Miguel A. de Avillez Dieter Breitschwerdt

Dept. Mathematics, University of Évora, Portugal ZAA, Technical University Berlin, Germany

The Importance of the Atomic History in Time-Dependent Simulations of the Interstellar Gas

�2

Parallel AMR Coarse resolution = 8 pc Higher resolution = 0.5 pc Effective grids of 20003 cells Evolution time = 500 Myr Cut through the Galactic midplane

Free electrons distribution

THERMAL + DYNAMICAL EVOLUTION OF THE ISM

➔ Ionizing

➔ Recombining

➔ Cooling

➔ Turbulent mixing

➔ Conductive interfaces

➔ Particles acceleration (DSA)

➔ Non-equilibrium plasmas ➔ Thermal + Non-thermal ➔ Feedback

LARGE RANGE OF SCALES TO CONSIDER

�3

Visc

ous

Dis

sipa

tion

500 250 75−100 −210

!4

Thermal translational

energy

Energy stored in (or delivered) from excited states

Total energy loss (gain) is not synchronized with equivalent decrease (increase) of temperature.

Feed into the momentum equation

Affects the dynamics

INTERNAL ENERGY

@⇢e

@t+r · [(⇢e+ Pth)~v] = ⇢~v · ~g +r · (rT ) + �SN +H� nenH⇤(T )

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

⇢e =3

2(ntot + ne)kBT +

X

Z

ZX

z=1

nZ,z

z�1X

l=0

�Z,l

!+X

Z

ZX

z=1

2

4X

j=no+1

nZ,z,j��Ej,no

�Z,z

3

5

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

Energy stored in (or delivered) from high ionization stages

@⇢~v

@t+r · (⇢~v~v + Pth) = �⇢g + S⇢~v

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

INTERNAL ENERGY & ADIABATIC PARAMETER

�5

� =cpcv

⇢u =3

2(ntot + ne)kBT +

X

Z

ZX

z=1

nZ,z

z�1X

l=0

�Z,l

!+X

Z

ZX

z=1

2

4X

j=no+1

nZ,z,j��Ej,no

�Z,z

3

5

AAACyHicdVFdb9MwFHXC1ygf68YjLxYVUqeWKumQtpdKEzAJ8VSkdZtoQuS4TuPViSP7BtRGftlP3BtP/BXcpBuwwZUsH59z7r22b1wIrsHzfjjuvfsPHj7aetx68vTZ8+32zu6plqWibEKlkOo8JpoJnrMJcBDsvFCMZLFgZ/Hi/Vo/+8aU5jI/gWXBwozMc55wSsBSUftnoFKJy1GQKEKrfVMNTTePKpBgenZnZg8vouqdOe kFusyi6otp9tXIN1/tyXos2V8ZEwiWQLdRxciz6uqNb4JxytcGYQLF5yns/adOnT1tuItRXVUa0/NvGvQvblp8YAIIbh1bZ//aeV3+93Xqcxi1O97AqwPfBf4GdNAmxlH7KphJWmYsByqI1lPfKyCsiAJOBTOtoNSsIHRB5mxqYU4ypsOqHoTBry0zw4lUduWAa/bPjIpkWi+z2DozAqm+ra3Jf2nTEpLDsOJ5UQLLadMoKQUGiddTxTOuGAWxtIBQxe1dMU2JHSnY2bfsJ/i3n3wXnA4H/v5g+Plt52i4+Y4t9BK9Ql3kowN0hD6iMZog6hw7Cwec0v3kFu53d9lYXWeT8wL9Fe7lL02s4qc=

All fluid elements have the same atomic history

SIMULATIONS OF THE ISM WITH FIXED COOLING

!6

➔ Maxwell-Boltzmann distribution

➔ Temperature equilibration ions and electrons ➔ Include a fixed cooling function (of a gas parcel)

➔ Adiabatic parameter constant (5/3) ➔ Internal energy includes only the thermal component

➔ Neglect the feedback of dynamics

102

103

104

105

106

107

108

109

T [K]

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

ΛP

roc [

erg

cm

3 s

-1]

BremRRDREII2γ

LinesTotal

NEIIsochoric: solid linesIsobaric: dashed lines

102

103

104

105

106

107

108

109

T [K]

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

ΛP

roc [

erg

cm

3 s

-1]

