Giant Star-Forming Regions - mpia-hd.mpg.de€¦ · Lect. 3 2-Nov-2012 Introduction to the Physics...

University of Heidelberg, Center for Astronomy

Giant Star-Forming Regions

Dimitrios A. Gouliermis

Lecture #8 Physical Processes in

Ionized Hydrogen Regions Part III

Giant Star-Forming Regions Gouliermis & Klessen

(tentative) Schedule of the Course

WS 2012 - 2013 Lecture 8 2

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 I Phases of the ISM; Transitions; Introduction to cooling mechanisms

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

Lect. 4 9-Nov-2012 Introduction to the Physics of the ISM III 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; Photo-ionization & Recombination of hydrogen; Photoionization Equilibrium

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

Lect. 8 7-Dec-2012 Physical Processes in HII Regions III T & n measurements in HII Regions; Secondary Ionization; Dielectronic Recombination; Free-free emission

Lect. 9 14-Dec-2012 Photodissociation regions (PDR) Ionization & Energy Balance; Dissociation of Molecular Hydrogen; Structure; Observations

Lect. 10 11-Jan-2012 Stellar Feedback Processes Dynamics of the ISM; Ionization fronts; Expansion of HII regions; Shocks & Bubbles

Lect. 11 18-Jan-2012 Star Formation Collapse & fragmentation of Molecular Clouds: Cores & Disks; Protostars and YSOs; PMS evolution

Lect. 12 25-Jan-2012 Stellar Content of HII Regions Hot Massive Stars (Rotation; Binarity; Spectral features); Pre--Main-Sequence (PMS) Stars (Characteristics)

Lect. 13 1-Feb-2012 Stellar Clusters and Associations Young Stellar Systems; Stellar Initial Mass Function; Stellar Cluster dynamics & survival; runaway stars


Physical Processes in HII Regions Part III

In this Lecture •  More of Spectral Diagnostics •  Thermal Bremmstralung emission •  Secondary Ionizations of Trace Species •  Charge Exchange & Dielectronic Recombination

WS 2012 - 2013 3 Lecture 8

•  Literature –  B.T. Draine, Physics of the Interstellar and Intergalactic Medium, Ch. 3, 13 –  A.G.G.M Tielens, The Physics and Chemistry of the Interstellar Medium, Ch. 7 –  G.B. Rybicki & A.P. Lightman, Radiative Processes in Astrophysics, Ch. 6 –  T.L. Wilson, K. Rohlfs & S. Hüttemeister, Tools Of Radio Astronomy


Spectral Diagnostics in HII Regions

•  Hydrogen & Helium Recombination Lines (UV, optical, near-IR, Radio)

•  Collisionally Excited Lines of heavy ions (Optical, mid-IR)

•  Free-free Continuum Emission; Bremsstrahlung (far-IR, Radio)

WS 2012 - 2013 Lecture 8 4


Optical Spectra of HII Regions

WS 2012 - 2013 Lecture 8 5

Optical & UV spectrum of the Orion Nebula showing prominent forbidden and recombination lines, from Baldwin et al. 1991, Astroph. J., 374, 580


IR Spectra of HII Regions

WS 2012 - 2013 Lecture 8 6

The continuum emission is due to warm dust with superimposed the IR emission bands due to large PAHs (lecture 5). Absorption bands due to silicates and ices located in a foreground cold molecular cloud are also visible. The line spectrum shows HI recombination lines and far-IR ionic fine-structure lines (lecture 7), as well as those originating in the photodissociation region (lecture 9). Spectrum from E. Peeters, et al., 2002, Astron. & Astroph., 381, p. 571.


IR/Radio Spectra of HII Regions

WS 2012 - 2013 Lecture 8 7

The IR continuum spectrum, peaking around 100 µm (dashed line), is due to dust. The free-free emission at radio wavelengths (solid line) shows the well-known optically thin behavior at long wavelengths (flux ~ν2) and the optically thick behavior for shorter wavelengths (flux ~ν−0.1). The observations drop below the extrapolated free-free (and free-bound) continuum at the shortest wave- length owing to dust absorption. Spectrum from G. Wynn Williams, 1974, IAU Symposium No 60, p. 259.


