High‐ and Low‐Velocity Magnetized Outflows in the Star Formation Process in a Gravitationally...

HIGH- AND LOW-VELOCITY MAGNETIZED OUTFLOWS IN THE STAR FORMATION PROCESSIN A GRAVITATIONALLY COLLAPSING CLOUD

Masahiro N. Machida,1Shu-ichiro Inutsuka,

1and Tomoaki Matsumoto

2

Received 2007 May 14; accepted 2007 December 11

ABSTRACT

The driving mechanisms of low- and high-velocity outflows in star formation processes are studied using three-dimensional resistive MHD simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform mag-netic field, we calculate cloud evolution from the molecular cloud core (nc ¼ 104 cm�3) to the stellar core (nc ¼1022 cm�3), where nc denotes the central density. In the collapsing cloud core, we found two distinct flows: low-velocityflows (�5 km s�1) with a wide opening angle, driven from the adiabatic core when the central density exceeds nck1012 cm�3; and high-velocity flows (�30 km s�1) with good collimation, driven from the protostar when the centraldensity exceeds nck 1021 cm�3. High-velocity flows are enclosed by low-velocity flows after protostar formation.The difference in the degree of collimation between the two flows is caused by the strength of the magnetic field andconfiguration of the magnetic field lines. The magnetic field around an adiabatic core is strong and has an hourglassconfiguration; therefore, flows from the adiabatic core are driven mainly by the magnetocentrifugal mechanism andguided by the hourglass-like field lines. In contrast, the magnetic field around the protostar is weak and has a straightconfiguration owing to ohmic dissipation in the high-density gas region. Therefore, flows from the protostar are drivenmainly by the magnetic pressure gradient force and guided by straight field lines. Differing depth of the gravitationalpotential between the adiabatic core and the protostar causes the difference of flow speed. Low-velocity flows maycorrespond to the observed molecular outflows, while high-velocity flows may correspond to the observed optical jets.We suggest that the protostellar outflow and the jet are driven by different cores, rather than the outflow being entrainedby the jet.

Subject headinggs: ISM: clouds — ISM: jets and outflows — ISM: magnetic fields — MHD — stars: formation

1. INTRODUCTION

Since Snell discovered an outflow from a protostar in 1980(Snell et al. 1980), over 300 outflows have been found in manystar-forming regions (Wu et al. 2004). Recently, outflows frombrown dwarf (Whelan et al. 2005) and O-type stars (Beuther &Shepherd 2005) were discovered. These observations indicatethat outflow is ubiquitous in the star formation process. The flowsfrom the protostars have a collimation factor (i.e., length/widthor major /minor radius of the outflow) of H /R ¼ 3 to >20 (Arceet al. 2007), where H and R are the height and radius of the flow,respectively. There is a clear trend toward higher collimation athigher flow velocity (Arce et al. 2007). Since flows from the pro-tostar have various morphological and kinematical properties,they cannot be explained by a single-class model. The flows thatoriginated from the protostar are typically classified into two types:molecular outflow observed mainly with CO molecules (Arceet al. 2007), and optical jet observed by optical emission (Pudritzet al. 2007). Molecular outflows observed by CO line emissionexhibit awide opening angle (e.g., Belloche et al. 2002) and slowervelocity (10Y50 km s�1; Richer et al. 2000; Arce et al. 2007),while optical jets observed by optical emission exhibit good col-limation and higher velocity (100Y500 km; Bally et al. 2007).For convenience, we call the former an outflow and the latter a jetin the following. Observations indicate that around each proto-star, high-speed jets with a narrow opening angle are enclosed bya low-velocity outflowwith a wide opening angle (e.g., Mundt &Fried 1983).

What mechanism drives the outflow and the jet in the star for-mation process? During star formation, neither radiation northermal pressure from the protostar can supply sufficient kineticenergy and momentum for driving the outflow and the jet (Wuet al. 2004; Pudritz et al. 2007). These flows (outflows and jets)are considered to be driven by release of the gravitational energymediated by the Lorentz and centrifugal forces (e.g., Blandford& Payne 1982; Shu et al. 1994). However, we could not under-stand what are the drivers of these flows: the protostar, the cir-cumstellar disk near or far from the protostar, or the adiabaticcore formed before the protostar formation. It is difficult to di-rectly observe the driving points of the outflow and the jet be-cause they are embedded in the dense cloud at several AU fromthe protostar. Furthermore, we cannot analytically investigate thedriving mechanisms of the outflow and the jet in detail becausethey have a large spatial scale and density contrast, and these flowsare influenced by closely related Lorentz, centrifugal, thermalpressure gradient, and gravitational forces. Therefore, numericalsimulation is the most effective tool for investigating the drivingmechanisms of the outflow and the jet.Blandford & Payne (1982) showed that centrifugally driven

flow from the disk is possible if the poloidal component of themagnetic fieldmakes an angle of less than 60

�(i.e., the diskwind

model). Pudritz & Norman (1983, 1986) proposed this model asthe mechanism for the protostellar jet. Subsequently many nu-merical simulations (e.g., Kudoh& Shibata 1997a, 1997b), whichshowed that a disk could drive the flow, confirmed the disk windmechanism around the protostar (see Konigl & Pudritz 2000;Pudritz et al. 2007). Shu et al. (1994) proposed the X-wind model,in which the jet is driven in close proximity to the protostar. Boththe disk wind and the X-wind are driven magnetocentrifugallyfrom open magnetic field lines anchored on rapidly rotating cir-cumstellar disks. The difference between these models lies in

1 Department of Physics, Graduate School of Science, Kyoto University,Sakyo-ku, Kyoto 606-8502, Japan; [email protected], [email protected].

2 Faculty of Humanity andEnvironment,HoseiUniversity, Fujimi, Chiyoda-ku,Tokyo 102-8160, Japan; [email protected].

1088

The Astrophysical Journal, 676:1088Y1108, 2008 April 1

# 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

where the field lines are anchored: near the radius of magneto-spherical truncation on the disk for the X-wind and over awider range of disk radii for the disk wind (Shang et al. 2007).The flow speeds derived from both X-wind and disk wind the-ories correspond to the Kepler speed at their driving point onthe circumstellar disk. Thus, thesemodels have not clearly showedthe two velocity components of observed optical jet and mo-lecular outflow. Many people believe that molecular outflow(i.e., slow speed and wide opening angle flow) is entrained bythe optical jet (i.e., high speed and narrow opening angle flow)and that the optical jet is driven by either the disk wind or theX-wind (e.g., Arce et al. 2007). However, almost all simulations,except for a few studies, calculate the evolution of the circum-stellar disk (i.e., jet driving) after the protostar grows up suffi-ciently and provide the idealized boundary, density profile ofthe disk, distribution of the magnetic field and velocity, ac-cretion rate, etc. After the protostar is formed, we cannot judgewhether these configurations are realized. Therefore, to acquireadequate information about the protostar and to understand thedriving mechanism of the jet and the outflow, we should cal-culate cloud evolution from the molecular cloud until the pro-tostar is formed.

Simulations of cloud evolution from the molecular cloudcore to stellar core formation show that the low-velocity flow isdriven from the adiabatic core formed before protostar formation(Tomisaka 1998, 2000, 2002;Burkert&Balsara 2001;Matsumoto& Tomisaka 2004; Machida et al. 2004, 2005a; Fromang et al.2006;Banerjee&Pudritz 2006;Hennebelle&Fromang 2008) andthat the high-velocity flow is driven from another core (Tomisaka2002; Banerjee & Pudritz 2006; Machida et al. 2006a, 2007a).Assuming spherical symmetry, the evolution frommolecular cloudto stellar core has been investigated bymany authors (e.g., Larson1969; Winkler & Newman 1980a, 1980b; Masunaga et al. 1998;Masunaga & Inutsuka 2000), and they determined the density,velocity, and temperature structures of the collapsing cloud andstellar core. They have shown that the adiabatic core (or the firstcore) with a radius of �1 AU forms when the central densityreaches nc ’ 1011 cm�3 because the gas becomes optically thickand the thermal pressure increases. Bate (1998) and Whitehouse& Bate (2006) calculated the stellar core formation from the mo-lecular cloud core using smoothed particle hydrodynamics (SPH)simulations. However, no outflow appears in their calculationsbecause they ignored the magnetic effect. The evolution of themagnetized cloud until the formation of the adiabatic core (here-after the first core) was investigated by Machida et al. (2004,2005a, 2005b, 2006b), Hosking&Whitworth (2004),Matsumoto& Tomisaka (2004), Ziegler (2005), and Fromang et al. (2006).The low-velocity outflow appears after the first core formation inMachida et al. (2004, 2005a), Matsumoto & Tomisaka (2004),and Fromang et al. (2006). Tomisaka (1998, 2000, 2002) andBanerjee& Pudritz (2006) investigated the evolution of themag-netized clouds up to protostar formation. They calculated thecloud evolution from the molecular cloud (nc ’ 102Y106 cm�3)to protostar formation (nc ’ 1022 cm�3). In their calculations, twodistinct flows appeared: low-velocity flow (v ’ 2 km s�1) drivenfrom the first core, and high-velocity flow (v ’ 30 km s�1) drivenfrom the second core (i.e., the protostar). They expected thatlow-velocity flow would be observed as molecular outflow andhigh-velocity flow as an optical jet. They adopted ideal MHDapproximation, which is valid in the low-density gas region (nP1012 cm�3); however, it is not valid in the high-density gas region(nk 1012 cm�3). Nakano et al. (2002) found significant magneticflux loss for 1012 cm�3P nP1015 cm�3 by ohmic dissipation.Therefore, Tomisaka (1998, 2000, 2002) and Banerjee & Pudritz

(2006) overestimated the magnetic flux of the cloud, particularlyin the high-density gas region.

There are two predictions concerning driving jets and outflows:one is that the outflow is entrained by the jet, and another is thatthe outflow and jet are driven from different objects. These pre-dictions aremutually conflicting. In this paper we calculate cloudevolution from the molecular cloud core (nc ¼ 104 cm�3, rc ¼4:6 ; 104 AU) to stellar core formation (nc ’ 1022 cm�3, rc ’1 R�) using the three-dimensional resistive MHD nested gridmethod, study the formation process of jets and outflows, andshow the driving mechanisms of these flows. The numericalmethod of our computations and our model framework are givenin x 2, and the numerical results are presented in x 3. We discussthe driving mechanism of the outflow and the jet in x 4, and wesummarize our conclusions in x 5.

