Turbulence in HII Regions
Jane Arthur
Instituto de Radioastronomı́a y Astrofı́sica, UNAM
Principal Collaborators:
Sac-Nicté Medina, MPIfR, Bonn
Will Henney, IRyA, UNAM
Papers:
Medina et al., 2014, MNRAS 445, 1797
Arthur et al., 2016, MNRAS 463, 2864
6 Years of ISM-SPP: What have we learned?, 15 Feb 2017
DGAPA-PAPIIT Project IN112816
Goal is to describe 3D velocity and density fields from
observed surface brightness maps and line-of-sight velocities.
Possible turbulence in the Orion Nebula?
• In particular, want to investigate and characterize turbulence in
the ionized gas of the Orion Nebula.
• Spectral lines show broadening larger than the thermal
component, suggesting disordered motions along the line of sight.
• Interpreted as turbulence using structure functions by von
Hoerner (1951), Munch (1958) and Castañeda (1988) but the
resolution was not good enough to confirm or characterize the
turbulence.
• Possible driving mechanisms include shear flows at edge of stellar
wind bubble; photoevaporated flows from neutral globules.
• Also a way of testing whether our numerical simulations are
missing any key ingredients.
Orion Nebula
[O III] λ5007 Å
Line core
components
A + B only
ONC systemic velocity
Line intensity
4000
3000
Line core
components
2000
A
B
1000
C
0
−40
−20
0
20
Back-scattered
component
40
60
Heliocentric velocity, km/s
Arthur et al. (2016)
NASA, C.R. O’Dell and S.K. Wong (Rice U.)
Ionization Stratification;
Brightness Fluctuations.
Multiple line components.
80
100
Statistical Tools
VELOCITY CENTROIDS
Vc (x, y ) = M1 /M0 ,
M0 and M1 are the zeroth and first order velocity moments of the
PPV cube.
STRUCTURE FUNCTION
von Hoerner (1951); Castañeda & O’Dell (1987)
Second-order structure function of the velocity centroids
P
2
pairs [Vc (r) − Vc (r + l)]
.
S2 (l) =
2 N(l)
σvc
VELOCITY CHANNEL ANALYSIS
Lazarian & Pogosyan (2000); Esquivel (2003)
• Spatial power spectra of the velocity channels of spectroscopic
PPV (or PV) data.
—Bin into N channels of width δv = (vmax − vmin )/N.
—Sum the spatial power spectra for each velocity slice.
• Thickest slice: N = 1 is total velocity-integrated surface
brightness.
• Thin slice: Thinnest useful slice depends on instrumental velocity
resolution, seeing and thermal broadening. Heavy ions are best.
Thickest channels → density fluctuations dominate.
Thin channels → velocity fluctuations dominate.
• For homogeneous, isotropic turbulence, the structure functions
and VCA lead to power-law relations with scale/wavenumber.
• There are relations between these power laws and the underlying
3D velocity and emissivity power spectra indices.
Relationship between Statistical Measures
Description
3D
3D
3D
2D
emissivity fluctuations
velocity fluctuations
structure function
structure function
Projection Smoothing
Sheetlike Emission
Intensity fluctuations
Very Thick Velocity Slice
Thin Velocity Slice
Shallow density nE > −3
Steep density nE < −3
Power-law
Index
nE
n
m3D
m2D
γ
γT
γt
Relationship
K’grov
Value
n = −3 − m3D
m3D = −3 − n
(a)
(a)
−11/3
2/3
m2D = m3D + 1
m2D ∼ m3D
(b)
(c)
5/3
2/3
γT ∼ nE
(d)
γt = γT + m3D /2
γt = −3 + m3D /2
(d)
(d)
(a) Kolmogorov (1941); (b) von Hoerner (1951);
(c) Castañeda & O’Dell (1987); (d) Lazarian & Pogosyan (2000)
−8/3
Analysis of a Simulation
Medina et al. 2014
Analysis of a Simulation
Medina et al. 2014
VCA is a more robust tool
3D Power Spectra
Structure Functions
xy
0.9
d2i
-3.0
SF power-law index
Power Spectrum Gradient
-2.8
vi
-3.2
di
T
-3.4
-3.6
100
[OIII]
0.7
0.5
[SII]
0.3
150
200
Time [103 yrs]
250
300
100
150
200
Time [x 103] yrs
250
300
VCA is a more robust tool
3D Power Spectra
VCA
-1.5
d2i
-3.0
vi
-3.2
di
T
-3.4
xy
[SII]-thin
-2.0
VCA power-law index
Power Spectrum Gradient
-2.8
[SII]-thick
-2.5
-3.0
[OIII]-thin
-3.5
[OIII]-thick
-3.6
100
150
200
3
Time [10 yrs]
250
300
-4.0
100
150
200
Time [x 103] yrs
250
300
Results: Simulations
• VCA recovers the power-law index of the 3D velocity and density
fluctuations: n ∼ nE ∼ −3.1 ± 0.1.
