Laboratory Astrophysics with lasers Chantal Stehlé
LERMA (Laboratoire d’Etudes de la Ma ère et du Rayonnement en Astrophysique et Atmosphères)
This work is partly supported by French state funds managed by the ANR within the Inves ssements d'Avenir programme under reference ANR-11-IDEX-0004-02. Plasma astrophysics see for instance Savin et al. « Lab astro white paper », 2010
Perimeter Methods • Microscopic physical • Experiments processes (opacity, EOS) • Theory, databases • • Mul scale, mul physics Numerical simula ons • Links to observa ons processes (e.g. magne c reconnec on, shock waves, instabili es …) Tools • Study of large scale scaled • Medium size lab. processes, (e.g. stellar jets) experiments • Large scale facili es (lasers and pinches ) • Super-compu ng ressources OUTLINE
• Introduc on • Stellar Opacity • EOS for gazeous planets • Scaling • Accre on & Ejec on processes in Young Stars • Conclusion Opacity for stellar interiors
From Turck Chièze et al. ApSS 2010 4 Opacity An example of opacity : For a optically thick medium, Hydrogen( Stehlé et al 1993) • LTE is ~ valid -> near blackbody radia on κν/ρ
• The monochroma c radia ve flux Fν is propor onal to the gradient of rad. Energy
and to 1/κν (The radia on tends to escape from regions
where κν is low, ie between lines) hν • The frequency averaged flux
linked to the Rosseland opacity κR.
1 3 dν dB (T) / dT 16 σ T dT 1 ∫ κ ν < F > = and = ν d dB (T) / dT 3 κ R dz κ R ∫ ν ν 5 CEPHEIDS: the enigma
Strong periodic (P~ 1 – 50 days) Rela on P-L : varia ons of luminosity L, Teff, and distance calibrator radius.
Enveloppe 2 The pulsa on (κ mechanism) log(κR in g/cm ) 2 • in the external part of the stellar envelope 1.5 • linked to an increase of the opacity 1 4 6 -7 -2 3 0.5 10 < T < 10 K (10 < ρ < 10 g/cm ) 0 Hence radia on is blocked in the internal layers, -> hea ng -> expansion and bea ng Core 34 32 30 28 log(External Mass in g )
2 In the 90’, no code was able Temperature in K, κ in cm /g for M* = 5 M8, Y=0.25, Z=0.08, to reproduce the pulsa on. Teff= 6400 , 5900 and 5500 K (Bono et al 1999). 6 CEPHEIDS : theory and experiments
A synerge c approach combining : Later on, results from the 1. A revised theore cal calcula on Opacity Project -> confirma on of the opacity ( Baldnell et al. MNRAS 2005) (OPAL project, Iglesias et al. ApJ 1990)
2. A new calcula on of the stellar structure with the new opaci es sets (Moskalik P. et all, ApJ 1992)
3. An experimental measurement of the Fe opacity (Da Silva et al 1992) Principle of an opacity measurement
T (hν) = exp (–kν ρ d)
Spectrometer : Transmission Difficul es • TAMPER ( CH) Avoid the satura on of the Sample spectra TAMPER ( CH) • Small temperature gradients (uniformity) • LTE Radia ve hea ng X ray backligh ng Revisited Cepheids opaci es
Exp. Exp. + new calculation -> importance of the transitions Δn = 0 (Da Silva et al. PRL 1992) (neglected in the previous opacities).
OPAL Iglesias et al. ApJ 1990
Δn=0 -3 3 (3-3) Fe : 8 10 g/cm , 25 eV
New opaci es introduced in the cepheid model.
-> A be er agreement between the observed and calculated pulsa on periods New opaci es : was obtained 9 Differences for T > 105 K (bumps) (Moskalik P. et al, ApJ 1992 ) Current work on massive stars: 10-30 eV , 10-3 g/cm3
… s mulated by asteroseismology space missions COROT, KEPLER, … PLATO .