2. MODEL

Our initial settings are almost the same as those of Machidaet al. (2006a, 2006b, 2007a). To study cloud evolution, we usethe three-dimensional resistive MHD nested grid code. We solvethe resistive MHD equations including self-gravity:

@�

@tþ: = �vð Þ ¼ 0; ð1Þ

�@v

@tþ � v = :ð Þv ¼ �:P � 1

4�B < : < Bð Þ� �:�; ð2Þ

@B

@t¼ : < v < Bð Þ þ �92B; ð3Þ

92� ¼ 4�G�; ð4Þ

where �, v, P, B, �, and � denote the density, velocity, pressure,magnetic flux density, resistivity, and gravitational potential, re-spectively. The last term in equation (3) denotes the ohmic dis-sipation. The magnetic evolution in dynamical collapsing cloudsis investigated by many authors (e.g., Nakano et al. 2002; Tassis&Mouschovias 2007a, 2007b), including detailed estimation ofthe chemical evolution and ionization degree. We quantitativelyestimate the resistivity � according to Nakano et al. (2002) andassume that � is a function of density and temperature. For resis-tivity (�), we use the value adopted in Machida et al. (2006a,2007a). Note that the change in dust grain properties (size dis-tribution, etc.) should change the ionization degree, and that isthe reason why we adopted parameterization of the resistivity inour previous work (see Machida et al. 2007a).

As the gas pressure, we use a barotropic equation of state. Thethermal evolution of gas in star-forming clouds has been investi-gated bymany authors, including the detailed radiative process un-der spherical symmetry (e.g., Larson 1969; Tohline 1982;Winkler& Newman 1980a, 1980b; Masunaga et al. 1998; Masunaga &Inutsuka 2000), and in recent three-dimensional calculations (e.g.,Whitehouse & Bate 2006; Stamatellos et al. 2007). To mimic thetemperature evolution determined byMasunaga& Inutsuka (2000),we adopt the piecewise polytropic equation of state as

P ¼

c2s �; � < �c;

c2s �c�

�c

� �7=5

; �c < � < �d ;

c2s �c�d�c

� �7=5 �

�d

� �1:1

; �d < � < �e;

c2s �c�d�c

� �7=5 �e�d

� �1:1 �

�e

� �5=3

; � > �e;

8>>>>>>>>>>><>>>>>>>>>>>:

ð5Þ

HIGH- AND LOW-VELOCITY OUTFLOWS 1089

where cs ¼ 190 m s�1, �c ¼ 3:84 ; 10�13 g cm�3 (ncri ¼1011 cm�3), �d ¼ 3:84 ; 10�8 g cm�3 (nd ¼ 1016 cm�3), and�e ¼ 3:84 ; 10�3 g cm�3 (ne ¼ 1021 cm�3). For convenience,wedefine ‘‘the protostar formation epoch’’ as that at which the cen-tral density (nc) reaches nc ¼ 1021 cm�3. We also call the periodfor which nc < 1011 cm�3 ‘‘the isothermal phase,’’ the period forwhich 1011 cm�3 < nc < 1016 cm�3 ‘‘the adiabatic phase,’’ theperiod for which 1016 cm�3 < nc < 1021 cm�3 ‘‘the second col-lapse phase,’’ and the period for which nc > 1021 cm�3 ‘‘the pro-tostellar phase.’’

In this paper we adopt a spherical cloud with a critical Bonnor-Ebert (Ebert 1955; Bonnor 1956) density profile having �BE ¼3:841 ; 10�20 g cm�3 (nBE ¼ 104 cm�3) of the central (number)density as the initial condition. The critical radius for a Bonnor-Ebert sphere Rc ¼ 6:45cs(4�G�BE;0)

�1/2 corresponds to Rc ¼4:58 ; 104 AU for our settings. Initially, the cloud rotates rigidly(�0) around the z-axis and has a uniform magnetic field (B0 ¼17 �G) parallel to the z-axis (or rotation axis). To promote con-traction, we increase the density by 70% from the critical Bonnor-Ebert sphere. The initial central density is therefore �0 ¼ 6:53 ;10�20 g cm�3 (n0 ¼ 1:7 ; 104 cm�3).

The initial model is characterized by a single nondimensionalparameter !. This parameter is related to the cloud’s rotation rateand is defined using an initial central density �0 as

! ¼ �0= 4�G�0ð Þ1=2: ð6Þ

The model parameters !, magnetic field B0, angular velocity�0,total mass inside the critical radiusM0, and the ratio of the ther-mal �0, rotational �0, and magnetic �0 energies to the gravita-tional energy3 are summarized in Table 1.

We adopt the nested gridmethod (for details seeMachida et al.2005b, 2006b) to obtain high spatial resolution near the center.Each level of a rectangular grid has the same number of cells(64 ; 64 ; 32), although the cell width h(l ) depends on the gridlevel l. The cell width is reduced by a factor of 1

2as the grid level

increases by 1 (l ! l þ 1). We assumemirror symmetry with re-spect to z ¼ 0. The highest level of a grid changes dynamically.We begin our calculations with four grid levels (l ¼ 1, 2, 3, 4).The box size of the initial finest grid l ¼ 4 is chosen to be 2Rc,where Rc denotes the radius of the critical Bonnor-Ebert sphere.The coarsest grid l ¼ 1, therefore, has a box size of 24Rc. Aboundary condition is imposed at r ¼ 24Rc, such that the mag-netic field and ambient gas rotate at an angular velocity of �0

(for details see Matsumoto & Tomisaka 2004). A new finer gridis generated whenever the minimum local Jeans length kJ be-comes smaller than 8h(lmax). The maximum level of grids is re-stricted to lmax ¼ 30. Since the density is highest in the finestgrid, the generation of a new grid ensures the Jeans condition ofTruelove et al. (1997) with a margin of safety factor of 2. We

adopted the hyperbolic divergenceB cleaningmethod of Dedneret al. (2002).

3. RESULTS

Assuming spherical symmetry, many authors investigated theevolution from molecular cloud to stellar core using radiationhydrodynamic calculations (e.g., Larson 1969;Winkler&Newman1980a, 1980b;Masunaga et al. 1998;Masunaga& Inutsuka 2000).We briefly summarize the evolution of the collapsing cloud core,according to their calculations. The molecular gas obeys the iso-thermal equation of state with a temperature of �10 K until nc ’5 ; 1010 cm�3 (isothermal phase), then the cloud collapses al-most adiabatically for 5 ; 1010 cm�3P ncP 1016 cm�3 (adiabaticphase). A quasi-static core (i.e., the first core) with �10�2 M�forms in the adiabatic phase. Subsequently dissociation of mo-lecular hydrogen when the density exceeds nck 1016 cm�3 trig-gers further gravitational collapse (i.e., second collapse). Finally,the second core (i.e., protostar) with �10�3 M� forms at nc ’1021 cm�3. The protostar increases its mass for the subsequentgas accretion phase.In this study we calculated the cloud evolution from the mo-

lecular cloud core with nc ¼ 1:7 ; 104 cm�3 to form a protostarwith nc ’ 1022 cm�3.Machida et al. (2004, 2005a, 2005b, 2006b)investigated cloud evolution in the isothermal and early adia-batic phases. The evolution of the magnetic field and angularvelocity in the collapsing cloud for 104 cm�3P ncP 1023 cm�3

was shown by Machida et al. (2007a). Therefore, this paperfocuses mainly on the cloud evolution after the first core for-mation (nck 1011 cm�3) because we are interested in the drivingmechanism of the outflow and the jet. We parameterized angu-lar velocity, magnetic field strength, and the ratio of thermal togravitational energy of the initial cloud for 80 models. Cloudevolutions are typically classified into three types when the low-velocity flow (i.e., outflow) or high-velocity flow (i.e., jet) ap-pears in the collapsing cloud.We also found that cloud evolutiondepends on the ratio of the angular velocity to the magnetic field(�0/B0) but does not depend on the ratio of thermal to gravitationalenergy, especially after the first core formation (nck 1011 cm�3).Observations indicate that molecular cloud cores have largemagnetic energies and small rotational energies (Crutcher 1999;Caselli et al. 2002). In these types of clouds, cloud evolution issensitive to the initial angular velocity, as shown in Machidaet al. (2005b, 2006b, 2007a). In the following, we show onlythree typical models in which the initial clouds have the samemagnetic field strengths and ratios of thermal to gravitationalenergy, but different angular velocities (slow, moderate, andrapid rotation rate).In the collapsing clouds,we observe two distinct flows as shown

in Tomisaka (2002) and Banerjee & Pudritz (2006). These flowsare respectively driven by the first core and second core. Theflows driven by the first cores have speeds of several kilometersper second, while the flows from the second cores have speeds ofseveral tens of kilometers per second. In this paper, for conve-nience,we call the flow from the first core ‘‘the low-velocity flow’’

TABLE 1

Model Parameters and Calculation Results

Model !

B0

(�G)

�0

(s�1)

M0

(M�) �0 �0 �0

Bf

( kG)

Pf

(days)

SR......................... 0.003 17 7.0 ; 10�16 7.6 0.5 3 ; 10�5 0.96 2.18 3.0

MR ....................... 0.03 17 7.0 ; 10�15 7.6 0.5 3 ; 10�3 0.96 0.40 2.1

RR ........................ 0.3 17 7.0 ; 10�14 7.6 0.5 3 ; 10�1 0.96 . . . . . .

3 Representing the thermal, rotational, magnetic, and gravitational energiesasU,K,M, andW, the relative factors against the gravitational energy are definedas �0 ¼ U /jW j, �0 ¼ K/jW j, and �0 ¼ M /jW j.

MACHIDA, INUTSUKA, & MATSUMOTO1090 Vol. 676

and flow from the second core ‘‘the high-velocity flow.’’ Westart with the evolution of the cloud with initially slowest ro-tation in x 3.1. In this cloud, only the high-velocity flow ap-pears. The cloud evolution with initially moderate rotation isshown in x 3.2, in which the collapsing cloud shows both of thelow-velocity and high-velocity flows. In x 3.3, the cloud evo-lution with initially rapid rotation is shown. In this cloud, we cansee only the low-velocity flow because of numerical limitation.We summarize the relationship between cloud rotation and flowsin x 3.4.

3.1. Cloud Evolution with Slow Rotation

3.1.1. First Core and Protostar Formation

Figure 1 shows the cloud evolution for model SR after the firstcore formation. Model SR has a parameter of ! ¼ 0:003, whichmeans that the initial cloud has small rotation energy; the ratioof the rotational to gravitational energy is �0 ¼ 3 ; 10�5 (seeTable 1). Table 1 shows that, in model SR, the rotational energyis much smaller than the thermal and magnetic energy in its initialstate.

