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Pulsars; evolution of stellar magnetism

JD L

07/05/09

Leverhulme Lectures on Stellar Magnetism


Discovery of pulsars








First pulsar discovered accidentally in radio study of scintillating (small angular diameter) radio sources by Jocelyn Bell and Tony Hewish First pulsar had periodic repetitive radio pulses, P = 1.3 s Uncertainty at first about "clock": rotation, pulsation, orbital motion Short period requires very small clock ­ a white dwarf or neutron star (e.g. shortest orbital period for double white dwarf is of order seconds) Several more soon found, various periods, all of a few sec

07/05/09

Leverhulme Lectures on Stellar Magnetism


Discovery of CP 1919+21

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Leverhulme Lectures on Stellar Magnetism


Crab Nebula pulsar


Discovery of Crab Nebula pulsar provided important clues
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association with a known supernova (1054) short period of 0.033 sec ruled out all white dwarf models: if we guess that clock is rotation and require that equatorial velocity v is no more than Keplerian, P = 2R/v satisfies 42R3/ P2 < GM => > 3 / GP2 ~ 1011 gm/cm3, much higher than density of white dwarf (106 gm/cm3) therefore clock must be a neutron star pulse period soon found to be slowing down (4 x 10-13 s/s) presence of pulsar at centre of bright nebula with no visible energy source suggests pulsar is strongly magnetised neutron star that is slowing down by radiating lowfrequency EM waves
Leverhulme Lectures on Stellar Magnetism

07/05/09


Rotationally powered emission region in Crab Nebula






Composite image of supernova remnant from SN 1054 explosion Pulsar is blue star at centre, powering EM radiation from nebula ­ a macrowave oven Xray ­ blue Visible ­ green Radio red

07/05/09

Leverhulme Lectures on Stellar Magnetism


Energy loss from a pulsar




Suppose that a pulsar is basically a rapidly rotating magnetic neutron star which loses rotational energy by EM radiation Radiated energy given by Larmor formula, Prad = 2 (d2m /dt2)2 / 3c3 where m = BR3 is the perpendicular component of the magnetic moment of the field in the star If m = m0 exp(it) then d2m / dt2 = 2m so Prad = 2 (2m)2 /3c3 = 2 (BR3)2 (2 /P)4 /3c
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This power is taken from rotational energy, and is radiated as very lowfrequency EM waves: dErot /dt = d(I2/2) /dt = d(2 2I /P2) /dt = 42I Pdot /P3 = Prad where Pdot = dP/dt and I ~ 2 MR2/5 With known I, and measured P and Pdot, we can solve for B!
Leverhulme Lectures on Stellar Magnetism



07/05/09


Finally, field strength of a pulsar




Solving the energy loss equation for the field B required to supply the radiative energy loss from rotational deceleration B ~ (3c3I /82R6)1/2 (P Pdot)1/2 Using values for the Crab pulsar, B ~ 4 x 1012 G This value is typical for many pulsars Assuming that the field B is approximately constant in time, solving for P Pdot = P dP/dt, writing P dP = const x dt, and integrating from t = 0, we find predicted evolution of P(t): [P2 ­ P02]/2 = 82R6 B2 /3c3I t = (P Pdot) t. If P0 is much smaller than P and can be neglected, solving for t leads to an estimated age of t = P/(2 Pdot)

07/05/09

Leverhulme Lectures on Stellar Magnetism


The PPdot diagram








The PPdot diagram provides important insight into pulsar evolution If B stays constant, pulsars should evolve along lines of constant B, to greater and greater ages and steadily smaller energy loss rates Distribution of pulsars shows that this is too simple: field decay may occur. Pulsar field seem to be fossils
Leverhulme Lectures on Stellar Magnetism

07/05/09


The Lives of the Pulsars






Most current pulsars were formed in corecollapse SN explosions with fields around 1 TG, and evolve (perhaps with slow field decay), converting rotational energy into VLF radiation and thus slowing down, until after a few hundred Myr they no longer make radio beams Some pulsars (often "millisecond pulsars") are formed in interacting binary systems ­ when fresh material and angular momentum are dropped on a preexisting neutron star, it is spun up and is able to pulse again even with a much reduced field of order 100 MG A few pulsars form (perhaps from massive stars with extremely large fields on MS) with >100 TG fields, and have emission powered by energy release of magnetic decay
Leverhulme Lectures on Stellar Magnetism

07/05/09


Overview of evolution of stellar magnetic fields


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We have a good general picture of stellar evolution ~1 M0: ISM > T Tau > MS > RG > HB > AGB > PN > WD ~10 M0: ISM > HAeBe > MS > RSG > SN > NS (And don't forget that evolution in close binaries can be very different) How do magnetic fields evolve during this stellar evolution? We have basically two different kinds of questions How do fields evolve during a given evolution stage, such as main sequence or neutron star phases, and How do fields evolve between phases we know something about, through still uncharted phases such as the red giant? We now have some answers to the first type of question, but very little to the second
Leverhulme Lectures on Stellar Magnetism



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07/05/09


Star formation and premain sequence










We know fields of G to mG are present in ISM, where they have energy density similar to the values for kinetic and gravitational energy densities If fully retained as fossil, this flux would give ~100 MG on MS, so much flux must be lost, greatly reducing importance of fields Theory tells us that fields transfer angular momentum and this is probably the main way that protostars lose enough angular momentum to contract to stellar dimensions But little is known about field nature or evolution until the premain sequence (T Tau and Herbig AeBe) phase Probably the fields of T Tau stars are dynamos. Fields in more massive PMS stars could be due to protostar dynamos, or fossil remnants, or more complex processes....
Leverhulme Lectures on Stellar Magnetism