Further experiments : e.g. on LULI 2000 going for Fe and Ni, in the condi ons of the enveloppes of these massive stars (Loisel et al. 2009, Blenski et al. 2011, Turck- Chièze et al. 2011)
Taken from Loisel PhD thesis, 2011
Increasing work on theore cal calcula ons !! From Turck Chièze et al. ApSS 2010 What about the sun ? Like other stars, the sun oscillates. The heliosismologic observa ons (SOHO ) allows to
compute the sound speed csound versus radius R. However: if one compares these csound “observed” values with the theore cal ones, using revised solar abundances (Asplund et al. ApJ 2005), Results with new opaci es the disagreement for R /R¤ > 0.5, is larger than with the previous set of abundances (Grevesse & Sauval Sp.Sc.Rev. 1998)
(Basu & An a 2008 , Bahcal et al. 2005, Turck-Chièze et al. 2011, Piau & Couvidat 2011) Results with old opaci es A « lack » of opacity … ???
Differences between sound velocity between the solar models and the helioseismic results (Bahcall et al 2005) 11
The ques on of the solar opacity in the radia ve zone …..
in the radia ve zone ( below 0.71 R⊙ ) 106 < T ~ <15 106 K, 1 <ρ <150 g/cm3
This requires high energy installa ons !
21 -3 • Sandia ( Z ): Fe at T ~ 150 eV and Ne ~ 7 10 cm (Bailey et al. 2009) -> higher Fe opacity than predicted ! (Bailey et al , Nature 2015 ) 1.2 Opacity x 104 cm2 g-1 Comparison of Fe opacity : 6 0.8 Te = 2.11 10 K, 22 -3 Ne = 3.1 10 cm , 0.4 experimental in black (from Bailey et al., RSI 2015) 0 8 9 10 11 12 Å
• NIF : projects for C, N, O at T > 200 eV and ρ > 0.2 g/cm3 (Keiter et al. 2013) Equa on of state for planets
See also talk of K. Falk
Taken from h p://katjafalk.blogspot.fr/2011/10/my-dphil- research-project.html EOS for gaseous planets & exoplanets
P = P(ρ,T) (PV ≠ NkT at high pressure)
Mandatory to understand log T (K) the forma on, evolu on and 5 H+ structure 4 H atomic of planets and exoplanets.
3
For gaseous planets, H + He (10%) solid -> EOS of Hydrogen and He plays 2 a crucial role Log P(bar) Jupiter, 1 Complex: from molecular Saturn 2 4 6 8 to metallic state From Guillot, Ann. Rev. Earth& Plan. Sc. 2005 around 1 Mbar, 5000 K Jupiter See also talk of K. Falk Interior : a non ideal plasma • From molecular liquid to metallic H • H-He phase separa on (T < 5000 K, P ~few Mbar) 165 -170 K 1Mbar Molecular H2
Inhomogeneous ? 1) An outer helium-poor envelope 8300 -6800 K (He abundance constrained by 2 Mbar spectroscopic measurements of the atmosphere, GALILEO) Metallic H 2) An inner envelope, assumed to coincide with a metallic H region
3) A central dense core 15000 -21000 K of unknown mass and composi on Rock- ice 40 Mbar core
15 From T. Guillot, Science, 1999 S ll large uncertain es EOS + observa onal constraints -> computa on of the internal structure
Mcore/Mplanet
Uncertainty concerning the mass of the core : even solu ons with no solid core ( Mcore =0 ) do exist. -> impact on the forma on scenario.
Saumon & Guillot 2004 : « Improved astrophysical data will not be sufficient, however it is important to reduce the uncertain es surrounding the EOS of hydrogen in the 1 to 30 Mbar range ».
