Goddard Space Flight Center A Neutron Star Oscillation

Goddard Space Flight Center A Neutron Star Oscillation Mode During a Superburst Tod Strohmayer, NASA’s Goddard Space Flight Center with Simin Mahmoodifar (University of Maryland) An l=7, m=4 toroidal mode (Anna Watts) n(2 t 0) = 29. 8 (R 10)-1 (1. 71 - 0. 71 M 1. 4/R 10)1/2 Hz (0. 87 - 0. 13 M 1. 4/R 102) n(lt 0) = n(2 t 0) [ l(l+1)/6 ]1/2 [1 + (B/Bm)2 ]-1/2

Neutron Star Seismology Goddard Space Flight Center Brightness pattern for an l=2, m=1 g-mode (slow rotation limit). • Stellar oscillations are a powerful probe of internal structure (e. g. helioseismology). • For example, p-modes sense the sound speed. Mode frequencies scale as < ρ >1/2 (thus M and R). • Solid crust supports torsional shear modes, ltn for n = 0 modes, effective wavelength is R, for n > 0 it is DR, if Vs = constant, then fn=0 / fn>0 ~ DR/R, constrain crust thickness (magnetar QPOs). • g-modes supported by buoyancy (thermal and density gradients), can probe R, and envelope structure.

Rotating Neutron Stars: r-modes Goddard Space Flight Center Mode displacement for l=m=2 r-mode ωr = 2 mΩ/(l(l + 1)) • r-modes are a subset of the inertial modes supported by rotation (Coriolis force, analogous to Rossby waves on Earth). • Retrograde in frame rotating with the star, prograde in inertial frame, thus unstable to CFS gravitational radiation instability. • Modes damped by viscous processes (shear, bulk), depends on phases of dense matter in the interior. • Spin-down torque on the star, viscous damping heats the star.

Goddard Space Flight Center R-mode Patterns in Co-rotating and Inertial Frames Ω Co-rotating frame retrograde pattern. Ω Inertial frame prograde pattern.

Goddard Space Flight Center r-modes: Potential Probe of Dense Neutron Star Matter • As spin rate increases r-mode frequencies diverge from slow spin limit of 2Ω/3 (in rotating frame). • Spin dependence of frequency is sensitive to EOS and phase of dense matter.

Goddard Space Flight Center How Might Non-radial Oscillations be Observed? • Pulsation modes can modulate the temperature (flux) across the neutron star’s surface – coupled with spin can produce flux modulation at mode’s inertial frame frequency (Lee & Strohmayer, Heyl 2005). • Surface displacements generated by pulsation modes can periodically distort the X-ray emitting hot-spot (Numata & Lee 2010). Works for transverse (quasitoroidal) displacements. Such modes include surface g-modes, and r-modes. • Since hot-spot rotates with the star, the modulation frequency seen by a distant observer is the co-rotating frame frequency (Strohmayer & Mahmoodifar 2014, Ap. J, 784, 72). 4 U 1636 -536 Superburst

Goddard Space Flight Center Coherent Searches for Pulsation Modes • Use orbit model to remove time delays associated with neutron star’s orbital motion. Observer is effectively at the binary’s center of mass. • “Coherence Recovery, ” improves sensitive to weak, coherent signals. Narrow band signal is not “smeared” into many Fourier bins. • “Targeted” search for r-modes and surface g-modes. Spin frequency is known, so search mode frequency range (relative to spin) that is expected theoretically. Keeps Ntrial low and thus improves overall sensitivity. 0. 417 ≤ σ / Ω ≤ 0. 757 (rotating frame) 1. 243 ≤ σ / Ω ≤ 1. 583 (inertial frame) • Bin light curve using corrected times (4096 Hz sampling). • Create power spectra using 4 energy ranges (focusing on superburst thermal component).

Goddard Space Flight Center 4 U 1636 -535: February 2001 Superburst • Orbital period known (3. 79 hr), fit for other parameters; νspin, vns and epoch of T 90 (Strohmayer & Markwardt 2002). • Barycenter, then remove orbital time delays. Poster 122. 27 (Keek et al. ) • 582 Hz spin pulsations detected for ~800 s near burst peak. • Frequency drift consistent with orbital motion of the neutron star. pulsation interval

4 U 1636 -535 Superburst Light Curve Goddard Space Flight Center Nbins ≈ (Δν/ν) = (vns/c) = (0. 5/582)*835/(1/8000) = 5700!

Coherent Search in the Superburst Goddard Space Flight Center 1. 43546 x nspin Estimated significance: 2. 5 x 10 -4

835 Hz Coherent Modulation Goddard Space Flight Center • Folded light curve at 835. 644 Hz, profile well fit by a sinusoid, • A + B sin (ϕ - ϕ 0), modulation amplitude B/A = 0. 19 ± 0. 04 %, • Noise power distribution consistent with expected. • Extensive Monte Carlo simulations confirm analytic estimate.

