THE PECULIAR EVOLUTIONARY HISTORY OF IGR J IN TERZAN 5 A. Patruno Reporter: Long Jiang ( 姜龙 )

Frequency of 11 Hz Period of 21.3 hr & e < Companion mass M > 0.4M Location in a globular cluster B in the range of 10^9–10^10 G μ= 5 × 10^26, B <5 × 10^8 G Didier Barret In its spin-up epoch (Papitto et al. 2011). New accreting pulsar, discovered in 2010 October If it is a primordial binary, then its spin frequency & magnetic field are surprising low since the globular cluster Terzan 5 is about 12 Gyr old; Ferraro et al. 2009

The magneto-dipole torque dominated epoch Spun-down by wind torques Its present spin-up epoch, early phase EVOLUTIONARY HISTORY OF IGR J

Srinivasan et al. noted that many NS binary evolution scenarios have an early first mass transfer epoch when the companion, not yet filling its Roche lobe, is losing mass by a stellar wind, some of which is captured by the NS in a weak quasi-spherical accretion with low specific angular momentum. The NS will be spinning down by wind torques in this epoch, thus reducing its dipole field in proportion to its rotation rate. The wind spin-down epoch starts when the wind of the companion penetrates the light cylinder, ends when the companion fills its Roche lobe. Wind accretion

The average mass accretion rate is M˙ = 2 × 10^17 g s^−1, in agreement with the value reported by Degenaar & Wijnands (2011). The spin-up age up to the present is where Δ is the (unknown) duty cycle of the binary. If we assume Δ ∼ 0.01, the maximum estimated time in the spin-up epoch up to now is ≈5 × 10^7 yr corresponding to ν i = 814 Hz Even if the system were already in equilibrium at ν = 11 Hz then it must have reached equilibrium in the short time Duration of the Roche Lobe Overflow Epoch

the dipole spin-down proceeds with a constant dipole moment and braking index 3: where c is the speed of light and I is the NS moment of inertia. The duration of the dipole spin-down epoch, until the rotation rate Ω1 is reached is given by Duration of the Dipole Spin-down Epoch

Newborn NSs have a distribution of rotation rates Ω 0 ∼ 1– 300 rad s^−1 and dipole magnetic moments μ 0 ∼ 10^29– 10^30 G cm^3 (Faucher-Gigu`ere & Kaspi 2006). Then the dipole spin-down age is ∼ 10^7 yr. The captured wind loses angular momentum in a shock and will accrete toward the NS down to a stopping radius ∼ r A. The wind will be able to affect the torque on the NS when r A < r LC ≡ c /Ω 1 the rotation rate Ω 1 at the beginning of the wind spin-down epoch is

The NS is spinning rapidly within this wind of low specific angular momentum. Take a constant torque, giving the spin-down rate: Since the magnetic moment does not change after the wind spin-down epoch, μ 2 at the end of the wind spin-down epoch is just the magnetic moment in the present RLOF spin-up epoch as estimated above. By assuming that Ω(tsd) = Ω 2 << Ω 1 and μ 2 <<μ 1, we obtain where we have assumed that μ 1 = μ 0 as found at the end of the previous section. Duration of the Wind Accretion Spin-down Epoch

The Wind Accretion Rate The wind mass-loss rate from a ∼ 1M main-sequence companion is M˙ wind ∼ 10^12 g s^−1, M˙ wind ∼ 10^13 g s^−1 for sub-giant stars. Only a fraction of this wind will be captured to flow toward the NS, ∼ 10^−2 However, since the orbit of IGR J shows stringent upper limits on the eccentricity tidal circularization has probably already taken place and it is likely that the donor star is rotating synchronously with the orbit, since the circularization timescale is typically larger than the synchronization timescale (see, for example, Hurley et al. 2002). The large rotation of the donor can boost the wind loss rate by a large factor of the order of 10^2–3 when compared with typical isolated stars of similar mass at the same evolutionary stage. The captured wind might therefore be comparably higher, with values of M˙ wNS ∼ 10^13–14 g s^−1. the spin-down epoch lasts for a time 10^7–8 yr, much shorter than the age of the cluster ( ∼ 10^10 yr) for an assumed μ1 = μ0 = 10^29–30 Gcm^3. If more wind is accreted, the wind spin-down epoch would be further shortened if the wind still carries low angular momentum. If the wind has instead large angular momentum because it is focused through the Lagrangian point L1, the RLOF epoch would be further shortened.

