Giant Star-Forming Regions · Gouliermis & Klessen Giant Star-Forming Regions Effects of Dust:...

University of Heidelberg, Center for Astronomy

Giant Star-Forming Regions

Dimitrios A. Gouliermis

Lecture #5 Interstellar Dust

Giant Star-Forming Regions Gouliermis & Klessen

(tentative) Schedule of the Course

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Lect. 1 19-Oct-2012 Course Overview Motivation for the Course/Schedule; Overview of Physical Processes in HII Regions; Classification of HII regions

Lect. 2 26-Oct-2012 Introduction to the Physics of the ISM Phases of the ISM; Transitions; Introduction to cooling mechanisms

Lect. 3 2-Nov-2012 Introduction to the Physics of the ISM Atomic Transitions; Gas Cooling; Collisional Excitation

Lect. 4 9-Nov-2012 Introduction to the Physics of the ISM Gas Heating; Photo-ionization; Photo-electric heating; PAHs

Lect. 5 16-Nov-2012 Interstellar Dust Composition, Spectral Features, Grain Size Distributions, Extinction

Lect. 6 23-Nov-2012 Physical Processes in HII Regions I Radiative Processes; Strömgren Theory; Photo-ionization & Recombination of hydrogen; Dust

Lect. 7 30-Nov-2012 Physical Processes in HII Regions II Thermal Properties; Heating and Cooling of HII Regions; Forbidden lines and Line Diagnostics

Lect. 8 7-Dec-2012 Photodissociation regions (PDR) Ionization & Energy Balance; Dissociation of Molecular Hydrogen; Structure; Observations

Lect. 9 14-Dec-2012 Stellar Feedback Processes Dynamics of the ISM; Ionization fronts; Expansion of HII regions; Stellar Winds and Supernovas

Lect. 10 11-Jan-2012 Stellar Content of HII Regions I Massive Stellar Evolution; Mass-Loss; Rotation; Binary interaction; Spectral features of OB stars; Runaway stars - Stellar Cluster dynamics

Lect. 11 18-Jan-2012 Stellar Content of HII Regions II Pre--Main-Sequence (PMS) Stars; Young Stellar Systems; Stellar Initial Mass Function; Age determination & History

Lect. 12 25-Jan-2012 Star Formation (SF) Isothermal shperes and Jeans mass; Molecular Cores collapse; Protostars

Lect. 13 1-Feb-2012 Star Formation PMS Stellar Evolution/Contraction; Characteristics of T Tauri stars; Herbig Ae/Be Stars; Multiple SF


Interstellar Dust

In this Lecture •  Dust historic overview •  Extinction Absorption, Scattering •  Extinction Curve •  Scattering Theory •  Spectral Features of Dust •  Grain Size distributions - Models

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Historic Overview of Dust •  Presence of nebular gas was long accepted but the existence of

absorbing interstellar dust remained controversial into the 20th cy. •  W. Herschel (1738-1822) found with star counts only few stars in some

directions; later proven by E. E. Barnard to host dark clouds. •  R. J. Trumpler demonstrated in 1930 interstellar absorption by

comparing luminosity distances & angular diameter distances for open clusters:

–  Angular diameter distances are systematically smaller

–  Discrepancy grows with distance –  Distant clusters are redder –  Estimated ~ 2 mag/kpc absorption –  Attributed it to Rayleigh scattering

by tiny grains (25Å)

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R. J. Trumpler 1930, Pub. Astron. Soc. Passific, Vol. 42, p. 214


Historic Overview of Dust •  The advent of photoelectric photometry (1940-1954) led to the discovery

and quantification of interstellar reddening by precise comparison of stars of the same type

•  Interstellar reddening is ascribed to the continuous (with wavelength) absorption of small macroscopic particles, quantified by the extinction Aλ, i.e., by the difference in magnitudes:

–  Aλ, varies roughly as λ–1.5 from 0.3-2.3 µm –  The condition, 2πa/λ ~ 1, suggests particle sizes a ~ 0.1μm

•  Starlight is polarized in regions of high extinction with one polarization state selectively removed by scattering from small elongated conducting or dielectric particles aligned in the galactic magnetic field

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Evidence for Interstellar Dust •  Extinction, reddening, polarization of starlight