Possible Mode Identifications • g-modes in envelope above the solid crust. Piro & Bildsten (2004) and Strohmayer & Lee (1996) computed modes in accreting, nuclear burning envelopes (e-mechanism). Mode frequencies 20 – 30 Hz, but modes modified by fast rotation (Bildsten et al. 1996; Piro & Bildsten 2004). • latitudinal dependence of Coriolis force “squeezes” modes closer to equator. • Observed frequency (835 Hz) is larger than spin, so, if |m|=1, need prograde (m=-1) mode (this is a Kelvin mode), but frequency is not high enough to reach observed (likely rules out l=1). So, |m|=2. Then l=2, m=2 or l=2, m=1 appear plausible. Goddard Space Flight Center Piro & Bildsten (2004)

Goddard Space Flight Center Implications for Neutron Star Mass in 4 U 1636 -536 • If intrinsic mode frequency is constant then detection suggests vns = 134. 5 ± 0. 2 km/sec. • High velocity suggests ``light” neutron star, interesting as low mass end constrains core collapse physics (Lattimer 2012).

Conclusions, Future Work Goddard Space Flight Center • Detection of global neutron star oscillation modes would open a new window on neutron star interiors and cold ultra-dense matter. • Accreting Millisecond Pulsars (AMXPs) are good search candidates. Spin and orbits known. Mode-driven perturbations to hot spot. • Several initial searches reported (Strohmayer & Mahmoodifar 2014), additional searches using all RXTE archival data for AMXPs underway (including SAX J 1808). • For interpretation, need better r-mode (and g-mode) computations for realistic NS models with fast rotation and solid crusts. • Light curve calculations for g-modes, to explore “visibility” of modes squeezed closer to equator. • Larger colleting areas needed to improve sensitivities, ESA’s LOFT, and NASA’s NICER (Special Session Wed 1: 30) can contribute.

backup Goddard Space Flight Center

An r-mode in the Superburst Goddard Space Flight Center

Goddard Space Flight Center An r-mode in the Superburst: Amplitude Conundrum

Goddard Space Flight Center Neutron Star Oscillations: perturbing the hot-spot Numata & Lee (2010) • Surface displacements generated by pulsation modes can periodically distort the X-ray emitting hot-spot (Numata & Lee 2010). • Distortion is maximized for modes with dominant transverse (quasi-toroidal) displacements. • Such modes include surface gmodes, and r-modes. • Since hot-spot rotates with the star, the modulation frequency seen by a distant observer is the co-rotating frame frequency.

Goddard Space Flight Center Accreting Millisecond X-ray Pulsars (AMXPs) Romanova et al. (2009) • Accretion stream close to spin axis produces X-ray hot-spot, spin modulation generates pulsations. (Lamb et al. 2009, Patruno & Watts 2011).

Goddard Space Flight Center Pulsation Searches in AMXPs: XTE J 1751− 305 • Discovered in April 2002 with RXTE/PCA Galactic Bulge monitoring program (Markwardt et al. 2002), 435 Hz spin period. Strohmayer & Mahmoodifar ar. Xiv: 1310. 5147 • Pulse timing revealed a 42. 4 min orbital period, with a very low mass dwarf (likely He) companion.

XTE J 1751− 305 Search con’t Goddard Space Flight Center Can do targeted search in the frequency range where r-modes (and g-modes) are theoretically expected. Fast spin increases frequency (k 1), crust interactions decrease, k 2 , (Yoshida & Lee 2000). Psig = 1. 6 x 10 -3

Goddard Space Flight Center Pulsations: Light curves and Power Spectra r-mode frequency encoded in the light curve at co-rotating frame frequency, 2Ω/3 (Numata & Lee 2010). • Light curve modulation amplitude proportional to mode displacement amplitude • Observed modulation, aj, can constrain A.

XTE J 1751− 305 Search con’t Goddard Space Flight Center • Light curve calculations and modeling can connect observed amplitude, aj, to mode amplitude (Numata & Lee 2010). • Implied modulation amplitude of 7. 5 x 10 -4, signal ~coherent over ~5 day light curve. • No other broader bandwidth signals detected. Amplitude limit at ~2 x 10 -4.

Search in XTE J 1814− 338 Goddard Space Flight Center • Discovered in June 2003, 314. 4 Hz spin frequency, 4. 275 hr orbital period. • Pulsar has strong first harmonic. • Carried out similar search as for J 1751. No candidate signals found. Set upper limit on amplitude of ~8 x 10 -4.

Results for NGC 6440 X-2 Goddard Space Flight Center • Pulsar observed in only 4 RXTE orbits (not as much data as for J 1751 and J 1814). • No candidate signals detected, with upper limits on the modulation amplitude of ~3 x 10 -3. • RXTE Bulge scans caught glimpses of faint, recurrent transient in NGC 6440 (X-2) in August 2009. Pulsations seen at 205. 9 Hz.

Future Capabilities: LOFT Goddard Space Flight Center • Sensitivity for coherent search scales ~ 1 / (Ntot)1/2. • LOFT/LAD 10 -12 m 2 (3 – 15 ke. V) • 20 -30 x count rate of RXTE/PCA • Likely can reach aamp ~ 1 – 2 x 10 -5 ESA M 3 candidate mission, study report (“yellow book”) recently submitted, down-select in early 2014. Potential launch 2022.

r-mode spin-down limits Goddard Space Flight Center

The Neutron Star Equation of State Goddard Space Flight Center Demorest & Ransom 2011 • High mass measurements, limit softening of EOS from hyperons, quarks, other exotic stuff. • Most good mass measurements at low end, and systems not conducive to radius estimates, EOS not constrained strongly. • Need either masses for higher mass systems (accretors), and/or possibility to get R (AMPs).