Neutron Star F-modes James Clark, Ian Jones What f-mode GW signals - PowerPoint PPT Presentation

Neutron Star F-modes James Clark, Ian Jones What f-mode GW signals look like from a data analyst’s point of view Wednesday, 30 May 12

Outline Isolated NS f-modes History & context Parameter Space Rotation Plans 2 Wednesday, 30 May 12

F-modes Assume something excites fundamental (f)-mode oscillations in a neutron star Gravitational wave signal should look something like: Generally, each mode (i.e., value of m) has its own amplitude, frequency, phase and decay time Energy in each mode (i.e., amplitude) depends on excitation mechanism 3 Wednesday, 30 May 12

Energetics (the bad news / disclaimer) (LSC/Virgo) F-mode GW analyses have concentrated on pulsar glitches and magnetar flares. In the grand scheme of things not the most energetic events: Pulsar glitches (e.g., Abadie et al, Phys. Rev. D83 (2011) 042001): absolute upper bound on energy from size of glitch / rotation rate ~10 42 erg (slightly) more realistic estimate from a 2-component model ~10 38 erg SGR flares: Zink, Lasky & Kokkotas (2011): E fmode ~10 41-43 erg 4 Wednesday, 30 May 12

Previous F-mode Searches August 2006 Vela Glitch Seearch (Abadie et al 2011): E 90%2,0 = 5.0 x10 44 erg Considered each mode separately (i.e. only a single mode excited) and inferred intrinsic upper limit from sky-location & orientation Marginalised over unknown f-mode frequency with uniform prior in [1,3] kHz Magnetar searches (most recently Abadie et al 2011): E 90%iso = 1.4 x10 47 erg Assumed isotropic emission, nominal source distance 1 kpc Circular polarisation, fixed frequency (for upper limit, search is broadband) @ 1090 Hz Note: aLIGO will be ~100x more sensitive (in energy), still only beginning to probe upper bounds of plausible energies ET ‘only’ ~1e4 x more sensitive (in energy)... 5 Wednesday, 30 May 12

F-modes: this work In all previous searches (e.g., Vela glitch, SGR searches), assume: f-mode frequency in inertial frame = frequency in co-rotating frame and harmonics m are degenerate in frequency frequency and damping time are totally independent parameters emission is isotropic or only a single mode excited (only affects interpretation) Here, we start exploring relaxing these assumptions by considering: mode frequencies & damping times are EoS-dependent functions of mass and radius mode frequency in inertial frame for non-axisymmetric modes (i.e., |m|>0) is a function of spin frequency 6 Wednesday, 30 May 12

F-mode parameters f-mode frequency & decay time determined by mean density & compactness (M/R) Andersson & Kokkotas (1998), Benhar et al (2005) consider various EoS and fit for frequency & decay time: ✓ ¯ ¯ M 3  ◆� 1 M (1/s) = a τ − b τ ¯ ¯ R 4 R τ 0 Most recent results in Gaertig & Kokkotas (2011) Previous GW analyses assume frequency is ~1-3 kHz, decay time ~50-500 ms, but no correlation However, not totally ignorant about masses & radii: Idea / plan: use NS observations to inform f-mode parameter space 7 Wednesday, 30 May 12

F-mode parameters Idea : choose GW signal parameters (for injections & searches) based on our knowledge of the stellar parameters which determine them potential benefits: sensible parameter space for searches, more astrophysical injection populations, informed priors for parameter estimation.. Before considering observations, can get constraints from theory Allowed compactnesses: 1 M sun minimum 0 . 115 . M R . 0 . 35 mass & rotation causality limit Allowed densities 2 . 25 × 10 14 . ρ 0 g cm − 3 . 6 . 29 × 10 15 minimum mass & causality 8 Wednesday, 30 May 12

Neutron Star Parameters Steiner et al 2010 consider mass/radius of 6 neutron stars Use photospheric radius expansion in 3 Type-1 X-ray bursters & thermal X-ray spectra from 3 LMXBs See little correlation of radius with mass over a wide range of masses Mass distribution of neutron stars from Lattimer & Prakash 2007 9 Wednesday, 30 May 12

