Cooling-induced structure formation in collapsars
Aldo Batta
Advisor: William Henry Lee Alardín
Instituto de Astronomía UNAM
Kyoto, Japan 2013

Aldo Batta (IA UNAM)

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Kyoto, Japan 2013

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1

GRB variabilities
GRBs & variability
Variability in Collapsars

2

Variability from cooling-induced structure formation
Accretion flow evolution
Structure formation events

3

What we’ve learned so far

4Work in Progress and Future Work

Aldo Batta (IA UNAM)

Cooling-induced Structures in the Collapsar

Kyoto, Japan 20132 / 22GRBs & Variability
Most GRBs contain flares or flickers with intense variations in flux on a time scale of a few
milliseconds, much shorter than the duration of the burst (Walker et al., 2000; McBreen et al., 2001;
Nakar & Piran, 2002).

• Central engine region must be smaller
than ∼ 1200 km• Correlation between variability &luminosity of the bursts (Fenimore &Ramirez-Ruiz, 2000)• There are relatively long quiescentperiods of several seconds with noactivity (Ramirez-Ruiz and Merloni, 2001).

• Variability is likely due to a
combination of several physicalprocesses.
Fig. 1 The light curve of GRB 920627. The total duration of the burst is 52
sec, while typical pulses are 0.8 sec wide. Two quiescent periods lasting ∼10s are marked by horizontal solid bold lines (Piran 2004).
Aldo Batta (IA UNAM)

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Kyoto, Japan 20133 / 22GRBs & Variability
If the GRB is powered by hypercritical accretion onto compact objects, the flow will exhibit
fluctuations on small spatial scales, which could in turn be reflected in the power output of thecentral engine and ultimately in the high-energy prompt emission.

Fig. 2 Fireball model explaining a GRB from the combination of aninternal shock wave and an external shock wave occurring at different
places.
Aldo Batta (IA UNAM)

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4 / 22GRBs & Variability
If the GRB is powered by hypercritical accretion onto compact objects, the flow will exhibit
fluctuations on small spatial scales, which could in turn be reflected in the power output of thecentral engine and ultimately in the high-energy prompt emission.

Variability sources (NS disruption)• Hydrodynamical or magnetic instabilities
in the accretion disk.
(Perna et al. 2006; Proga & Zhang 2006; Taylor et al. 2010;
Carballido & Lee 2011; Batta & Lee 2013)• Fall back at late times of material strippedfrom a tidally disrupted neutron star(Rosswog 2007; Lee et al. 2009)• Internal shocks between shells in the flow.
(Panaitescu et al. 1999; Ramirez-Ruiz et al. 2001; Bosnjak et
al. 2009; Mendoza et al. 2009)
Fig. 2 Fireball model explaining a GRB from the combination of aninternal shock wave and an external shock wave occurring at different
places.
Aldo Batta (IA UNAM)

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If the GRB is powered by hypercritical accretion onto compact objects, the flow will exhibit
fluctuations on small spatial scales, which could in turn be reflected in the power output of thecentral engine and ultimately in the high-energy prompt emission.

Variability sources (massive star)• Hydrodynamical or magnetic instabilities
in the accretion disk.
(Perna et al. 2006; Proga & Zhang 2006; Taylor et al. 2010;
Carballido & Lee 2011; Batta & Lee 2013)• Internal shocks between shells in the flow.
(Panaitescu et al. 1999; Ramirez-Ruiz et al. 2001; Bosnjak et
al. 2009; Mendoza et al. 2009)• Progenitor properties (Kumar et al. 2008; Perna &MacFadyen 2010; Lopez-Camara et al. 2010, Lindner et al.,2010)

• Interaction of relativistic jet with stellar
envelope before breakout. (Aloy et al., 2000;
Fig. 2 Fireball model explaining a GRB from the combination of aninternal shock wave and an external shock wave occurring at different
places.
Aldo Batta (IA UNAM)

Morsony, 2010)

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Variability in Collapsars
Internal shocks

Collision between shocks• Faster shells collide with slower ones andproduce the observed γ rays. (Rees &Meszaros,1994; Sari & Piran 1997)• Variability time scales depends on theshell thickness as δt ∼ L/c (Sari, 1999)• The observed variability time scale δt,reflects the variability of the source L/c,
while the overall duration of the burst
reflects the overall duration of the activityof the “inner engine” (Piran, 2004)

Aldo Batta (IA UNAM)

Fig. 3 Internal shock model from Sari (1999). Faster shells collidewith slower ones and produce the observed γ rays. The variability
time scale is L/c and the duration of the burst is ∆/c.

