Pulsar Glitches: Gravitational waves at r-modes frequencies

Transcription

1 Pulsar Glitches: Gravitational waves at r-modes frequencies LIGO-G I. Santiago 1, J. Clark 2, I. Heng 1, I. Jones 3, Graham Woan 1 1 University of Glasgow, 2 Cardiff University, 3 University of Southampton 1

2 Overview Pulsar Glitches r-modes Signal Parameters Method Detectability Image: Combined Chandra X-ray Image of Vela Pulsar Jet (Credit: NASA/CXC/PSU/G.Pavlov et al.) 2 Summary and Future Work

3 Pulsar Glitches Previous Pulsar glitches searches focus on ring-down from f-modes [1-3 khz] Explore excitations in the r-modes frequencies for ring-down [2 Hz - 1 khz ] Signal characterized by a frequency and a decay time r-mode frequency is proportional to the Ωstar Quadrupole l = 2 has the strongest GW radiation and the strongest contribution to the mode function is l = m Lockitch et al, made some simulations using a simple neutron star model. Shift in the frequency of the modes for a sequence of stars of varying polytropic index n [1] f N = 2 3 Ω star [1] Lockitch, Friedman J., Andersson N fn Newtonian Frequencies 3

4 Pulsar Glitches 10 3 Pulsar with Glitches PSR J PSR J Spin Frequency [Hz] Vela Pulsar Crab Pulsar Distance [Kpc] From the ATNF database and Melatos et al, (2007) is possible to count 320 glitches in 116 Pulsars 10 of them have produced more than 5 observed glitches. (shown in green) Only one of them is a millisecond pulsar (PSR B ) 4

5 Signal Damping Time If the Pulsar has an internal temperature 10 8 K and considering a dissipation at a thin viscous boundary layer at the crust-core interface [4] the damping time τ may be in the order of 10 3 s Radius of the NS Fitting parameter for the shear viscosity NS spin frequency Fractional velocity mismatch at the crust/core interface Mass of the NS Internal Temperature of the NS Density at the crust-core interface of the NS [4] Levin Y., and Ushomirsky G,

6 Signal Damping Time F is the fitting parameter for the shear viscosity [2] Bildsten & Ushomirsky (2000) 10 6 Glitching Pulsars Damping Time [s] F=1 both n 0 and p + are normal F=1/15 if n 0 are superfluid and p + are normal PSR J F=5 both n 0 and p + are superfluid Spin Frequency [Hz] 6

7 Ω slippage Slow rotating stars Thin crust model Extracted from Figure 1 in Levin & Ushomisrky 2000 Rapid rotating stars δu/u = Fractional velocity mismatch at the crust/core interface The spin frequency is normalized with the Keplerian rotational frequency Ωk For slow rotating stars the minimum value δu/u ~ 1 and doesn t participate in the variation of τvbl, but for rapid rotating stars it should have a value of 0.1 7

8 Method We assume that the evolution of the r-mode is dominated by dissipative processes, so the mode can be considered to decay with a e-folding time τdiss. GRR = Gravitational Radiation Reaction And we can calculate E GW = c3 G 1 20 r2 ω 2 h 2 0τ diss Equation 1: Total Energy emitted in GW For the r-modes it is interesting to parameterise the mode amplitude in terms of the dimensionless number α such as in Owen, et al (1998), h 0 = 8π 5 Ė GW = c3 G G c 5 1 r αω3 MR 3 J Equation 3: Amplitude of the GW 1 10 r2 ω 2 (h 0 e t/τ diss ) 2 Equation 2: GW Luminosity 8

9 Method Ẽ = 1 2 α2 Ω 2 MR 2 J Equation 4: Energy of the mode E glitch = 1 Ω IΩ2 Ẽ = E glitch 2 Ω Equation 5: Energy of the glitch The Energy of a glitch as a function of the Ω, the rotational frequency of the star, can be equal to the energy of the mode, that leads to α = 2Ĩ J 1/2 1/2 Ω Ω/Ω = Ω /2 Equation 6: The estimate of the mode 9

10 Method A relation between the glitch energy and the total radiated gravitational wave energy can be obtain by combining the equations shown earlier E GW = τ diss E glitch τ GRR It is important to point out that there is a very steep frequency scaling E GW = f 11/2 E glitch. Inserting the expression for α into the h0 equation in terms of the Eglitch h 0 = G c 5 π r Ω2 M 1/2 R 2 J 1/2 E 1/2 glitch and h rss = h 0 τvbl 10

11 Energy and h0 estimation Observed parameters Known Glitches Known Glitches h0 h Spin Frequency [Hz] Distance to the sources [pc] 11

12 Energy and h0 estimation Observed parameters Pulsars with N glitches > Pulsars with N glitches > h h Spin Frequency [Hz] Distance to the sources [pc] 12

13 hrss Glitching Pulsars h rss and detectors sensitivity curves h[f] PSR J Frequency [Hz] 13

14 hrss Glitching Pulsars h rss and detectors sensitivity curves h[f] Frequency [Hz] 14

15 Optimistic Plot Optimistic h rss of Glitches in Pulsars and detectors sensitivity curves PSR J h[f] Frequency [Hz] Assuming a Eglitch = 4.95 x which is the Vela glitch strength 15

16 Recent glitches Glitching Pulsars h rss and detectors sensitivity curves h[f] LHO S6 Adv LIGO (Opt NS NS) ET B sensitivity curve ET C sensitivity curve h rss of Glitches registered after 1 Jan Frequency [Hz] 16

17 Other models Bennet, et al. (2010), propose a signal that decays over days to weeks (10 5 to 10 8 s) Propose that the SNR depends on the buoyancy, compressibility and viscosity of the NS interior Detection can be possible by the second and third generation interferometers Prix et al. (2011) propose a method for this kind of signal 17

18 Summary and Future Work This r-modes study is still in a feasibility stage, but we re looking at what can be learnt from this type of search using parameter estimation in advanced detectors. Investigating emissions of long duration gravitational waves and high frequencies (few hundred Hz) associated with pulsar glitches Investigate methods to search for these signals 18