Similar situa on for Saturn MZ/Mplanet (Helled and Guillot, ApJ 2013) Jupiter structure: core and mass of heavy
16 elements: solu on fi ng the observa onal constraints for 5 H- EOS ( Saumon Guillot, ApJ 2004) EOS Experiments • Sta c methods, e.g. diamond anvils (P < 1 Mbar, T < 10000 K) • Dynamic methods , e.g. lasers & pinches (P up to 100 Mbar, T up to 105 K) : genera on of a shock wave to compress the ma er, determina on of P, ρ, E, T. • A combina on of the two
Deriva on of EOS based on Rankine Hugoniot equa ons Pusher (u)
3 equa ons linking the post shock u, P, (u0=0), P0, quan es (u, P, ρ, E) , the velocity ρ, Ε ρ0, E0 of the shock D to the pre-shock condi ons D 3 Taking ρ0 = 1 g/cm , D ~ u = 1 km/s for P0 ~ 1 bar -> P ~ 100 Mbar
5 unknown parameters : u, P, ρ, E, D => 2 parameters to be measured .
17 Laser experiments on EOS
Strong pressure generated by laser abla on ablator Pusher which drives the pusher.
u, T, ρ u0=0 , Pusher : a metal foil and an thin layer of ablator T0, ρ0 on the top of it (abla on -> rocket launch) D Different diagnos cs, for instance : • VISAR for the shock velocity (D) (Celliers et al RSI, 2001) • Op cal pyrometry (SOP) or the shock temperature (T) (Cauble et al., ApJS, 2000) • Transverse radiography (D and u) (Cauble et al., ApJS, 2000) • Reflec vity measurement ( transi on to metallic state ) (Knudsen et al., Sc. 2015) • X-ray Thomson sca ering (ne, te, Ti, Z) (Falk et al. PRE, 2013)
Difficul es : • Uniformity and planarity of the shock -> (phase plate to smooth laser beam) • Sta onarity • Control of the ini al condi ons : no prehea ng
18 D2 EOS laser experiments
In 2000, work on cryogenic D2 by Cauble et al. (ApJS 127, 267, 2000) at NOVA at the high pressure , high temperature, insolator – metal transmission
NOVA drive beam Shock front 527 nm, 3 1014 W/cm2, few ns Interface
Pusher : Al + layer of CH (ablator)
Be window Time in ns Backligh ng Radiography
0 100 200 300 400 500 Distance in microns
Pyrometry => T U , U 19 p s Design of the cryogenic cell to measure proper es of the EOS of Deuterium Extensive study, in theory and experiments
300
250
200
D / H 150 2 2 100 Pressure in GPa
Pressure in GPa 50
10 100 1000 3 4 5 6 0 2 3 4 5 6 Compression ρ/ρ0 Compression ρ/ρ0 Calculated Hugoniots for D star ng with the 2 Principal Hugoniot of D2 and H2 : experiments ini al density of 0.717 g/cm3 (OMEGA ) and a selec on of theore cal results (from Hicks et al.. PRB 2009) (from Loubeyre et al. PRB 2012) Too large uncertain es in the measurements to constraint the various theore cal models
20 Similari es and Scaling Aircra in a wind tunnel at ONERA
21 HH47 seen by HST Similari es (Esirkepov & Bulanov, 2012) or, how to make the bridge between astrophysics and experiments ? Absolute similarity : same equa ons, same dimensionless quan es, and also scaled ini al condi ons (rather difficult ) Approximate similarity : only basic parameters are reproduced (common situa on) JETS - configura on simula on: global geometry + some physical processes - process simula on: local physical processes in astrophysical condi ons. EOS OPACITY Limited similarity (qualita ve scaling) (common situa on) dimensionless quan es, which are small compared to unity SHOCKS should be small in the model (or vice versa), but not necessarily by the same order of magnitude. Absolute similarity (1/3) Ryutov et al. PoP 2001
For a perfect fluid (no viscosity, no diffusion, no radia ve transport ..) : the system evolu on is fully determined : 1) By the Euler equa ons and ideal MHD ∂ρ +∇.ρu = 0 Mass conserva on ∂t % ∂u ( 1 ρ' + u.∇u* = −∇P − B× ∇ × B Impulse conserva on & ∂t ) 4π ∂u + u.∇P = −γP ∇.u Energy conserva on , with P /( 1) ∂t ε = γ − ∂B = ∇ × u × B ∂ t ρ(t=0, r) € € 2) and by the ini al condi ons : ρ(r)|0, u(r) |0 , P(r)|0 , B(r)|0
23 r Absolute similarity (2/3) Taking characteris cs length L*, density ρ*, pressure P*, the equa ons remain unchanged with the following change of variables r ρ P t P * ρ * B r = , ρ = , P = , t = , u = u , B = L* ρ * P * L* ρ * P * P *
THUS
€ ∗ ρ/ρ ∗ ρ/ρ1 2 The two systems evolve in iden cal way ( in dimensionless units) if
1) the ini al condi ons are geometrically similar ∗ ∗ r/L1 r/L2
2) the following 2 dimensionless numbers ρ * are the same for the two systems. u * = inv = Eu P *
2 B * 3) β =Ptherm/Pmag ~ P* / B* = cte = inv 24 P *
€ Absolute similarity (3/3) Validity condi ons All transport mechanisms mes must be negligible in comparison with the hydrodynamical me scales, i.e.
