harbor life). However, in order to support life the planet must orbit a star. Otherwise neither a planet, nor a moon, will ever gain enough energy to heat the surface up to temperatures that are livable.

Consequently, the possibility of a free-floating planetary object to be captured has to be es- timated. Another interesting theory was presented by Oxley & Woolfson (2000): A star may capture parts of a cloud and these parts then evolve into orbiting planets. This theory is more closely described in Section 4.3.

4.2 Possibility of a capture as a free-floating planet-like object

This possibility can be assumed to be zero. There is almost no chance that a developed free- floating planet-like object is captured by a star. For this it needs to be slowed down once it approaches the star. A possible scenario is a three-body problem such as in the case of Triton, Neptune’s moon, with a strange orbit around the planet, as described in Agnor & Hamilton (2006). If a globulette will evolve into a binary system this scenario is possible. However, there is no way to determine the possibility for a binary system developed out of a globulette with the present observational data. The resolution of nowadays instruments is just not good enough.

4.3 Possibility of a capture as a cloud

By smoothed-particle-hydrodynamics (SPH) modeling (Oxley & Woolfson 2000) it is shown that a cloud, close enough to a star, can result into some planets orbiting the star. Oxley & Woolfson included three different initial setups in their paper. They found always some condensations in their models, resulting in 3 − 5 captured planets of a few Jupiter masses. This is possible due to the friction of the cloud’s parts. They slow some parts of the cloud down, which are then captured and orbit the star further on, while the other parts carry the remaining momentum. These other parts also condense, escaping the star or dissipating into space. This capture mechanism is described in more detail in Appendix C.

Once a condensation is captured, it has an orbit of typically a few 1000 AU. According to

Oxley & Woolfson (2000) they migrate inwards due the friction of the gas around the star.

4.4 Computing the possibility of a star capturing a globulette In their analysis, Oxley & Woolfson used distances of 2700 and 1600 AU. As at 2700 AU, the captured cloud results in some condensations, it can be assumed that any cloud, as near as 2700 AU, will result into some objects orbiting the star. The authors say that the mechanism is stable against changing of parameters. Thus a cloud approaching a star at a distance of 2700 AU can be claimed to be captured by the star.

The initial globules in Oxley & Woolfson (2000) have a mass of (0.7 − 1.3) · 10

g, corre- sponding to 0.35 − 0.65M. The captured condensations have a mass of around 10M

. If we want to have condensations of at least 1M♁, the cloud must have a mass of some 53M♁. This value was just assumed due to comparison with the condensations in Oxley & Woolfson (2000) and the desired minimal mass of a captured planet.

4.4 Computing the possibility of a star capturing a globulette

Calculating the real situation is impossible with the current information. There is no information about where the smaller, not observable, globulettes are situated. Hence, simulations with ran- dom arrangements have to be made. In such a simulation, a number of stars and globulettes are arranged randomly in space. Then the computer program checks how many globulettes are close enough to a star.

Additionally, such a program can calculate the movement of the globulettes against the stars due to the stellar wind of the central cluster. The stars are much less affected to the stellar wind and the radiation pressure of the central cluster than the globulettes. This is due to the much smaller surface of the stars. See Section 1.6 for further explanation. For this reason the motion of the stars can be neglected compared to the motion of the globulettes.

To calculate the number of stars for the simulation, the stellar density of this area is needed.

The clusters with the high stellar densities are inside the nebulæ, where no globulettes can survive the strong radiation of the luminescent cluster stars. The globulettes have to be placed outside the plasma bubble, where there is normal galactic stellar density. So no more stars than the average number of stars per cubic parsec can be assumed for the region the globulettes pass by. The average stellar density in the galactic plane is given in Table 4.1.

Stars are not all the same. Their masses differ, and thus their forces of attraction do as well.

So the simulation must also consider different distances for stars of various spectral types. As a B-type star has much more mass than a brown dwarf it has a wider range of attraction for globulettes. For this reason their capture range is different for each spectral type.

By simply applying Kepler’s third law, one can derive the free-fall time for clouds to be:

τ

= 1 4

s 3π

2Gρ

, (4.1)

where G is the gravitational constant and ρ

is the mean density of the cloud.

Table 4.1 – The average decadic logarithm of the stellar density of the Milky Way. The density of all stars in the Milky Way is approximately 0.13 stars/pc

(Chabrier 2001). The stellar density of brown dwarfs is estimated by Chabrier (2002). Other stellar densities were extracted from Allen (1973).

Spectral type log (number density) Average mass in log stars/pc

in M/M

O-type -7.6 40

B-type -4 17

A-type -3.3 3.2

F-type -2.6 1.7

G-type -2.2 1.1

K-type -2.2 0.8

M-type -0.96 0.5

Giants -3.2 4.3

White dwarfs -2.3 1.26

Brown dwarfs -1 0.05

total -0.89

For initially uniform density clouds, the collapse time is also uniform throughout the cloud.

Equation (4.1) becomes incorrect for stellar formation due to inner forces, such as hydrostatic pressure or the pressure due to the nuclear fusion in the star. However, for this investigation it is enough to assume hydrostatic equilibrium throughout the globulettes, as shown in Grenman (2006).

The simulation should run over the time a globulette is about to collapse. The average free fall

time can be calculated, using the densities tabulated in Gahm et al. (2007) and Equation (4.1) to

be some 3 · 10

yr. On the other hand, some globulettes have a free fall time of over 5 · 10

yr. In

order to take into account all globulettes, the simulation should run for 500, 000 years.

5 Results

For all fitting issues I used the program Igor Pro in Version 6.1.2.1 from WaveMetrics (http:

//www.wavemetrics.com/). Igor provides the singular value decomposition algorithm for linear and polynomial fits. The data fits were applied with Equations (3.16 & 3.18) to the logarithmic representation of the data in Figure 3.4. For the fitting, absolute values were used.

As mentioned earlier both nebulæ were just surveyed for globulettes in some regions. Thus there may be some incompleteness in the histograms.

The capture simulation was carried out with a C++ program, I have written during writing this work. It considers all facts from Section 4.4, and a brief description is given in Section 5.4. The full program is available upon request.

The simulation plots in Figures 5.4 and 5.5 were done with the program 3D Grapher in Version 1.21 from RomanLab software (http://www.romanlab.com/3dg/).

5.1 Fitting the Carina Nebula size distribution

In Figure 5.1 the fit for the Carina Nebula (CN) is plotted. In the histogram, just four bins (i.e., from 0.25 to 1.25 kAU) follow a power law. Those four points were used to plot the logarithmic values, using Equation (3.16). The fit gave the coefficients, with 95 per cent confidence,

a

= 1.332±0.083

b

=−1.49 ±0.35. (5.1)

Thus the parameters for the power-function are

A

= 21.49±1.21

B

=−1.49±0.35. (5.2)

It has to be noted that the absolute numbers of the globulettes were used for fitting issues.

The fit quality can be determined with a χ

test. For the fit parameters in Equation (5.2) it is χ

= 0.25. For the 2 degrees of freedom (d f ), this gives a probability of the fit of

P χ

= 0.25, d f = 2
= 88 per cent, (5.3)

showing that the fit was good for these 4 points.