LIFE OF NEUTRON STARS WITH EVOLVING MAGNETIC FIELD Sergei Popov ICTP, Trieste (see a review in arXiv: 2109.05584) During last ~30 years many attempts have been made to build a model of “GRAND UNIFICATION FOR NEUTRON STARS”. Diversity of neutron stars Piresetal.2015 Main ingredients of a unified model: magnetic field evolution Aguilera et al. • Field decay Page et al. • Emerging magnetic field Pons et al. • Magnetic field topology Magnetic field decay Magnetic fields of NSs are expected to decay due to decay of currents which support them. Crustal field of core field? It is easy to decay in the crust. In the core the filed is in the form of superconducting vortices. They can decay only when they are moved into the crust (during spin-down). Still, in most of models strong fields decay. Field evolution in the core 2010.07673 Panels (a) and (b) present, respectively, poloidal and toroidal components of the relative velocity of muons and electrons. Panel (c) presents poloidal component of the velocity of electrons. The homogeneous magnetic field is directed upwards. Left figure – before the field is re-arranged. Right – after. Then the field evolves slower. 6 Period evolution with field decay astro-ph/9707318 An evolutionary track of a NS is very different in the case of decaying magnetic field. The most important feature is slow-down of spin-down. Finally, a NS can nearly freeze at some value of spin period. Several episodes of relatively rapid field decay can happen. Number of isolated accretors can be both decreased or increased in different models of field decay. But in any case their average periods become shorter and temperatures lower. 7 Magnetars, field decay, heating A model based on field-dependent decay of the magnetic moment of NSs can provide an evolutionary link between different populations (Pons et al.). P Pdot PSRs M7 Magnetars CCOs 8 Magnetic field decay vs. thermal evolution arxiv:0710.0854(Aguileraetal.) Magnetic field decay can be an important source of NS heating. Ohm and Hall decay Heat is carried by electrons. It is easier to transport heat along field lines. So, poles are hotter. (for light elements envelope the situation can be different). 9 Joule heating for everybody? arXiv:0710.4914(Aguileraetal.) It is important to understand the role of heating by the field decay for different types of INS. In the model by Pons et al. the effect is more important for NSs with larger initial B. Note, that the characteristic age estimates (P/2 Pdot) are different in the case of decaying field! 10 Magnetic field vs. temperature astro-ph/0607583 The line marks balance between heating due to the field decay and cooling. It is expected that a NS evolves downwards till it reaches the line, then the evolution proceeds along the line: Selection effects are not well studied here. A kind of population synthesis modeling is welcomed. Teff ~ Bd 1/2 Hall cascade and field evolution 12 astro-ph/0402392 advection Ohm Hall With only Hall term we have: Characteristic timescales Hall time scale strongly depends on the current value of the field. Ohmic decay depends on the conductivity Resistivity can be due to • Phonons • Impurities Aguilera et al. 2008 See Cumming et al. 2004 14 P-Pdot diagram and field decayChashkina,Popov2012.arXiv:1112.1123 τOhm=106 yrs τHall=104/(B0/1015 G) yrs 15 Decay parameters and P-Pdot τOhm=107 yrs τHall =102/(B0/1015 G) τOhm=106 yrs τHall =103/(B0/1015 G) τOhm=106 yrs τHall =104/(B0/1015 G) Longer time scale for the Hall field decay is favoured. It is interesting to look at HMXBs to see if it is possible to derive the effect of field decay and convergence. Chashkina,Popov2012.arXiv:1112.1123 16 Realistic tracks Popovetal.MNRAS2010 Using the model by Pons et al. (arXiv: 0812.3018) we plot realistic tracks for NS with masses 1.4 Msolar. Initial fields are: 3 1012, 1013, 3 1013, 1014, 3 1014, 1015 Color on the track encodes surface temperature. Tracks start at 103 years, and end at 2 106 years. See newer calculations in Gullon et al. 17 Joint description of NS evolution with decaying magnetic field The idea to describe all types of NSs with a unique model using one initial distribution (fields, periods, velocities) and to compare with observational data, i.e. to confront vs. all available observed distributions: - P-Pdot for PSRs and other isolated NSs - Log N – Log S for cooling close-by NSs - Luminosity distribution of magnetars (AXPs, SGRs) - …………….. The first step is done in Popov et al. (2010) The initial magnetic field distribution with ~13.25 and σ~0.6 gives a good fit. ~10% of magnetars. GRAND UNIFICATION FOR NEUTRON STARS 18 Cooling curves with decay Magnetic field distribution is more important than the mass distribution. 19 Observational evidence? Kaplan&vanKerkwijkarXiv:0909.5218 20 Extensive population synthesis: M7, magnetars, PSRs M7 M7 Magnetars PSRs Using one population it is difficult or impossible to find unique initial distribution for the magnetic field All three populations are compatible with a unique distribution. Of course, the result is model dependent. 