The density ( false colors) and velocity distribution (arrows)around the first core are plotted in the top and middle panels ofFigure 1. The plasma beta and magnetic fields around the firstcore are plotted in the bottom panels of Figure 1. We plottedshocked regions as dotted lines in the top and middle panels ofFigure 1. Since the first core is surrounded by the shock layer(Masunaga & Inutsuka 2000), dotted lines indicate the first core.For model SR, the first core forms when the central densityreaches nc ’ 1014 cm�3. The first core at its formation epoch hasa mass of 5:1 ; 10�3 M� and a radius of R ’ 0:71 AU, whichis equivalent to or slightly larger than that expected by one-dimensional radiation hydrodynamic calculations (Masunaga &Inutsuka 2000). Matsumoto & Hanawa (2003) showed that alarger first core forms in a rapidly rotating cloud because the cen-trifugal force suppresses the cloud collapse and the shock occursin the earlier adiabatic phase. However, the effect of centrifugalforce at the first core formation epoch is small in model SR be-cause a slowly rotating cloud is adopted as the initial state. Themagnetic effect slightly increases the mass and size of the firstcore, as shown in Machida et al. (2005b).

Figures 1a and 1b show the density and velocity distributionon z ¼ 0 and y ¼ 0 cut planes at nc ¼ 6:5 ; 1016 cm�3. Thesepanels indicate that the first core has a nearly spherical shape.To evaluate the core shape, we define the oblateness as "ob �(hlhs)

1/2/hz, where hl, hs, and hz are the major axis, minor axis,and z-axis, respectively, derived from the moment of inertia forthe high-density gas of � � 0:1�c according to Matsumoto &Hanawa (1999). Figure 2a shows the evolution of the oblatenessfor model SR as a solid line. The oblateness increases as the cloudcollapses in the isothermal phase (ncP 1014 cm�3) and has a peakof "ob ’ 10 (i.e., the ratio of the radial to vertical scale is about 10)at nc ’ 2 ; 108 cm�3. Therefore, the central region has a disklikestructure at this epoch. Since the cloud rotates slowly, the disk isformed mainly by the Lorentz force. Note that the magnetic en-ergy is comparable to both the thermal and gravitational energy atthe initial state (see Table 1). The oblateness oscillates around"ob ’ 10 for 2 ; 108 cm�3P ncP 1012 cm�3 and then begins todecrease (Fig. 2a). This decrease is caused by an increase in ther-mal energy. When the gas density reaches nc ’ 1011 cm�3, thecloud collapses adiabatically and thermal pressure increases. Theoblateness becomes "ob ’ 1 at the first core formation epoch (nc ’1014 cm�3), which indicates that the first core has a nearly sphericalshape, as shown in Figures 1a and 1b.

Figure 1c shows the plasma beta (�p � B2/8�c2s �) around thefirst core on the y ¼ 0 cut plane. This panel shows that the mag-netic energy inside the first core is extremely small (�p ’ 10Y104), while that outside the first core is comparable to the thermalenergy (�p < 1). As shown inMachida et al. (2006a, 2007a), themagnetic field is largely removed from the cloud core by ohmicdissipation for 1012 cm�3P ncP1015 cm�3. Figure 2b showsthe evolution of the magnetic flux density at the center of thecloud (Bc) for model SR (solid line). The growth rate of themagnetic flux density becomes small for 1012 cm�3P ncP1015 cm�3. The solid line in Figure 2c shows the magnetic fluxdensity normalized by the square root of the gas density at thecenter of the cloud (Bc/�

1/2c ) for model SR. In the ideal MHD

regime, the evolution of Bc/�1/2c depends on the geometry of the

collapse. This value, Bc/�1/2c, remains constant after a thin disk

forms because the magnetic field increases in proportion to thesquare root of the density when the disklike cloud collapses(B / �1/2; Scott & Black 1980). On the other hand, Bc/�1/2c

in-creases in proportion to �1/6 when the cloud collapses spherically(for details see Machida et al. 2006b). Thus, a rapid drop ofBc/�

1/2c for 1012 cm�3PncP1015 cm�3 indicates the removal

of the magnetic field from the center of the cloud by ohmic dis-sipation. Nakano et al. (2002) showed that the magnetic field islargely removed by ohmic dissipation for 1012 cm�3P ncP1016 cm�3. Since the first core forms at nc ’ 1012 cm�3 in thismodel, the first core is composed of the gas from which the mag-netic field is already removed. Therefore, the first core has a largeplasma beta (or weak magnetic field strength), as shown inFigure 1c.

Figures 1d and 1e show the density and velocity distributionsaround the first core at nc ¼ 6 ; 1020 cm�3 (second collapsephase). The cloud can collapse again for 1016 cm�3P ncP1021 cm�3 owing to dissociation of molecular hydrogen (i.e.,second collapse; Masunaga & Inutsuka 2000). The arrows inFigures 1d and 1e indicate that the cloud collapses intenselyaround its center. The size of first core at this epoch is slightlysmaller than that at the epoch of Figures 1a and 1b. However,the first core has a nearly spherical shape ("ob ’ 1 at nc ¼6 ; 1020 in Fig. 2a) because the anisotropic Lorentz and cen-trifugal forces are weaker than the isotropic forces of the grav-itational and thermal pressure gradient forces in this phase. TheLorentz force becomes weak due to magnetic dissipation, and aninitially small rotation rate produces a weaker centrifugal force.

Figure 2d shows the angular velocity normalized by the free-fall timescale at the center of the cloud, whose value correspondsto the ratio of the rotational to gravitational energy (Machidaet al. 2005b). When this value reaches �c/(4�G�c)1/2 ’ 0:2, therotational energy becomes comparable to the gravitational energy,and cloud rotation begins to affect cloud evolution (Matsumoto &Hanawa 2003; Machida et al. 2005b, 2006b). In model SR, theeffect of cloud rotation is significantly small in the second collapsephase (1016 cm�3P ncP 1020 cm�3) because �c/(4�G�c)

1/2T0:2. The magnetic field is again important for cloud evolutionafter the second collapse phase because ohmic dissipation be-comes less effective, and the magnetic field can be amplified.Figure 2c shows that Bc/�

1/2c has a minimum at nc ’ 1015 cm�3

and then continues to increase for nck 1015 cm�3. However, theplasma beta inside the first core reaches only �p � 100 at nc ’1021 cm�3 (Fig. 1f ); therefore, the magnetic energy is muchsmaller than the thermal energy, even in the second collapsephase.

Figures 1g and 1h show the density and velocity distributionsat nc ¼ 2:6 ; 1021 cm�3 (the protostar formation epoch). In ourcalculations, the first core (i.e., shock layer) does not disappear

HIGH- AND LOW-VELOCITY OUTFLOWS 1091No. 2, 2008

until the calculation ends. The second core (i.e., protostar;Masunaga& Inutsuka 2000) forms inside the first core in Figures 1g and 1h.Since both the magnetic field and angular velocity continue toincrease in the second collapse phase, the first core is slightlyflattened by both Lorentz and centrifugal forces at the protostarformation epoch, as shown in Figure 1h. However, the protostarhas an oblateness "ob ¼ 1:2 (Fig. 2a) at its formation epoch (nc ¼1021 cm�3) and therefore has a nearly spherical shape. The mag-netic field and rotation period reachBf ¼ 2:18 kGandPf ¼ 3 daysat the protostar formation epoch. In Table 1 we summarize themagnetic field strengths Bf and rotation periods Pf of each modelat the protostar formation epoch. The plasma beta around the

protostar (or inside the first core) becomes �p ’ 10Y103 (Fig. 1i).After the protostar formation (nck1021 cm�3), the plasma betabecomes large (�p ’ 103Y104) because the thermal energy be-comes large (see eq. [5]). The angular velocity normalized bythe free-fall timescale, however, reaches �c/(4�G�c)

1/2 ’ 0:2 atthe protostar formation epoch (Fig. 2d ); then, the cloud beginsto rotate rapidly, and the rotation significantly affects protostarevolution.

3.1.2. High-Velocity Flow from Protostar

Figure 3 shows cloud evolution after the protostar formationepoch (nc > 1021 cm�3). Figures 3aY3c show the protostar

Fig. 1.—Time sequence of model SR. (a, d, g) Density (color scale) and velocity distribution (arrows) on the cross section in the z ¼ 0 plane. (b, e, h) Density (colorscale) and velocity distribution (arrows) on the cross section in the y ¼ 0 plane. (c, f, i) Plasma beta (color scale and contours) and magnetic field (arrows) on the crosssection in the y ¼ 0 plane. Panels from left to right are snapshots at the stages of nc ¼ 6:5 ; 1016 cm�3 (l ¼ 20), 6:0 ; 1020 cm�3 (l ¼ 20), and 2:6 ; 1021 cm�3 (l ¼ 20),respectively, where l denotes the level of subgrid.White dotted lines in the top andmiddle panels show the shocked regions, which indicate the first core. The elapsed time,density at the center of the cloud, and arrow scale are denoted in each panel.


(i.e., second core) surrounded by the shock layer as a dotted line.Figure 3a shows the density and velocity distribution around theprotostar 170 days after the protostar formation epoch. The pro-tostar has a mass of 5:1 ; 10�4 M� and a radius of R ’ 0:75 R�at its formation epoch (nc ’ 1021 cm�3). The arrows in Figure 3ashow that the gas around the protostar accretes spherically ontothe protostar. Figure 3b shows the protostar 207 days after itsformation epoch. Figures 3a and 3b show that the protostar be-comes flat with time because the magnetic field and cloudrotation are amplified and affect protostar evolution, as shown inFigures 2c and 2d. Two shocks (outer and inner) are seen inFigure 3b. The outer shocks are located at z ’ �6 ; 10�3 AU,while the inner shocks corresponding to the protostar are locatedat z ’ �2 ; 10�3 AU. As shown in Figure 3c, the accretionspeed inside the outer shock ( jvj ’ 5 km s�1 in the region ofz < j2 ; 10�3j AU) is slower than that outside the outer shock(jvj ’ 20 km s�1 in the region of z > j2 ; 10�3jAU). This struc-ture of the shock and distribution of the density and velocity,shown in Figure 3b, is similar to ‘‘the magnetic bubble’’ inTomisaka (2002). He showed that the magnetic pressure is am-plified by the twisted magnetic field lines, and a bubble-likestructure is formed in the weakly magnetized collapsing cloud.