L* P* / ρ* Re = >> 1 Reynolds number v
L* P* / ρ* Pe = >> 1 Peclet number χ
L* P* / ρ* ReM = >> 1 Magnetic Reynolds number DM
χ, ν, DM, thermal, viscous and magne c diffusion coefficients
25 Crédit NASA
Jets from Young Stars
HST @ NASA Carina nebula
HST @ NASA Classical T Tauri Stars young: age < 10 Myr PROTOSTAR low mass: 0.1 < M* < 1 M¤ “cold”: Teff ~ 4000 K, Magne c Accre on field Topology disk • Star JET • Accre on disk -7 • Bipolar jets (Mejec~ 10 M¤/yr )
• Magne c field connec ng the star to the disk ( ~ 1 kG) • Accre on flows from the disk to the -8 star (Macc~ 10 M¤/an) Accre on columns Accre on & ejec on have an impact on the stellar evolu on and need to be well characterized Stellar jets
Propaga on A er launching, the jets are propaga ng almost hydrodynamically. Knots are associated to shocks (intrinsic variability, interac on with ISM..)
Typical condi ons :
vjet = 100 – 500 km/s,
0.32 light years ~ 20000 AU Mach number =vjet / csound >> 1 Length 1017 cm, radius 1015 cm, Density contrast ( jet/ISM) > 1
Launching HH 111 Linked to the effect of the disk rota on and the magne c field which is anchored in it Stellar jets Lebedev et al 2002
Hydrodynamical Propaga on
Several experiments, with lasers and Z pinches showing in par cular
• The effect of radia ve cooling on the collima on (Lebedev et al. ApJ 2002 at MAGPIE)
• The interac on with an ambiant medium (bow shock, see for instance Nicolai et al. APSS 2009 at PALS)
Nicolai et al APSS. 2009 Stellar jets
Launching scenario (Blandford et al. MNRAS, 1992)
Poloidal magne c field anchored in the rota ng disc. The ma er is magneto centrifugally accelerated into a wide angle conical wind; The magne c field lines become twisted and the toroidal component of B leads to self collima on.
Experiments : Need of a magne c field -> Z pinches
0.32 light years ~ 20000 AU (Lebedev et al. MNRAS 2005, A. Ciardi et al, PoP 2007, Suzuki-Vidal et al. APSS 2009) 298ns
However, this launching scenario is insufficient to explain collima on of the flow into a narrow jet-like
HH 111 form.
=> Experiments inves ga ng the poloidal collima on, (Albertazzi et al. Science 2014, Pisarczuk Phys. Scripta 1994 ) Albertazzi et al., Science 2014 A poloidal collima on of stellar jets Pulsed a er the launching phase ? (1/2) coils • Plas c target • Laser ( ELFIE @ LULI ) 0.5 ns, B 100 J, 1053 nm, 1012 W/cm2 ELFIE • Pulsed B : 0.2 MG, dura on 5 µs CH Diagnos cs : visible interferometry v ~ 100 km/s
1017 cm2
Simula ons -> T ~70 eV at the Ne dl ∫ posi on of the -2 Convergence of the Integrated Ne (cm ) at oblique shock plasma, oblique shock 20 ns at ~3 mm Albertazzi et al., Science 2014 A poloidal collima on of stellar jets a er the launching phase ? (2/2)
3D simulation of jet collimation in a young star system in a 5 mG axial magnetic field .
