Pulsar Ages and the Evolution of Pulsar Spin Velocity Alignment Aristeidis Noutsos Michael Kramer Simon Johnston Dominic Schnitzeler Evan Keane NS212b Bonn, 22 October
Previously on Pulsar Spin Velocity Alignment N.3.2 KS probability of rejecting uniformity = 99.8% Noutsos et al. (212), MNRAS S±9º S±9º S±9º S±9º Ψ Ψ Ψ v v v v S from pulsar polarisation data v from pulsar timing / VLBI.1 uniformity PSR 1 2 34 1 2 3 4 54 PSRs We used the polarisation and proper motion data of 54 pulsars to study the distribution of Ψ, the angle between S±9º and v We rejected that the orientations of pulsar spins and velocities are uncorrelated, with 99.8% probability
!"" #$%&' Chapter 2: Spin Velocity Alignment with Pulsar Age We examined the degree of spin velocity alignment for subsets of pulsars grouped according to characteristic age.5.4!"" +.196 =.694.352 = 4.5.4!"" #$%&'!#"""!"#"""!""#""" +.49 =.938.159 = 14.5.4 +.15 =.982.61 = 46.5.4 +.2 =.998.8 = 58 ".3.2.3.2.3.2.3.2.1.1.1.1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4.5.4 +.91 =.879.246 = 1.5.4 +.25 =.969.94 = 42.5.4 +.3 =.997.13 = 54!"".3.2.3.2.3.2.1.1.1 1 2 3 4 1 2 3 4 1 2 3 4.5.4 +.77 =.898.212 = 32.5.4 +.8 =.991.33 = 44!#""".3.2.3.2.1.1 1 2 3 4 1 2 3 4!"#""".5.4.3.2 +.16 =.979.54 = 12.1 1 2 3 4
!"" #$%&' Chapter 2: Spin Velocity Alignment with Pulsar Age We examined the degree of spin velocity alignment for subsets of pulsars grouped according to characteristic age.5.4!"" +.196 =.694.352 = 4.5.4!"" #$%&'!#"""!"#"""!""#""" +.49 =.938.159 = 14.5.4 +.15 =.982.61 = 46.5.4 +.2 =.998.8 = 58 ".3.2.3.2.3.2.3.2.1.1.1.1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4.5.4 +.91 =.879.246 = 1.5.4 +.25 =.969.94 = 42.5.4 +.3 =.997.13 = 54!"".3.2.3.2.3.2.1.1.1 1 2 3 4 1 2 3 4 1 2 3 4.5.4 +.77 =.898.212 = 32.5.4 +.8 =.991.33 = 44!#""".3.2.3.2.1.1 1 2 3 4 1 2 3 4!"#""".5.4.3.2 +.16 =.979.54 = 12.1 1 2 3 4
Chapter 2: Spin Velocity Alignment with Pulsar Age The probability of rejecting that S v are uncorrelated remains constant (within errors) across all pulsar characteristic ages 1.8! ().6.4.2 ~ t dyn 4 2 2 5-Myr pulsar trajectory in the Galactic potential! "!!"!#$!%&' 4 2 15 1 5 5 (!)*+,- "!)*+,-! " #$%! 1 1, 1, 1,! "#$%&' This is surprising since we expect the Galactic potential to significantly alter pulsar velocities on a dynamical timescale of t dyn = GMMW πr 2 MW δh and wash out any S v correlation 1/2 1 Myr But this is not what we see based on the above analysis
Pulsar Ages The characteristic ages of pulsars are known to be unreliable* P = KP 2 n t true = S147 PSR J538+2817 SNR centre P (n 1) P 1 P The distance and outward proper motion of PSR J538+2817 from the centre of S147 imply a true age of 3 4 kyr P n 1 t 2 kyr t 4 kyr t 6 kyr * They are calculated assuming: (i) The pulsar was born spinning infinitely fast P = (ii) The pulsar spins down by converting rotational energy to purely magnetic-dipole radiation n =3 (iii) The pulsar maintains a constant magnetic field K (B sin α) 2 = const. τ c = P 2 P Ng et al. (27) t true ~ 3 kyr τ c ~ 6 kyr Either or all of these assumptions are likely wrong for most pulsars. E.g. PSR J538+2817 was born with P 138 ms ( P ) and is 1x younger than τc.
