glitches in radio pulsars - uni-bonn.detauris/ns2012-2/espinoza_glitches.pdf · glitches in radio...

Glitches in radio pulsarsCristóbal EspinozaJodrell Bank Centre for Astrophysics

42000 44000 46000 48000 50000 52000 54000MJD (Days)

6.3945

6.39452

6.39454

6.39456

6.39458

6.3946

6.39462

6.39464

6.39466Fr

eque

ncy

(Hz)

?

Monday, 22 October 2012

Glitch 0

10

20

30

!!

("H

z)

-1500 -1000 -500 0 500 1000 1500Days from MJD=53737

-7380

-7360

-7340

-7320

-7300

-7280

-7260

! (1

0-15 H

z s-1

)•

∆ν

∆ν̇

10−3 ≤ ∆ν ≤ 100µHz


What can produce a glitch?Caused by crust rearrangements; cooling, slowdown re-shaping.

Caused by rapid angular momentum exchange between the inner superfluid and the Crust; result of halted vortex migration.

Caused by magnetic field stresses on the crust, driven by vortex migration.

(Anderson & Itoh 1975; Alpar et al. 1984; many many others)

(Baym et al. 1969)

(Ruderman et al. 1998)

INTERNAL OR CRUST PROCESS

M. Ruderman (2009)


0.001 0.01 0.1 1 10Period (s)

-21

-20

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

log(

Perio

d de

rivat

ive)

Glitch detectedMagnetar

100 TG

1 TG

0.01 TG

100 MG

1 Kyr

100 Kyr

10 Myr

1 Gyr

GlitchDetections

315 glitches in plot

378 detected so far http://www.jb.man.ac.uk/pulsar/glitches.html

~130 pulsars


http://www.jb.man.ac.uk/pulsar/glitches.html




Glitch spin-up rate(integrated glitch activity)[Lyne, Shemar & Graham-Smith (2000)]

ν̇glitch =�

i

�j ∆νij�

k Tk

Separate pulsars according to their spindown rate and estimate their spin-up rate:

j counts the glitches on pulsar iTk is the total time for which pulsar k has been observed (and sums over ALL pulsars in the group)

|ν̇|

622 pulsars observed for more than 3 yr


-2 0 2 4

0.0001

0.001

0.01

0.1

1

log |!| (10-15 Hz s-1)•

! N

g" (

yr -1

)

•

-2 0 2 4 60.001

0.01

0.1

1

0.01 0.1 1 10 100 1000 10000 100000 1x106

log |!| (10-15 Hz s-1)•

%

of

! r

eve

rsed

by

glit

ch

es

•

(b)-2 0 2 4 6

1x10-6

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100 1000 10000 100000 1x106|!| (10-15 Hz s-1)•

Glit

ch

sp

in-u

p

rate

(1

0-15 H

z s-1

)

(a)

Glitch activity grows linearly with spindown rate

Glitching rateEspinoza, Lyne, Stappers & Kramer (2011)


old pulsars

young pulsars

pulsar evolution?

ν̇glitch ∝

|ν̇|

ν̇glitch ∝ |ν̇|

3 regimes


-4 -3 -2 -1 0 1 2

0

10

20

30

40

50

60

Num

ber

0.0001 0.001 0.01 0.1 1 10 100

315 glitches

315 glitches (smaller bin)

Magnetars

log(!!) ["Hz]

!! ["Hz]

Bi-modal: two types of glitches?

Large glitches: seen mostly in Vela-like pulsars

Distribution of Frequency steps

(Espinoza et al. 2011)


Giant glitchersselected for showing large frequency and spindown rate steps

0.001 0.01 0.1 1 10 100 1000 10000

0.0001

0.001

0.01

0.1

1

10

100

Positive dF1 jump

Negative dF1 jump

!! ("

Hz)

|!!| (10-15 Hz s-1)·

old pulsars

young pulsars

ν̇glitch ∝

|ν̇|


Giant glitchersNarrow size distributions.

Quasi periodic behaviour. Waiting times consistent with reaching critical lag.

Permanent spindown

-1000 -500 0 500 1000Days from Glitch

-894

0-8

900

! (1

0-15 H

z s-1

)

•-1000 -500 0 500 1000

Days from Glitch

-295

00-2

9200

02

46

8

J2021+365154177

!!