–  dark clouds •  Scattered light

–  reflection nebulae –  diffuse galactic light

•  Continuum IR emission –  diffuse galactic emission correlated with HI & CO –  young and old stars with large infrared excesses

•  Depletion of refractory elements from the interstellar gas (e.g., Ca, Al, Fe, Si)

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Effects of Dust: Absorption

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Barnard 68 Dark Cloud. See ESO PR http://www.eso.org/public/news/eso9934/


Effects of Dust: Scattering

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The Pleiades Open Cluster. The nebulosity seen here is light reflected from the particles in a cloud of cold gas and dust into which the cluster has drifted. It appears blue because these tiny interstellar particles scatter blue light more efficiently than the longer wavelengths of red light and it is streaky because the particles have been aligned by magnetic fields between the stars. (Royal Observatory Edinburgh).


Extinction

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For simplicity, we consider homogeneous spherical dust particles of radius a and introduce the cross section for extinction:

where Qext(λ) is the efficiency factor for extinction. The optical depth along a line sight with volumetric dust density ndust is then

Extinction in magnitudes, Aλ, is defined in terms of the reduction in the intensity cause by the presence of the dust:

€

σ(λ) = πa2Qext (λ)

€

τλext = ndustσλ

ext∫ ds =σλext ndustds =∫ πa2Qext (λ)Ndust

€

I(λ) = I0(λ)exp −τλext[ ]

€

Aλ = −2.5log10 I(λ) /I0(λ)[ ] = 2.5log10(e)τλext =1.086τλ

ext


Extinction

•  In the optical/NIR the trend is λ–1.5.

•  There is a steep UV rise with peak at ~ 800 Å.

•  Strong features: λ = 220 nm, Δλ = 47 nm λ = 9.7µm, Δλ ~ 2-3µm (not visible on this plot)

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Schematic of relation of extinction in magnitudes versus wavelength in µm


Extinction Wavelength Dependence

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Wavelength dependence of extinction in the IR/optical region for the case RV = 3.1.

E. L. Fitzpatrick 1999, Pub. Astron. Soc. Passific, Vol. 111, pp. 63-75


Scattering & Absorption

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The extinction efficiency is the sum of scattering and absorption:

For spherical grains:

All of the Q’s and the albedo are functions of λ and a. The scattering phase function is

The amount and character of the scattering is expressed by the

corresponds to forward, isotropic, and back scattering

€

Qext =Qsca +Qabs

€

σabs = πa2Qabs σsca = πa2Qsca

σext = πa2Qext = πa2 Qabs +Qsca( )

€

albedo =σscaσext

=Qsca

Qext

€

g = cosϑ =I(ϑ)cosϑdΩ

0

π

∫

I(ϑ)dΩ0

π

∫

€

cosϑ =1,0,−1


Extinction Measurements

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The (“general”) extinction Aλ can also be written as terms of the brightness in magnitudes of a source, but this requires knowing its distance and luminosity:

The “normalized selective extinction” at any wavelength is also a common measure of extinction:

The extinction curve is steep in the diffuse ISM: RV = 3.1±0.2 and shallower in dark clouds: RV ~ 5

The “normalized extinction” : 1/RV, measures the steepness of the extinction curve

Instead we use the distance-independent “selective extinction”, which is the additional color excess due to extinction:

€

mλ = Mλ + 5logd − 5 + Aλ

€

E(B −V ) = A(B) − A(V ) = (B −V ) − (B −V )0

€

E(λ,V )E(B −V )

€

RV =A(V )

A(B) − A(V )=

A(V )E(B −V )


Interstellar Reddening

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Da Rio et al. 2009, Astroph. J., vol. 696, p. 528

Bik et al. 2012, Astroph. J., vol. 744, p. 87


Empirical Extinction Curves

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Based on extinction measurements from the UV to NIR. It Illustrates the effect of varying the normalized extinction 1/RV (which measures the slope of the extinction curve).

B. T. Draine 2003, Ann. Rev. Astron. & Astroph., Vol. 41, p. 241


Gas and Dust

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Correlation between gas column density (HI & H2) and interstellar reddening E(B-V) for 100 stars from the Copernicus atomic and molecular hydrogen survey. The solid line gives an average total hydrogen to E(B-V) ratio of NH = 5.8×1021 cm–2 mag–1 It measures of the dust-to-gas ratio for diffuse interstellar clouds.