Pulsar Kinematic Ages Alternatively, one can estimate pulsar ages independently of a spin-down model, based on the kinematic properties of individual pulsars, assuming pulsars are born close to the Galactic plane!"#$%&'.4.3.2.1 -.1 -.2 -.3 -.4!","-."/( *+!","12"/(! -8-6 -4-2 ("#$%&' 2 4 6-1 1 2 3 4 )"#$%&' 5 6
Pulsar Kinematic Ages We integrated the equations of motion for 52 pulsars, assuming they are moving through the Galactic potential of Paczynski (199) and using their present proper motions and locations (μ l, μ b, l, b, d) For each pulsar, we explored finite ranges of the unknown v r and z birth : v r = [ 5, +5] km s 1 z birth = [-1,+1] pc H(v birth ) Hobbs et al. (25) Arzoumanian et al. (22) +1 pc zbirth 1 pc v 1 t1 Δt = t kin v birth t we weighted the unknown v r using the distribution of v birth + R(z birth ) we weighted the unknown birth height using the distribution of OB stars (Reed 2) n OB = n e z /h OB! "#$%& '()*'+,-..1.1 z (kpc)
Pulsar Kinematic Ages The probability distribution of tkin comes from marginalising the joint probability of H(v birth ) and R(z birth ) over all v birth and z birth : +1 pc p(t kin )= L(v birth,t kin ) H(v birth ) R(z birth ) H(τ 1 t kin )dv birth dz birth 1 pc J837+61 J922+638 J1136+1551 p (t kin ).2.15.1.5 68% CL.8.6.4.2.15.1.5.1 1 1 1 1 1 1.1.1 1 1 1 most probable kinematic age characteristic age τ 1 =2τ c ln( P 1ms ) (integration limit) t kin / τ c p (t kin ) ~35% of the pulsars produced more than 1 intersection with the Galactic plane and p(tkin) was complex.2.15.1.5?.1 1 1 1 t kin / τ c
Spin Velocity Alignment with Pulsar Age Redux We have produced a data set of 52 kinematic ages This is the largest number of pulsar ages, estimated independently of a spindown model We have used the 33 most reliable estimates to examine again the degree of spin velocity alignment as a function of pulsar age
Spin Velocity Alignment with Pulsar Age Redux!"#$%&%''!($)''*(+,- Vela (~2 kyr).5!"#""".5 pks =.936.162.4.5 +.33 pks =.935.153.4 Npsr = 4.11.4.3.3.1.1.1.1 2 3 4 1 2 3 4 1 4.153.11.4.134 Npsr = 33.3.3.2.1.1.1 4 1 2 3 4 1.5.267 pks =.726.324.4 Npsr = 19 Npsr = 22.3.3.2.2.1.1 1 2 3 4 1 2 3 +.242 pks =.335.228.4 PSR B1952+32 (~51 kyr) 4.5!"#""" 4 +.174 pks =.791.4 3.5 +.98 2 3 4 pks =.937.4.2 2 3 +.47 pks =.956.2 1 2 Npsr = 3.3 1.5 Npsr = 11 +.33 pks =.935.4 3.5 +.5!$)$%&%''!($)''*(+,- 2.5 Crab (~1 kyr).3.2!#""" Npsr = 33.2 1.134.4.2 pks =.937 Npsr = 3.2!"" +.47 pks =.956 Npsr = 11.3!""#""".5 +.5 +.5 "!#""" estimates to examine again the degree of spin velocity alignment as a function of pulsar age!"" We have use the 33 most reliable Npsr = 3.3.2.1 PSR J538+2817 (~3 kyr) 1 2 3 4
Spin Velocity Alignment with Pulsar Age Redux!"#$%&%''!($)''*(+,- Vela (~2 kyr).5!"#""".5 pks =.936.162.4.5 +.33 pks =.935.153.4 Npsr = 4.11.4.3.3.1.1.1.1 2 3 4 1 2 3 4 1 4.153.11.4.134 Npsr = 33.3.3.2.1.1.1 4 1 2 3 4 1.5.267 pks =.726.324.4 Npsr = 19 Npsr = 22.3.3.2.2.1.1 1 2 3 4 1 2 3 +.242 pks =.335.228.4 PSR B1952+32 (~51 kyr) 4.5!"#""" 4 +.174 pks =.791.4 3.5 +.98 2 3 4 pks =.937.4.2 2 3 +.47 pks =.956.2 1 2 Npsr = 3.3 1.5 Npsr = 11 +.33 pks =.935.4 3.5 +.5!$)$%&%''!($)''*(+,- 2.5 Crab (~1 kyr).3.2!#""" Npsr = 33.2 1.134.4.2 pks =.937 Npsr = 3.2!"" +.47 pks =.956 Npsr = 11.3!""#""".5 +.5 +.5 "!#""" estimates to examine again the degree of spin velocity alignment as a function of pulsar age!"" We have use the 33 most reliable Npsr = 3.3.2.1 PSR J538+2817 (~3 kyr) 1 2 3 4
Spin Velocity Alignment with Pulsar Age Redux Now, the probability of rejecting uniformity shows a clear downwards trend For pulsars with tkin > tdyn, uniformity is not rejected 1.8 " )*.6.4.2 ~ t dyn 1 1 1, 1, 1,!!"# $%!&'( Our results suggest that if we use the more reliable kinematic ages instead of the characteristic ages for our sample of pulsars, then Young pulsars ( 1 Myr) maintain a strong correlation (pks ~ 95%) between their spin and velocity orientations Beyond tkin~1 Myr the correlation weakens and it completely disappears for tkin 1 Myr