• Multiple scales of energy injection are suggested since spectrum
of fluctuations is flatter than Kolmogorov prediction.
• [OIII] has a steeper thick slice VCA power law than the lower
ionization ions: suggests larger line-of-sight depth through [OIII]
emitting gas.
Emission-Line Atlas of the Orion Nebula
Garcı́a-Dı́az et al. 2007, 2008
Statistical Tools: Observations of the Orion Nebula
Velocity Channel Analysis: δvt = 4 km s−1
-1
-1
k [parsec ]
10
k [parsec ]
100
10
[NII] 6583 - Thin
1.00
[NII] 6583 - Thick
II
III
IV
3
k P(k)
I
100
0.10
γt2 = −2.30±0.08
γt3 = −4.14±0.11
0.01
0.10
k [arcsec-1]
γT2 = −2.58±0.09
γT3 = −4.14±0.13
0.01
0.10
k [arcsec-1]
Statistical Tools: Observations of the Orion Nebula
Velocity Channel Analysis: δvt = 4 km s−1
k [parsec-1]
10
k [parsec-1]
100
Hα 6563 - Thin
10
100
Hα 6563 - Thick
3
k P(k)
1.00
0.10
γt2 = −2.70±0.12
γt3 = −4.40±0.12
0.01
0.10
k [arcsec-1]
γT2 = −2.79±0.15
γT3 = −4.26±0.16
0.01
0.10
k [arcsec-1]
Statistical Tools: Observations of the Orion Nebula
Velocity Channel Analysis: δvt = 4 km s−1
k [parsec-1]
10
k [parsec-1]
100
[OIII] 5007 - Thin
10
100
[OIII] 5007 - Thick
k3P(k)
1.00
0.10
γt2 = −2.53±0.08
γt3 = −4.03±0.11
0.01
0.10
k [arcsec-1]
γT2 = −2.82±0.10
γT3 = −3.68±0.25
0.01
0.10
k [arcsec-1]
Regime II spectral indices and relationships
Emission
Line
[SII] λ6716
[SII] λ6731
[NII] λ6583
Hα λ6563
[OIII] λ5007
Thin
γt2
−2.72 ± 0.12
−2.69 ± 0.09
−2.30 ± 0.08
−2.70 ± 0.12
−2.53 ± 0.08
Thick
γT2
−3.06 ± 0.13
−3.03 ± 0.14
−2.58 ± 0.09
−2.79 ± 0.15
−2.82 ± 0.10
n
−3 − m3D
−3.56 ± 0.24
−3.62 ± 0.22
−3.56 ± 0.24
...
−3.58 ± 0.26
Conclusions: Orion Nebula
• We find consistent evidence of a Kolmogorov-type spectrum for
length scales 800 < l < 2200 (0.02 < l < 0.05 pc).
• We identify the characteristic lengthscale l = 0.05 pc as the
main driving scale of turbulence.
• We tentatively suggest a link with the autocorrelation length of
dense cores in Orion molecular filament (Kainulainen et al 2017).
• The similarity of the [NII] and [OIII] results suggests a similar
volume distribution for the low- and high-ionization gas: confined
to a thick shell and not filling the interior of the nebula.
Schematic Structure of the Orion Nebula
O’Dell et al, 2009, ApJ 137, 367
Causal Relationships
Gravitational
Instability
Thermal
Instability
Turbulence
Density
Fluctuations
Molecular
Feedback
Photoionization
Ionized
Extinction
Pressure Gradients
Bright Rims
Ordered
Velocity
Instabilities
Velocity
Fluctuations
Colliding Streams
Density
Fluctuations
Ionization,
Temperature
Fluctuations
Stellar Wind,
Jets,
Radiation
Pressure
Brightness
Fluctuations