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Variability in Collapsars
Relativistic Jet interactions
Jet & stellar envelope interaction(Morsony et al., 2010) 2D relativistic axisymmetric simulations in FLASH• Variability properties of the jet outside thestar are a combination of the variability
injected at the base of the jet and thevariability caused by the jet propagation
through the star.

• Variability injected by the engine ispreserved even if the jet is heavily shocked
inside the star.

• Even if the central engine releases a
constant luminosity, the power curveshows marked variability as a result of theinteraction between the jet and theprogenitor star.

Aldo Batta (IA UNAM)

Fig. 4 Light power curve of the uniform (red) and a variable energy
simulation (blue). Variations are present even for the uniform energy
input and at later times (& 5 s) the light curve and the variableenergy input are strongly correlated (Morsony et al., 2010).

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Variability in Collapsars
Progenitor Properties

Angular Momentum distribution• J(R) determines the duration of the initial
jet energy, and subsequent accretion ofouter layers via ADAF’s induce luminosity
decrease. (Kumar et al. 2008)• J(R) (and MBH ) determines if it’s possible toproduce temporal transitions between a QRI
and a centrifugally supported disk. (Lopez-Camara
et al. 2010)

Fig. 5 Neutrino Luminosity for simulations with J(R) = Jo + m(R/Rs ) for m = 1, 2, 3 (top) and For a simulation with two shells of lenght
δR with J > Jmin separated by a low angular momentum region (J < Jmin ) of lenght ∼ 2δR (López-Cámara et al. 2010).

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Variability in Collapsars
Progenitor Properties
Angular Momentum distribution• Transitions from J(R) < Jmin to
J(R) > Jmin (and viceversa) can induce
variations in the accretion flow andtherefore, the energy output.

• Such transitions could be obtained inprogenitors with unmixed layers, which
are able to produce quiescent periods
where Lν descends by one order ofmagnitude.

• Only models with tdiskI > tcross arepotentially observable to have a quiescentperiod.

• Duration of quiescent periods depends onthe mass contained on the shells (I,II &III)

Aldo Batta (IA UNAM)

Fig. 6 Specific angular momentum J(R) for model 16TI of Woosley& Heger (2006). Models with unmixed layers could have regionswith J > Jmin (region I) followed by regions of QRI with J < Jmin
(region II) and another region with J > Jmin (region III). At theedge of the CO shell, J > Jmin and a rise in L is attained(López-Cámara et al., 2010).

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Variability in Collapsars
Progenitor Properties

Angular momentum & mixing• Restrictions on the progenitors fromflaring activities. (Perna & MacFadyen, 2010)• Flaring activity has not been observed in alarge fraction of well monitored long
GRBs.

• The lack of flares indicates that themassive stars which produce GRBs aremostly well mixed, as expected in
low-metallicity, rapidly rotating massive
stars.

Aldo Batta (IA UNAM)

Fig. 6 Specific angular momentum J(R) for model 16TI of Woosley& Heger (2006). Models with unmixed layers could have regionswith J > Jmin (region I) followed by regions of QRI with J < Jmin
(region II) and another region with J > Jmin (region III). At theedge of the CO shell, J > Jmin and a rise in L is attained(López-Cámara et al., 2010).

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Variability in Collapsars
Hidrodynamical or magnetic instabilities in the accretion disk

• Energy release can be repeatedly stopped
and then restarted by the magnetic flux
accumulated around the accretor. (Proga &Zhang, 2006)• Episodes when the accretion resumes
correspond to X-ray flares discovered in a
number of GRBs.

• Variability due to turbulent motions

Fig. 7 General structural features of the inner MHD flow at three different

induced by the MRI. The dissipation isaccretion stages (Proga & Zhang, 2006). Left panel shows hyper-accretion
when forming a poloidal jet and a raising B intensity. Center panel shows
related to the local hydrodynamical
hyper-accretion ended due to the intense B. Right panel shows when thevariables, and as these vary in time, so will surface density of the flow becomes high enough to squash the magnetic
field and restart intense accretion.
the energy output. (Carballido & Lee, 2011)

Aldo Batta (IA UNAM)

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Variability in Collapsars
Hidrodynamical or magnetic instabilities in the accretion disk

• Disk fragmentation at large radii →disruption of fragments could produce
shorter flares separated by relatively longer
interval between flares. (Perna et al., 2006)

Fig. 8 Gravitational instabilities developed at the outer parts of the disk can
induce later accretion events when a clump gets close enough to the BH for
disruption (Batta & Lee 2013).