07/05/09


Field nature and evolution of lowmass stars during main sequence








Fields seem to be present generally in PMS stage ­ T Tau stars usually have fields of ~ 1 ­ 3 kG that control accretion from disk During MS we cannot detect fields directly yet except in fairly active stars, but ~all stars show activity indirectly through chromosphere (visible in Ca II K line) and Xray emission Level of activity increases with decreasing rotation period Loss of angular momentum through wind and mass ejections causes rotation to slow during MS, so field ­ and activity declines This is so predictable that it can be used to determine stellar ages (gyrochronology) Such fields are clearly produced by dynamo action, although details of dynamo are still quite obscure
Leverhulme Lectures on Stellar Magnetism

07/05/09


HK line emission, and presumably B, declines with age in low mass stars

07/05/09

Leverhulme Lectures on Stellar Magnetism


Field nature and evolution in massive stars during main sequence phase


Fields seem to be present at immediate premain sequence Only a few % of O, B, A stars are magnetic; fraction declines sharply below Teff ~ 10 000 K, vanishes below 7 000 K. Why? Fields sometimes present in only one star of SB. No fields found in SBs with periods below 3 d. Not obvious that fossil origin can explain all these features. Hint of binary origin or connection?? Fields associated with 10x (or more) deficiency in angular momentum (slow rotators), perhaps due to loss of rotation through stellar wind in PMS phase |B| is not correlated with 1/(rotation period) or depth of surface convection: unlikely to be current dynamo. Probably in fossil phase Field and flux both decline during MS with time scale somewhat shorter than main sequence time scale over x2 range of mass
Leverhulme Lectures on Stellar Magnetism









07/05/09


Evolution of field strength during main sequence phase of Ap stars






Stefano BagnuIo & I have obtained first sample of magnetic stars of known ages spanning full MS lifetime, by observing magnetic Aps in associations and clusters A typical result is at right. We see that field strength in this mass range seems to decline after an age of about 40 Myr ~ 0.2x(MS life) Decay rather fast to be Ohmic, but slow for instability... => ??
Leverhulme Lectures on Stellar Magnetism

07/05/09


Fields evolution through giant phases towards magnetic white dwarfs












During MS life of massive star, it is usually assumed that field is excluded from convective core However, perhaps enough radiative zone remains to anchor a fossil field even with red giant's deep envelope convection ­ one such star (EK Eri) seems to have been discovered Most giants known to have fields are in close binary systems (RS CVn, FK Com) and are forced to rotate rapidly by tidal coupling ­ hence they have dynamo fields based on rotation and convection Very weak field has been found in one single subgiant (beta Gem): not known if this is dynamo or fossil Global picture of field evolution through giant phase(s) still far from clear Recall Tout contention that WD fields may only arise in binaries
Leverhulme Lectures on Stellar Magnetism

07/05/09


Evolution of white dwarf fields


Once a single white dwarf is formed, its evolution is simply cooling. For typical WD (0.6 M0), cooling times are
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107 yr: Teff ~ 40 000 K, field decay modest during cooling 108 yr: Teff ~ 20 000 K, ditto 109 yr: Teff ~ 10 000 K, ditto 3x109 yr: Teff ~ 6 000 K, and cooling time longer than field decay time Thus for fossil evolution from start of WD stage, expect constant magnetic fraction for all but coolest WDs, where fraction should decline However, convection zones exist in nondegenerate outer layers of WD, so dynamo action might be possible, even though rotation velocities are very slow (<~ 10 km/s) Valyavin & Fabrika (1990s) report that frequency of fields increases as Teff declines ­ clearly not expected fossil behaviour. And we have seen that neutron star fields may decay as fossils....
Leverhulme Lectures on Stellar Magnetism

07/05/09


Finally ... overview


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07/05/09

Two families (or phases?) of magnetic fields: fossils and dynamos Fossil fields Upper main sequence (and some Herbig AeBe stars), white dwarfs, neutron stars Field strength unrelated, or inversely related, to rotation rate Fairly simple global field structure Field structure is static or evolves slowly over many years Associated chemical peculiarity may occur, due to vertical diffusion (gravity vs radiative acceleration) which requires suppression of competing mixing phenomena: internal mixing weak due to slow rotation, atmospheric mixing weak due to field stabilisation Close binary frequency is very strange (no Ap systems with P < 3 d)
Leverhulme Lectures on Stellar Magnetism


Overview 2


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Current dynamo fields Lower main sequence stars & active red giants (usually binary) Field strength directly related to rotation rate and presence of deep convection zone Field structure normally rather complex, like solar field Field structure usually changes within a few rotation periods Associated phenomena (chromospheric emission lines, e.g. in Ca II lines, starspots, and Xray emission) seem to be intrinsically linked to (powered by) presence and variability of dynamo field, and are stronger with more rapid rotation Phenomena closely connected with binarity, since rapid rotation is required and this may be enforced by close companion As a single star loses mass, angular momentum and field both decline
Leverhulme Lectures on Stellar Magnetism


Overview 3


One hypothesis is that these main types are independent: Fossil fields are left in some stars from formation, and persist until collapsed state (WD, NS) because of long decay time
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Statistics roughly right for WDs but probably not for NSs Leave binarity anomalies unexplained







Dynamo fields appears when physics (rotation, convection, shear) can drive dynamo, otherwise not Alternative 1: dynamo fields can persist into fossil phase (e.g. PMS dynamo leads to MS fossil, giant dynamo leads to WD or NS fossil) Alternative 2: dynamo fields are produced only (or mainly, or sometimes) in certain types of binaries (e.g. commonenvelope systems) and then appear in resulting system (cataclysmic variable such as AM Her) or even in a single (merged) star
Leverhulme Lectures on Stellar Magnetism

07/05/09


Thanks for your attention

07/05/09

Leverhulme Lectures on Stellar Magnetism