21 Magnetars bursting activity due to field decay 1101.1098 In the field decay model it is possible to study burst activity. Bursts occur due to crust cracking. The decaying field produce stresses in the crust that are not compensated by plastic deformations. When the stress level reaches a critical value the crust cracks, and energy can be released. At the moment the model is very simple, but this just the first step. 22 An illustrative model1204.4707 Poloidal Test illustrates the evolution of initially purely poloidal field 23 Another model Initially the poloidal field is large. Initially the toroidal field is large. If the toroidal field dominates initially then significant energy is transferred to the poloidal component during evolution. In the opposite case, when the poloidal component initially dominates, energy is not transferred. The toroidal component decouples. 1201.1346 Hall cascade and attractor http://www.physics.mcgill.ca/~kostasg/research.html Hall cascade can reach the stage of so-called Hall attractor, where the field decay stalls for some time (Gourgouliatos, Cumming). GourgouliatosandCumming2013 Evolution of different components 1311.7004 Hall attractor mainly consists of dipole and octupole (+l5) New studies of the hall cascade1501.05149 New calculations support the idea of a kind of stable configuration. Core and crust field evolution 27 1709.09167 Hall attractor is confirmed. Magnetic field decay on P-Pdot diagram Igoshev,Popov(2014).arXiv:1407.6269 It is not clear if magnetic field significantly decays during at least some episodes of lifetime of normal radio pulsars. Modified pulsar current Igoshev,Popov(2014) We applied our methods to large observed samples of radio pulsars to study field decay in these objects: - ATNF catalogue (Manchester et al. 2005). - PMSS (Parkes Multibeam and Swinburne surveys) (Manchester et al. 2001). We reconstructed the magnetic field decay in the range of true (statistical) ages: 8 104 < t < 3.5 105 yrs In this range, the field decays roughly by a factor of two. With an exponential fit this corresponds to the decay time scale ~4 105 yrs. Note, this decay is limited in time. Thermal evolution. Low fields All types of heating are neglected. Calculations are made by Shternin et al. (2011). We fit the numerical results to perform a population synthesis of radio pulsars with decaying field. Also valid when the Hall cascade is off. Magnetic field evolution Igoshev,Popov(2015) All inclusive: - Hall - Phonons - Impurities arXiv:1507.07962 What kind of decay do we see? Ohmic decay due to phonons Hall cascade Both time scales fit, and in both cases we can switch off decay at ~106 yrs either due to cooling, or due to the Hall attractor. Comparison of different optionsIgoshev,Popov(2015) We think that in the range ~105 – 106 yrs in the case of normal pulsars we see mostly Ohmic decay, which then disappears as NSs cool down. arXiv:1507.07962 Getting close to the attractor Temperature maps Pure dipole Dipole + octupole (Model 1) Dipole+octupole+l5 arXiv:1610.05050 New results in 2009.04331 36 SXP 1062 A peculiar source was discovered in SMC. Be/Xray binary, P=1062 sec. A SNR is found. Age ~104 yrs. (1110.6404; 1112.0491) Typically, it can take ~1 Myr for a NS with B~1012 G to start accretion. 37 Evolution of SXP 1062 1112.2507 B0= 4 1014, 1014, 7 1013, 4 1013, 1013 G A model of a NS with initial field ~1014 G which decayed down to ~1013 G can explain the data on SXP 1062. Many other scenarios have been proposed. We need new observational data. Some new data in arXiv: 1706.05002 Accreting magnetars 1709.10385 Typically magnetic fields of neutron stars in accreting X-ray binaries are estimated with indirect methods. • Spin-up • Spin-down • Equilibrium period • Accretion model • ……. Field evolution in a magnetar 1709.10385 Parameters of ULX M82 X-2 1709.10385 41 Anti-magnetars Note, that there is no room for antimagnetars from the point of view of birthrate in many studies of different NS populations. Ho1210.7112 New results 1301.2717 Spins and derivative are measured for PSR J0821-4300 and PSR J1210-5226 42 Evolution of CCOs Among young isolated NSs about 1/3 can be related to CCOs. If they are anti-magnetars, then we can expect that 1/3 of NSs in HMXBs are also low-magnetized objects. They are expected to have short spin periods. However, there are no many sources with such properties. The only good example - SAX J0635+0533. An old CCO? Possible solution: emergence of magnetic field (see physics in Ho 2011, Vigano, Pons 2012). 1011 1013 B HMXBs Chashkina, Popov 2012 Popov et al. MNRAS 2010 B PSRs+ Magnetars+ Close-by coolers CCOs 1010 1012 Halpern, Gotthelf 43 Observations vs. theoryChashkina,Popov(2012) We use observations of Be/X-ray binaries in SMC to derive magnetic field estimates, and compare them with prediction of the Pons et al. model. 44 Where are old CCOs? Yakovlev,Pethick2004 According to cooling studies they have to be bright till at least 105 years. But only one candidate (2XMM J104608.7-594306 Pires et al.) to be a low-B cooling NS is known (Calvera is also a possible candidate). We propose that a large set of data on HMXBs and cooling NSs is in favour of field emergence on the time scale 104 ≤ τ ≤ 105 years (arXiv:1206.2819). Some PSRs with “additional heating” can be descendants of CCOs with emerged field. 