Spectral lines Diagnostics: e– Density •  Density is estimated from recombination lines in the optical (i.e., Hα

at 6562 Å), infrared (i.e., Brα at 4.05 µm), or radio (i.e., H109α or H137β near 6 cm) or from the free–free continuum in the radio.

•  The line strength directly yields the emission measure, EM:

•  For a homogeneous nebula, the emission measure can be translated into a density by adopting a scale size,

•  The optical and IR lines have to be corrected for dust extinction first. For inhomogeneous nebulae, the emission measure is of course weighted towards higher density regions.

WS 2012 - 2013 Lecture 8 8

€

EM = nenpdl0

L

∫ , in homogeneous nebulas : EM = n2L

€

nrms =EMcm−6pc⎛

⎝ ⎜

⎞

⎠ ⎟ pcL

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2


Spectral lines Diagnostics: IR

•  The intensities of both lines scale with density and their ratio is constant and independent of the density. In between the two critical densities, the ratio is a good measure of the density.

WS 2012 - 2013 Lecture 8 9


Spectral lines Diagnostics: e– Temperature •  Collisionally excited lines originating from different terms will have

different excitation energies and thus their relative intensities are sensitive to the electron temperature.

•  The electron temperature can be determined from the optically thick portion of the radio spectrum, which yields the electron temperature directly from the brightness temperature.

WS 2012 - 2013 Lecture 8 10


Combined Line Diagnostics: Optical/IR

WS 2012 - 2013 Lecture 8 11

Calculated variation of [OIII] forbidden-line relative-intensity ratios as functions of T and logne. From Dinerstein et al. 1985, Astroph. J., 291, 561


Other Ionization Mechanisms •  Apart from radiative ionization from UV & X-rays photons,

there are few more basic methods for ionizing the gas: 1. Cosmic rays

2. Collisional Ionization

3. Charge Exchange

•  Cosmic rays are important only in cool radiation-shielded regions of interstellar clouds.

•  Otherwise the main processes are radiative and collisional ionization.

WS 2012 - 2013 Lecture 8 12

€

X +CR→X + + e− +CR

€

X + e− →X + + 2e−

€

X +Y + →X + +Y


Ionization of Trace Species •  Generalizing the ionization balance of H and He to species

with multiple ionization stages implies that there will be a set of ionization equations linking sequential ionization stages.

•  The dependence of the ionization cross section on photon energy becomes more complex and a second channel for recombination – dielectronic recombination – opens up.

•  Solving the ionization balance equations for each charge for each species requires a redundant set of equations.

•  Therefore, one equation is replaced by a conservation law

where imax is the maximum ionization charge considered and Aj is the gas phase abundance of species Xj.

WS 2012 - 2013 Lecture 8 13

€

n(X ji )

i=0

imax

∑ = A jn


Ionization of Trace Species •  Because of resonances, ionization to different levels of the ion,

and inner shell ionization, the ionization cross section of heavy species can be complex:

where αT the cross section at the ionization threshold νT, and a and b are fitting parameters.

•  Radiative recombination is like that for H and He where, after capture of the electron, the resulting exiting species stabilizes through the emission of a photon.

•  In dielectronic recombination, the incoming electron excites a bound electron to an excited electronic state. The long-lived, doubly-excited species then relaxes radiatively. The rate coefficient depends on the resonance character of the reaction.

WS 2012 - 2013 Lecture 8 14

€

α(ν) = αT b ννT

⎛

⎝ ⎜

⎞

⎠ ⎟

−a

+ (1− b) ννT

⎛

⎝ ⎜

⎞

⎠ ⎟

−a−1⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ with ν > νT


Secondary Ionizations in diffuse ISM •  The initial kinetic energy of a photoelectron ejected from

shell s of an atom or ion is Epe = hν − Is, where Is is the threshold energy for photoionization from shell s.