("Hz

)

-28.

7-2

8.5

! (1

0-15 H

z s-1

)

•

-1500-1000-500 0 50010001500

00.

005

0.01

J1847-013054784.449

!!

("Hz

)

-1500-1000-500 0 500 1000 1500

010

2030 J2229+6114

53064

-184

.7-1

84.4

! (1

0-15 H

z s-1

)

•

-1500-1000-500 0 50010001500

01

23

4 B1838-0453388

!!

("Hz

)

-88.

6-8

8.3

! (1

0-15 H

z s-1

)

•

-1500-1000-500 0 50010001500

00.

020.

040.

06 B1822-0952056

!!

("Hz

)

-1000 -500 0 500 1000Days from Glitch

-295

00-2

9300

-1500-1000-500 0 50010001500

05

10

J2229+611454110

-296

0-2

920

-1500-1000-500 0 50010001500

020

40

B1853+0154123

-117

7-1

176

-117

5

-1500-1000-500 0 50010001500

01

2

J1841-052453562

-89

-88.

2-1500-1000-500 0 50010001500

00.

050.

10.

15

B1822-0954114.96

-28.

45-2

8.4

-28.

35-1500-1000-500 0 50010001500

00.

10.

2 B1859+0151318

-203

.15

-203

.05-1500-1000-500 0 50010001500

00.

1

J1845-031652128

-734

0-7

260-1500-1000-500 0 50010001500

010

2030

40 B1823-1353737

-255

-250

-1500-1000-500 0 50010001500

00.

10.

20.

3 J1913+083254653.908

-203

.5-2

03.1

-1500-1000-500 0 50010001500

00.

20.

4

J1845-031654170

-805

-800

-795-1500-1000-500 0 50010001500

010

2030 J1838-0453

52162

-1500-1000-500 0 50010001500

020

40

B2334+6153642

-1000 -500 0 500 1000Days from Glitch

-800

-790

-780

0.01 0.1 1 100

0.2

0.4

0.6

0.8

1

!! ["Hz]

P(!!)

Vela

J0537-6910

B1338-62

Crab

B1737-30

J0631+1036

Modelling pulsar glitches 13

1e-13 1e-12 1e-11 1e-10 1e-09| ! |

100

1000

10000

Wai

ting

time

(day

s)

J0537-6910

J0729-1448

B2334+61

Vela

.(Hz/s)

Figure 14. We plot the approximate waiting time betweenglitches for the pulsars that have shown multiple giant glitches, asa function of the spin down rate. We also include two pulsars thathave shown only one glitch but also have a long baseline for theobservations and can thus provide us with an interesting lowerlimit on the waiting time. The data appears consistent with thenotion that giant glitches can occur once a critical lag of approxi-mately !" = 10!2 is reached. In fact the Vela like pulsars glitchevery few years, but the X-ray pulsar J0527-6910, which is spin-ning down approximately an order of magnitude faster glitchesevery few months, while the lower limits on slower pulsars indi-cate that they may glitch every decade. In fact the data appearsto be well described by a fit of the form y=A/x, as shown inthe figure, with y the waiting time in seconds, x the frequencyderivative and A = 1.082212 ! 10!3 Hz.

weak in the crust, possibly due to the fact that not all vor-tices are free, but rather that the strong pinning force givesrise to a situation in which most vortices are pinned andonly a small fraction can ’creep’ outwards. Only once themaximum unpinning lag is exceeded can the vortices moveout freely; a process which can excite Kelvin oscillations andgive rise to a strong drag and recoupling of the two compo-nents on a very short timescale, i.e. a glitch. The short termpost-glitch relaxation of the Vela, on the other hand, sug-gests that the magnitude of the drag in the core of the NS isconsistent with theoretical expectations for electron scatter-ing of magnetised vortex cores. Our model does not supportthe notion that, at least on short timescales, a significantnumber of vortices is pinned in the core (as could, for ex-ample, be the case if one has a type II superconductor andvortices cannot cross fluxtubes, e!ectively decoupling thecore and the crust). A detailed analysis of the case in whichthe core consists of a type II superconductor will be a focusof future work in order to obtain more quantitative resultsand constraints on NS interior physics. Some vortices thatcross the core may however be weakly pinned to the crust,and vortex repinning and creep (also in the core) may playa role on the longer timescales associated with the recovery.