45 How the field is buried 1212.0464 t=60 msec Recent model 46 1809.07057 47 Emerging field: modelingHo2011 1D model of field emergence Dashed – crustal, dotted – core field 48 Another model Vigano,Pons1206.2014 2D model with field decay Ohmic diffusion dominates in field emergence, but Hall term also can be important. Calculations confirm that emergence on the time scale 103-105 years is possible. B0p=1014 G 49 Emerged pulsars in the P-Pdot diagram Emerged pulsars are expected to have P~0.1-0.5 sec B~1011-1012 G Negative braking indices or at least n<2. About 20-40 of such objects are known. Parameters of emerged PSRs: similar to “injected” PSRs (Vivekanand, Narayan, Ostriker). The existence of significant fraction of “injected” pulsars formally do not contradict recent pulsar current studies (Vranesevic, Melrose 2011). Part of PSRs supposed to be born with long (0.1-0.5 s) spin periods can be matured CCOs. Espinozaetal.arXiv:1109.2740,1211.5276 50 Evolution of PSRs with evolving field 1209.2273 Three stages: 1. n<=3 Standard + emerging field 2. n>3 Ohmic field decay 3. oscillating and large n – Hall drift 51 Buried field in Kes79? 1110.3129 Very large pulse fraction (64%) in the anti-magnetar Kes 79. Large sub-surface magnetic field can explain the existence of compact hot spots. Then the field must have been buried in a fall-back episode. The idea is to reconstruct surface temperature distribution, and then calculate which field configuration can produce it. Hidden magnetar in RCW103 521504.03279 Not so hidden! 53 1607.04107 1607.04264 Typical SGR activity was reported. Pulsar timing Recently, Parthasarathy et al. (2019) presented detailed timing of 85 pulsars. For many of them braking indices were measured. We analyze different approaches to explain these results, and conclude that the best explanation is related to an episode of field decay in young, still relatively hot, NSs. Braking index measurements Parthasarathy et al. (2020) MNRAS 494, 2012 Braking and P-Pdot 1702.03616 n=2.7 n=1 n=6 For constant field n=3. n>3 can be an indication of decaying fields. Parthasarathyetal.(2020)MNRAS494,2012 Large braking indices due to field decay P0=0.04 s P0=0.16 s M=1.32 Msun 2008.11737 Field decay is due to phonons Lighter NSs (M~1-1.2 Msun) have higher temperatures, and so – more rapid field decay due to phonons at ages ~few kyrs. This can explain large braking indices of radio pulsars. 2008.11737 What we have We analyzed different models to explain large braking indices recently measured for a sample of normal radio pulsars. We conclude that these results can be better explained in the model of magnetic field decay in low-mass NSs due to scatter of electrons off crystal phonons. These findings are in correspondence with our previous results on magnetic field decay in young normal radio pulsars. 2008.11737 60 Conclusions • Decaying magnetic field results in additional heating of a NS and decreasing its spin-down rate. • Field decay can be more important for large initial fields, for “standard” fields (~1012 G) it is not important, but can be detectable. Recent studies indicate that in the life of normal radio pulsars there is a period when their magnetic field decay. • It is possible to describe different types of young NSs (PSRs, magnetars, M7 etc.) in the model with decaying magnetic field. • Re-merging magnetic field can be an important ingredient. • With re-emerging field we can add to the general picture also CCOs. • Hall cascade (and attractor) can be an important ingredient of the field evolution: - At the moment we cannot state that we see the Hall attractor in the population of normal radio pulsars; - Also, we do not see that any of the M7 are at the Hall attractor stage with properties predicted by GC2013; - Probably, the attractor stage is reached later, or its properties are different form the predicted ones. 61 Papers to read • Cumming et al. “Magnetic field evolution in neutron star crust due to Hall effect and Ohmic decay” astro-ph/0402392 • Pons, Vigano “Magnetic, thermal and rotational evolution of isolated neutron stars” arXiv: 1911.03095 • Gusakov et al. “Magnetic field evolution timescales in superconducting neutron stars” arXiv: 2010.07673 SEE A REVIEW in arXiv: 2109.05584 Core field evolution 62 1705.00508,1805.03956 Typical timescales for the magnetic field dissipation as functions of temperature and the magnetic field strength. Field evolution due to ambipolar diffusion 63 1906.06076 Hypothesis: field decay in MSPs is caused by ambipolar diffusion in the NS core in the non-superfluid/superconductor regime. The magnetic field is transported by the charged particles at the ambipolar diffusion velocity Evolution on the P-Pdot diagram 64 1906.06076 Different types of companions 65 1906.06076 66 Wide initial spin period distribution 1301.1265 Based on kinematic ages. Mean age – few million years. Note, that in Popov & Turolla (2012) only NSs in SNRs were used, i.e. the sample is much younger! Can it explain the difference? 67 Magnetic field decay and P0 Igoshev,Popov2013 One can suspect that magnetic field decay can influence the reconstruction of the initial spin period distribution. Exponential field decay with τ=5 Myrs. =0.3 s, σP=0.15 s; =12.65, σB=0.55 τ<107 yrs, 105