In model SR, the high-velocity flow appears 215 days after theprotostar formation epoch. Figure 3c shows that the gas flows outfrom the central region along the vertical axis. The red lines inFigures 3bY3f indicate the border between the inflow and the out-flow. Inside the red lines, the gas flows out from the central re-gion (vz w 0 for zw 0), and outside the red lines, it flows into thecentral region (vzM 0 for zw 0). The high-velocity flow has amaximum speed of vHVF ’ 17 km s�1 at the same epoch as inFigure 3c. The high-velocity flow has an elongated structure and

height-to-radius ratio of H /R � 3 in Figure 3c. The height-to-radius ratio increases with time. Figures 3d and 3e show the high-velocity flow extending in the vertical direction keeping almostthe same horizontal scale (R ¼ 0:012AU in Fig. 3d and 0.018AUin Fig. 3e). The high-velocity flow extends up to H ¼ 0:043 AUwith a maximum speed of vHVF ’ 22 km s�1 at tc ¼ 229 days(Fig. 3d ), while it extends up to H ¼ 0:1 AU with vHVF ’26 km s�1 at tc ¼ 226 days (Fig. 3e), where tc is the elapsed timefrom the protostar formation epoch (nc ¼ 1021 cm�3). Figure 3fshows the structure of the high-velocity flow at the end of thecalculation. Note the butterfly-like density distribution (whitedensity contour), which is caused by the strong mass ejectionfrom the protostar. The high-velocity flow has a well-collimatedstructure at this epoch. The height-to-radius ratio of the high-velocity flow reaches H /R ’ 10. In Figure 3f, the high-velocityflow penetrates the first core, shown as a thick dotted line, andextends up to the outside of the first core. At the end of the cal-culation, the high-velocity flow reaches 0.2 AUwith a maximumspeed of vHVF ’ 32 km s�1.

Figure 4 shows the shape of the high-velocity flow ( purpleisovelocity surface) and magnetic field lines (streamlines) at thesame epoch as Figure 3f but with a different grid size (left panel:l ¼ 22; right panel: l ¼ 24). The left panel of Figure 4 confirmsthat the high-velocity flow has a well-collimated structure show-ing that the high-velocity flow is strongly coiled by the magneticfield lines, with the bow shocks clearly visible near the upper andlower boundaries. The right panel of Figure 4 provides a close-up view of the left panel, indicating that the high-velocity flowis driven from the protostar, which is shown by a red isodensitysurface. We can see ripping density contours on the projectedwall caused by strong mass ejection (Machida et al. 2006a).

Fig. 2.—(a) Oblateness ("ob) within � < 0:1�c. (b) Thick lines: Magnetic flux density (Bc; left axis). Thin lines: Rotation period (P; right axis). (c) Magnetic fieldnormalized by the square root of the density (Bc/�1/2c

) in units of the initial sound speed cs;0. (d ) Angular velocity normalized by the free-fall timescale [�c/(4�G�c)1/2] at the

center of the cloud against the central number density (nc) for models SR, MR, and RR.


At the end of the calculation, the protostar in model SR has amass of 4:04 ; 10�3 M� and a radius of 1.07 R�, while the massflowing out from the protostar is Mout ¼ 5:23 ; 10�5 M�. Theprotostar is surrounded by a disk with a mass of 2:8 ; 10�4 M�and a radius of 3.16 R�. At the same epoch, the protostar and

high-velocity flow have the angular momenta of Jcore ¼ 4:23 ;1047 g cm2 s�1 and Jout ¼ 1:55 ; 1046 g cm2 s�1, respectively.Therefore, the specific angularmomenta of the protostar and high-velocity flow are jcore ¼ 5:25 ; 1016 cm2 s�1 and jout ¼ 1:49 ;1017 cm�3, respectively. This indicates that the high-velocity flow

Fig. 3.—Time sequence of model SR after the protostar formation epoch. The density (color scale) and velocity distribution (arrows) on the cross section in the y ¼ 0plane are plotted in each panel. Panels (a)Y ( f ) are snapshots at the stages of (a) tc ¼ 170 days (l ¼ 26), (b) 207 days (l ¼ 26), (c) 221 days (l ¼ 25), (d ) 229 days (l ¼ 24),(e) 236 days (l ¼ 23), and ( f ) 265 days (l ¼ 22), where tc denotes the elapsed time after protostar formation (nc ¼ 1021 cm�3). Red thick lines indicate the border betweenthe high-velocity flow and the accretion flow (i.e., contour of vz ¼ 0). White dotted lines in panels (a)Y (c) indicate the second core (i.e., protostar), while the white dottedline in panel ( f ) indicates the first core. The elapsed time after protostar formation (tc), the elapsed time from the initial (t), gas density at the center of the cloud (nc), arrowscale, and grid scale are denoted in each panel. The level of the subgrid is shown in the upper left corner.


largely removes the angular momentum from the protostar.Machida et al. (2007a) showed that, at its formation epoch, theprotostar has a short rotation period compared with the observa-tion. The high-velocity flow may be one of the mechanisms forthe angular momentum transfer after protostar formation.

3.2. Cloud Evolution with Moderate Rotation

3.2.1. First Core and Protostar Formation

Figure 5 shows the cloud evolution for model MR after firstcore formation. Model MR has a parameter of ! ¼ 0:03. Theratio of the rotational to gravitational energy for model MR is�0 ¼ 3 ; 10�3, which is 100 times larger than that for model SRat its initial state (see Table 1). In model MR, the first core formsat nc ’ 1014 cm�3 and has a mass of M � 0:01M� and a radiusof R � 1 AU. Figures 5a and 1a show that the first core of modelMR is larger than that of model SR because the centrifugalforce for model MR is stronger. The angular velocity, nor-malized by free-fall timescale at the center of the cloud, saturates�c/(4�G�c)

1/2 ’ 0:2 for nck 1014 cm�3 (Fig. 2d ). This indicatesthat cloud rotation significantly affects cloud evolution after thecentral density reaches nc ’ 1014 cm�3. Due to the rotation (orthe centrifugal force), the first core for model MR has a moreoblate structure than that for model SR, as shown in Figure 5b.The evolution of the oblateness for model MR is almost thesame as that for model SR for ncP 1014 cm�3. On the otherhand, the oblateness increases after the central density reaches

nc ’ 1015 cm�3, while it maintains "ob ’ 1 for nck 1014 cm�3 inmodel SR. Figure 5c shows the plasma beta around the first coreat nc ¼ 3:2 ; 1016 cm�3. The plasma beta for model MR is aslarge as that for model SR (�p ¼ 10Y103) at the first core for-mation epoch (Fig. 5c). Thus, the magnetic field slightly affectscloud evolution inside the first core at this epoch.

Figures 5d and 5e show the density and velocity distribution atnc ¼ 1:2 ; 1018 cm�3 (the second collapse phase). The arrows inFigure 5d show that the cloud collapses while rotating: however,it collapses only in the radial direction for model SR (Fig. 1). Theazimuthal component of the velocity (v�) inside the first core iscomparable to or larger than the radial one (vr) in model MR,while the azimuthal component of the velocity is much smallerthan the radial one in model SR. Since the gas cloud inside thefirst core rotates rapidly, the central region increases its oblate-ness as the cloud collapses (Fig. 2a). Therefore, the central re-gion has a more oblate or disklike structure, similar to the firstcore shown in Saigo & Tomisaka (2006), in which they inves-tigated the equilibrium state of the rotating first cores. In general,since the angular momentum is transferred by magnetic brakingin themagnetized clouds (Basu&Mouschovias 1994), the cloudrotation slows with time. In this model, however, the cloud ro-tation hardly slows because the magnetic energy around the firstcore is too small to effectively work the magnetic braking. Thesmall energy of the magnetic field is realized by ohmic dissipa-tion. Therefore, the cloud around the first core has a large plasmabeta (�p > 10; Fig. 5c). Figure 2c compares the magnetic field

Fig. 4.—Bird’s-eye view of model SR at the same epoch as Fig. 3f, but with different scales of 0:35 AU (left) and 0:087 AU (right). The structure of the high-densityregion (� > 0:1�c; red isodensity surface) and magnetic field lines (black and white streamlines) are plotted in each panel. The structure of the jet is shown by the purpleisovelocity surface in which the gas is outflowing from the center. The density contours ( false color and contour lines) and velocity vectors (thin arrows) on the midplaneof x ¼ 0, y ¼ 0, and z ¼ 0 are, respectively, projected in each wall surface.


normalized by the density at the center of the cloud (Bc/�1/2c ) for

model MR (dashed line), which is smaller than that for modelSR (solid line) because the cloud collapses maintaining the disk-like structure in model MR, while that in model SR collapsesspherically. The growth rate of the magnetic field depends on thegeometry of the collapse and is much larger for a spherical col-lapse than for a disklike collapse (Machida et al. 2005b, 2006b).As a result, the protostar has a magnetic field of Bf ¼ 0:4 kG formodelMR, which is 5 times smaller than that for model SR at theprotostar formation epoch (see Table 1).

Figures 5g and 5h show the density and velocity distribution atnc ¼ 2:3 ; 1021 cm�3 (the protostar formation epoch). In eachpanel, the protostar (i.e., the second core) is represented by a red

dotted line. InmodelMR, the protostar forms at nc ’ 2 ;1020 cm�3

and has a mass of M ’ 3:6 ; 10�4 M� and a radius of R ¼1:5 R�. As shown in Figure 5h, at the protostar formation epoch,the first core sags downward in the center in a concave structuresimilar to model C in Saigo & Tomisaka (2006). This concavestructure is considered to be caused by rapid rotation and an in-crease in the density of the first core (for details see Saigo &Tomisaka 2006). As shown in Figure 5h, since the gas densityfalls below ncP 1012 cm�3 in the regions just above and belowthe first core at the center of the cloud (jxj < 0:1 AU), ohmicdissipation is less effective in these regions. Note that ohmic dis-sipation is effective for 1012 cm�3P ncP 1015 cm�3 (Nakanoet al. 2002). Therefore, the magnetic field is strong around the

Fig. 5.—Same as Fig. 2, but for model MR. Panels from left to right are snapshots at the stages of nc ¼ 3:2 ; 1016 cm�3 (l ¼ 20), 1:2 ; 1018 cm�3 (l ¼ 20), and 2:3 ;1021 cm�3 (l ¼ 20), respectively. Thewhite dotted lines in top andmiddle panels indicate the first core, while the red dotted lines in panels (g) and (h) indicate the protostar.


protostar (�p ’ 0:1). Since the central region becomes increas-ingly thinner and has an increasingly concave structure over time,the magnetic field around the protostar barely dissipates throughohmic dissipation. Therefore, in model MR, the torsional Alfvenwave generated by the rotation of the protostar can be transferredoutside without dissipation. In model SR, however, the magneticfield dissipates and the plasma beta maintains a high value(�p ’ 10Y103) around the protostar because the cloud collapsesspherically with slow rotation and ohmic dissipation is effectivearound the protostar. Figure 5h shows that the low-velocity flowsare driven near the first core. The region where the low-velocityflow appears in Figure 5h corresponds to the low plasma betaregion (�pP 0:1) shown in Figure 5i.