Savage & Mathis 1979, Ann. Rev. Astron. & Astroph., Vol. 17, p. 33


Dust-to-Gas Ratio

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Extinction measurements of local diffuse clouds yield:

Remember that Aλ=1.086τλext and

where ρdust / ρgas is the dust-to-gas ratio, mdust is the mean mass of a dust grain, and mgas is the mean gas particle mass per H nucleus ~ 1.4 mH. Extracting mean values from the integral gives

or , with RV = A(V) / E(B-V):

€

NH

E(B −V )≡N(HI) + 2N(H2)

E(B −V )≈ 5.8 ×1021 atoms mag−1 cm−2, RV ≈ 3.1

€

A(V ) ≈ NH

1.8 ×1022 mag cm2

€

τλext = ndustσλ

ext∫ ds =σλext (ρdust /mdust )ds⇒∫

τλext =σλ

ext nH(ρdust /ρgas)(mgas /mdust )∫ ds

€

τλext = ρdust /ρgas mgas /mdust Qλ

extπa2NH


Dust-to-Gas Ratio

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Another order of magnitude result is to rewrite Aλ=1.086τλext as

and to divide by the gas column NH to obtain the mean extinction cross section per H nucleus

If we assume that the visual extinction is due to “classical grains” of sizes a = 0.1 μm (e.g., 2πα ~ λ), with Qλ

ext ~ 1, and a typical specific (internal) grain mass density ρgr ~ 2.5 gr cm–3, we arrive at a dust-to-gas ratio of: €

A(V ) =1.0863mgasQλ

ext

4ρdaρdust /ρgas NH

€

ρdust /ρgas ≈ 0.01

€

A(V ) =1.086NdσVext

€

Nd

NHσVext ~ 5 ×10−22cm−2


EM Scattering by small particles •  Gustav Mie in 1908 solved Maxwell’s Equations for scattering by

a uniform sphere of radius a and a complex refractive index m m = n – ik with m = m(λ).

•  The mathematical basis is a multipole expansion in terms of spherical harmonics (EM modes of a sphere). The solution takes the form of an analytical infinite series (el. dipole, magn. dipole / el. quadrupole, magn. quadrupole / el. octupole, …).

•  Basic parameter is x = 2πa/λ, i.e., radius in terms of wavelength –  x << 1: long wavelength: diffraction limit - need only a few terms –  x >> 1: short wavelengths: geometrical optics limit - need many terms

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Original Study: G. Mie, “Beiträge zur Optik trüber Medien - speziell kolloidaler Metallösungen”, Annalen der Physik, Band 25, No. 3, pp. 377-445 (1908).

Classic reference: H.C. van de Hulst, “Light Scattering by Small Particles”, Wiley, New York, 1957 (1981, Dover)


Asymptotic Mie Formulas for x << 1

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€

Qabs = −4x Im m2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟ ∝ λ−2

Qsca =83x 4 Re m2 −1

m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟

2⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ ∝ λ−4

In this long wavelength or Rayleigh limit, the absorption cross section depends only on the mass of the grain:

€

σabs =Qabsπa2 ∝ a3 ∝ mdust


Mie Scattering & Absorption

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The extinction and scattering efficiency calculated using Mie theory for spherical grains plotted as a function of the size parameter, x = 2πα/λ.

H.C. van der Hulst, 1981, Light Scattering by Small Particles, (New York: Dover)


Dust-to-Gas Ratio (Purcell)

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Purcell (1969, ApJ 158, 433) used the Kramers-Kronig relations to relate the integrated extinction coefficient to the (constant) index m and the dust column Nd:

Purcell reintroduced the extinction Aλ and derives a relation between it and the dust column:

This provides only a lower limit on grain volume for other shapes; spherical grains have been assumed here.

€

Qextdλ0

∞

∫ = 4π 2a m2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟

τext =Qextπa2Nd , Nd = ρdL /md

τextdλ0

∞

∫ = 4π 3a3Ndm2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟

€

Aλ =1.086 τλ =1.086 Qextπa2Nd


Dust-to-Gas Ratio (Purcell)

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This Kramers-Kronig result involves integrated quantities. So, by integrating the above we get :

where mgr is the mass of an individual grain and L is the distance along the line of sight.