An isotropic wind of H from the combined star–disk system with a mass ejection rate of 10−8 M☉/year and velocity 200 km/s is embedded in an initially axial (z) magnetic field
X ray emission map Ideal MHD Approximate similarity Labo astro Dim. less numbers Labo Astro 15 r (cm) 1 10 Euler 1 - 8 10 – 22 ρ (g/cm3) 5 10-4 5 10-18 => 20 ns Alfven, Reynolds >>1 >>1 correspond B( Gauss) 2 105 10-2 Peclet >>1 >>1 to 6 yrs
Vjet (km/s) ~ 100 100-500 Albertazzi , PHD mansucript 2014
Conclusion : a « small » longitudinal field of few mG allow to collimate the flow. This also explains the observed sta c X ray emission spot near the star (Güdel et al. AA 2010) From magnetospheric From Long et accre on in young al. 2011 stars to radia ve shock waves From Long et al. 2011
From Orlando et al. 2013 Accre on to the star From Romanova The scenario • Ma er channeled by B (500 -1000G) from the disk to the photosphere -> magnetospheric columns • Free fall velocity (200 -500 km/s) • Impact the atmosphere -> strong shock at ~1 MK
Accre on B stream
Corona Only indirect observa onnal signatures : 300-500 km/s n < 1010 cm-3 • X rays (shock at the atmosphere, Ardiroffi et al 2007) 107 K • Lines shi ed by Doppler (column, Ardila et al 2013) • Brillant spots (atmosphere, Dona et al 2010)
1 - 5 106K
Hot slab X rays
1010-1015 cm-3 Global simula ons (1/2)
B= 50 G B= 500 G 6 12 T in log scale 10 4 U= 500 km/s 8
cm) cm) 9 9 2 6
z(10 z(10 4
0 2
0 0 2 4 6 8 10 r(109cm) 0 2 4 6 8 10 r(109cm) Orlando et al,A&A 2014 Global simula ons of the column in its surrounding show that the magne c field strength and topology play a drama c role.
Open ques ons 1) Accretion rate deduced from X ray: too low ( not enough X rays! ) 2) Quasi Periodic Oscillations seen in the simulations but not observed.
chromosphere 35
RADIATION ON
Te up to 30 eV, equal Temperature before and after the front Global simula ons (2/2)
Accre on shocks , with T ~ 1 MK, are strongly radia ve
• Standard simula ons assume that the shock is op cally thin to radia on
• Differences in the shock dynamics and structure when radia on is included in the simula on. Radia on trapping may even suppress the oscilla ons (de Sa, PHD thesis 2014)
Need of 1) Radia ve hydrodynamics simula ons 2) a good knowledge of radia ve shocks Radia ve shocks Radia ve shocks in short
Strong shocks (M>>1), Thin – Thin regime which are structured by radia on T Op cally thin hν D Radia ve T cooling
hν hν
Thick – Thick regime
Post shock Pre-shock T Pre-shock hea ng hν Op cally thick Strong Absorp on 2 Tshock ~ Dshock Radia ve precursor 38 Two radia ve regimes Michaut & al. Astrophys. Space Sci. 322, 2009 1. The flux-dominated regime : The radia on flux - Frad - is non-negligible, compared with the flux of material energy : Frad > (Pth + ρε)D This is regime the most common regime, as it is accessible with kJ class lasers ( LULI, OMEGA, PALS), In Xenon, v < 150 km/s
2. The pressure dominated regime :
At very high T, the radia on pressure - Prad - (which is a factor 1/c smaller than the radia on flux), may exceed the material pressure Prad > Pth
Few experiments, were v > 200 km/s, are trying to reach this regime (Diziere et al APSS 2011 at GEKKO).