Aldo Batta (IA UNAM)

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Kyoto, Japan 20138 / 22

Variability in Collapsars
Hidrodynamical or magnetic instabilities in the accretion disk

• Gravitational instabilities due to neutrino
cooling allow spiral structure and clumps
to form at the accretion disk. ( Taylor et al. 2010;
Batta & Lee 2013)• Cooling efficiency determines whether
gravitational instabilities develop.

• Neutrino cooling efficiency is determinedby the rotation rate of the progenitor.
(Lopez-Cámara et al. 2009)

Fig. 9 Density at the equatorial plane for times at 0.8 s (left) and 1.3 s (right) for simulations of Taylor et al. (2010) (top) and Batta et al.
(2013) (bottom). Spiral structure forms at earlier times at the accretion disk, and gas clumps form after substantial cooling has taken place.
Formation of structure depends on the efficiency of the cooling mechanism (i.e. the rotation rate in neutrino cooling).

Aldo Batta (IA UNAM)

Cooling-induced Structures in the Collapsar

Kyoto, Japan 20138 / 22Our goals• 3D hydrodynamical simulations (SPH) to study effects of self gravity and cooling on theevolution of the accretion flow in a collapsar scenario.

• What’s the effect of structure formation in the accretion flow evolution?
⇒ the effect on the engine’s energy output.

Aldo Batta (IA UNAM)

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Physical setup
Towards a Collapsar scenario
3D SPH simulation to study effects of self gravity and cooling on the morphology and evolutionof the accretion flow in a collapsar accretion disk
4.5M Polytropic stars, whose 2M innermost mass is collapsed into a BH

• BH cannot move
• Rigid body rotation (below breakup)& modified BH potential.

• Modified version of GADGET-2
code (Springel 2005) based on SPH.

Fig. 10 Density at the XY plane for the 4.5M polytropic star with its
innnermost 2M turned into a BH.
Aldo Batta (IA UNAM)

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Physical setup
Towards a Collapsar scenario
PW potential & Angular Momentum Distribution
Paczynski-Wiita (PW) potential that reproduces
the position of the innermost stable circular orbit
Risco = 3rg = 6GMBH /c2Φ=−GMr − rgMinimum angular momentum of the envelope isdetermined by the innermost stable circular orbit(ISCO) Risco = 3rg = 6GMBH /c2 and gas velocity∼cFig. 11 Keplerian angular momentum distribution for a test
particle in a Newtonian (red line), a Paczynski-Wiita (greenline) and a Schwarzschild BH potential (blue line).

Aldo Batta (IA UNAM)

Jmin = Risco c
6GMAN∼ 1016 (M/M ) cm2 s−1=c
J > Jmin (but below breakup)
Material at r ≤ 3rg is considered accreted

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Physical setup
Towards a Collapsar scenario
β Cooling
The Neutrino Cooling time-scale
Temperatures and densities estimated near theBH can reach: ρ ' 1011 g cm−3 , T ' 1011 K

Gas orbits the BH ∼ β times before cooling down.

tcool = βtdisk

→

du
u
=−
dt
tcool

Estimate tν → for T and ρ expected.
non-degenerate relativistic e± , and ionized H
ideal gas cooled by e− capture and pairannihilation.
Neutrino Cooling Timescale
u=

3 kTρ
11
+ aT 42 µmp
496qν ' 5 × 1033 T11+ 9.0 × 1023 ρT11tν = u/qν
Fig. 12 Neutrino Cooling timescale obtained from assuming an
ideal gas, radiation pressure and non-degenerate relativistic
electrons and positrons.
Aldo Batta (IA UNAM)

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Accretion flow evolution
Models with increasing cooling efficiency show more, and more intense events, where Lc
increases significantly.

Lc =

X dui
i

dt

=−

1 X
tcool

ui

i

• Intense variations in Lc imply an important
increase in ui (compressions or shock).

• Increase in ui may be due to structureformation.