Kinematic Ages as Probes of Pulsar Evolution The derived kinematic ages can serve as an estimate of the pulsars true age: n =1+2 τ c t kin 1 P P n 1 t true t kin Hence, we can used them to test the standard assumptions of magnetic-dipole braking and infinitesimal birth periods By comparing tkin with τc, we can express the braking index as a function of P and vice versa.35.3.25.2.15.1.5.35.3.25.2.15.1.5.35.3.25.2.15.1.5.35.3.25.2.15.1.5 5% 16% 12% 29% 29% 18% 1% 21% 25% 21% 33 pulsars 9% 1 1 2 3 4 5 6 7 8 9 n n P / P = P/P = P / P = P/P =.1 P / P = P/P =.1 P / P = P/P =.5 P P = P 1 p(p ) [x1 3 ] 2.5 2. 1.5 1..5 1.8.6.4.2 n 1 2 tkin τ c 1 n 1 27 pulsars n=3 25 5 75 1 125 P,3 (ms) P,3 = P ^ P, 3 = 63 1 t kin τ c +728 35 Popov & Turolla (212) ms (a) (b)
Epilogue
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution:
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined the distribution of braking indices for our sample, for different P
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined the distribution of braking indices for our sample, for different P the distribution of P, assuming magnetic-dipole braking (n = 3)
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined the distribution of braking indices for our sample, for different P the distribution of P, assuming magnetic-dipole braking (n = 3) the dependence of spin velocity alignment on P
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined the distribution of braking indices for our sample, for different P the distribution of P, assuming magnetic-dipole braking (n = 3) the dependence of spin velocity alignment on P The observed preference for n = 1 is an artefact of assuming P = ; relaxing this assumption yields a more uniform distribution of n
Epilogue If we take pulsar characteristic ages at face value, spin velocity alignment does not become weaker with increasing age! this is the opposite of what is expected for pulsars travelling through the Galactic potential We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.! this is the largest sample of independently estimated pulsar ages If we use the kinematic ages to study the evolution of spin velocity alignment, we see a clear decorrelation between the spin and velocity orientations for ages > 1 Myr! this the expected for the Milky Way, with the above virialisation time scale Kinematic ages are potentially a powerful probe of pulsar evolution: Using the tkin/τc ratios, we examined the distribution of braking indices for our sample, for different P the distribution of P, assuming magnetic-dipole braking (n = 3) the dependence of spin velocity alignment on P The observed preference for n = 1 is an artefact of assuming P = ; relaxing this assumption yields a more uniform distribution of n The predictions of SN-kick models favouring alignment for short P need to be tested with more data
Coming Soon VLBA pulsar astrometry (PSR π, eπ) 2 Path of Pulsar B95+8 Pulsar absolute polarisation data (Effelsberg, Parkes, LOFAR, etc.) 1999.855 Y (mas) -2 1999.373 1998.874 + -4 1998.331-6 Model Data -3-2 -1 1 2 3 X (mas) 1s more spin velocity orientations will allow for a better statistics and hence a better understanding of the process of spin velocity alignment Don t miss! We are currently using our method for calculating pulsar kinematic ages with the 233 pulsar proper motions from Hobbs et al. (25) as well as other measurements from the literature (MSc degree, Oliver Lux)