Bok Globule

A Bok globule is a compact, isolated, and optically opaque dark cloud of cold molecular gas (predominantly H₂ and He) and sub-micrometer interstellar dust grains found within the disk of the Milky Way and nearby star-forming galaxies. First identified as probable sites of stellar birth by Dutch-American astronomer Bart Jan Bok and Edith F. Reilly in 1947—building upon the pioneering wide-field photographic dark-nebula catalogs compiled by Edward Emerson Barnard in 1919 and 1927—Bok globules appear at optical wavelengths as sharply bounded, ink-black silhouettes projected against rich background stellar fields or bright H II emission nebulae (such as the Orion Nebula, the Lagoon Nebula M8, and IC 2944). Because they lack the crowded, turbulent environment of giant molecular cloud complexes, Bok globules represent the simplest, cleanest laboratories in observational astronomy for studying the hydrostatic equilibrium, astrochemical freeze-out, magnetic support, and inside-out gravitational collapse of individual star-forming cores into T Tauri stars and protoplanetary disks.

Typical Bok globules have characteristic linear diameters of D ≈ 0.1 to 1.0 parsec (20,000 to 200,000 astronomical units), total gas-plus-dust masses of M ≈ 2 to 50 M_☉ (occasionally reaching 100 M_☉ in larger globules), and central molecular hydrogen number densities of n(H₂) ≈ 10⁴ to 10⁶ cm⁻³. Because sub-micrometer silicate and carbonaceous dust grains (comprising ~1% of the cloud mass) efficiently absorb and scatter ultraviolet and visible photons from the ambient interstellar radiation field (ISRF), the interior of a Bok globule exhibits visual extinctions of A_V ≈ 10 to >50 magnitudes (corresponding to H₂ column densities of N(H₂) ≈ 10²² to 5 × 10²² cm⁻² via the standard Bohlin gas-to-extinction relation N(H₂) / A_V ≈ 0.94 × 10²¹ cm⁻² mag⁻¹).

Shielded from external photoelectric heating by this thick dust blanket and cooled internally by rotational line emission from carbon monoxide (¹²CO, ¹³CO, C¹⁸O) and thermal continuum emission from dust grains at far-infrared and submillimeter wavelengths (λ ≈ 100 μm to 1.3 mm), the interior kinetic gas and dust temperatures of starless Bok globules drop to T ≈ 8 to 15 K—among the coldest macroscopic environments in the universe outside of the Boomerang Nebula.

The NICE / NICER Near-Infrared Extinction Technique

How is the internal density profile ρ(r) of a completely opaque starless globule measured? In 2001, João Alves, Charles Lada, and Elizabeth Lada pioneered the Near-Infrared Color Excess (NICE and NICER) method using deep J (1.25 μm), H (1.65 μm), and K_s (2.16 μm) imaging of the iconic starless globule Barnard 68 (B68, d ≈ 125 pc) with the Very Large Telescope. Because dust extinction at near-infrared K_s wavelengths is roughly one-tenth of visual extinction (A_K ≈ 0.112 A_V), background giant stars shining through the globule remain detectable in the near-infrared, but their (H − K_s) colors are systematically reddened in direct proportion to the dust column density along each pencil-beam line of sight.

Unlike supersonic giant molecular clouds (where non-thermal turbulent velocity dispersions Δv_turb ≫ c_s dominate internal pressure support), the interior of a quiescent Bok globule exhibits subsonic or transonic turbulence: non-thermal spectral line widths match or fall below the isothermal sound speed c_s = (k_BT / μm_H)^1/2 ≈ 0.19 km s⁻¹ (for mean molecular weight μ = 2.33 at T = 10 K). Consequently, a starless Bok globule bounded by an external ambient pressure P_ext is governed by the equation of isothermal hydrostatic equilibrium analyzed by William Bonnor (1956) and Rolf Ebert (1955):

(1 / r²) d/dr [(r² / ρ) (dP / dr)] = −4π G ρ, with P = ρ c_s²

Introducing the dimensionless radius ξ = r (4π G ρ_c / c_s²)^1/2 and dimensionless logarithmic density contrast ψ(ξ) = −ln(ρ / ρ_c) reduces this to the isothermal Lane–Emden equation, which describes a Bonnor–Ebert sphere Featuring a flat constant-density inner core (ξ ≲ 2) that transitions smoothly to an outer envelope falling off as ρ(r) ∝ r⁻².

The Critical Bonnor–Ebert Stability Threshold (ξ_max = 6.451)

As established by Bonnor (1956) and Ebert (1955) in close analogy with the Jeans instability, a pressure-bounded isothermal sphere remains hydrostatically stable against radial perturbations only so long as its dimensionless outer boundary radius ξ_max and center-to-edge density contrast ρ_c / ρ_edge remain below a strict critical threshold:

ξ_max,crit = 6.451, (ρ_c / ρ_edge)_crit = 14.04

At this stability boundary, the critical Bonnor–Ebert mass is:

M_BE,crit = 1.18 (c_s⁴ / (G³ P_ext)^1/2) ≈ 1.8 M_☉ × (T / 10 K)² (P_ext / k_B / 3 × 10⁴ K cm⁻³)^−1/2

In the cold (T ≤ 10 K), dense (n(H₂) ≥ 3 × 10⁴ cm⁻³) central regions of a prestellar Bok globule such as Barnard 68, the collision timescale of gas-phase molecules with dust grains becomes shorter than the dynamical free-fall time t_ff = (3π / 32*G*ρ)^1/2 ≈ 10⁵ yr. Consequently, carbon- and sulfur-bearing molecules—most notably carbon monoxide (CO, C¹⁸O) and carbon monosulfide (CS)—condense onto cold silicate grain mantles (molecular freeze-out or depletion), leaving a central "CO hole" in millimeter rotational emission maps while solid CO ice is converted via atomic H surface addition into formaldehyde (H₂CO) and methanol (CH₃OH) ices.

