Radiation Pressure and Ionization Feedback

Larson & Starrfield (1971) first explored the idea that the pressure and ionization caused by radiation could inhibit accretion onto a forming massive star, finding an upper mass limit of

50−60M_⊙. This pioneering work was soon followed by simulations of the effect of radiation

pressure on dust grains in accreting matter (Kahn, 1974; Yorke, 1977; Wolfire & Cassinelli, 1987). These studies gave upper limits to the mass which could be accreted, or suggested that the dust around the stars must be altered, or that the accretion must be variable, to

1.2. The Formation of Massive Stars

allow sufficient accretion to make a massive star. However, these early simulations assumed that the accretion was spherically symmetric. Instead, it is likely that accretion proceeds through a disk (see Section 1.2.4 concerning observations of disks around massive stars). In this case, radiation pressure can then be funneled out perpendicular to the disk plane, creating a ‘flashlight’ effect (e.g. Yorke & Sonnhalter, 2002).

Another way to overcome radiation pressure is to simply increase the accretion rate above

the values assumed for low-mass stars (>10−5_M

⊙ yr−1). This would push material inside

the dust destruction radius, so that then, having its main source of opacity removed, it could accrete unimpeded onto the protostar. The expected rise in temperature of the circumstellar material around a massive star would also increase the sublimation radius, aiding this effect. This is supported by modelling of several massive “Hot Cores" (see Section 1.2.3.b) by Osorio

et al. (1999), who found higher accretion rates for these objects (¦6_×10−4M_⊙yr−1).

In addition, varying the dust grain properties, such as increasing the average dust grain size, or lowering the effective opacity of the surrounding material, can allow material to con- tinue accreting. One way the effective opacity can be reduced is to accrete material in ‘blobs’ rather than continuously, the extreme form of this being the coalescence of two protostars to produce one higher mass object (e.g. Bonnell et al., 1998), which will be discussed further in Section 1.2.2.

Recent 3D simulations of the accretion onto forming massive stars have also suggested that outflow cavities and Rayleigh-Taylor instabilities in the interface between the radiation bubble and the accreting material (or accretion ‘fingers’) can also allow matter to be more efficiently accreted, and therefore overcome radiation pressure (e.g. Krumholz et al., 2005b). The interaction between an accretion flow and ionizing radiation was first discussed by Walmsley (1995), who found an expression for the mass accretion rate required to ‘choke

off’ the formation of an HII region1_:

˙ Mcrit= € 8πNphotGM⋆m2H/α Š1/2 , (1.5)

where N_phot is the ionizing photon flux from the star,mH is the mass of a hydrogen atom,

andαis the recombination coefficient to excited states of hydrogen. This work was extended

1_{The factor of two difference to his equation accounts for the assumption that the accreting material is in free-fall}

Chapter 1. Introduction

by Keto (2002) and Omukai & Inutsuka (2002), who found that, for a given accretion rate ˙

M⋆, the radius of equilibrium can be expressed as:

R_HII=R⋆exp

h€_˙ M_crit/M˙⋆

Š2i

. (1.6)

Accretion can therefore occur through an HII region, so that there is an ionized gas accretion flow onto the star. Hence the development of an HII region may not immediately halt the accretion process. If accretion can occur through an HII region, this infers that as the star accretes mass and therefore increases in luminosity, the HII region must accordingly evolve.

Taking R_HII from equation 1.6 above as the radius of ionization equilibrium, andR_G=

GM_∗/2c_s2 to be the gravitational radius of the accretion flow, which is the radius at which

gravity balances the outward pressure of the ionized gas, the evolution of a spherically sym-

metric HII region can be followed (c.f. Keto, 2002). At early times, whenR_HII < R_G, the

HII region is “trapped” within the accretion flow, and the HII region is a stationary R-type

ionization front. For a 10 M_⊙ B star, and a sound speed c_s of _∼ 10 kms−1 in ionized gas,

R_G∼40 AU; therefore an HII region would be confined by accretion into a very small region

surrounding the star. As material is further accreted onto the star, R_HII can increase until

it is greater than R_G, which itself increases more slowly as mass is added to the star. At

the point whereR_HII>R_G the HII region halts further accretion and begins hydrodynamical

expansion.

However, it is again possible to relax the assumption of spherical symmetry for the ac- creting gas. Recently, Keto (2007) introduced an ionized accretion flow through a disk. To

conserve angular momentum, the disk forms atR_D, where the infall velocity equals the rota-

tional velocity and the centrifugal and gravitational forces balance: RD=GM⋆/υ2rot, where

υrot is the rotational velocity of the disk atRD. The stages of the evolution of the HII region

are then very similar to the spherical case described above, except that due to higher densi-

ties in the disk,R_HII is now a function of the angle from the disk axis. At first the protostar

has not reached the main sequence, soR_HII =0 and accretion proceeds through a massive

molecular disk. When the star reaches the main sequence and its UV radiation ‘turns on’, the HII region can expand more rapidly in the direction of the poles while the HII region is trapped along the midplane. As the protostar accretes more material, the HII region will expand to completely engulf the disk, and to ionize more of the actual disk itself. Finally

1.2. The Formation of Massive Stars

the HII region will start expanding along the disk via thermal pressures, and halt accretion

through the disk; this will occur whenR_HII along the disk equalsR_G. Ifυ_rot>p2cs, so that

the radius of disk formation is within the gravitational radius, all of the accreting material within the disk will have been ionized before accretion is halted.

The picture above can also apply to models of photoevaporating disks (Hollenbach et al., 1994). In a similar way to the photoevaporation of low-mass disks (see Section 1.1.3.c), and the ionized accretion scenario described above, the ionized gas is bound to the star within

the gravitational radiusR_G. Outside this radius, the sound speed in the ionized upper layers

of the disk (∼10 kms−1) exceeds the escape velocity, and the ionized gas expands away from

the disk as a wind with a velocity of∼10−50 kms−1.

If the ram pressure of the stellar wind from the central source exceeds the thermal pres- sure of the photoevaporative ‘disk wind’ then the upper layers of the disk are also removed

within R_G so that the ionizing radiation can travel further into the disk. In addition, the

disk wind is pushed out and concentrated by the ram pressure of the stellar wind to radii

larger thanR_G. From this model, Hollenbach et al. (1994) calculated that disks with masses

2₋10 M_⊙would have lifetimes of¦105yr.

These calculations were also supported by simulations by Yorke & Welz (1996) and Rich- ling & Yorke (1997), who also found that the combination of the ionized stellar and disk wind were hydrodynamically focused perpendicular to the disk, suggesting that this could be an outflow collimating mechanism which may act instead or in conjunction with the effect of magnetic fields.