Another e!ect which will have an impact on the post-glitch recovery is the Ekman flow at the crust-core inter-face. This e!ect has been shown to be important in fittingthe post glitch recovery of the Vela and Crab pulsars byvan Eysden & Melatos (2010) and future adaptations of our

model should relax the rigid rotation assumption for thecharged component and include the e!ect of Ekman pump-ing. Further developments should also include more realisticmodels for the drag parameters in the star, as the densitydependence of the coupling strength clearly has an impacton the amount of angular momentum that can be exchangedon di!erent timescales. Truly quantitative results could thenbe obtained with the use of realistic equations of state to-gether with consistent estimates of the pinning force, suchas those of (Grill & Pizzochero 2011) and (Grill 2011).

Note that we have assumed that a giant glitch onlyoccurs when the maximum critical lag is reached. If unpin-ning could be triggered earlier, this could generate smallerglitches. In fact cellular automaton models have shown thatthe waiting time and size distributions of pulsar glitches canbe successfully explained by vortex avalanche dynamics, re-lated to random unpinning events (Warszawski & Melatos2010; Melatos & Warszawski 2009; Warszawski & Melatos2011). It would thus be of great interest to use our long-termhydrodynamical models, with realistic pinning forces, as abackground for such cellular automaton models that modelthe short-term vortex dynamics. Such a model could thenalso be extended to model not only large pulsar glitches,but more generally pulsar timing noise, an issue that is ofgreat importance for the current e!orts to detects GWs withpulsar timing arrays (Hobbs et al. 2010).

Finally, the next generation of radio telescopes, such asLOFAR and the SKA, is likely to provide much more precisetiming data for radio pulsars and is likely to set much morestringent constraints on the glitch rise time and short termrelaxation, thus allowing us to test our models and probethe coupling between the interior superfluid and the crustof the NS with unprecedented precision.

ACKNOWLEDGMENTS

This work was supported by CompStar, a Research Net-working Programme of the European Science Foundation.

BH would like to thank Cristobal Espinoza, DanaiAntonopoulou and Fabrizio Grill for stimulating discussionson pulsar glitch observations and pinning force calculation.BH also acknowledges support from the European Union viaa Marie-Curie IEF fellowship and from the European Sci-ence Foundation (ESF) for the activity entitled ”The NewPhysics of Compact Stars” (COMPSTAR) under exchangegrant 2449.

TS acknowledges support from EU FP6 Transfer ofKnowledge project “Astrophysics of Neutron Stars” (AS-TRONS, MTKD-CT-2006-042722).

REFERENCES

Adams P.W., Cieplak M., Glaberson W.I., 1984., Phys RevB, 32, 171

Alexov A. et al., 2011, A&A 530, A80Anderson P.W., Alpar M.A., Pines D., Shaham J., 1982,Pil.Mag. A, 45, 227

Anderson P.W., Itoh N., 1975., Nature, 256, 25Andersson G., Comer G.L., C.Q.G., 2006, 23, 5505

(Haskell et al. 2012) (Espinoza et al. 2011)

rate changes


PERMANENT CHANGES ( )THE CRAB AND VELA PULSARS

CRAB VELAν̇(t) ν̇(t)

RESIDUALS RESIDUALS

∆ν̇p

~36 YR ~14 YR

ν̇


0.001 0.01 0.1 1 10 100 1000 10000

0.0001

0.001

0.01

0.1

1

10

100

!! ("

Hz)

|!!| (10-15 Hz s-1)·

1 day

7 days

0.001 ph

0.0001 ph

Small glitchesMeet detection issuesPresent in all pulsars, but preferably in low spin-down rate ones

jumps appear smaller...

Do not seem to show significant permanent steps.

Small glitches with large jumps may go undetected

∆ν̇

∆ν̇

∆ν̇


10Timing no ise

Timing noise refers to unmodelled deviations from a simple spindown model, appearing as a random wandering of the phase residuals. As pictured by Lyne+2010, most timing noise could be caused by changes, with both signs, of the spindown rate.