•  In a fully ionized nebula, an energetic photoelectron slows down by Coulomb scattering off thermal electrons, with all of its initial kinetic energy eventually converted to heat.

•  If there are bound electrons present (H atoms), the photo-electron can also excite electrons to excited bound states (1s → 2p) by collisional excitation, or to free electron states (H → H+ + e−) by collisional ionization.

•  The collisional ionizations by both the photoelectron and energetic secondary electrons are referred to as secondary ionizations.

WS 2012 - 2013 Lecture 8 15


Collisional Ionization •  To understand the effects of energetic electrons in a

partially ionized gas, it is necessary to carry out a statistical study of slowing-down process.

WS 2012 - 2013 Lecture 8 16

•  Cross sections for electronic ionization are generally much larger than for photoionization, but they are much harder to calculate (even for H) and to measure, at least for the moderate energies (1-100 eV) of astrophysical interest.

Standard shape of an electronic ionization cross section.


Collisional Ionization of heavy Ions •  The role of collisional ionization for ion X

depends on the ratio of kBT to the ionization potential IP(X). In this context, we should keep in mind these basic conversion factors:

WS 2012 - 2013 Lecture 8 17

€

kBT =T

11605eV

€

hν =chλ

=12.397eV Aλ


Collisional Ionization of heavy Ions

WS 2012 - 2013 Lecture 8 18

The rate coefficient for collisional ionization by the thermal electrons in a plasma is:

€

kC.I. = σC.I.(E)υfEdEI

∞

∫ =8kTπme

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

σC.I.(E)EkTI

∞

∫ e−E / kT dEkT

The collisional ionization cross section rises smoothly from zero at the threshold energy I. For moderate energies I < E ≤ 3I, the actual cross section can often be approximated by the simple form

€

σC.I.(E) ≈ Cπa02 1− I

E⎛

⎝ ⎜

⎞

⎠ ⎟

a0 = 2/mee2 = 5.292 ×10−9cm :[ Bohr radius]

For this simple form, the thermal rate coefficient is readily calculated and is given by

€

kC.I. = Cπa02 8kTπme

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

e−I / kT = 5.466 ×10−9CT41/ 2e−I / kT cm3s−1 T4 ≡

T104 K

⎡

⎣ ⎢ ⎤

⎦ ⎥


Ionization Structure of Trace Species

WS 2012 - 2013 Lecture 8 19

Onion-like shell structures of sequential ionization stages. Except near the boundary of the HII region, the transition from one stage of ionization to the next is quite gradual.

As for H & He, the ionization structure of O & N is layered with the highest ionization closest to the star and lower ionization progressively further away.

The calculated ionization structure of oxygen and nitrogen for an O4 star (right) and an O8 star (left) at a density of 103 cm−3.


Collisional Ionization Cross Sections

WS 2012 - 2013 Lecture 8 20

Collisional Ionization Cross Sections Calculations: Bell, K.L., et al. 1983, J. Phys. Chem. Ref. Data, 12, 891 Lennon, M.A., et al. 1988, J. Phys. Chem. Ref. Data, 17, 1285

Collisional Ionization Models: Shapiro & Moore 1976, Astroph. J., 207, 460 (SM76) Sutherland & Dopita 1993, Astroph. J. Suppl. Ser., 88, 253 (SD93)

Cooling functions for the Collisional Ionization under equilibrium and non-equilibrium conditions in plasmas with 104 ≤ T ≤ 106K (SM76) and 104 ≤ T ≤ 108.5K (SD93).