3.2.2. Low- and High-Velocity Flows from First Core and Protostar

Figure 6 shows the evolution of low-velocity flow for modelMR. Figures 6aY6c show the density and velocity distributionaround the first core on the y ¼ 0 plane. The gas accretes onto thefirst core (white dotted lines) in the whole region outside the firstcore (Fig. 6a), while the gas in the regions above and below thefirst core (inside the red lines) outflows from the central region(Fig. 6b). In the ideal MHD regime, the low-velocity flow in thecollapsing cloud appears in close proximity to the first core(Tomisaka 2002; Matsumoto & Tomisaka 2004; Machida et al.2004, 2005a; Banerjee & Pudritz 2006). However, as shown inFigure 6b, the low-velocity flow appears far from the first core inthe nonideal MHD regime because the magnetic field near thefirst core is not well coupled with the neutral gas due to ohmicdissipation. Thus, the torsional Alfven wave caused by the ro-tation of the first core is not effectively transferred. However, the

torsional Alfven wave generated far from the first core canmaintain itself because the gas density is low and ohmic dissi-pation is less effective in these regions. As the cloud collapses,the low-velocity flow can be driven even near the first core, asshown in Figure 6c, because in these regions, the gas densitygradually decreases and ohmic dissipation becomes less ef-fective over time, as shown in Figures 5b, 5e, and 5h. Finally,the low-velocity flow is anchored by the first core, as seen inthe ideal MHD calculations. At the end of the calculation, thelow-velocity flow has a maximum speed of 3.2 km s�1, whichis comparable to the results of idealMHD calculations (Tomisaka2002). Therefore, the low-velocity flow in our calculation(the nonideal MHD calculation) differs from that of the idealMHD calculation in the early phase, while the features of low-velocity flow are almost the same (e.g., the shape and speed)for both the nonideal and ideal MHD calculations in the laterphase.

Figure 7 shows the evolution of a high-velocity flow drivenfrom the protostar. In this figure, the first core and protostar (i.e.,the second core) are shown as dotted white and red lines, re-spectively. The protostar has a disklike structure, while the firstcore has a concave shape (Fig. 7a). The gas flows out from theregions above and below the protostar (Fig. 7b). Figure 7b showshornlike structures at z ¼ �0:1 AU, which are caused by strongmass ejection. This panel shows that only the gas located in theregions just above and below the protostars flows out from theprotostar, while a large fraction of the gas accretes onto the pro-tostar. At the end of the calculation, a high-velocity flow with amaximum velocity of 17.2 km s�1 is driven from the protostar, asshown in Figure 7c.

Fig. 6.—Time sequence of the outflow driven from the first core for model MR. The density (color scale) and velocity distribution (arrows) on the cross section inthe y ¼ 0 plane are plotted in each panel. Panels (a)Y(c) are snapshots at the stages of (a) nc ¼ 2:5 ; 1016 cm�3 (l ¼ 17Y19), (b) 1:5 ; 1017 cm�3 (l ¼ 17Y19), and(c) 1:2 ; 1023 cm�3 (l ¼ 17Y19). White dotted lines indicate the first core. Red solid lines indicate the border between the low-velocity flow and accretion flow (i.e.,contour of vz ¼ 0). The elapsed time from the initial (t), density at the center of the cloud (nc), and arrow scale are denoted in each panel.


Figures 8aY8c show the density (color and contours) and ve-locity distributions (arrows) around the protostar for model MR.The velocity of the z-component (vz; color and contours) andmagnetic field (arrows) corresponding to each of Figures 8aY8care plotted in Figures 8eY8f. The first core and protostar (i.e.,second core) are plotted as dotted white and red lines, respec-tively. The low-velocity flow extends from the region just abovethe first core to the outside of the l ¼ 17 grid boundary (Fig. 8a).In model MR, the low-velocity flow extends to 7 AU at the endof the calculation.

There are two velocity peaks in Figure 8d. The upper one(peak 1) has a velocity of vz ’ 2:5 km s�1 at (x; z) ’ (�0:7 AU;5 AU), while the lower one (peak 2) has a velocity of vz ’3 km s�1 at (x; z) ’ (�0:2 AU; 1 AU). Figures 8b and 8e pro-vide close-up views of Figures 8a and 8d. In Figure 8e, strongflows (peak 3) appear near the surface of the first core [(x; z) ’( � 0:1 AU; 0:3 AU)]. Figures 8c and 8f show close-up viewsof Figures 8b and 8e. A flow with high speed is driven from theregion above the protostar in Figure 8c, corresponding to peak 4in Figure 8f. This peak (peak 4) has a velocity of vz ’ 15 km s�1

at (x; z) ’ (�0:02 AU; 0:08 AU). The bottom panels of Fig-ure 8 show four velocity peaks (peaks 1Y4). These peaks implythat speeds (strength) of theseflows changewith time because theyrepresent a history of the flows. We confirmed that peaks 1 and 2appear before protostar formation, and peaks 3 and 4 appear afterprotostar formation. We also confirmed that each peak is relatedto the oscillation of each core. For example, peaks 1 and 2 appearevery time the first core oscillates. It is, therefore, considered thatthe outer peaks (peaks 1 and 2) originate from the first core, whilethe inner peaks (peaks 3 and 4) originate from the protostar. Thus,in our definition, the outer peaks correspond to the low-velocityflow, while the inner peaks correspond to the high-velocity flow.

Figure 9 shows the structure of the low- and high-velocityflows and the configuration of the magnetic field lines. It alsoshows the shapes of the first core (left panel; the projecteddensity contours on the wall) and the protostar (right panel; thered isosurface). The purple and blue surfaces in Figure 9 indicatethe isovelocity surface of vz ¼ 0:5 and 7 km s�1, respectively.The flow inside the purple isovelocity surface has a velocity ofvz > 0:5 km s�1 ( low-velocity component [LVC]), while the flowinside the blue isovelocity surface has a velocity of vz > 7 km s�1

(high-velocity component [HVC]). The HVC is enclosed by theLVC. The LVC flow is mainly driven from the first core, whilethe HVC flow is mainly driven from the protostar. The LVC andHVC are strongly coiled by the magnetic field lines anchored tothe first core and protostar, respectively.In model MR, the protostar has a mass of 4:52 ; 10�3 M� and

a radius of 1.07 R�, while at the end of the calculation, the massflowing out from the protostar is Mout ¼ 1:42 ; 10�3 M�. Theprotostar is surrounded by the disk with a mass of 2:0 ; 10�3 M�and a radius of 8.2 R�. At the same epoch, the protostar andoutflowing gas ( low- and high-velocity flows) have angularmomenta of Jcore ¼ 1:53 ; 1048 g cm2 s�1 and Jout ¼ 1:93 ;1048 g cm2 s�1, respectively. Therefore, the specific angularmomenta of the protostar and outflowing gas (i.e., the low- andhigh-velocity flows) are jcore ¼ 1:67 ; 1017 cm2 s�1 and jout ¼6:82 ; 1017 cm�3, respectively.

3.3. Cloud Evolution with Rapid Rotation

3.3.1. First Core Formation

Figure 10 shows the cloud evolution for model RR after thefirst core formation. Model RR has a parameter of ! ¼ 0:3. Theratio of the rotational to gravitational energy for model RR is

Fig. 7.—Time sequence of the high-velocity flow driven from the protostar for modelMR. The density (color scale) and velocity distribution (arrows) on the cross sectionin the y ¼ 0 plane are plotted in each panel. Panels (a)Y (c) are snapshots at the stages of (a) nc ¼ 2:5 ; 1020 cm�3 (l ¼ 21Y23), (b) 1:1 ; 1022 cm�3 (l ¼ 21Y23), and(c) 1:2 ; 1023 cm�3 (l ¼ 21Y23). The first core and second core (or protostar) are shownbywhite and red dotted lines, respectively. Red thick lines indicate the border between thehigh-velocity flowand accretionflow (i.e., contour of vz ¼ 0). The elapsed time from the initial (t), density at the center of the cloud (nc), and arrow scale are denoted in each panel.


�0 ¼ 0:3, which is 104 times larger than that for the initialstage of model SR (Table 1). The first core forms at nc ’ 8 ;1012 cm�3 and has a mass of M ’ 0:026 M� and a radius ofR ’ 5:68 AU at its formation epoch. The mass and size of thefirst core for model RR are larger than those for models SR andMR because the cloud is rotating rapidly. The cloud in model RRhas �c/(4�G�c)

1/2 ’ 0:2 in the initial stage and maintains thisvalue for ncP1012 cm�3, as shown in Figure 2d, which indicatesthat the centrifugal force significantly affects the formation of thefirst core. Owing to rapid rotation, the cloud has a disklike struc-ture near the center, as shown in Figure 10a. The oblateness ofmodel RR increases rapidly, as shown by the dotted line in Fig-ure 2a, and saturates "ob ’ 5Y6 for nc ’ 107 cm�3. In this model,the first core has a disklike shape at its formation epoch. Then,the disklike first core deforms to a ring, and the ring fragmentsinto several pieces at nc ’ 3 ; 1014 cm�3. Machida et al. (2004,

2005a) showed that fragmentation occurs in the rapidly rotatingcloud. Since we focus on the mechanism of the outflow and jet,we stopped the calculation when fragmentation occurred. We willdiscuss the fragmentation process of the first and second cores ina subsequent paper (Machida et al. 2007b).