Increasing |∆ν̇|∆ν̇ = 0.00 ∆ν̇ = −0.01 ∆ν̇ = −0.1 ∆ν̇ = −0.3 ∆ν̇ = −1.0

×10−15

Hz s−1 Increasing |∆ν̇|×10

−15Hz s

−1

fit until glitch

overall fit

∆ν̇ > 0

∆ν̇ < 0

∆ν̇ = 0.00

∆ν̇ = −0.01 ∆ν̇ = −0.1 ∆ν̇ = −0.3∆ν̇ = −1.0

∆ν̇ = 0.00

∆ν̇ = −0.01 ∆ν̇ = −0.01∆ν̇ = −0.1 ∆ν̇ = −0.1∆ν̇ = −0.3 ∆ν̇ = −0.3∆ν̇ = −1.0 ∆ν̇ = −1.0∆ν̇ = 0.00

∆ν̇ = 0.01∆ν̇ = 0.00 ∆ν̇ = 0.1 ∆ν̇ = 0.3 ∆ν̇ = 1.0∆ν̇ = 0.00 ∆ν̇ = 0.01 ∆ν̇ = 0.3∆ν̇ = 0.1 ∆ν̇ = 1.0

Glitches and timing noise can be confused.Small glitches might remain undetected because they look like timing noise and timing noise might be confused with glitches (and reported as glitches with unusual properties).

∆ν̇ > 0 & ∆ν̇ < 0

Residuals for ∆ν = 0.003µHz (ν, ν̇ fit until glitch epoch) Residuals for ∆ν = 0.003µHz (ν, ν̇ fit entire data span)

Residuals for ∆ν = 0.0µHz (ν, ν̇ fit entire data span)Residuals for ∆ν = 0.0µHz (ν, ν̇ fit until glitch epoch)

0.001 0.01 0.1 1 10 100 1000 10000

0.0001

0.001

0.01

0.1

1

10

100

All glitches (dF1 < 0)The Crab pulsar

!! ("

Hz)

|!!| (10-15 Hz s-1)·

1 day

samplin

g

0.1 milli periods RMS

(!! < 0)·

10

Characterising glitches and timing irregularities in pulsars and magnetars

Gl i tches

C. M. Espinoza1*, D. Antonopoulou2^, B. W. Stappers1, A. Watts2

Glitches are unresolved positive steps in pulsar spin frequency, normally accompanied by a change in the spindown rate. After some glitches the frequency and the spin-down rate relax back to the pre-glitch state on timescales of up to ~100 days. These events are thought to be caused by the interaction of the neutron star crust with the internal neutron superfluid.

1Jodrell Bank Centre for Astrophysics, UK2Astronomical Institute "Anton Pannekoek"*[email protected], ^[email protected]

Timing no ise

φg = −∆νp∆t−∆ν̇p∆t2

2+ τ2d |∆ν̇d|

�e∆t/τd − 1

�

Here is what a glitch looks like

Many recent detections of small events show unusual properties, like positive spindown rate jumps [Yuan+2010, Chukwude+2010, Espinoza+2011]. We focus on these small events and study, for the first time, how they are detected and measured, with the suspicion that some of them are signatures of a different physical mechanism and should instead be classified as a different phenomena, namely timing noise. After the glitch, the

phase residuals can be described by a parabola plus a decaying term.

Timing noise refers to unmodelled deviations from a simple spindown model, appearing as a random wandering of the phase residuals. As pictured by Lyne+2010, most timing noise could be caused by changes, with both signs, of the spindown rate.

By demanding at least one datapoint before and that is larger than the typical RMS of the residuals (see the first figure) we can define glitch detection limits.

These plots show all detected glitches in three particular pulsars [JBCA glitch catalogue], and the detection limits corresponding to each pulsar, reflecting the regular observations carried out at Jodrell Bank observatory.

Yuan+2010, MNRAS, 404, 289Chukwude+2010, MNRAS, 406, 1907Espinoza+2011, MNRAS, 414, 1679

-40 -20 0 20 40 60 80 100Time since glitch (Days)

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

Phas

e re

sidu

als

in a phase residuals plot, for a model that describes

the rotation up until the glitch epoch.

