GammaRay Burst afterglow plateaus

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Gamma-Ray Burst afterglow plateaus
Gravitational Waves probing the millisecond
magnetar scenario
Alessandra Corsi Peter Mészáros
University of Rome Sapienza Penn State
University
GWDAW 13 San Juan - 2009, January 19-23
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Outline of the talk

• Standard GRB progenitor scenarios and
  expectations for the associated GW signals
• GRB afterglow plateaus and the magnetar
  progenitor scenario
• Evolution of the magnetars spin down under the
  effect of a secular bar-mode instability
• Associated afterglow plateau and corresponding GW
  signal

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Can we observe closer to the central engine?
Swift and other satellites, optical and radio
telescopes
1013 cm
1016 cm
4
GW-GRB searches the standard scenario
In-spiral last few minutes in the band
accessible to LIGO and Virgo Merger and
ring-down few ms duration (burst-type signals)
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GW emission from GRB progenitors standard
scenario
Advanced LIGO
Advanced LIGO
Kobayashi Meszaros 2003
Fryer et al. 1999, Belczynski et al. 2002
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Are there other plausible progenitor scenarios?
(and why do we need them?)
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Recent Swift results flares plateaus
Zhang et al., 2006
Evidence for a prolonged central engine
activity! Flares and plateaus are commonly
observed in long GRBs, and also found in some
short GRBs
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How to account for a prolonged activity?

• Newborn magnetars among the scenarios proposed
  to account for shallow decays or plateaus
  observed in GRB afterglows.
• Independent support to this scenario SN2006aj,
  associated with the nearby (?140 Mpc)
  sub-energetic GRB 060218 ? the SN-GRB connection
  may extend to a range of masses much broader than
  previously thought, possibly involving two
  different mechanisms a collapsar for the more
  massive stars collapsing to a BH, and a newborn
  NS for the less massive ones (Mazzali et al.,
  2006).
• Dai Lu, 1998 there are at least two
  possibilities for having a strongly magnetic
  millisecond pulsar created during a GRB (i) an
  accreting white dwarf collapsing to a rotating
  NS, whose magnetic field is amplified by flux
  conservation, with an initial fireball occurring
  during the NS birth (relevant for long GRBs)
  (ii) NS binaries merging into a massive, highly
  magnetized and rapidly spinning NS, with a
  fireball produced e.g. via neutrino/anti-neutrino
  process.

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The magnetar scenario for GRBs
Assuming the spin-down is mainly due to
electromagnetic dipolar radiation and to GW
radiation, the spin-down law reads (Shapiro
Teukolsky 1983) I ? (d?/dt) - (B2R6?4)/(6c3)
- (32 G I2 ?2 ?6)/(5c5)
In previous works aimed to explain the em
plateaus (e.g. Dai Lu 1998, Zhang Meszaros
2001, Fan Dong 2006, Yu Huang 2007), this
term was neglected or considered as an
alternative limiting case, with ?const.
The energy input into the fireball is due to the
EM dipolar emission only

• angular frequency
• B dipolar field strength at the poles
• I moment of inertia
• R stellar radius
• ellipticity of the NS

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Considering only dipole losses and a star with
fixed shape

• I ? (d?/dt) -(B2R6?4)/(6c3)
• ?(t) ?0 (1T/Tem)-1/2
  L(T)L0(1T/Tem)-2
• Plateau duration
• Tem? 2x103 s (I/1045 g cm2) (B/ 1015 G)-2?/(2? 1
  kHz)-2 (R/10 km)-6
• Visibility condition L0 x Tem ? Eimp

Zhang Meszaros 2001
?0
L0
L0(T/Tem)-2
?0(T/Tem)-1/2
Tem
Tem
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What happens including GW losses in the spin-down?
?
?
a3
a1
?
a2
a3
a2
a1
Initial configuration Maclaurin spheroid a1a2?a3
Evolution Riemann-S ellipsoid a1?a2?a3
We have studied the contribution of GW losses to
the spin-down, under the hypothesis that a
secular bar-mode instability does set in the
newborn magnetar. According to the analytical
formulation given by Lai Shapiro (1995), we
follow the NS quasi-static evolution under the
effect of gravitational radiation, i.e. along an
equilibrium sequence of compressible Riemann-S
ellipsoids evolving toward a stationary football.
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General scenario