3.3.2. Low-Velocity Flow from First Core

Figure 10b shows the density and velocity distribution aroundthe center of the cloud 330.3 yr after the first core formation.This panel shows that the low-velocity flow (i.e., the flow from thefirst core) is driven from the center of the cloud. The low-velocityflow extends up to 120 AU with a maximum speed of vLVF ’2:5 km s�1 at this epoch. Figure 10c shows the structure of thelow-velocity flow 476.1 yr after the first core formation. At theend of the calculation, this flow extends up to 200 AU witha maximum speed of vLVF ¼ 3:1 km s�1. Figures 10b, 3, and

Fig. 8.—(a, b, c) Density (color scale and white contours) and velocity distribution (arrows) on the cross section in the y ¼ 0 plane for modelMR at the same epoch asFig. 6c. (d, e, f ) Vertical component of the velocity (vz; color scale and contours) and magnetic field (arrows) with the same scale as each panel above. The characters of‘‘peak’’ indicate the position where vz has a local peak. The first core and second core (or protostar) are shown by thewhite and red dotted lines, respectively. Red thick linesindicate the border between the outflow and accretion flow (i.e., contour of vz ¼ 0).


8 show that the opening angle of the low-velocity flow for modelRR is larger than that of the high-velocity flow (i.e., the flow fromthe protostar) for models SR and MR. The height-to-radiusratio of the low-velocity flow is H /R ’ 2:2 (Fig. 10b) to 2.5(Fig. 10c) in model RR, while that of the high-velocity flow isH /R ’ 10 in model SR. In model RR, the low-velocity flowmaintains its shape (i.e.,H /R � constant) regardless of time,whilethe high-velocity flow in model SR becomes slender along thevertical axis with time (i.e., H /R increases with time).

Figure 11 shows the density and velocity distribution on they ¼ 0 (top panels) and z ¼ 0 (bottom panels) planes at the sameepoch as Figure 10c, but with different grid scales. Figure 11cis 16 times magnification of Figure 11a and shows the ripping

density contours caused by the strong mass ejection from the cen-ter of the cloud. Since the low-velocity flow interrupts gas ac-cretion in the regions above and below the central core, the gasaccretes onto the central region only via a thin disk (Fig. 11a).The top panel in Figure 11b shows the low-velocity flow drivennear the first core (dotted line). At this epoch, the first core, whichhas a disklike shape at the formation epoch, has deformed to aringlike shape (Fig. 11b, bottom panel ). As shown in Figure 11c,the density of the first core exceeds nck 1012 cm�3, while the den-sity of the ambient gas outside the first core is ncP 1012 cm�3.Since ohmic dissipation is effective for 1012 cm�3P ncP1015 cm�3 (Nakano et al. 2002), the dissipation of the magneticfield becomes effective inside the first core, while it is barely

Fig. 9.—Bird’s-eye view of model MR at the same epoch as Figs. 6c and 7c, but with different scales of 2:8 AU (left) and 1:4 AU (right). The structure of the high-density region (� > 0:1�c; red isodensity surface) andmagnetic field lines (black and white streamlines) are plotted in each panel. The structures of the high-velocity flow(v > 7 km s�1) and low-velocity flow (v > 0:5 km s�1) are shown by purple and blue isovelocity surfaces, respectively. The density contours ( false color and contourlines) and velocity vectors (thin arrows) on the midplane of x ¼ 0, y ¼ 0, and z ¼ 0 are, respectively, projected in each wall surface.

Fig. 10.—Time sequence of model RR. The density (color scale) and velocity distribution (arrows) on the cross section in the y ¼ 0 plane are plotted. Panels (a)Y (c) aresnapshots at the stages of (a) nc ¼ 1:7 ; 1012 cm�3 (l ¼ 12Y14), (b) 2:7 ; 1014 cm�3 (l ¼ 12Y16), and (c) 5:5 ; 1014 cm�3 (l ¼ 16Y17). Red thick lines indicate the borderbetween the outflow and accretion flow (i.e., contour of vz ¼ 0). The elapsed time after the first core formation (tc), elapsed time from the initial (t), density at the center ofthe cloud (nc), and arrow scale are denoted in each panel.


dissipated by ohmic dissipation outside the first core. Therefore,the magnetic field lines can be twisted just outside the first core,and the torsional Alfven wave transfers to the outside, as shownin the ideal MHD calculations (Tomisaka 2002; Banerjee &Pudritz 2006).

Figure 12 shows the shape of the low-velocity flow (blueisovelocity surface) and the configuration of the magnetic fieldlines (streamlines) at the same epoch as Figure 11. This figureshows that the magnetic field lines are strongly twisted inside thelow-velocity flow,while they are loosely twisted outside the low-velocity flow. Due to rapid rotation, the first core forms at a lowerdensity for model RR (nc ’ 8 ; 1012 cm�3) than for models SRand MR (nc ’ 1014 cm�3); therefore, ohmic dissipation is lesseffective outside the first core in model RR. The magnetic fieldlines anchored to the rapidly rotating first core are effectivelytwisted, and the Lorentz force can drive the strong flow nearthe first core. We stopped the calculation for model RR at nc ’1015 cm�3 because fragmentation occurred. Thus, we cannotdetermine further cloud evolution for model RR. Each fragmenthas a small spin angular momentum because of redistribution ofthe angular momentum (spin and orbital angular momenta) forfragmentation (Machida et al. 2005a), and the magnetic fieldis dissipated by ohmic dissipation in each fragment. Thus, weexpect that each fragment traces a similar evolution to modelsSR and MR.

Inmodel RR, the first core has amass of 9:42 ; 10�2 M� and aradius of 5.32 AU, while the mass flowing out from the first coreis Mout ¼ 6:01 ; 10�3 M� at the end of the calculation. At the

same epoch, the first core and low-velocity flow have the angularmomenta of Jcore ¼ 8:48 ; 1051 g cm2 s�1 and JLVF ¼ 4:95 ;1050 g cm2 s�1, respectively. Therefore, the specific angular mo-menta of the first core and low-velocity flow are jcore ¼ 4:52 ;1019 cm2 s�1 and jLVF ¼ 4:14 ; 1019 cm�3, respectively. Thus,in model RR, the low-velocity flow largely removes the angularmomentum from the first core.

3.4. Low-/High-Velocity Flows and Initial Cloud Rotations

In the previous sections we showed the evolutions of threedifferent clouds, while we investigated the cloud evolutions of80 models in total. As shown in Machida et al. (2005b, 2006b,2007a), cloud evolution depends only on the initial angular veloc-ity in the magnetic forceYdominant clouds �0/B0 < �cri/Bcri �0:39G1/2c�1

s , where�0, B0, and cs are the initial angular velocity,magnetic flux density, and sound speed, respectively. Our choiceof these strongly magnetized clouds is supported by observa-tions (Crutcher 1999; Caselli et al. 2002). From our calculations,we found that the emergence conditions for the low- and high-velocity flows fall into three categories, depending on the initialrotation rate !:

1. !k0:01, both low- and high-velocity flows can be drivenfrom each core.

2. 0:002P!P 0:01, only a high-velocity flow can be drivenfrom the protostar.

3. !P0:002, neither low-velocity nor high-velocity flow canbe driven from each core.

Fig. 11.—Density (color scale and white contours) and velocity distribution (arrows) on the cross section in the y ¼ 0 plane (top) and z ¼ 0 plane (bottom) at the sameepoch as Fig. 10c, but with different grid levels of (a) l ¼ 13, (b) l ¼ 15, and (c) l ¼ 17, respectively. White dotted lines indicate the first core. Red thick lines indicate theborder between the outflow and accretion flow (i.e., contour of vz ¼ 0).


The low-velocity flow always appears when condition 1 is satis-fied. However, the high-velocity flow does not appear in somemodels even when condition 1 or condition 2 is satisfied. Thus,condition 1 is the necessary and sufficient condition for drivinglow-velocity flow, while conditions 1 and 2 are the necessarycondition for driving high-velocity flow. For example, although24 models satisfy condition 2, the high-velocity flow appearedonly in nine models. Although we followed the evolution of the

accreting protostar up to �200 CPU hr for each model, we didnot observe any sign of the high-velocity flow in 15 (24� 9)models. After the protostar is formed, the magnetic field becomesstrong in the regions above the poles of the protostar; thus, theplasma beta becomes �T1 in these regions. Therefore, it isdifficult to calculate for a long period after protostar formationbecause the time step becomes significantly short owing tothe increased Alfven speed. Therefore, we could not determine

Fig. 12.—Bird’s-eye view of model RR (l ¼ 12) at the same epoch as Fig. 10c. The structure of the high-density region (n > 1012 cm�3; red isodensity surface) andmagnetic field lines (black and white streamlines) are plotted. The structure of the outflow is shown by the blue isovelocity surface inside which the gas is outflowing fromthe center. The density contours ( false color and contour lines) and velocity vectors (thin arrows) on the midplane of x ¼ 0, y ¼ 0, and z ¼ 0 are, respectively, projected ineach wall surface.


the reason the high-velocity flow does not appear in some models.We could not determine if the high-velocity flow would neverappear in those models or if it might appear much later. To clar-ify the long-term evolutions, we need to develop a calculationmethod with implicit time integration.

4. DISCUSSION

4.1. Driving Mechanism of Molecular Outflow and Optical Jet

In this paper, for convenience, we called the flows driven fromthe first core the low-velocity flow and the flows driven from theprotostar (i.e., the second core) the high-velocity flow.We expectthat the low-velocity flow evolves to the observedmolecular out-flow and the high-velocity flow evolves to the optical jet. InmodelSR, no low-velocity flow appears because the initial cloud rotatesslowly, and the rotation rate is not sufficiently amplified at the firstcore formation epoch. On the other hand, we cannot observe thehigh-velocity flow driven from the protostar inmodel RR becausewe stopped calculation once it showed fragmentation. In modelMR, both the low- and high-velocity flows appear. In this section,to investigate the driving mechanism of the outflow and the jetobserved in the star-forming regions, we focus on the flows thatappeared inmodels SR (the low-velocity flow) and RR (the high-velocity flow).We do not discuss the flows inmodelMR becauseit is difficult to separate the high-velocity flow from the low-velocity flow as shown in Figures 6Y9.