Glitch

Increasing |∆ν̇|∆ν̇ = 0.00 ∆ν̇ = −0.01 ∆ν̇ = −0.1 ∆ν̇ = −0.3 ∆ν̇ = −1.0

×10−15

Hz s−1

The panels below show how the glitch signature is lost as the size of the spindown rate jump increases.

tup

φm

Increasing |∆ν̇|×10−15

Hz s−1

Is the time at which the residuals become positive.

Is the minimum value reached by the phase residuals.

tup

φm

fit until glitch

overall fit

∆ν̇ > 0

∆ν̇ < 0

∆ν̇ = 0.00

∆ν̇ = −0.01 ∆ν̇ = −0.1 ∆ν̇ = −0.3∆ν̇ = −1.0

∆ν̇ = 0.00

∆ν̇ = −0.01 ∆ν̇ = −0.01∆ν̇ = −0.1 ∆ν̇ = −0.1∆ν̇ = −0.3 ∆ν̇ = −0.3∆ν̇ = −1.0 ∆ν̇ = −1.0∆ν̇ = 0.00

∆ν̇ = 0.01∆ν̇ = 0.00 ∆ν̇ = 0.1 ∆ν̇ = 0.3 ∆ν̇ = 1.0∆ν̇ = 0.00 ∆ν̇ = 0.01 ∆ν̇ = 0.3∆ν̇ = 0.1 ∆ν̇ = 1.0

Glitches and timing noise can be confused.Small glitches might remain undetected because they look like timing noise and timing noise might be confused with glitches (and reported as glitches with unusual properties).

What can we detect/have detected ? ∆νmin ←→ ∆ν̇min

tup

φm

The plots also show all detected glitches, in more than 100 pulsars.

The distribution of glitches in the space is determined by our ability to detect them.Glitches below the lines wouldn’t be detected.

∆ν̇ — ∆ν

Lyne+2010, Science, 329, 408Glitch catalogue: http://www.jb.man.ac.uk/pulsar/glitches.html

∆ν̇ > 0 & ∆ν̇ < 0

IAU Symposium 291| Beijing, August 2012

Residuals for ∆ν = 0.003µHz (ν, ν̇ fit until glitch epoch) Residuals for ∆ν = 0.003µHz (ν, ν̇ fit entire data span)

Residuals for ∆ν = 0.0µHz (ν, ν̇ fit entire data span)Residuals for ∆ν = 0.0µHz (ν, ν̇ fit until glitch epoch)

The two segmented lines represent lower limits determined by observing cadence and the RMS of the timing residuals

∆ν > 0 & ∆ν̇ < 0

0.001 0.01 0.1 1 10 100 1000 10000

0.0001

0.001

0.01

0.1

1

10

100All glitches (dF1 < 0)J0631+1036 (dF1<0.0)J0631+1036 (dF1>0.0)

!! ("

Hz)

|!!| (10-15 Hz s-1)·

3 milli periods RMS

10 day

samplin

g

(!! < 0)(!! < 0)(!! > 0)

··

·

0.001 0.01 0.1 1 10 100 1000 10000

0.0001

0.001

0.01

0.1

1

10

100All glitches (dF1 < 0)B1737-30 (dF1<0.0)B1737-30 (dF1>0.0)

!! ("

Hz)

|!!| (10-15 Hz s-1)·

10 day

samplin

g

0.8 milli periods RMS

(!! < 0)(!! < 0)(!! > 0)

·

··

Study of the small glitches population is complicated because of contamination by other phenomena

UNDERSTANDING OF JUMPS BECOMES IMPORTANT∆ν̇


Summary: what we know about glitches

All pulsars can glitch. But different pulsars glitch different.

Pulsar with faster spindown rates glitch more often.

The cumulative effect over time is larger for pulsars with large (linearly) and it represents ~%1 of the spindown rate.

-distribution is bimodal. Some pulsars only exhibit large glitches.

∆νν̇

∆ν


Future work...or in progress

Any trend involving -jumps? Re-measure and improve error determinations.

Are all glitches followed by a permanent change?

How is the size distribution towards lower end?

ν̇

ν̇


FIN


glitches in radio pulsars - uni-bonn.detauris/ns2012-2/espinoza_glitches.pdf · glitches in radio...

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