galaxy formation with sphs: a novel mode of positive feedback...galaxy formation with sphs - cooling...

Galaxy formation with SPHS: a novel mode of positive feedback

Alexander HobbsETH Zürich

w. Justin Read (Uni. Surrey), Chris Power (UWA), Andrina Nicola (ETH Zürich)

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So what is SPHS?

SPHS - Smoothed Particle Hydrodynamics with a higher order dissipation Switch(Read & Hayfield 2012)

Friday, 12 July 13

So what is SPHS?

SPHS - Smoothed Particle Hydrodynamics with a higher order dissipation Switch(Read & Hayfield 2012)

‘Classic’ SPHcf. Springel (2005)

Ritchie & Thomas 2001Price 2008Wadsley et al. 2008Cullen & Dehnen 2010Hopkins 2012Kawata et al. 2013a“Anarchy”

Other flavours:

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Smoothed particle hydrodynamics (SPH)

- Solves equations of hydrodynamics on interpolation points that move with the flow - ‘particles’

- Advantages include:1. Lagrangian

2. Galilean invariant

3. Manifestly conservative

4. Easy to implement

5. Couples well to N-body approach

j

i- Variable smoothing lengths

refine resolution on density

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...is great

Figure credit: J. Shaye, OWLS project

Figure credit: D. Price, Monash Uni

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...but there are problems to fix

1. Force error in momentum equation

2. Multi-valued fluid quantities preventing mixing of phases

3. Overly viscous

4. Noisy

−40 −20 0 20 4020

4060

80100

x

y

Kelvin-Helmholtz instability:

Figure credit: Read et al. 2010b

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12 Oscar Agertz et al.

Figure 9. Each frame shows a density slice through the cloud center at times t = 0.5, 1.0 and 1.5 τKH with densities varying from low(blue) to high (red). The grid (Enzo) simulation (left) shows instabilities developing on the surface causing the cloud to fragment, whilethese features are absent in the SPH (Gasoline) simulation (middle and right).

Figure 10. Evolution of the cloud with ‘analytic’ initial conditions using the CHARM code. Each frame shows a density slice throughthe cloud center at times t = 0.24, 0.9, 1.7 and 2.5 τKH with densities varying from low (red) to high (blue).

hand side can create or diffuse vorticity. The first term is thebaroclinic term which is non vanishing if we have non-alignedpressure and density gradients. This is the case in obliqueshocks like in the bow shock of our cloud simulation. Thesecond term is responsible for diffusing vorticity in space i.e.taking local vorticity and spreading it into the general flow.This means that as soon as we have viscosity, we will dampenvorticity. Especially important is the vorticity generated inthe post shock flow, which should act to destabilize the cloudtogether with the surface instabilities.

A study on how AV dampens small scale vorticity wasmade by Dolag et al. (2005). By using a low viscosity formu-lation of SPH they find higher levels of turbulent gas motionsin the ICM and noted that shocked clouds tend to be unsta-ble at earlier times. However, by looking at their Figure 3we note that the overall difference in the cloud evolution issmall. As we will see in the tests carried out below, loweringthe AV does not necessarily lead to improved results.

In order to understand the effect of artificial viscosityin our cloud-wind test we have performed three simulationswith modified setting of the viscosity coefficients. These areGas 10mAV1, Gas 10mAV2 and Gas 10AV3, see Table 1for viscosity values. A simulation using the Balsara switchbut with the standard (α = 1.0, β = 2.0) was also per-

formed. Fig. 11 shows the outcome of the simulations att = 0.25, 0.75, 1.5 and 2.25 τKH. We can directly see the im-pact these terms have on the stability of the simulation.The standard α = 1.0, β = 2.0 is the most stable one, mostprobably due to the unphysical use of the α bulk viscos-ity. The use of α = 0 and β = 2.0 or the Balsara switchrenders very similar visual results. This is because the Bal-sara switch turns of viscosity where |∇·v|/(|∇·v+|∇×v|) issignificant, which is the case for shearing flows like on thesurface of the cloud. Note that this is a very noisy quantitywhen measured using only 32 neighbours. By further lower-ing the shock capturing β viscosity we make the cloud evenmore unstable but it is not clear how physical this solutionis. The shock front gets more blurred and we see strong postshock ringing effects. The reason for the increased instabil-ity in the α = 0, β = 0.5, and α = 0, β = 0.1 case is mostprobably due to high speed particles traveling through thepoorly captured shock region and transferring momentuminside the cloud, perturbing it in an unphysical way.