At the end of the calculation, the high-velocity flow has awell-collimated structure with high speed (vjet ’ 30 km s�1) anda large height-to-radius ratio of H /rk 20. The H /r ratio of the

high-velocity flow increases with time, as shown in xx 3.1.2 and3.2.2. The low-velocity flow, however, has a wide opening anglewith slow speed (vout ’ 3 km s�1) and expands outwardly, main-taining the height-to-radius ratio of H /r ’ 2Y2:5. The differenceof the speeds between the low- and high-velocity flows can beunderstood from the difference in the gravitational potential. Inmodel SR, the protostar has a mass of M ’ 4:04 ; 10�3 M� anda radius of R ’ 1:07 R� at the end of the calculation. TheKeplerspeed corresponding to themass and radius is vKepler ¼ 26 km s�1,which is comparable to the speed of the high-velocity flow inmodel SR (v jet ’ 30 km s�1). On the other hand, at the end ofthe calculation for model RR, the first core has a mass of M ’9:42 ; 10�2 M� and a radius of R ’ 5:32 AU. Thus, the Keplerspeed of the first core is vKepler ¼ 3:96 km s�1, which is com-parable to the speed of the low-velocity flow (vout ’ 3 km s�1).As a result, both the low- and high-velocity flows have flowspeeds similar to the Kepler speed of their respective cores. Sincewe calculated the evolutions of low- and high-velocity flows for ashort duration, the following discussion may be limited to veryearly stages of protostar evolution (for details see x 4.3).

4.1.1. High-Velocity Flow Driven from the Protostar

The difference in the degree of collimation between the low-and high-velocity flows (thewell-collimated structure of the high-velocity flow and the wide opening angle of the low-velocityflow) can be understood from the difference in their drivingmechanisms and the configuration of the magnetic field linesaround their drivers (i.e., the first core and protostar). Figure 13shows the shapes of the high-velocity flow (model SR; left panels)

Fig. 13.—Ratio of the toroidal to poloidal component of the magnetic field (Btoroidal/Bpoloidal; color and contours) and velocity vector (arrows) are plotted in the z > 0region for models with initially slow rotation (model SR; left panels) and rapid rotation (model RR; right panels). The plasma beta (�p; color and contours) and magneticfield (arrows) are plotted in the z < 0 region for the same models. Red thick lines indicate the border between the outflow and accretion flow (i.e., the shapes of the high-velocity flow and low-velocity flow).


and low-velocity flow (model RR; right panels) with thick redlines indicating the border between the accretion and the out-flow. This shows that the collimation of the high-velocity flow isstronger than that of the low-velocity flow.

First, we discuss the collimation and driving mechanism ofthe high-velocity flow. The top panels of Figure 13 show theratio of the toroidal to poloidal components of the magnetic field(Btoroidal/Bpoloidal) at each mesh point around the low-velocityflow (model SR; left) and the high-velocity flow (model RR;right). In Figure 13a, the toroidal field dominates the poloidalfield inside the high-velocity flow (Btoroidal/Bpoloidal ’ 10), whilethe toroidal field barely exists outside the high-velocity flow(Btoroidal/BpoloidalP 0:01). In model SR, the magnetic field is dis-sipated by ohmic dissipation and decoupled from the neutral gasinside the first core (or outside the second core), as shown inFigure 1i. Thus, the magnetic field lines are relaxed by the mag-netic tension force and are almost straight (Bz 3Br; B� in thecylindrical coordinates) because magnetic field lines move freely,irrespective of the neutral gas. Even after the magnetic field iswell coupled with the neutral gas for nck 1015 cm�3, the straightmagnetic field lines are distributed around the protostar, whichreflects past ohmic dissipation. Therefore, the vertical compo-nent of the magnetic field (Bz) is dominant outside the protostar.The bottom panels in Figure 13 show the plasma beta around thehigh-velocity flow (left; model SR) and the low-velocity flow(right; model RR). Figure 13b shows that the magnetic field isweak (�p ’ 10) outside the high-velocity flow (outside the redline), while it is very strong (�pP 0:01) inside the high-velocityflow (inside the red line), compared to the thermal pressure. Thesharing motion between the protostar and ambient gas amplifiesthe magnetic field inside the high-velocity flow, since the formedprotostar rapidly rotates because the magnetic braking is less ef-fective, explained in x 3.1. In general, when the magnetic field isweak around the driver, it is considered that the magnetic pres-sure gradient force dominates the magnetocentrifugal force interms of driving the flow (Uchida & Shibata 1985; Tomisaka2002).

To investigate the drivingmechanism of low- and high-velocityflow, we calculate the Lorentz (FLorentz), centrifugal (Fcentrifugal),and thermal pressure gradient (Fpressure) forces parallel to thepoloidal component of the magnetic field (Bp). When the self-gravity term in equation (5) is ignored, the equation of motioncan be rewritten as

�@v

@t¼ �� v = :ð Þ �:P � 1

4�B < v < Bð Þ½ : ð7Þ

We consider the dot product between each term on the left-handside of equation (7) and the poloidal component of the magneticfield (Bp). Thus, each force parallel to Bp is written as

Fcentrifugal � � v = :ð Þ = ep�� ; ð8Þ

Fthermal � :P = ep�� ; ð9Þ

FLorentz �1

4�B < v < Bð Þ = ep�� ; ð10Þ

where ep � Bp/jBpj. In the left panels of Figure 14 we plot theratio of the Lorentz to the centrifugal force (FLorentz/Fcentrifugal;Fig. 14a) and the ratio of the Lorentz to the thermal pressuregradient force (FLorentz/Fthermal; Fig. 14b) in the outflowing re-gion at each mesh point, where the outflowing region is de-fined as meshes with vz > 0:1 km s�1 for z > 0. Figures 14c and14d show the plots for the same ratios of FLorentz/Fcentrifugal andFLorentz/Fthermal in the accreting region (vz < 0:1 km s�1 for z >

0). In Figure 14, red crosses and lines are data from the regionaround the high-velocity flow in model SR, while black dia-monds and lines are data from the region around the low-velocityflow in model RR. In Figure 14, left panels show that, insidethe high-velocity flow (red crosses and line), the Lorentz forceis equivalent to the centrifugal force (FLorentz/Fcentrifugal ’ 1;Fig. 14a), while the Lorentz force is about�30Y40 times strongerthan the thermal pressure gradient force (FLorentz/Fcentrifugal ’30Y40; Fig. 14b). In the accreting region around the high-velocityflow (red crosses and lines inFigs. 14c and 14d ), the Lorentz forceismuchweaker than both the centrifugal (FLorentz/Fcentrifugal ’ 10�5

to 10�4) and thermal pressure gradient forces (FLorentz/Fpressure ’10�6 to 10�4). Thus, the Lorentz force is not effective in theaccreting regions.In model SR, a rapidly rotating protostar forms because the

magnetic field around the center of the cloud is weak and mag-netic braking is less effective. Thus, the magnetic field linesanchored to the protostar make a strong toroidal field for therapid rotation of the protostar. The toroidal field caused by theprotostar transmits in the vertical direction as the torsional Alfvenwave, generating a large magnetic pressure gradient along thevertical axis. The high-velocity flow is considered to be drivenby this strong magnetic pressure gradient force. In general, thehigh-velocity flow has good collimationwhen themagnetic pres-sure gradient force is dominant (Btoroidal 3Bpoloidal) for drivingthe flow because the magnetic field lines are pinched by the to-roidal field, as shown by Tomisaka (2002). Furthermore, the high-velocity flow in model SR is guided by the straight configurationof the magnetic field lines (Bz 3Br; B�) outside the outflowingregion. Thus, the well-collimated jet (i.e., the high-velocity flow)is caused by both the driving mechanism of the magnetic pres-sure gradient and the straight configuration of the magnetic fieldlines around the protostar.

4.1.2. Low-Velocity Flow Driven from the First Core

Figures 13c and 13d show the ratio of the toroidal to poloidalcomponents of the magnetic field (Btoroidal/Bpoloidal; Fig. 13c) andthe plasma beta (�p; Fig. 13d) around the low-velocity flow formodel RR. The toroidal field is �3Y5 times stronger than thepoloidal field (Btoroidal/Bpoloidal ’ 3Y5) inside the low-velocity flow(inside the red line). However, this ratio is smaller than that of thehigh-velocity flow (Btoroidal/Bpoloidal ’ 10; model SR) because therotation rate in model RR, which causes the toroidal field, is smallaround the first core, due to effective magnetic braking. Outsidethe low-velocity flow, however, the poloidal field is slightlylarger than the toroidal field (Btoroidal/Bpoloidal ’ 0:3). Figure 13cshows that the magnetic energy is larger than the thermal energyinside the low-velocity flow (�pP 0:01), while the magnetic en-ergy is comparable to or slightly weaker than the thermal energyoutside the low-velocity flow (�p � 0:1Y1). The gas around thefirst core has a density range of 108 cm�3PncP1012 cm�3 inmodel RR (Fig. 10). Since ohmic dissipation is ineffective in thisregion, the magnetic energy becomes comparable to the thermalenergy as demonstrated by Machida et al. (2005b, 2006b). Afterthe first core formation, the toroidal field can be amplified be-cause the rotational timescale is shorter than the collapsing time-scale and the magnetic field lines begin to twist (Machida et al.2006c). Therefore, the magnetic energy inside the low-velocityflow (or near the first core) becomes larger than that outside thisregion (or far from the first core).As shown in Figures 14a and 14b, the centrifugal force

is dominant over the Lorentz and thermal pressure gradientforces inside the low-velocity flow (FLorentz/Fcentrifugal < 1 andFLorentz/Fthermalk 1; black diamonds and lines), while it is


comparable to the Lorentz force inside the high-velocity flow(red crosses and lines). Outside the low-velocity flow, boththe centrifugal and thermal pressure gradient forces are strongerthan the Lorentz force (Fcentrifugal ’ Fthermal > FLorentz), sinceFLorentz/Fcentrifugal ’ 0:1 (Fig. 14c) and FLorentz/Fthermal ’ 0:1(Fig. 14d ). These results indicate that the low-velocity flow inmodel RR ismainly driven by themagnetocentrifugal mechanism( Blandford & Payne 1982), which causes the loosely pinchedmagnetic field lines inside the low-velocity flow. In addition, be-fore the low-velocity flow appears, the magnetic field lines aroundthe first core expand sideways toward the rotation axis from thecenter of the cloud, whose shape looks like a capital letter U or V,as shown by Tomisaka (2002). Thus, the collimation of the mag-netic field lines becomes worse with distance from the center, asshown in Figure 8a of Machida et al. (2007a). Since the low-velocity flow traces this configuration of the magnetic field lines,it does not have good collimation and the low-velocity flowdriven from the first core has a wide opening angle because ofthe magnetocentrifugal driving mechanism and the configura-tion of the magnetic field lines. The former realizes the loosely

pinched magnetic field lines, and the latter swells the low-velocity flow.