Recombinations of Ions with e–

1. Radiative recombination (discussed in Lecture 6)

2. Dielectronic recombination

3. Charge exchange

4. Three-body recombination

5. Dissociative recombination

6. Neutralization by grain

WS 2012 - 2013 Lecture 8 21

€

X + + e− →X + hν

€

X + + e− →X ** →X + hν

€

X + + e− + e− →X + e−

€

AB+ + e− →A + B

€

X + + grain→X + grain+

€

X + +Y →X +Y +


Dielectronic Recombination

WS 2012 - 2013 Lecture 8 22

•  Rather than making a direct radiative transition on capture,

a doubly-excited configuration X** my be formed before radiating:

•  If the ion has at least one bound electron it is possible for the incoming electron to transfer energy to the bound electron, promoting it to an excited state, and removing enough energy from the first electron that it too can be captured in an excited state. The ion now has two electrons in excited states, a process known as dielectronic recombination.

•  As long as the energy has not been radiated away, the process is reversible: the doubly excited electronic state is capable of autoionizing.

€

X + + e− →X + hν

€

X + + e− →X ** →X + hν



WS 2012 - 2013 Lecture 8 23

•  The rate coefficient for dielectronic recombination depends on detailed atomic physics: the initial cross section for capture to a doubly excited state, and the probabilities per unit time of autoionization and spontaneous radiative decay.

•  Dielectronic recombination is important in high-temperature plasmas, where it exceeds the radiative recombination rate.

•  Dielectronic recombination is important at the ~104K temperatures of H II regions for selected ions, including recombination of MgII, CIII.



WS 2012 - 2013 Lecture 8 24

Modern Calculations including radiative and dielectronic recombination: Badnell 2006, Astroph. J. Suppl. Ser., 167, 334.

Recent work on dielectronic recombination: Colgan et al. 2004, Astr. & Astrophys., 417, 1183 Mitnik & Badnell 2004, Astr. & Astrophys., 425, 1153 Zatsarinny et al. 2004, Astr. & Astrophys., 417, 1173

RR DR


Charge Exchange •  Electronic recombination is a slow process (Lecture 6):

•  Particle reactions are often many orders of magnitude stronger, e.g., fast charge exchange of an ion and an abundant neutral (rate coefficient ~10–9 cm3s–1 for n>2) is more important than recombination with electrons.

•  Therefore, besides photo-ionization, charge exchange reactions of the type

with Yk being H or He, can also be important.

WS 2012 - 2013 Lecture 8 25

€

β2(8000K, H) = 3 ×10−13cm3s−1

€

X ji +Yk

0 ⇔ X ji−1 +Yk

+1


Charge Exchange •  In view of the small energy difference between the IPs of H0

and O0 (0.0197 eV), the charge exchange reaction between O(3P0) and H+ is very important.

•  From detailed balance the relation between the forward and backward rate coefficients (kf= 2×10–9 cm3 s–1 & kb) is:

•  When neutral hydrogen is abundant – as in the ionization front – the O/O+ ratio is very closely tied to the H/H+ ratio.

•  These charge exchange reactions can be included in the ionization balance.

WS 2012 - 2013 Lecture 8 26

€

O+ +H →H+ +O H+ +O →O+ +H (exothermic) (endothermic)

€

kb =89kf exp[−220 /T]


Charge Exchange

WS 2012 - 2013 Lecture 8 27

There are three different fine-structure levels of OI that could be produced when an electron is exchanged.

O+ O0

Σg = 4×2 = 8 Σg = 3×3 = 9 (g: statistical weights) Detailed Rate Coefficients calculated by

Stancil et al. 1999, A&AS, 140, 225


The O+/O Ratio

WS 2012 - 2013 Lecture 8 28

•  For T >> 300K, the exponential in the Milne relation between the forward (O++H) and backward (H++O) reactions is ~1. Therefore only the statistical weights matter:

•  Therefore the O/O+ ratio is the H+/H ratio multiplied by the ratio of rate coefficients:

•  At temperatures T ≤ 300K, ionized oxygen is suppressed by charge transfer reactions with H0.

•  For T ≥ 103K, the oxygen ionization fraction will be close to the hydrogen ionization fraction. This applies in HII regions.

