1. Gravitational Waves from Magnetars
Sandro Mereghetti
INAF – IASF Milano

2. See review: Mereghetti 2008, A&A Rev. 15, 225
What is a Magnetar ?
Isolated neutron stars where the main source of energy is the magnetic field
[ most observed NS have B = G and are powered by accretion, rotational energy, residual internal heat ]
In Magnetars external field: B = G
internal field: B > G
See review: Mereghetti 2008, A&A Rev. 15, 225
[ arXiv: ]

3. Magnetars emit: “Persistent” X-rays short bursts of soft gamma-rays
Lx~ erg/s
~1-200 keV
pulsed at few seconds,
spin-down
short bursts of soft gamma-rays
Lx ~ erg/s
kT~30-40 keV
durations ~ sec
Giant Flares
Lx > 1044 erg/s
very rare events (only three observed )
Hurley et al. 1999

4. Period – Period derivative plot for Magnetars
(Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters )
NOTE : vertical bars indicate Pdot variability range

5. GW from rotating neutron stars
Rotational deformation
Konno et al. 2000,
Normal pulsars are very weak GW emitters (ellipticity too small)
Magnetars have larger deformations, but (for most of their life) rotate too slowly
Magnetic deformation

6. Some possibilities for GW emission from magnetars
1) Magnetar formation
the high magnetic field of magnetars is thought to result from a highly efficient dynamo requiring P<3 ms at birth
What is the magnetars birth rate ?

7. Magnetars birthrate ~ a few every 104 years large uncertainties:
small statistics (~10 persistent sources)
uncertain lifetimes (~104 yrs ?),
number and duty cycle of transient magnetars
Keane & Kramer, 2008, MNRAS
Birthrate of radio PSR and core collapse SN (1-3 / century) already in reasonable agreement  no much room for other populations of NS
Magnetars ~ / century i.e. up to ~10% of radio PSRs
See also:
Gill & Heyl 2007, MNRAS 381, (~0.22 / century + transients)
Muno et al. 2008, ApJ 680, (~0.3 – 6 / century )

8. Some possibilities for GW emission from magnetars
1) Magnetar formation
the high magnetic field of magnetars is thought to result from a highly efficient dynamo requiring P<3 ms at birth
What is the magnetars birth rate ?
too small for Galactic events, but OK if detectable up to the Virgo cluster (~2000 galaxies at 20 Mpc)
What is the GW luminosity of a magnetar formation event ?
depends on intensity and geometry of internal and external field

9. Some possibilities for GW emission from magnetars
1) Magnetar formation (Stella et al. 2005, Dall’Osso et al 2008)
the high magnetic field of magnetars is thought to result from a highly efficient dynamo requiring P<3 ms at birth
~1 / year expected in Virgo Cluster
2) Giant Flares (Andersson & Kokkotas 1998, de Freitas Pacheco 1998, Ioka 2001)
extremely energetic events related to giant crustal fractures (“starquakes”)
fast oscillations observed during giant flares – seismic oscillations

10. 3 Giant Flares from SGRs 1979 March 5 - SGR 0626-66
Initial spike: erg Pulsating tail: erg
1998 August SGR
Initial spike: > erg Pulsating tail: erg
2004 December 27 – SGR
Initial spike: erg Pulsating tail: erg
(Hurley et al. 2005, Palmer et al. 2005, Mereghetti et al. 2005, Terasawa et al. 2005, Boggs et al. 2007, Frederiks et al. 2007)

11. Implications of December 2004 Giant Flare
E ~ ergs emitted in the Dec 2004 GF from SGR
[~100 times more energetic than the other two observed GFs ]
This sets a lower limit on the internal magnetic energy, depending on the number of such events in a magnetar’s lifetime (Stella et al. 2005):
1 such event in ~30 yrs from 5 SGRs  recurrence time ~15 yrs/magnetar
~70 events like Dec 2004 GF in ~104 yrs magnetar lifetime
 total energy release ~ ergs (independent of beaming)
B > G [ up to ~1016 G including also neutrino luminosity]
CAVEATs:
recurrence time is probably longer (including AXP and transients )
uncertainties in GF flux (and spectrum) measurement due to its exceptional brightness
distance of SGR could be smaller than the assumed 15 kpc

13. 2.8 light seconds Peak affected by instrument saturation
Mereghetti et al. 2005, ApJ 624, L105
Initial giant pulse backscattered by the Moon
SGR
Giant Flare
2004 Dec 2004

14. SGR
distance
No direct methods ! Based on possible associations with other objects
Distance of G (which is not a SNR, but a wind nebula powered by the LBV star) is well determined 15.1 [ ] kpc.
d of SGR assumes that it is a member of the cluster of massive stars to which also the LBV belongs.
~ 15 kpc
(Corbel & Eikenberry 2004)
(Bibby et al. 2008)