• Non-axisymmetric instabilities can develop in
  rapidly rotating fluid bodies when the ratio
  ?T/W of rotational-to-gravitational potential
  energy is sufficiently large
• ??0.27 ? dynamical instability (possibly a
  burst-type signal)
• 0.14???0.27 ? lm2 bar-mode oscillations
  become secularly unstable due to viscosity or
  gravitational radiation reaction

??7x104 (M/1.4 M?)-3 (R/10 km)4 (?-0.14)/0.01-5
s TGW?few ?
For a given value of ?, one has fmax ? M1/2
R-3/2 fmax100 Hz for ?0.15, n1, M1.4 M?,
R10 km fmax600 Hz for ?0.25, n1, M1.4 M?,
R10 km
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Results dipole losses plus secular bar-mode
?0.18, n1, M1.4 M?, R20km, B3x1015 G

• Tem?5.4x103 s (dashed lines) and TGW?3??104 s
  (dash-dotted lines)
• The inclusion of GW losses (dash-dotted line)
  speeds-up the process, causing ? to decay
  somewhat earlier (solid lines)
• Depending on the particular parameters choice,
  one has Tplt?Min(TGW, Tem). Setting Tplt equal to
  its observed value, this relation provides a
  constrain on the parameters of the problem.

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Effect of magnetic dipole losses on the X-ray
light curve
We can then predict the effect of the NS dipole
losses on the fireball dynamics dRf/dt2c?2
d?/dt -3/2 (?/Rf) dRf/dt 3/2 Ldip
(4?nISMmpc2R3 ?)-1 Rffireball
radius nISMinterstellar medium number
density ?fireball Lorentz factor
GRB X-ray light curves are qualitatively compared
with our theoretical energy input model. Data
points are rescaled in flux and corrected for the
cosmological time delay. The blue, purple, and
light-green data points are from GRB061121,
GRB070420 and GRB080905b. Red data points are
from the short GRB 051221a.
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GW signal associated to the em plateau
h(t)4 G ?2 I ?/(c4d) hcf(t) h(t) (df/dt)-0.5

• We have ?max5 at d70-80 Mpc, or d100-120 Mpc
  assuming, as a rule-of-thumb, that knowledge of
  the GRB trigger time reduces the detection
  threshold of a factor of 1.5 (Kochanek Piran
  1993 Cutler Thorne 2002).
• Higher confidence in a detection
  lt?gt(2/5)0.5?max? 5 in each of a 3-detectors
  network with similar hrms (Cutler Flanagan
  1994). With the help of the GRB trigger time ?
  compensating for the (2/5)0.5 factor, this gives
  d ? 70 - 80 Mpc.

_at_ 70 Mpc
Virgo
Adv Virgo/LIGO
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Some comments on the nearest GRBs

• Currently observed GRB 980425 _at_ 40 Mpc, GRB
  060218 _at_ 140 Mpc (and sub-luminos, nearby GRBs
  are expected to occur with a higher rate than
  normal GRBs, INTEGRAL catalog probably include
  some few more events, and future missions like
  EXIST and Janus could enlarge the sample).
• Some other nearby candidate events GRB 050906
  (short) _at_ 130 Mpc? GRB 070201 in M31? GRB081215a
  in M31?
• Expectations for short GRBs Our best-fit
  model to the current observations predicts that
  about 3 of the SHBs observed by BATSE are within
  100 Mpc while about 1 are within 50 Mpc. Given
  that Swift detects 10 SHBs per yr, and that its
  threshold is comparable to that of BATSE, the
  expected rate of simultaneous detections of an
  SHB and a GW signal is 0.3 (0.1) per year
  (Nakar, Gal-Yam, Fox 2006). If we consider the
  GBM on-board GLAST, the rate of SHB within 100
  Mpc is expected to be of about 1 per year.