Because gas-phase CO normally destroys the trihydrogen cation H₃⁺ (via H₃⁺ + CO → HCO⁺ + H₂), the freeze-out of CO in the core center allows H₃⁺ to react instead with trace deuterated hydrogen (HD) via the exothermic reaction:

H₃⁺ + HD ⇌ H₂D⁺ + H₂ + ΔE (232 K)

At T = 10 K, the backward reaction is thermally suppressed, driving extreme deuterium fractionation (enhancing the D/H ratio in N₂D⁺ / N₂H⁺ and DCO⁺ / HCO⁺ by four orders of magnitude above the cosmic elemental ratio D/H ≈ 1.5 × 10⁻⁵) and leaving nitrogen hydrides (N₂H⁺, N₂D⁺, and ammonia NH₃, which resist freeze-out to higher densities) as the primary kinematic tracers of the dense core center.

Once a supercritical Bok globule loses residual magnetic support via ambipolar diffusion (mapped via submillimeter dust-polarization vectors from Planck, JCMT/POL-2, and ALMA), it undergoes inside-out gravitational collapse as formulated analytically by Frank Shu in 1977: an expansion wave propagates outward at the sound speed c_s, inside of which gas falls freely toward the central Class 0 protostar with density ρ(r) ∝ r^−3/2 and infall velocity v(r) ∝ r^−1/2. In high-resolution millimeter spectroscopy of Barnard 335, this collapse produces the classic double-peaked, blue-skewed infall line profile in optically thick lines (such as CS and HCO⁺): redshifted emission from the near, infalling front hemisphere is self-absorbed by cold static outer gas, making the blueshifted peak from the far, infalling hemisphere systematically brighter than the redshifted peak.

In addition to thermal gas pressure, interstellar magnetic fields (B ≈ 10 to 300 μG) thread Bok globules and regulate both their collapse timescale and the angular momentum of their nascent protoplanetary disks. Non-spherical silicate and carbonaceous dust grains spinning inside a Bok globule experience radiative torque (RAT) alignment, orienting their long axes perpendicular to the local magnetic field vector B. Consequently, background starlight transmitted through the outer envelope of a globule becomes linearly polarized parallel to B via dichroic extinction in the optical and near-infrared, whereas thermal continuum radiation emitted by cold dust grains at submillimeter wavelengths (λ ≈ 450 μm to 1.3 mm) is linearly polarized perpendicular to B (rotating the observed polarization vectors by 90° maps the plane-of-sky magnetic field morphology).

Applying the Davis–Chandrasekhar–Fermi (DCF) method—which relates the dispersion δθ of dust polarization angles to the ratio of turbulent velocity dispersion σ_v and the Alfvén wave speed v_A = B / (4πρ)^1/2—alongside OH and CN Zeeman splitting measurements reveals the dimensionless mass-to-magnetic-flux ratio λ_B:

λ_B = (M / Φ_B) / (M / Φ_B)_crit = 2π G^1/2 μ m_H N(H₂) / B

In starless subcritical globules, λ_B ≲ 1 and uniform magnetic field lines resist gravitational contraction; in collapsing Class 0 globules such as Barnard 335 and CB 26, λ_B ≈ 2 to 4, and inward gravitational infall drags the field lines into a pinched hourglass magnetic morphology that channels collimated bipolar molecular outflows and Herbig-Haro object jets along the magnetic poles while braking excess disk rotation.

1. Bok, B. J., & Reilly, E. F. (1947). "Small dark nebulae." The Astrophysical Journal, 105, 255–257. https://doi.org/10.1086/144901
2. Bonnor, W. B. (1956). "Boyle's Law and gravitational instability." Monthly Notices of the Royal Astronomical Society, 116(3), 351–359. https://doi.org/10.1093/mnras/116.3.351
3. Shu, F. H. (1977). "Self-similar collapse of isothermal spheres and star formation." The Astrophysical Journal, 214, 488–497. https://doi.org/10.1086/155274
4. Alves, J. F., Lada, C. J., & Lada, E. A. (2001). "Internal structure of a cold dark molecular cloud inferred from the extinction of background starlight." Nature, 409(6817), 159–161. https://doi.org/10.1038/35051509
5. Bergin, E. A., & Tafalla, M. (2007). "Cold dark clouds: The initial conditions for star formation." Annual Review of Astronomy and Astrophysics, 45, 339–396. https://doi.org/10.1146/annurev.astro.45.071206.100404