11ns front front
Shocked gas precursor
cold Te up to 30 eV, equal Temperature before and after the front
11ns
Shock front : large compression (~ 30 ) : caused by shock, ionisation & radiation
40 Calculations using MULTI 1D (Ramis et al. 1988) How to produce them ?
Similar to EOS experiments, but in low Pusher density gases ablator • Gases at low pressure ( < 1 bar), ρ ~ 10-2 - 10-3 g/cm3 2 High atomic weight, Tshock ~ 3 m D /(16 k) Reighard et al. ‘06
• ~ 1 ns laser, usually the visible • 1014 W/cm2 on the target (-> 50-150 km/s) • Piston with abla ng material 2 Pistons 4 mm long on a shield channel Difficul es . • Target manufacturing: piston, windows, control of gas leakage • If 1D, uniformity of the laser • Dense post shock (opaque to visible) Rad shock target for counter-propaga ng rad shock waves at PALS (Credit Stehlé) Some results 2002 @ LULI ( ~ 60 km/s) visible me resolved interferometry -> precursor : • Shock velocity • 2D effects in the precursor : In a similar regime at PALS : radia on losses at the windows Gonzalez et al. LPB 2006 reduce the velocity of the precursor Stehlé et al. LPB 2010 (Fleury et al, LPB 2002, Bouquet et al PRL 2005)….
2009 @ Rochester ( ~150 km/s)
point source X ray imaging -> shock front In a similar regime at OMEGA • Radia on from the front ablates the Reighard et al. PoP 2006, 2007 Drake et al. HEDP 2010 , 2011 tube walls (wall shock) Doss et al, HEDP 2010 • Perturba ons near the front shock. Visco et al. , PRL 2012 (Doss et al. 2009)
2012 and 2014 @ PALS ( ~ 50 km/s) XRL radiography @ 21 nm -> shock, post shock , precursor • Structures in the precursor -> need of good opaci es • possible instabili es in the post shock (Stehlé et al. Op cs Comm. 2012, Chaulagain et al HEDP 2014) A test case for simula ons
Van der Holst, HEDP 2013 (V= 150 km/s) Cotelo et al, HEDP 2014 (V= 48 km/s) comparison to Doss et al. 2009 at OMEGA comparison to Chaulagain et al. 2014 at PALS 0 700 um
Material
Te(keV) Te(eV)
AMR CRASH-2D (radia on diffusion) AMR ARWEN-2D (Discrete-ordinate radia on 1bar, 3500 J at 0.35 um; t= 13 ns transport method ) Material and AMR levels : Xenon (black), Be ( blue) , polyimide (green) … 0.3 bar, 60 J at 1.315 um; t= 13 ns Te(keV) in logarithmic scale Material: Au (orange), CH (dark blue), Xe (blue) Te(eV) in linear scale
Gonzalez et al., A&A 2009 (V= 60 km/s) comparison to Gonzalez et al. LPB 2006, at PALS HERACLES-2D Eulerian, M1 model 0.2 bar, 200 J at 0.438 um; t= 50 ns, 40% reflec vity at the walls Te(eV) in linear scale, Xenon only.
43 Conclusions A lot of applica ons to astrophysics
• Star forma on (jets, accre on shocks), • stellar interiors ( EOS and opacity) , • planetary interiors ( EOS)
But also Review paper : • ISM (ionisa on fronts and instabili es), Remington et al. Rev. • Supernovae explosions and remnants ( nstabili es), Mod. Phys. 2006 • Compact objects( accre on on cataclysmic variables ), • Sun atmospheres (magne c reconnec on) ,
Topic mostly driven by ns high energy lasers
For high intensity lasers, open field of research : • Collision less shocks, Review paper : • High energy par cle beams interac on with plasmas, Ersikepov et al. EAS, 2012 • Genera on of ultra high magne c fields ( > 1 Ggauss), • Ultra fast (rela vis c) shock waves, etc.