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Conclusions (I)

• Our results point to a new class of GW signals
  to be searched for in coincidence with GRB
  triggers. Nearby GRBs with EisoO(1050 ergs)
  would produce a GW signal that could be detected
  by the adv Virgo/LIGO, emitted in association
  with an observed X-ray light-curve plateau, over
  relatively long timescales.
• The peak amplitude of the GW signal would be
  delayed with respect to the GRB trigger, thus
  offering GW interferometers the challenging
  possibility of catching its signature on the fly.
  This would be relevant to call for a follow-up
  with optical and radio telescopes.
• For GW detectors, our results are relevant in
  the light of the fact that (I) Virgo and LIGO
  are already active on GRB-GW searches (e.g.
  Acernese et al. 2008 Abbott et al. 2008) (II)
  Virgo and LIGO are exchanging data and getting
  prepared to develop online analyses soon, in
  their enhanced configuration (III) Adv detectors
  should arrive in ?2013-2015.

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Conclusions (II)

• The GW signal is linked to an em signature. The
  NS properties, such as M and R, determine both
  the duration Tplt and luminosity Ldip,i of the
  observed afterglow plateau, as well as the
  initial frequency and amplitude h of the
  associated GW signal. Thus, a correlation does
  exist with the em emission, apart from the
  trigger itself, which GW detectors might use to
  enhance the confidence of an eventual detection.
  Moreover, the presence of such a GW signal may
  confirm us the GRB/magnetar scenario.

??7x104 (M/1.4 M?)-3 (R/10 km)4 (?-0.14)/0.01-5
s
Tem? 2x103 s (I/1045 g cm2) (B/ 1015 G)-2?/(2? 1
kHz)-2 (R/10 km)-6 Tplt?Min(TGW,Tem)
Visibility condition Ldip,i xTplt ? Eimp
fmax ? M1/2 R-3/2
Ldip,i(Bi2Ri6?i4)/(6c3)
h(t)4 G ?2 I ?/(c4d)
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The End
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The secular timescale
Lai Shapiro, 1995
Secular instability growth time due to
gravitational radiation as a function of ? for a
NS modeled as a compressible Maclaurin spheroid,
with M1.4 M? and R10 km. Solid, dotted and
dashed lines correspond to the bar-mode (m2)
instability for polytropic index n0, n0.5 and
n1 respectively. The long-dashed line is for n0
and m3.
??2x10-5 (M/1.4 M?)-3 (R/10 km)4 (?-?sec)-5
Starting from a secularly unstable Maclaurin
spheroid, a little perturbation will cause the
star to evolve along a Riemann-S sequence on a
timescale TGW of the order of few ?
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Maximum frequency of the emitted GW signal
Lai Shapiro, 1995
Maximum frequency of the GWs radiated during the
evolution of a NS from an unstable Maclaurin
spheroid to a stable Dedekind ellipsoid ad a
function of ?. Values of M1.4 M? and R10 km
are assumed. Solid, dotted and dashed lines
correspond to polytropic indices of n0, n0.5
and n1 respectively.
For a given value of ?, one has fmax ? M1/2 R-3/2
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Immediate neighborhood of the source
GRBs EM signal and GWs
d ? 1013 cm from the source
EM signal
GW emission
Source position, distance and trigger time

Structure and density of the surrounding medium
short vs long, compact binaries vs massive
progenitors Total energy output hints on the
disk mass of the bh accretion disk system
powering the GRB
Amplitude of the GW signal hints on the masses
(e.g. chirp or mass ratio), total energy output
in GWs
Nature of the progenitor
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The secular evolution
Lai Shapiro, 1995
? angular frequency of the ellipsoidal
figure ?angular frequency of the internal
fluid motions
The problem depends on some initial parameters,
which also set the relevant physical scales -
polytropic index n - total mass M of the NS -
length unit R0 (radius of the non-rotating,
spherical equilibrium polytrope) - ratio ? of
kinetic to gravitational potential energy (or
internal fluid circulation) - intensity of the
dipolar magnetic field
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GW signals expected in the standard scenario 3
phases

• In-spiral expected only for short GRBs, the
  emitted GWs are in the frequency band accessible
  to VIRGO LIGO only for the last few minutes of
  in-spiral (e.g. Cutler Flanagan 1994).
• Merger associated to a burst-type signal, with
  duration of the order of few ms. It can occur in
  long GRBs if dynamical instabilities develop into
  the collapsing core or in the disc, and naturally
  occurs in short GRBs.
• Ring-down burst-type signal, due to GW emission
  associated with the BH deformations. Damped
  oscillation, with duration of the order of few ms.