Fig. 13 Logarithm of the energy loss rate Lc (bottom panel) in erg/s for models β2.6 (blue line), β1.3 (pink line), β0.67 (black line) and
β0.132 (orange line). Shaded regions show episodes when both Lc and dMBH /dt show an intense increase.
Aldo Batta (IA UNAM)

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Accretion flow evolution
Intense variations in Lc and Ṁ coincide in time ⇒ structure formation is increasing accretion(or vice versa).

Fig. 13 Logarithm of the energy loss rate Lc (bottom panel) in erg/s for models β2.6 (blue line), β1.3 (pink line), β0.67 (black line) and
β0.132 (orange line). Shaded regions show episodes when both Lc and dMBH /dt show an intense increase.
Aldo Batta (IA UNAM)

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Accretion flow evolution

Fig. 13 Logarithm of the energy loss rate Lc (bottom panel) in erg/s for models β2.6 (blue line), β1.3 (pink line), β0.67 (black line) and
β0.132 (orange line). Shaded regions show episodes when both Lc and dMBH /dt show an intense increase.

Aldo Batta (IA UNAM)

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Ṁ, Lc & Pr Characteristic Frequencies

Fig. 14 Logarithm of the renormalized Fourier’s transform power |F(ν)|2 of the mass accretion rate Ṁ (blue line), the energy loss rate Lc(red line) and the cylindrical radial component of momentum Pr (black line) versus inverse frequency 1/ν (time), for the adiabatic case, andmodels β13.4, β2.68 and β1.34 (we only show the transform of Lc for cooled models). The spectrum of the mass accretion rate Ṁ shows
power at intrinsic time scales of t ' 0.2 and 0.05 s that also appear in the spectrum of Lc . Increasing the cooling efficiency alters the position
and intensity of the peaks time scales and in model β1.34 an additional peak is present at t ' 0.02 s.

Aldo Batta (IA UNAM)

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Ṁ, Lc & Pr Characteristic Frequencies

Fig. 15 Logarithm of the renormalized Fourier’s transform power |F(ν)|2 of the mass accretion rate Ṁ (blue line), the energy loss rate Lc(red line) and the cylindrical radial component of momentum Pr (black line) versus 1/ν (time), for models β0.67, β0.134, β0.067 and theisothermal case. More efficient cooling seems to increase the number of intense peaks appearing also at shorter time scales (higher
frequencies).

Aldo Batta (IA UNAM)

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Kyoto, Japan 201315 / 22β0.67 Model, tcool = 0.061 s
Animation with SPLASH Price (2007)

Aldo Batta (IA UNAM)

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Kyoto, Japan 201316 / 22β0.134 Model, tcool = 0.0123 s
Animation with SPLASH Price (2007)

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Characterizing structure formation events
Study the evolution of non-axisymmetric Fourier transform (FT) on theR Rinstabilities →azimuthal distribution of mass ΦM =ρ(φ, r, z)dz r dr as in (Zurek & Benz, 1986), by
defining the amplitude of the m mode by:
Z 2π
1
Cm =
eimφ ΦM dφ
2π 0
Relative power |cm |2 = |Cm |2 /|C0 |2 indicates the intensity of m spiral arms compared to thedisk integrated mass. Which should be visible on density maps.
Check for unstable regions at the disk → Toomre parameter
QT =

κcs
πGΣ

where κ = (∂W/∂r)1/2 is the epicyclic frequency obtained from first order perturbations in
the disk material subject to the effective potential W(r) = φ(r) + l2 /2r2 , Σ(r, φ) is thesuperficial density of the disk and cs is the local sound speed.

Aldo Batta (IA UNAM)

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201318 / 22β1.3 Model, tcool = 0.123 s• The relative power |c2 |2 has the mostintense peak at t ' 0.85 s where intense
variations on Ṁ and Lc become
noticeable.

• Increasing cooling efficiency → earlier
structure formation

Fig. 16 Relative power |cm |2 (m = 1, 2, 3, 4) for theazimuthal distribution of mass ΦM Fourier transform of
β1.3 model. At t ' 8 s there’s an ongoing increase in modem = 2 reaching a maximum at t ' 0.9 s.
Aldo Batta (IA UNAM)

Fig. 17 Mass accretion and energy loss rates for β1.3 model.
(Top and bottom panel respectively).

