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Neutron Stars Nanda Rea Institute for Space Sciences (ICE), CSIC-IEEC, Barcelona, ES Anton Pannekoek Institute, University of Amsterdam, NL Early history 1931 Chandrasekhar argued that WDs collapse at masses > 1.4 M . (Chandrasekhar

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Nanda Rea

Institute for Space Sciences (ICE), CSIC-IEEC, Barcelona, ES Anton Pannekoek Institute, University of Amsterdam, NL

Neutron Stars

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Early history

  • 1934 Baade & Zwicky proposed the existence of NS, they

predicted their formation due to supernova explosion and their radius of ~10 km . (Baade & Zwicky 1934, Proc.Nat.Acad.Sci.)

  • 1932 Chadwick discovers the neutron, recognized as a new

elementary particle. (Chadwick1932, proceedings of the RAS)

  • 1939 Oppenheimer & Volkoff defined the first equation of state

for a NS of mass ~1.4 M€, a radius of ~10 km and a density of ~1014 gr/cm3 (Oppenheimer & Volkoff, Phys.Rev)

  • 1931 Chandrasekhar argued that WDs collapse at masses > 1.4

M€. (Chandrasekhar 1931, ApJ)

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Early history

  • 1967 Pacini predicted electromagnetic waves from rotating

NSs and that such star might be powering the Crab nebula. (Pacini

1967 and 1968, Nature)

  • 1934 Baade & Zwicky proposed the existence of NS, they

predicted their formation due to supernova explosion and their radius of ~10 km . (Baade & Zwicky 1934, Proc.Nat.Acad.Sci.)

  • 1932 Chadwick discovers the neutron, recognized as a new

elementary particle. (Chadwick1932, proceedings of the RAS)

  • 1939 Oppenheimer & Volkoff defined the first equation of state

for a NS of mass ~1.4 M€, a radius of ~10 km and a density of ~1014 gr/cm3 (Oppenheimer & Volkoff, Phys.Rev)

  • 1931 Chandrasekhar argued that WDs collapse at masses > 1.4

M€. (Chandrasekhar 1931, ApJ)

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Institute of Space Sciences, Barcelona, Spain

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Early history

  • 1968 Hewish & Bell studing interplanetary scintillation observed

a periodicity of 1.337s, discovering the first pulsar: PSR 1919+21.

(Hewish et al. 1968, Nature)

  • 1967 Pacini predicted electromagnetic waves from rotating

NSs and that such star might be powering the Crab nebula. (Pacini

1967 and 1968, Nature)

  • 1934 Baade & Zwicky proposed the existence of NS, they

predicted their formation due to supernova explosion and their radius of ~10 km . (Baade & Zwicky 1934, Proc.Nat.Acad.Sci.)

  • 1932 Chadwick discovers the neutron, recognized as a new

elementary particle. (Chadwick1932, proceedings of the RAS)

  • 1939 Oppenheimer & Volkoff defined the first equation of state

for a NS of mass ~1.4 M€, a radius of ~10 km and a density of ~1014 gr/cm3 (Oppenheimer & Volkoff, Phys.Rev)

  • 1931 Chandrasekhar argued that WDs collapse at masses > 1.4

M€. (Chandrasekhar 1931, ApJ)

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Curiosity…

Charles Schisler 1931 – 2011 (Bluffon, South Carolina)

Independent US Navy discovery of pulsars in August 1967, and the first dis covery of the Crab pulsar, with the Clear Antenna in Alaska. Na Nanda nda Rea ea - In

Institute of Space Sciences, Barcelona, Spain

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50 years of pulsars

Credit: S. Serrano Elorduy N. Rea (ICE, CSIC-IEEC)

Rea 2017, Nature Astronomy, Vol. 1 p 827

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Birth of a neutron star

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Westerlund 1

  • Via dynamos/instabilities in the stellar core
  • As fossil fields from a magnetic progenitor
  • From massive star binary progenitors

Magnetic field formation in neutron stars

(Obergaulinger, Janka & Aloy 2015, MNRAS)

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Neutron star composition

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Rotating magnetic dipole

Magnetic field estimate

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

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Magnetars XDINSs CCOs Rotation Powered Isolated Pulsars Binary millisecond pulsars

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The most dense rigid body known to date: As dense as a nucleus, with a central pressure 10000000000000000000000000 times the atmospheric pressure on Earth.

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The most dense rigid body known to date: As dense as a nucleus, with a central pressure 10000000000000000000000000 times the atmospheric pressure on Earth. The fastest known rotating body in the Universe: 1.3959546744700354+/-0.0000000000000003ms

Tangential velocity 0.15c

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The most dense rigid body known to date: As dense as a nucleus, with a central pressure 10000000000000000000000000 times the atmospheric pressure on Earth. The fastest known rotating body in the Universe: 1.3959546744700354+/-0.0000000000000003ms The roundest known circle in the Universe: Is the orbit of a pulsar around a normal star: PSR J1909-3744’s orbit it is round to 5micron (1/10 of a human hair) to 567000km.

Tangential velocity 0.15c

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The most stable clocks in the Universe: Pulsar arrivals are so precise and stable that beats atomic and quantum optical clocks.

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The most magnetic objects in the Universe: The magnetar: SGR 1806-20 has a magnetic field is 100000000 times larger than the highest B-field we can reproduce on Earth. The most stable clocks in the Universe: Pulsar arrivals are so precise and stable that beats atomic and quantum optical clocks.

