Fluctuations in ISM Thermal Pressures Measured from C I

Observations

Edward B. JenkinsPrinceton University

Observatory

Fundamentals …• Most of the free carbon atoms in the ISM are

singly ionized, but a small fraction of the ions have recombined into the neutral form.

• The ground electronic state of C I is split into three fine-structure levels with small energy separations.

• Our objective is to study the relative populations of these three levels, which are influenced by local conditions (density & temperature.

Fine-structure Levels in the Ground State of C I

3P0 (E = 0 cm-1, g = 1)

3P1 (E = 16.4 cm-1, g = 3)

3P2 (E = 43.4 cm-1, g = 5)

C IC I*

C I**

Upper Electronic Levels

Collisionally Induced Transitions

Optical Pumping (by Starlight)Spontaneous Radiative

Decays

E/k = 23.6 KE/k = 23.6 K

E/k = 62.4 KE/k = 62.4 K

C I Absorption Features in the UV Spectrum of λ Cep Recorded at a Resolution of 1.5 km s-1 by STIS on HST

From Jenkins & Tripp (2001: ApJS, 137, 297)

Col

umn

dens

ity p

er u

nit

velo

city

[10

13 c

m-2 (

km s

-1)-1

]

Velocity (km s-1)

C I

C I*

C I**

λ Cep

Most Useful Way to Express Fine-structure Population Ratios

• n(C I)total = n(C I) + n(C I*) + n(C I**)

• f1 n(C I*)/n(C I)total

• f2 n(C I**)/n(C I)total

f1f2Then consider the plot:

Collision partners at a given density and temperature are expected to yield specific values of f1 and f2

n(H) = 10 cm-3

n(H) = 100 cm-3

n(H) = 1000 cm-3

n(H) = 104 cm-3

n(H) = 105 cm-3

Collisional Excitation by Neutral H

T = 100 K

Collisional Excitation by Neutral H Plus Optical

Pumping by the Average Galactic Starlight Field

n(H) = 10 cm-3

n(H) = 100 cm-3

n(H) = 1000 cm-3

n(H) = 104 cm-3

Collisional Excitation by Neutral H Plus Optical Pumping by 10X the

Average Galactic Starlight Field

n(H) = 10 cm-3

n(H) = 100 cm-3

n(H) = 1000 cm-3

n(H) = 104 cm-3

Tracks for Different Temperatures

n(H) = 100 cm-3

T = 30 K

T = 60 K

T = 120 K

T = 240 K

Tracks for Different Temperatures

T = 30 K

T = 60 K

T = 120 K

T = 240 K

p/k = 104 cm-3 K

(Back to simple f1f2 diag.)

Cloud 1

Cloud 2

A Theorem on how to deal with superpositions

A Theorem on how to deal with superpositions

C I-weighted “Center of

Mass” gives Composite

f1,f2

Allowed Region for Composite

Results

P/k

Results

• Original observations reported by Jenkins & Tripp (2001) included 21 stars.

• We have now expanded this survey to about 100 stars by downloading from the MAST archive all suitable STIS observations that used the highest resolution echelle spectrograph (E140H).

• The archival results have somewhat lower velocity resolution because the standard entrance aperture was usually used (instead of the extremely narrow slit chosen for the Jenkins & Tripp survey).

Composite over all velocities and stars:

f1 = 0.217, f2 = 0.073

T = 20K

T = 40K

T = 80K

T = 160K

H II reg.

T = 20K

T = 40K

T = 80K

T = 160K

H II reg.

Note: HISA-land is down here

VLSR

VDifferential Galactic Rotation

Positive Velocities

Negative VelocitiesAllowed Velocities

Sun

Target

KinematicsKinematicsKinematicsKinematicsC

olu

mn

de

nsi

ty p

er

un

it ve

loci

ty [

1013

cm

-2 (

km s

-1)-1

]

Velocity (km s-1)

C I

C I*

C I**

λ Cep

(heliocentric)

Allowed VelocitiesComposite f1 = 0.203, f2 = 0.063

T = 20K

T = 40K

T = 80K

T = 160K

H II reg.

Positive VelocitiesPositive VelocitiesNegative Velocities

Composite f1 = 0.231, f2 = 0.082 for both velocity intervals

T = 20K

T = 40K

T = 80K

T = 160K

H II reg.

eff = 0.72

Barytropic index

(Wolfire, Hollenbach, McKee, Tielens & Bakes 1995, ApJ 443, 152)

Gamma_eff on f1f2 (0.72)

Gamma_eff on f1f2 (0.72, 0.90)

Log-normal Distribution of Mass vs. Density

Rel

ativ

e M

ass

Fra

ctio

n

n(H I) (cm-3)

Observed composite f1, f2

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

H IC I

Observed composite f1, f2

H IC I

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

Observed composite f1, f2

H IC I

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

Observed composite f1, f2

H IC I

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

Observed composite f1, f2

H IC I

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

Observed composite f1, f2

H IC I

Log-normal distribution of H I mass fraction vs. n(H), with γeff = 5/3

Obs.

Model for a random Model for a random mixture of high and mixture of high and low pressure gaslow pressure gas

Obs.

Pressure Distribution Function

p/k (cm-3 K)

Rel

ativ

e M

ass

Fra

ctio

n

H I mass fraction

Note: The width of this peak is a lower limit, since the observations at each velocity probably exhibit some averaging of pressure extremes along the straight portion of the f1-f2 curve.

Note: The width of this peak is a lower limit, since the observations at each velocity probably exhibit some averaging of pressure extremes along the straight portion of the f1-f2 curve.

The width and central pressure of this peak are not well known, but the height of the peak is well determined.

The width and central pressure of this peak are not well known, but the height of the peak is well determined.

Pressure Distribution Function

p/k (cm-3 K)

Rel

ativ

e M

ass

Fra

ctio

n

C I mass fractionH I mass fraction

A Question to Consider About the High Pressure Component

• Could this component arise simply from the action of radiation or mass loss from the target stars (or their associations) either of which could compress the gas?

• Probably not: recall that negative velocity material behaved in much the same way as positive velocity material

Except for some gas parcels that have only high pressures

Blue = neg. vel.Red = pos. vel.

HS0624+6907HS0624+6907 Galactic Coordinates: l = Galactic Coordinates: l =

145.7145.7°°, b = +23.4, b = +23.4°°

Nearest O- or B-type star to the line Nearest O- or B-type star to the line

of sight: 43 Cam (V = 5.14, of sight: 43 Cam (V = 5.14,

spectral type: B7IV), about 2spectral type: B7IV), about 2° away° away

p/k (cm-3 K)

Rel

ativ

e M

ass

Fra

ctio

nImplications on the Existence of Small

Neutral Stuctures

Tcool = 15,000 yr (for T = 60 K)

Tcool = 2,500 yr

Rapid Compression

• High pressure component mass fraction is low (~10-3), relative to most of the gas.

• It has n(H I) ~ 103 −104 cm-3 and T ≥ 100 K.

• Tcool ≤ 2500 yr, which implies a typical dimension of only 0.00025 pc (i.e., 50 AU), or less, if crossing-time velocities are of order 10 km s-1 and the compression is nearly adiabatic.

Implications on the Existence of Small Neutral Stuctures