We have performed simulations similar in spirit to theSPH ones using Enzo-ZEUS. There is formally no need forlinear viscosity using this method except for hyper-sonicflows, but it is interesting to study the effect of loweringQAV in the same way as β. Fig 12 shows density slices from

c© 0000 RAS, MNRAS 000, 000–000

A 1:10 density ratio gas sphere in a wind tunnel (Mach 2.7), initially in pressure eq.

The “blob test”

Agertz et al. 2007Friday, 12 July 13


Force error in momentum equation

Multi-valued fluid quantities preventing mixing of phases

Overly viscous

Noisy

were

1.

2.

3.

4.

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Multi-valued fluid quantities preventing mixing of phases

Overly viscous

Noisy

were

1.

2.

3.

4.

Error reduced w. 442 neighbours + stable high-order HOCT kernel

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Overly viscous

Noisy

were

1.

2.

3.

4.


Multi-valued pressures eliminated using advance warning high order switch and conservative dissipation

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Noisy

were

1.

2.

3.

4.


Multi-valued pressures eliminated using advance warning high order switch and conservative dissipationSame high order switch gives lower viscosity away from shocks

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...but there are problems to fixwere

1.

2.

3.

4.


Multi-valued pressures eliminated using advance warning high order switch and conservative dissipationSame high order switch gives lower viscosity away from shocks

Larger neighbour number + high-order HOCT kernel gives lower noise

+ Saitoh & Makino (2008) timestep limiter

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0 20 40 60 80 100

0.8

0.9

1.0

1.1

1.2

1.3

y

PP 0

SPH-HOCT442

Multivalued pressures - the problem

Read, Hayfield & Agertz 2010 (RHA10); Read & Hayfield 2012Friday, 12 July 13

P

A1,m1,v1...A2,m2,v2...

Read, Hayfield & Agertz 2010 (RHA10); Read & Hayfield 2012; Ritchie & Thomas 2001; Price 2008; Wadsley et al. 2008; Cullen & Dehnen 2010

Multivalued fluid quantities - the need for dissipation

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`

Read & Hayfield 2012

SPHS tests - Sedov-Taylor blast wave

SPHS-442

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Read & Hayfield 2012Friday, 12 July 13

`


SPHS tests - KH instability 1:8 density contrast

SPHS-442

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`

SPHS tests - Blob test

SPHS-442

Read & Hayfield 2012Friday, 12 July 13

Power, Read & Hobbs 2013 - http://arxiv.org/abs/1307.0668

SPHS science tests - Santa Barbara test

x8

SPH-32 SPHS-442

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SPH-32 SPHS-442

x128

Power, Read & Hobbs 2013 - http://arxiv.org/abs/1307.0668Friday, 12 July 13

http://arxiv.org/abs/1307.0668http://arxiv.org/abs/1307.0668


Power, Read & Hobbs 2013 - http://arxiv.org/abs/1307.0668Friday, 12 July 13



Power, Read & Hobbs 2013 - http://arxiv.org/abs/1307.0668

see also Wadsley (2008)

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...and finally...