€

Aλdλ0

∞

∫L

= 3π 21.086 m2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟ ndVgr , Vgr =

4π3a3

ndVgr =ndmgr

mgr /Vgr=ρd

ρgr=

spatial average dust densitydensity of a grain

•  The integrated extinction Aλ measures the mean dust density. •  We get the mean Dust-to-Gas mass ratio by dividing the integral by

ρgas = mgasnH = mgasNH/L, with mgas = 1.35mH, the gas particle mass.


Dust-to-Gas Ratio Estimation

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We assume silicate grains with a real index of 1.5 and internal density ρgr= 2.5 g cm–3 and use the empirical extinction law, A(V) ≈ NH / 1.8×1021 mag cm2 to obtain

€

1L

Aλdλ0

∞

∫ = 3π 21.086 m2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟ ρdust

ρgas

(NH /L)mgas

ρgr⇒

ρdust

ρgas=

Aλdλ0

∞

∫NH

3π 21.086 m2 −1m2 + 2⎛

⎝ ⎜

⎞

⎠ ⎟ mgas

ρgr

⎡

⎣ ⎢

⎤

⎦ ⎥

−1

€

ρdust

ρgas=19.2

Aλdλ0

∞

∫NH

With the approximation A ~ λ–1.5 for λ > 0.25μm, the dust-to-gas ratio is ~ 0.004, and if we guess that the UV contributes another 50-100%, we would get a ratio of ~ 0.06-0.08. Spitzer calculates a ratio of ~ 0.006.


Implications of the Dust-to-Gas Ratio •  A significant fraction of heavy elements are in interstellar

dust grains. •  The mass fraction of heavy elements is Z = 0.016×Solar.

Therefore, ~ 40% are in grains, or even larger fraction when abundant volatile elements are excluded

•  Typical grain models include –  Silicates: Mg, Si, Fe, O (20%) in (Mg,Fe)2SiO4, etc. –  Carbonaceous material (graphite & organics): C (60%) –  Some SiC

•  The presence of C and Si are supported by dust spectral features, as discussed later.

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Features in the Extinction Curve

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2175 Å (~220 nm) Feature (Aromatic C ?)

9.7 µm Silicate Feature


The 220 nm Feature •  Ubiquitous in the Milky Way

–  217.5 ± 47 nm (fixed wavelength) –  width varies (10%) as does strength

•  Graphite has a strong UV resonance due to π-orbital valence electrons

–  But why is the feature so uniform?

•  220 nm bump is weak in the SMC bar, presumably due to reduced C abundance

•  Hydroxylated (+OH) Mg2SiO4 (forsterite) also has a 220 nm feature.

•  The actual carrier of the 220 nm feature has not been identified.

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See also: Cecchi-Pestellini & Williams 2012, Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 113, p. 2310

Fitzpatrick & Massa 2007, Astrophys. J., vol. 663, p. 320


The 220 nm Feature

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Fitzpatrick & Massa (1986, ApJ, 307, 286) showed that the observed 2175Å feature can be accurately fit with a Drude profile:

Because the expected oscillator strength per molecule is fX ≤ 0.5, it can be concluded that the carrier molecule must contain one or more elements from {C,O,Mg,Si,Fe}, as these are the only condensible elements with sufficiently high abundances nX/nH ≥ 2 × 10−5 in the ISM.

€

ΔCext (λ) =C0γ

2

(λ /λ0 − λ0 /λ)2 + γ 2 ,

peaking at λ0 = 217.5 nm (λ0−1 = 4.60 µm−1)

and with a broadening parameter γ = 0.216(corresponding to FWHM γλ0 = 46.9 nm)


The 220 nm Feature

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Hypothesis #2 (see e.g. models by Weingartner & Draine 2001, ApJ, 548, 296; Li & Draine 2001, ApJ, 554, 778):

Large PAH molecules. The carbon atom skeleton of PAHs is very similar to a portion of a graphite sheet, with similar electronic wavefunctions. So, PAH molecules generally have strong π → π∗ absorption in the 2000–2500 Å.

Required abundance: C/H = 6.0 × 10−5 in PAH molecules or clusters containing from 20 to 105 C atoms. Absorption profiles are not known for the sizes characteristic of the interstellar PAHs, but one would expect a similar π → π∗ oscillator strength per C as for graphite, or f ≈ 0.16.