Signal Parameters We have: some prior distribution for mass, radius distribution of neutron stars p(M,R|I) A mapping between mass, radius and frequency and decay time: ✓ ¯ ¯ M 3  ◆� 1 M (1/s) = a τ − b τ ¯ ¯ R 4 R τ 0 trivial to write down prior on frequency and decay time: I’m lazy, simple-minded: take a 2-D Gaussian on mass and radius with 10 Wednesday, 30 May 12

Signal Parameters Recall that f-mode searches have all taken uniform, independent priors on frequency and decay time! 11 Wednesday, 30 May 12

Oscillations In Rotating Stars l=2 has 2l+1=5 m indices in spherical harmonics Different m’s have different projections onto detector so, in Vela glitch search (known orientation), give upper limits in terms of different m’s In a rotating star, frequency of m th mode: ω 2 ,m = ω 2 , 0 − m σ Ω No good model for how energy is distributed across modes (for Vela, single mode excitation was an assumption ; for SGR searches, it’s just used for upper limit simulations) Potentially 5 modes with different frequencies, amplitudes, phases & decay times 12 Wednesday, 30 May 12

Splitting Resolvability Stated that frequency of m th mode is: ∆ ω rot = m σ Ω ω 2 ,m = ω 2 , 0 − ∆ ω rot with σ ~1. But if Δω rot is smaller than frequency resolution Δω res of any reasonable search then there’s not much to study Mode calculations indicate duration of f-mode ~0.5 s - sensible to search over this time-scale T obs , so resolution of a search is: ∆ ω res = 2 π T obs Parameterising, ratio of splitting to resolution is ✓ f star ◆ ✓ T obs ◆ ∆ ω rot ∼ 0 . 5 ∆ ω res 0 . 5 s 1 Hz So, anything spinning faster than ~2 Hz (i.e., not magnetars) has resolvable rotation-induced f-mode splitting 13 Wednesday, 30 May 12

splitting Ω vs B -field Magnetic fields also break symmetries, mode degeneracies. How important? Magnitude of rotational splitting ~rotation freq., B-field splitting ~ mode freq x magnetic / gravitational energy: E mag ∆ ω mag ∼ ω 0 ∆ ω rot ∼ Ω magnetic effect: rotational effect: E grav Compare size of magnetic splitting / rotational splitting for fiducial NS: � 2 ⇣ ⌘ ∆ ω mag B 1 Hz ∆ ω rot ∼ 4 . 2 × 10 − 9 � 10 12 G f star ‘Normal’ pulsars (e.g., Crab): f star ∼ 1 Hz , B ∼ 10 12 G , ∆ ω mag / ∆ rot ∼ 10 − 9 f star ∼ 30 Hz , B ∼ 10 12 G , ∆ ω mag / ∆ rot ∼ 10 − 10 Young pulsars (e.g., Vela): f star ∼ 300 Hz , B ∼ 10 9 G , ∆ ω mag / ∆ rot ∼ 10 − 17 LMXBs & MSPs: f star ∼ 0 . 2 Hz , B ∼ 10 15 G , ∆ ω mag / ∆ rot ∼ 10 − 2 Magnetars: Conclusion: for these studies, assume ‘normal’ B-field, so rotational splitting is dominant effect 14 Wednesday, 30 May 12

Rotation Demonstration Wednesday, 30 May 12

Going Forward Close to having a more complete, astrophysical f-mode waveform Energy is still a problem Want to explore: impact of mode-split waveforms on burst pipelines (does time-frequency clustering still work well? optimal time-frequency resolution?) constraints on burst searches, based on parameter space (i.e., priors) Impact on parameter estimation Parameter estimation for inverse problem (mass, radius recovery from f-modes) Extend the informed signal priors to (e.g.,) r-modes 16 Wednesday, 30 May 12

Wish-list A quantitative idea of the uncertainties in the fits for f-mode parameters More energetic f-modes, other mode types? Complete picture for which modes (m’s) and which mode types (e.g., f vs r, g etc) are excited Also beginning to think along the same lines for post-merger HMNSs we do burst searches: can we see post-merger oscillations? e.g., trigger a burst analysis from a BNS inspiral signal... A high-frequency (>1 kHz) GW detector?? Clearly worth thinking about a good figure of merit for bursts accessible in the kHz regime... 17 Wednesday, 30 May 12