15. Magnetars formation Outer dipole field B~1014-15 G
(Duncan & Thompson 1992)
Very strong internal B-fields in a newborn differentially rotating fast-spinning neutron star
For initial spin periods of Pi∼1–2 ms, differential rotation can store ∼1052 (Pi /1 ms)2 ergs,
that can be converted into a magnetic field of up to 3x1017 (Pi /1ms)-1 G. Bd Bt
Outer dipole field B~ G
Inner toroidal field B > 1015 G

16. Toroidal inner field: prolate shape with ellipticity -6
Toroidal inner field: prolate shape with ellipticity -6.4x10-4 (Bt / G)2
Poloidal inner B-field :
Oblate star
Toroidal inner B-field :
Prolate star

17. Outer dipole field Inner toroidal field
Symmetry axis of deformed star, in general, not (exactly) coaligned with the spin axis
Viscous damping of free precession leads to an orthogonal rotator within ~1 day from birth
Condition for fast orthogonalization for different initial periods (1, 2.6 ms) and initial angles (1, 2 degrees)
(Dall’Osso, Shore & Stella 2008, MNRAS )
Inner toroidal field
Outer dipole field

18. Advanced LIGO/Virgo expected S/N for newborn magnetar in Virgo Cluster
(Dall’Osso, Shore & Stella 2008, arXiv: )

19. (Dall’Osso, Shore & Stella 2008, arXiv:0811.4311)
Dependence on initial spin period
Pi = 0.97 ms
Pi = 1.13 ms
Pi = 2 ms
Pi = 2.58 ms
(Dall’Osso, Shore & Stella 2008, arXiv: )
Competition between dipole emission and GW energy losses
The maximum S/N depends only on initial period

20. There is no evidence that the SNRs associated to Magnetars are more energetic than “standard” SNRs Vink & Kuiper 2006, MNRAS 370, L14

21. long orthogonalization timescale
E SNR > 1051 ergs
long orthogonalization timescale
Outer dipole field
Inner toroidal field

22. (Dall’Osso, Shore & Stella 2008, arXiv:0811.4311)
Pi = 1 ms
Pi = 1.13 ms
S/N = 9
S/N = 8
S/N = 7
Pi = 2 ms
Pi = 2.6 ms

23. Conclusions
Gravitational waves can be revealed from newly born magnetars in the Virgo Cluster with advanced GW detectors
…but this requires a favorable combination of initial spin period, dipole strength of external field, and internal magnetic energy
Expected rate close to 1 per year [depending on fraction of magnetars satisfying above constraints]
GW from Galactic magnetars possibly associated to oscillations after Giant Flares
for upper limits see Baggio et al , Abbot et al. 2007, 2008

24. EXTRA SLIDES

27. Radio (unpulsed) Transient emission after (Giant) Flares
Seen in two SGRs, but possibly present in all bright flares
SGR VLA GHz
Frail et al. 1999, Nature

28. Radio emission after SGR 1806 giant flare
Gelfand 2007
200 mJy 7 days after GF
Gaensler et al. 2005
Cameron et al. 2005
Granot et al. 2006
Gelfand 2007

30. SGR Giant Flare of Dec 27, 2004
UHECR  High E neutrons can travel several kpc before decaying and arrive to earth (or produce n that maintain directionality)
n flux depends on barion load of fireball (Ioka et al. 2005)
Upper limits on n
Auger (Anchordoqui et al. 2007, ICRC)
AMANDA (Zornoza et al. 2006, Achterberg et al. 2006)
RICE (Besson et al. 2007)

31. Discovery of QPO (Quasi Periodic Oscillations) in the tail of the Dec 27 Giant Flare
Israel et al. 2005, ApJ 628, L53

32. High Frequency Oscillations in Giant Flares
– 43 Hz (Barat etal.1983)
– 90 Hz, ~18 Hz, ~30 Hz (Israel et al. 2005) Hz (Watt & Strohmayer 2006)
– 84 Hz, 28 Hz, 53 Hz, 155 Hz (Strohmayer & Watt 2005)
Large scale NS crust fractures trigger global seismic oscillations (analogous to earthquakes)
Torsional modes of NS crust  potentially important diagnostic for NS
Caveats:
Magnetic field coupling between crust and core  magnetic stresses would significantly reduce the mode amplitude in less than 1 sec and redistribute the energy within the liquid core (Levin 2006) or lead to global MHD oscillations (Glampedakis et al. 2006)
Other possibilities? B confined in the crust or QPO originate in magnetosphere