Hypothesis #1 (see e.g. models by Draine & Lee 1984, ApJ, 285, 89):

Some form of graphitic carbon is responsible for the observed feature. The C atoms in graphite are bound to one another in hexagonal sheets.

Absorption of a photon can excite the delocalized π-orbital electron to an excited orbital (π∗); this π → π∗ transition is responsible for the absorption feature peaking at ~ 2175Å. Required abundance: C/H = 5.8 × 10−5


Silicate Minerals •  Silicates have strong absorption resonances near

10 µm due to the Si-O bond stretching mode. –  It is virtually certain that the interstellar 9.7 µm feature is

produced by interstellar silicates (absorption as well as emission is observed).

–  The 10 µm emission feature is observed in outflows from cool O-rich stars

•  Their expanding atmospheres condense silicates •  It is absent in the outflows from C-rich stars, where the O needed

for silicates is all locked up in CO •  A broad feature at 18 µm can be identified with the O-Si-O

bending mode in silicates

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Grain Populations •  There are at least three components associated with the

optical/IR extinction, the 220 nm bump, and the FUV extinction rise.

•  The Aλ rise from NIR/optical to the NUV requires a ~ 150 nm –  But if there were only 150 nm grains present, Aλ for λ< 200 nm

would be approximately constant.

•  The steep rise in FUV extinction down to 80 nm requires a ~ λ /2π ~ 15 nm, otherwise Qext would be flat.

•  The 220 nm bump implies a specific (still unknown) carrier –  symmetry and constancy of λ0 imply absorption in the small

particle limit a ≤ 10 nm. –  small graphite spheroids a ≈ 3 nm, b/a = 1.6 might work,

except for variation in central wavelength

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Grain Size Distribution •  Grain size distribution is likely to be continuous

(c.f. physical [coagulation] theory for small particle generation) •  Mathis, Rumpl & Nordseick (1977, ApJ 217 425) proposed

power law distributions of graphite and silicate grains in approximately equal numbers

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€

dnda

∝ AnHa−3.5, amin < a < amax

amax = 250 nm, set by NIR & Visibleamin = 5 nm, set by FUV extinction curve

•  MRN power law has most of the mass in large particles & most of the area in small particles:

€

M ∝ a3 dnda∫ da∝ amax

0.5 − amin0.5 A ∝ a2 dn

da∫ da∝ amin−0.5 − amax

−0.5


Grain Size Distribution

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•  Two component model: 5 nm < a < 250 nm –  Graphite: 60% of C –  “Astronomical silicate”: 90% of Si, 95% Mg, 94% Fe & 16% O

Draine & Lee 1984, Astrophys. J., vol. 285, p. 89

Extinction expressed as cross-section Comparison with other models


Graphites

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Absorption Coefficients for spherical graphite grains of various sizes

sub-micron wavelengths NIR-FIR wavelengths

€

For a ≤ 0.1λ Qabs ∝ aFor a ≤ 0.3µm absoprion cross - section is independent of Tgrain


Silicates

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10 and 20 µm Absorption silicate features

Absorption Coefficients for spherical grains of “astronomical” silicates

sub-micron wavelengths NIR-FIR wavelengths

Varying grain sizes for Silicates


The Model by Weingartner & Draine 2001

(ApJ 548 296)

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NIR-FIR cross-sections sub-micron cross-sections

The dashed green lines show the asymptotic behavior of the absorption (∝λ−2) and scattering (∝λ−4) cross sections (see slide #19).


The Model by Weingartner & Draine 2001

(ApJ 548 296)

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Size distributions for carbonaceous-silicate grain model for Milky Way dust with RV = 3.1, but with abundances decreased by a factor 0.93 to reproduce the AIc/NH relation.

NOTE: Extinction in the I-band vs. H2 column density (Bohlin et al. 1978, ApJ, 224, 132): AIc/NH ≈ 2.96 × 10−22 mag cm2 for RV = 3.1.


Summary •  The shape of the interstellar extinction curve

contains information about the size and chemical composition of interstellar dust grains.

•  The relatively smooth variation of the extinction with wavelength from 0.1 to 3 µm indicates that a wide distribution of grain sizes are involved.

•  The relatively large dust-to-gas ratio indicates that a substantial fraction of the heavy elements are bound up in dust.

•  The 220 nm bump and the 9.7 &18 µm features Indicate that dust contains C and Si, respectively.

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