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201319 / 22β1.3 Model, tcool = 0.123 sFig. 16 Relative power |cm |2 (m = 1, 2, 3, 4) for theazimuthal distribution of mass ΦM Fourier transform of
β1.3 model. At t ' 8 s there’s an ongoing increase in modem = 2 reaching a maximum at t ' 0.9 s.
Aldo Batta (IA UNAM)

Fig. 18 Evolution of the Toomre parameter Q for the β1.3
model at times ' 0.8 s. There are two distinguishable spiral arm
with Q . 1 (∆t ' 0.023 s between snapshots).

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201319 / 22β1.3 Model, tcool = 0.123 sFig. 16 Relative power |cm |2 (m = 1, 2, 3, 4) for theazimuthal distribution of mass ΦM Fourier transform of
β1.3 model. At t ' 8 s there’s an ongoing increase in modem = 2 reaching a maximum at t ' 0.9 s.
Aldo Batta (IA UNAM)

Fig. 19 Evolution of the Toomre parameter Q for the β1.3
model at times ' 0.9 s. The spiral structure reaches Q < 0.1,
afterwards the spiral arm breaks into several arms.

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201319 / 22β0.67 Model, tcool = 0.061 s• The relative powers |cm |2 have an intense
peak at t ' 0.5 s.

• The number of intense variations on Ṁ
and Lc increases with cooling efficiency

Fig. 20 Relative power |cm |2 = |Cm |2 /|C0 |2(m = 1, 2, 3, 4) for the azimuthal distribution of mass ΦM
Fourier transform of β0.67 model. All modes show animportant increase at t ' 0.5 s.
Aldo Batta (IA UNAM)

Fig. 21 Mass accretion and energy loss rates for β0.67 model.
(Top and bottom panel respectively)

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201320 / 22β0.67 Model, tcool = 0.061 s

Fig. 20 Relative power |cm |2 = |Cm |2 /|C0 |2(m = 1, 2, 3, 4) for the azimuthal distribution of mass ΦM
Fourier transform of β0.67 model. All modes show animportant increase at t ' 0.5 s.
Aldo Batta (IA UNAM)

Fig. 22 Evolution of the Toomre parameter Q for the β0.67
model at times ' 0.5 s. Formation of structure is triggered atearly times but does not survive for too long. There are
noticeable spiral structures forming at the disk.

Cooling-induced Structures in the Collapsar

Kyoto, Japan 201320 / 22β0.67 Model, tcool = 0.061 s

Fig. 20 Relative power |cm |2 = |Cm |2 /|C0 |2(m = 1, 2, 3, 4) for the azimuthal distribution of mass ΦM
Fourier transform of β0.67 model. All modes show animportant increase at t ' 0.5 s.
Aldo Batta (IA UNAM)

Fig. 23 Evolution of the Toomre parameter Q for the β0.67
model at times ' 0.5 s. Formation of structure is triggered atearly times but does not survive for too long. There are
noticeable spiral structures forming at the disk.

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What we’ve learned so far• The spiral structure and gas clumps formed induce intense variations in both Ṁ and Lc ,but may also break the symmetry in the gravitational interaction between the disk and the
BH.

• Duration, intensity and characteristic timescales depend on the cooling efficiency, more
effective cooling ⇒ more frequent and intense variations.

• Time variations obtained from our collapsar engine, could explain & 10−3 s − 10−1 svariations imprinted on GRBs.

• The available power to drive a GRB is present in the system (how it eventually manages
to do so is a different matter).
Integrated energy losses obtained range from 1051 to 1054 erg for adiabatic to isothermal models ("neutrino" energy release). The
R
integrated accretion energy Eacc = Ṁc2 dt ranges from 1054 to 3 × 1054 erg.

• More details in:
Cooling-induced structure formation and evolution in collapsars,
A. Batta & W. Lee, 2013 (in arXiv, accepted in MNRAS)

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What if the BH is able to move?
• The BH moves a few km around the CM.
• When the first structure formation event occurs, there is an intense kick that changes
considerably the BH-CM distance.

Fig. 24 BH position relative to the center of mass on the XY plane (left panel), evolution of the distance between the BH and the center ofmass in the XY plane (right panel).

Aldo Batta (IA UNAM)

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What if the BH is able to move?
• The BH moves a few km around the CM.
• When the first structure formation event occurs, there is an intense kick that changes
considerably the BH-CM distance.

Fig. 25 Fourier transform of the BH position relative to the center of mass on the XY plane (left panel), and FFT of the disk’s radial
component of the lineal momentum Pr in the XY plane (right panel).

Aldo Batta (IA UNAM)

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