Conclusions The dipole spin-down timescale is about a few 10^7 yr for typical new born pulsar. The wind accretion spin-down epoch last for yr relate to the accretion rate The time elapsed in RLOF has been very short, since the time required to spin up a 1 Hz NS to 11 Hz with a spin frequency derivative of 10 −12 Hz s −1 and a duty cycle of 0.01 is a few 10^7 yr. Based on these findings we conclude that IGR J is in an exceptionally early RLOF phase. The total spin-up timescale to transform IGR J from a slow pulsar ( ∼ 1Hz) into a millisecond one (ν > 100 Hz) is 10^8–10^9 yr. Since the current RLOF phase will last for ∼ 10^9 yr, we would expect to observe today ∼ 1–10 accreting millisecond pulsars that have followed a similar evolutionary history as IGR J

CONSTRAINTS ON THE DONOR MASS AND BINARY PARAMETERS The mass function has been reported in Papitto et al. (2011) and corresponds to a minimum donor mass of 0.4 M for a NS of 1.4M. Terzan 5 is composed by two populations of stars: (Z = 0.01, Y = 0.26, 12 ± 1 Gyr ) and (Z = 0.03, Y = 0.29, 6 ± 2 Gyr) The minimum orbital separation of the system is A ≈ 0.02 AU. The Roche lobe approximation of Eggleton (1983): M d = 0.4,M NS = 1.2, R L =1.1R s. M d = 1, M ns = 2, the maximum Roche lobe radius will be 1.8R s

The turnoff mass of the metal-poor population of Terzan 5 is 0.9M (Ferraro et al. 2009) To fill the Roche lobe, therefore, any possible donor star of IGR J has to be an evolved star that has left the main sequence and has increased its radius to fit its Roche lobe. The donor star mass falls in the range of M, and is likely to be a subgiant. This result strongly constrains the orbital separation of the system to be in the range 0.023–0.026 AU for a total mass of the binary between 2.1 (1.2M NS and 0.9M donor) and 3M (2M NS and 1M donor). The inclination i of the binary is then constrained by using the projected semimajor axis of IGR J Identical considerations apply if the donor star belongs to the metal- rich population, with the difference being that the turnoff mass will be higher by a few tenths of solar mass and the inclination smaller by a few degrees.

Other formation scenarios: Accretion-Induced Collapse (AIC) In this scenario a ONeMg white dwarf accretes matter until its mass exceeds the Chandrasekhar limit and it collapses to form an NS via electron captures on Mg and Ne nuclei. In this case the binary must have gone through a preliminary contact phase during which the white dwarf was accreting from a donor star in in RLOF. During the collapse about 0.2 M are ejected from the binary which causes a sudden expansion of the orbit turning the system into a detached binary. A gravitational NS mass larger than 1.25M would immediately rule out the AIC scenario.

Frequency of 11 Hz Location in a globular cluster B in the range of 10^9–10^10 G μ= 5 × 10^26, B <5 × 10^8 G Didier Barret In its spin-up epoch, accretion rate ~ 0.2 Edd Surprising properties If it is a primordial binary, then its spin frequency & magnetic field are surprising low since the globular cluster Terzan 5 is about 12 Gyr old; Ferraro et al Terzan 5 is (1 − 4) × 10 6 M ⊙ pc^−3, 2-8 times of NGC known MSPs in NGC 6440 (Eight new MSPs in NGC 6440 and NGC 6441)

Formation from close encounter

Formation rate Take NGC 6440 for example (F. Verbunt): 5*10^5M ⊙ pc -3, R c ~0.24pc, V dis ~13km/s ~10 -4 f x=2 ~10 -3 f x=1 dN = C 0 m -1-x dm (Initial mass function)

Spin-up & Spin-down The minus sign in the equation implies that the sense of the orbital angular momentum is the same as that of the rotation of the neutron star.

Evolution history epochTimescaleRotate frequencyMagnetic FieldDuty cycle Spin-up1~10 8 yrF 1 - F 2 B 1 - B 2 Δ1Δ1 Spin-down~10 8 yrF 2 - F 3 B 2 - B 3 Δ2Δ2 Spin-up2~10 6 yrF 3 - F 4 B 3 - B 4 Δ2Δ2 F 1 ~1Hz F 2 ~100Hz F 3 ~0.1Hz F 4 ~11Hz (Reversed to F 1,2,3 ) B 1 ~10 12 G B 2 ~ G B 3 = B 4 = B f Δ 1 ~ Δ 2 ~ 0.1

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