BremRRDREII2γLinesTotal

CIE

Not correct

!7

THERMAL + DYNAMICAL SIMULATIONS OF THE ISM

Mass Conservation

Energy Conservation

Momentum Conservation

Maxwell Equations

Equation of StateInternal Energy

Charge ConservationCooling

Ionization Structure

τdyn=τth? StopYesNo

τth

τdyn

Γ-Λ

ρ, u, τdyn

Cosmic Rays

Wave field

DY

NA

MIC

AL

+ T

HE

RM

AL

EV

OLU

TIO

N

@⇢

@t+r · (⇢~v) = S⇢

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

@⇢XZ,z@t

+r · (⇢XZ,z~v) = ⇢SZ,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

IONIZATION STRUCTURE + LEVEL POPULATIONS

�8

RZ,z = ne⇣↵rr

Z,z+ ↵dr

Z,z

⌘+

X

Z̃,z̃

↵ceZ̃,z̃

ñZ̃,z̃

IZ,z = ⇣Z,z + ne⇣Ceii

Z,z+ Cea

Z,z

⌘+

X

Z̃,z̃

CceZ̃,z̃

ñZ̃,z̃

⇣Z,z = ⇣phZ,z

+ ⇣cZ,z

+ ⇣peZ,z

dnZ,zdt

= IZ,z�1nZ,z�1 ��IZ,z +RZ,z

�nZ,z +RZ,z+1nZ,z+1

dnZ,z,jdt

=X

mj

Dexcn!j �X

j>m

Dexcj!m �X

jm

⇣Cd,X

jmnX +Ajm

⌘nZ,z,j �

X

j

PROCESSES + COMPUTING TIME

!9

➔ Non-equilibrium ionization: H, He, C, N, O, Ne, Mg, Si, S, Ar, Fe + H, C, O chemistry

➔ 70-level ions ➔ Abundances (solar and pre-solar)

➔ Equal and/or different temperature for electrons and ions ➔ Thermal and non-thermal particle distributions (e.g., kappa, n, cosmic rays)

➔ Rates calculated from cross sections on the fly

➔ Excitation/deexcitation rates calculated from collision strengths (R-Matrix calculations) ➔ Calculations are made in accelerators/coprocessors while CPUs are idle for 10-5 s

➔ Parallel computing - dynamical model in CPUs + thermal model in GPUs/Xeon Phi

➔ Electron impact ionization (total and shell), inner-shell excitation auto-ionization

➔ Radiative (RR) and dielectronic (DR) recombination followed by cascades ➔ Charge-transfer reactions ➔ Photoionisation + Auger photoelectrons + Secondaries

➔ Continuum (bremsstrahlung, free–bound, two-photon) ➔ Line (permitted, semi-forbidden, forbidden) emission

!10

➔ 3D multi-fluid HD or MHD evolution over 500 Myr

➔ Grid: 1 kpc × 1kpc × ± 15 kpc Δx=0.25 pc and 0.5 pc (40003 cells per kpc3)

➔ Density distribution from observations (Dickey & Lockman 91, Ferriere 98)

➔ Star Formation based on thresholds: n > 100 cm-3 & T

!11

➔ Background heating due to diffuse UV photon field calculated from the stars

➔ Galactic gravitational field by stars (Kuijken & Gilmore 1989) + self gravity

➔ Heat conduction (Dalton & Balbus 1993)

➔ Magnetic field (random + mean components 6 μG)

THERMAL + DYNAMICAL MODEL

HISTORY OF THE PLASMA

�12

Avillez+Breitschwerdt (2012)

�13

➡ Jenkins (2013): FUSE observations of UV spectra of 44 hot subdwarf stars a few hundred parsecs away from the Sun

✓ Compare column densities of ArI to those go OI

✓ The measured deficiency [ArI/OI]=-0.427 below the expectation for a fully neutral medium

✓ Implies that the electron density ne~0.04 cm-3 if n(H)=0.5 cm-3

➡ Dispersion measurements against pulsars of known distances (Berkhuijsen+ 2008; Gaensler+ 2008; Schnitzeler 2012, see also Avillez+2012):

✓ Electrons have a clumpy distribution

✓ Log ne has a Gaussian PDF

✓ ne (z=0 pc)=0.02-0.04 cm-3

CAN WE TRUST THESE SIMULATIONS? ELECTRONS

ne~0.033 cm-3

14

Dispersion is constant with d

Electrons: clumpy distribution.

From pulsars DMs up to 8 kpc from Sun

CAN WE TRUST THESE SIMULATIONS? ELECTRONS

Avillez+ 2012, 2019

33 pulsars at |z|

FINAL REMARKS

�15

➔ Full blown simulations imply ten most abundant elements (112 ions), thermal and non-thermal electron/proton distributions, large database of cross sections and collision strengths.

➔ CRs ISM simulations must include DSA and full calculation of ionisation, recombination and excitation/deexcitation rates using cross sections and the local electron/proton distribution function

HD/MHD/CR-MHD + ATOMIC/MOLECULAR PHYSICS

➔ Cooling time < Recombination time of ions

➔ Plasma keeps a record of its history - Need to include all the ions

➔ The ionization structure varies in space and time and depends on the ICs

➔ The cooling paths can be quite different for plasmas with the same initial temperature, but having different evolution histories;