€

n(H)n(O+)kf = n(H+)n(O)kb

€

n(O+)n(O)

= kb

kf

n(H+)n(H)


The O+/O Ratio

WS 2012 - 2013 Lecture 8 29

•  The excited fine-structure levels are efficiently depopulated by spontaneous decay for low densities. At high densities with nH ≥ 104 cm–3 collisions will ensure that the O0 fine structure levels 3P2,1,0 are populated according to a thermal distribution.


Radio Observations of the ISM •  HII Regions (~104K)

–  Continuum Radiation: Free-free emission –  Line Emission: Radio Recombination Lines of H, He

and heavier elements. •  Hot Plasmas (≥105.5K: Coronal; HIM; SNRs)

–  Synchrotron emission from highly-relativistic electrons (Non-thermal)

•  Warm (WNM) & Cool HI (CNM), Diffuse H2 –  HI 21-cm emission, absorption

•  Diffuse & Dense H2 –  CO 2.6 mm & CO lines emission

WS 2012 - 2013 Lecture 8 30


Bremsstrahlung Radiation

WS 2012 - 2013 Lecture 8 31

It is the electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon due to conservation of energy.

Bremsstrahlung has a continuous spectrum, which becomes more intense and shifts toward higher frequencies as the change of the energy of the accelerated particles increases.

In thermal equilibrium the absorption coefficient κν and the emissivity jν must satisfy Kirchhoff’s law: κν = jν /Bν(T), where Bν is the Planck function. The absorption (attenuation) coefficient due to free–free absorption is:

where gff the Gaunt factor for free-free emission

€

κν = neni16π 2Zi

2e6

(6π mekT)3 / 2ν 2cgff


Thermal Equilibrium @ Radio

WS 2012 - 2013 Lecture 8 32

At radio frequencies hν/kT~ν(GHz)/20T(K)<<1 for typical HII temperatures. In this case the Rayleigh-Jeans approximation of the Planck function applies and the specific intensity Iν of the HII region is expressed as a function of the brightness temperature TB as:

€

Iν = Bν (TB) = 2ν 2kTB /c2

€

dTBdτν

= −TB +Te

€

TB(ν) = Te(1− e−τν ) +TB(0)

The transfer equation of thermal emission in these circumstances with Te being the kinetic or electron temperature of the nebula and τν the optical depth along the line-of-site, is:

For an isothermal nebula the specific intensity expressed in brightness temperature is:

with TB(0) being the background sky temperature at the frequency of interest.


Bremsstrahlung Radiation Diagnosis

WS 2012 - 2013 Lecture 8 33

The radio brightness of the HII region is measured once the source optical depth is known. Opacity is provided by the free-free absorption, which is computed by analysis of the inverse process, i.e., free-free emission and application of Kirchhoff’s law. The flux density at an optically thin nebula is:

€

Sν =6.51×10−15

D2(cm) ν 0.1(Hz)neni

T 0.35∫ dV (cm3) (Jy)

€

Ne2 =1.54 ×1014 Sν (Jy)D

2ν 0.1T 0.35 /V

If we assume that the nebula is isothermal and homogeneous an estimate of the mean-square electron density is given by:

Assumptions about the geometry and distance of the nebula must be made. Once these are made the total mass of the nebula is also measured. Important extracted information from the flux density of the nebula is the Spectral Type of the source.


Bremsstrahlung Diagnostics Notes

•  For the realistic case of an inhomogeneous nebula the above equations must be rewritten to take into account the density distribution within each nebula.

•  The spectral shape – the dependence of flux density to frequency – takes the form Sν ∝ να, where α has a value between the optically thin (α = –0.1) and optically thick (α = +2) limits.

•  For a power-law density distribution N(R) ∝ R–γ, as the density distribution steepens, the spectral index α will be more close to the optically thick limit.