4.2. Dependence on the Initial Magnetic Field Strengthand Rotation Rate

In this paper we investigated cloud evolution with the samemagnetic field strengths (Bini ¼ 17 �G) but different rotation rates(�ini ¼ 7 ; 10�16 s�1 [model SR], 7 ; 10�15 s�1 [model MR],and 7 ; 10�14 s�1 [model RR]). As shown in the previous sec-tion, the speeds of flows depend on the mass and size of theirdrivers. The mass and size of the first and second cores at theirformation epochs depend on the initial rotation rate. Therefore,the speeds of the flows depend on the initial rotation rate of thecloud core. For example, in a rapidly rotating cloud, the first coreforms at lower density with larger size. When the first core has alarger size and lower density, the flow from the first core becomesrelatively slow because the gravitational potential is shallow. Onthe other hand, a slowly rotating cloud produces a first core withsmaller size and higher density. In this case, flow has a relativelyhigh speed, owing to the deep gravitational potential of the first

Fig. 14.—Ratio of each force for models SR andRR at the end of the calculation. (a) Ratio of the Lorentz to the centrifugal forces (FLorentz/Fcentrifugal) at eachmesh pointin the regionwith vz > 0:1 km s�1 (i.e., the outflow region). (b) Ratio of the Lorentz to the thermal pressure gradient forces (FLorentz/Fthermal) in the regionwith vz > 0:1 km s�1

(i.e., the outflow region). (c) Ratio of the Lorentz to the centrifugal forces (FLorentz/Fcentrifugal) in the regionwith vz < 0:1 km s�1 (i.e., the inflow region). (d ) Ratio of the Lorentzto the centrifugal forces (FLorentz/Fcentrifugal) in the region with vz < 0:1 km s�1 (i.e., the inflow region). The horizontal axis means the number of the cell. The symbols arethe data from models RR (black diamonds) and SR (red crosses). The thick lines are the average of adjacent 100 cells for models RR (black lines) and SR (red lines). Thehorizontal dotted lines indicate the value at which each force equals.


core. Thus, the flow from the first core has higher speed in a moreslowly (rapidly) rotating cloud. In addition, a cloud with an ex-tremely low rotation rate produces no flow from the first corebecause the first core has such a small angular momentum at itsformation epoch that the magnetic field lines are barely twisted.The speed of the flow from the protostar, however, depends onthe initial rotation rate only slightly because the angular mo-mentum around the center of the cloud converges to a certain valueby the time the protostar (i.e., second core) is formed (Machidaet al. 2007a). Thus, the variation caused by the rotation of theinitial cloud does not remain so much at the protostar formationepoch. Note that the properties of the flowmight possibly changemuch later because we followed the evolution of these flows foronly a short period.

Does the difference of magnetic field strength in the initialcloud affect the properties of these flows?Machida et al. (2005b,2006b) showed that the evolution of the molecular cloud de-pends only on the ratio of the angular velocity to the magneticflux density of the initial cloud (�ini/Bini). Initial differences inthe distribution of the density, velocity, andmagnetic field hardlyaffect cloud evolution, especially once the central region becomesadiabatic (nck1011 cm�3). Cloud evolution is controlled by themagnetic field when �ini/Bini < 0:39G1/2c�1

s , while it is con-trolled by the rotation when �ini/Bini > 0:39G1/2c�1

s (Machidaet al. 2006b). Although we can choose arbitrary parameters of�ini and Bini, observations indicate that the magnetic energy ismuch larger than the rotation energy in many molecular clouds(Crutcher 1999; Caselli et al. 2002), and clouds have �ini/Bini >0:39G1/2c�1

s (i.e., themagnetic forceYdominant clouds inMachidaet al. 2005b). In magnetic forceYdominant clouds, the magneticfield converges to a specific value in the isothermal phase (themagnetic fluxYspin relation;Machida et al. 2005b, 2006b, 2007a).Thus, cloud evolution does not depend much on the initial mag-netic field strength. As a result, flows with similar properties mayappear in clouds with different initial magnetic fields when theyhave the same initial angular velocities.

4.3. Duration of Driving Outflow

As shown in x 4.1, we expect that the low-velocity flow drivenfrom the first core corresponds to the observed molecular out-flow. After the first core formation epoch, the collapse timescalebecomes longer than the rotational timescale, the magnetic fieldlines are strongly twisted for the rotating first core, and low-velocity flow appears as shown in x 3.2.2. Observations haveshown that molecular outflows have lifetimes of �6 ; 104 yr( Wu et al. 2004). However, since we followed cloud evolutiononly through the very early phase, we could not determinewhetherlow-velocity flow (i.e., outflow) continues to be driven for a longtime. The spherical symmetric calculation indicates that the firstcore disappears �1000 yr after its formation epoch. In modelRR, we followed cloud evolution for �800 yr after the first coreis formed. In this model, the first core remains until the end of thecalculation. The low-velocity flow that appears just after the firstcore formation epoch continues to be driven from the first core.The rotating first cores seem to have lifetimes of several thou-sand years or more (e.g., Saigo& Tomisaka 2006). Thus, the flowdriven from these cores may maintain itself for several thousandyears. Note that it is expected that a high-velocity flow (i.e., jet)will continue to be driven from the protostar once it appears be-cause the protostar does not disappear.

After the first core disappeared,we could not determinewhetherthe low-velocity flow continues to be driven. Saigo & Tomisaka(2006) suggested that after the first core disappears, the remnantof the first core forms a disklike structure or torus. Low-velocity

flow may continue to be driven from these objects even afterthe disappearance of the first core. However, if the low-velocityflow does not continue after the first core disappears, then low-velocity flow, as shown in this paper, might be a transient phe-nomenon, in which the flow is driven only for �1000 yr. In thiscase, the flow from the first core, whichwe call low-velocity flowin this paper, might be a special phenomenon that would be ob-served only in limited numbers of young stellar objects. To under-stand the duration of the flow driven from the first core, furtherlong-term calculations, possibly with an implicit code, are nec-essary. At present we conjecture that the low-velocity flow cor-responding to the molecular outflow will be driven for k104 yr.

5. SUMMARY

Observation shows that the molecular outflows have wideopening angles and low flow speeds, while the optical jets havegood collimation and high flow speeds. Molecular outflow hasbeen considered to be entrained by the optical jet driven from acircumstellar disk around the protostar. In this paper we calcu-lated the cloud evolution from the molecular cloud core to pro-tostar formation. As a result of calculations, we found that twodistinct flows ( low- and high-velocity flows) are driven fromdifferent objects (the first and second cores) and the observedfeatures of molecular outflow and the optical jet (flow speed andcollimation factor) were naturally reproduced. Thus, we expectthat the low-velocity flow from the first core corresponds to themolecular outflow, while the high-velocity flow from the pro-tostar corresponds to the optical jet.Our results show that the flow appearing around the first core

has a wide opening angle and slow speed, while the flow ap-pearing around the protostar has a well-collimated structure andhigh speed, as shown in Figure 15. The speed difference is causedby the difference of the depth in the gravitational potential. Theflow speed corresponds to the Kepler speed of each object (thefirst and the second cores). Because the first core has a shallowgravitational potential, its flow is slower. The flow driven fromthe protostar, which has a deeper gravitational potential, has ahigh speed. In our calculations, the low- and high-velocity flowshave speeds of vLVF ’ 3 km s�1 and vHVF ’ 30 km s�1, re-spectively. These speeds are slower than those of observations.Typically, observed molecular outflow and the optical jet havespeeds of vout;obs ’ 30 km s�1 and vjet;obs ’ 100 km s�1, re-spectively. However, since the first and second cores (protostar)havemasses ofMBrst core ¼ 0:01 M� andMsecond core ’ 10�3 M�,respectively, at the end of the calculations, each core increases itsmass in the subsequent gas accretion phase. The Kepler speedincreases with the square root of the mass of the central object ata fixed radius.When themass of each core increases by 100 times,the Kepler speed increases 10 times. Thus, the speed of the low-and high-velocity flows may increase by 10 times and reachvLVF ’ 30 km s�1 and vHVF ¼ 300 km s�1, respectively, whichcorrespond to typical observed values.The low-velocity flow (i.e., molecular outflow) has a wide

opening angle, while the high-velocity flow (i.e., optical jet) hasa well-collimated structure. This is caused by both the configu-ration of the magnetic field lines around the drivers and theirdrivingmechanisms. Themagnetic field lines around the first corehave an hourglass configuration because they converge to thecloud center as the cloud collapses, and ohmic dissipation isineffective before the first core formation. In addition, the cen-trifugal force is more dominant than the Lorentz force in the low-velocity flow (molecular outflow). Thus, the flow appearing nearthe first core is mainly driven by the magnetocentrifugal windmechanism (disk wind). On the other hand, near the protostar,


the magnetic field lines are straight, and the magnetic pressuregradientmechanism ismore effective for driving the high-velocityflow (optical jet). There is little analytical study about the mag-netic pressureYdriven jet, while there aremany analytical studiesabout disk wind mechanism (e.g., Blandford & Payne 1982).The magnetic field lines are stretched by the magnetic tensionforce near the protostar because the magnetic field is decoupledfrom the neutral gas.However, themagnetic field lines are stronglytwisted in the region in close proximity to the protostar, wherethemagnetic field is coupledwith the neutral gas again. Thus, thestrong toroidal field generated around the protostar can drive thehigh-velocity flow (optical jet), which is guided by the straightconfiguration of the magnetic field.

Our results do not completely reject the well-known conceptthat the observedmolecular outflow is entrained by the optical jetor a similar high-speed flow because our calculations cover the

formation and evolution of the jet and outflow only in the earlystar formation phase. Further long-term calculations are neededto understand the mechanism of the optical jet and molecularoutflow in more detail.

We have greatly benefited from the discussion with T. Nakanoand K. Saigo.We also thank T. Hanawa for making a contributionto the nested grid code. Numerical computations were carried outonVPP5000 at theCenter for ComputationalAstrophysics, CfCA,of the National Astronomical Observatory of Japan. This work issupported by the Grant-in-Aid for the 21st Century COE ‘‘Cen-ter for Diversity and Universality in Physics’’ from the Ministryof Education, Culture, Sports, Science and Technology (MEXT)of Japan and partially supported by the Grants-in-Aid fromMEXT (15740118, 16077202, 18740113, 18740104).

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High‐ and Low‐Velocity Magnetized Outflows in the Star Formation Process in a Gravitationally...

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