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Galaxy formation with SPHS

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- Cooling hot gaseous halo (e.g., Kaufmann et al. 2006, 2007, 2009) forming MW

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- Cooling hot gaseous halo (e.g., Kaufmann et al. 2006, 2007, 2009) forming MW - Late (smooth) accretion mode corresponding to main disk formation phase

(Abadi et al. 2003, Sommer-Larsen et al. 2003, Governato et al. 2004)


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rs = 40 kpcrt = 200 kpc

Mhalo ≈ 1.9 x 1012 MsunMgas ≈ 1.9 x 1011 Msun

Dehnen & McLaughlin (2005)

Mastropietro et al. (2005), Kaufmann et al. (2007)

- Late (smooth) accretion mode corresponding to main disk formation phase(Abadi et al. 2003, Sommer-Larsen et al. 2003, Governato et al. 2004)

λ = 0.038jgas ∝ r1.0

Peebles 1969, Bullock et al. 2001b


- Cooling hot gaseous halo (e.g., Kaufmann et al. 2006, 2007, 2009) forming MW

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Simulation

100

T(K)

ρ

Stars form on polytrope

above a fixed density threshold

ICs relaxed with adiabatic EQS to eliminate Poisson noise

- Tfloor = 100 K

Radiative cooling

- Ensure Jeans mass resolved with Mres = Nres msph

- Mgas ≈ 4 x 104 Msun

- Using HOCT442 kernel (reduces particle noise)

- Mres ≈ 5 x 106 Msun 100 atoms cm3

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SPHS SPH

Hobbs, Read, Power & Cole 2013; http://arxiv.org/abs/1207.3814Friday, 12 July 13


-1.0 -0.5 0.0 0.5 1.0Jz/Jc

0

200

400

600

800

1000

Nstars

-1.0 -0.5 0.0 0.5 1.0Jz/Jc

0

200

400

600

800

1000

Ngas

Stars Gas

SPH

SPHS

SPHS

SPH

Hobbs, Read, Power & Cole 2013; http://arxiv.org/abs/1207.3814Friday, 12 July 13


0.8 Gyr

SPHS-442 | 5M

Hobbs, Read, Power & Cole 2013; http://arxiv.org/abs/1207.3814

80 kpc

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Hobbs, Read, Power & Cole 2013; http://arxiv.org/abs/1207.3814

Filaments Disc

SNe ejecta

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2.2

1.1

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1.1

2.2

rb

xr2

r1

MW

θ1 φ

φ

x

v

vθ2

R R

∴

∴ 1.1

Gas condensing

N

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Hobbs, Read & Nicola, in prep.

SPHS-96 | 1M rfinal < 1.0 1.0 < rfinal < 2.0 2.0 < rfinal < 5.0 5.0 < rfinal < 10.0

80 kpc

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In conclusion, we have shown that SPHS:

Presents a practical method that is not subject toprohibitive numerical cost (Hobbs et al. 2013)

Corrects for fundamental limitations in ‘classic’ SPHrelating to mixing of multiple phases within the fluid (Agertz et al. 2007)

-

-

Forms an entropy core in the SB test (Power, Read & Hobbs 2013)(puts to rest AMR vs. SPH controversy for this problem)

-

Eliminates spurious cold clumps in SPH simulations and paves the way toward a new mode of disc feeding (Hobbs et al. 2013)

-

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SNe-driven fragmenting filament

- Qualitatively similar to break-up of ‘cold-mode’cosmological streams (Keres et al. 2009, Keres & Hernquist 2009)

- Overdensity allows for non-linear mode of collapse- Different progenitors (SNe vs. large-scale cosmological flows)- Different scales (50 kpc --> galaxy vs. > 200 kpc --> 40 kpc)- Different temperatures (104 K vs 105 K)

- Form of positive feedback whereby SNe give rise to cold gasflows that feed the disc and fuel further star formation

- Filaments can have preferentially low angular momentumand are efficient at bringing gas from 50 kpc 1 kpc in tff

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What’s next?

- Inclusion of metals (metal line cooling, metal diffusion)

- Cosmological setting

- SMBH feeding

- may alter condensation of filaments from ambient gas- can determine if feeding mode provides a source of pristine gas

- more realistic ICs- self-consistent phase of disc growth

- does this feeding mode occur on smaller scales?

- Cast as a sub-grid model?

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Thank you

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galaxy formation with sphs: a novel mode of positive feedback...galaxy formation with sphs - cooling...

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