WS 2012 - 2013 Lecture 8 34

Source: Radio observations of HII regions by R. L. Brown, in Spectroscopy of Astrophysical Plasmas, A. Dalgarno & D. Layzer (eds.), Cambridge (1987)


Radio Recombination Lines

WS 2012 - 2013 Lecture 8 35

Source: Radio observations of HII regions by R. L. Brown, in Spectroscopy of Astrophysical Plasmas, A. Dalgarno & D. Layzer (eds.), Cambridge (1987)

In a hydrogen plasma, collisional processes will maintain a population of H atoms in very high quantum states with principal quantum number n ≥ 100 – the Rydberg states – populated mainly by three-body collisional processes:

€

H+ + e− + e− →H(n) + e−

The three-body recombination rate ensures that a significant population of high-n levels of H are in collisional equilibrium (LTE) with the electrons and protons. Recombinations in such highly excited atoms leads to downward cascades each accompanied by a photon emission seen in radio.


Heart & Soul nebula (NASA/WISE)

100 pc 1.56o

W5

W4

W3

W3 Main (LBT/LUCI)

1 pc


Magnetic Fields

WS 2012 - 2013 Lecture 8 37

Interstellar magnetic field: The magnetic field resulting from electric currents in the interstellar medium; it guides the cosmic rays, and in some parts of the ISM, the magnetic field is strong enough to be dynamically important.

Synchrotron radiation is generated by astronomical objects, typically when relativistic electrons spiral (and hence change velocity) through magnetic fields. Two of its characteristics include non-thermal power-law spectra, and polarization.

Synchrotron emission is important in the pulsar wind nebulae (plerions). Pulsed emission γ-ray radiation from the Crab nebula has been observed up to ≥25 GeV, due to synchrotron emission by electrons trapped in the strong magnetic field around the pulsar. Polarization in the Crab at energies from 0.1 to 1.0 MeV illustrates a typical synchrotron radiation.


Anisotropic plasmas: Faraday rotation

WS 2012 - 2013 Lecture 8 38

In an anisotropic plasma with a (tangled) magnetic field the cyclotron frequency becomes important:

In such a plasma the propagation speed of the waves depends on their polarization. A linearly polarized wave will change its angle by an amount

This is known as Faraday rotation. Through the frequency dependency of ∆θ we can find B||, or a lower limit to it. If the field is so strong that ∆θ varies by close to 90° within the bandwidth of our measurement, the wave is depolarized.

€

Δϑ =2πe3

m2c 2ω 2 nB||0

d

∫ ds€

ωB =eB0mc


(realistic?) Schedule of the Course

WS 2012 - 2013 Lecture 8 39

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 I Phases of the ISM; Transitions; Introduction to cooling mechanisms

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

Lect. 4 9-Nov-2012 Introduction to the Physics of the ISM III 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; Photo-ionization & Recombination of hydrogen; Photoionization Equilibrium

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

Lect. 8 7-Dec-2012 Physical Processes in HII Regions III T & n measurements in HII Regions; Secondary Ionization; Dielectronic Recombination; Free-free emission

Lect. 9 14-Dec-2012 Photodissociation regions (PDR) Ionization & Energy Balance; Dissociation of Molecular Hydrogen; Structure; Observations

Lect. 10 11-Jan-2012 Stellar Feedback Processes Dynamics of the ISM; Ionization fronts; Expansion of HII regions; Shocks & Bubbles

Lect. 11 18-Jan-2012 Star Formation Collapse & fragmentation of Molecular Clouds: Cores & Disks; Protostars and YSOs; PMS evolution

Lect. 12 25-Jan-2012 Stellar Content of HII Regions Hot Massive Stars (Rotation; Binarity; Spectral features); Pre--Main-Sequence (PMS) Stars (Characteristics)

Lect. 13 1-Feb-2012 Stellar Clusters and Associations Young Stellar Systems; Stellar Initial Mass Function; Stellar Cluster dynamics & survival; runaway stars

Giant Star-Forming Regions - mpia-hd.mpg.de€¦ · Lect. 3 2-Nov-2012 Introduction to the Physics...

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