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The most magnetic objects in the Universe: The magnetar: SGR 1806-20 has a magnetic field is 100000000 times larger than the highest B-field we can reproduce on Earth. The most stable clocks in the Universe: Pulsar arrivals are so precise and stable that beats atomic and quantum optical clocks. The most precise tests of General Relativity: Binary pulsar systems holds the Guiness for having tested GR at 0.05% confidence level. Einstein is right so far…

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The least expensive Gravitation Waves detector: Observing regularly millisecond pulsars we might detect GWs (International Pulsar Timing Array).

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The least expensive Gravitation Waves detector: Observing regularly millisecond pulsars we might detect GWs (International Pulsar Timing Array). The least expensive Solar System planet mass determination: Observing pulsars systematically planet masses are measured as precisely as dedicated satellites.

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The least expensive Gravitation Waves detector: Observing regularly millisecond pulsars we might detect GWs (International Pulsar Timing Array). The least expensive Solar System planet mass determination: Observing pulsars systematically planet masses are measured as precisely as dedicated satellites. Our future GPS in space: Pulsar clocks are so precise that will be our unique GPS system when travelling in space with no connection with Earth.

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Pulsar Timing Technique

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The great potential of pulsar timing

1) Pulsar periods can be measured with extraordinary precision: e.g. PSR J0437-4715 has a period of :

17 s 17 signi nificant nt digits! ! 0.00575745192436238 0.00575745192436238 ± 0.00000000000000005 s 0.00000000000000005 s

2) Exploiting an event which repeats a huge number of times in a reasonable time-span Tobs 3) Rotational stability of some pulsars is comparable to the best artificial clocks

a 3-ms pulsar performs Tobs/Pspin ~ 1010 cycles a year by coherently counting all of them, one gets an accuracy after 1 YEAR of obs ΔPerror/Pspin = Δterror/ Tobs = 0.01 Pspin / Tobs = 10-12 Na Nanda nda Rea ea - In

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The great potential of pulsar timing

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Acquisition of the pulsar time series

tbe

begi gin

tend

end

07346100374221775320153201532110233030367162

digitization @ 1 or 2 or 4 or 8 or 16 bits

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The great potential of pulsar timing

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Dispersion of the radio waves due to scattering

ne

Free electrons in Interstellar Medium

t2−t1 ∝ (ν2-2 −ν1-2) DM DM = nedl

∫

L

L

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De-dispersion of the pulsar time series De-dispersion of the pulsar time series

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The great potential of pulsar timing

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Time

0 phase 1 Folding Integrated profile

Period search and folding of the pulsar time series

Fourier spectrum Frequency Na Nanda nda Rea ea - In

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The great potential of pulsar timing

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Pulsar times should be reported to a stable reference clock: the Solar System Barycenter (SSB)

tSSB : Time calculated at the Solar System Barycenter tobs : Time measure at the Radio Antenna tclk : Observatory clock correction, usually via GPS D/f2 : Dispersion Measure term ΔR : Roemer delay (propagation) to SSB ΔS : Shapiro delay in Solar-System ΔE : Einstein delay at Earth Na Nanda nda Rea ea - In

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Pulsar times should be reported to a stable reference clock: the Solar System Barycenter (SSB)

D / f 2 = [ DM / (2.41 · 10-16) s ] / f 2

ΔR = + ( r · n ) ( r · n )2

  • | r |2

c 2 c d

→ → → → →

ΔS = - 2 Tsun log10 ( 1 + cos θ )

dΔE G mi (vEarth-SSB)2 dt c2 ri 2c2

= Σi ( )+

Gravity of other planets. This is where we can measure planet masses. Solar gravitational dwell changes wave paths. Earth path around the Sun wit h respect to the pulsar Dispersion measure correction Na Nanda nda Rea ea - In

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Pulsar Timing modelling can now start…

Time Time residual Time Time Na Nanda nda Rea ea - In

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Pulsar Timing modelling can now start…

  • Spin parameters: period, first derivative, second derivative…
  • Astrometric parameters: position, proper motion, parallax

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Pulsar Sound

PSR B0833-45 (Vela Pulsar): rotating with a period of 89 millisec

  • nds or about 11 times a second

PSR B0531+21(Crab Pulsar): rotating with a period of 33 millisec

  • nds or about 30 times a second

PSR J0437-4715: binary system with a pulsar rotating about 174 times a second PSR B1937+21 (the F flat pulsar): rotating at 0.00155780644887275 seconds, or about 642 times a second Na Nanda nda Rea ea - In

Institute of Space Sciences, Barcelona, Spain

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

Magnetars

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40

1 G – The Earth magnetic field measured at the North pole 100 G – A common hand-held magnet like used to stick papers on a refrigerator 107 G – The strongest man-made field ever achieved, made using focussed explosive charges, lasting only 4-8 s 104 G – The magnetic field used for an MRI in the hospitals 1012 G – Typical neutron star magnetic fields 4.4x1013 G – Electron critical magnetic field 10 14 -1015 G: Magnetars overtake this limit…

Magnetars

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Swift-XRT INTEGRAL COMPTEL Fermi-LAT Abdo et al. 2010

  • About 25 X-ray pulsars with Lx~1033-1036erg s-1
  • X-ray luminosity generally larger than the

rotational energy loss rate

  • soft and hard X-ray emission (0.5-200 keV);

thermal + non-thermal spectrum

  • persistent or transients
  • rotating with P~0.3-12 s
  • magnetic fields of B~1013-1015 Gauss
  • flaring activity in soft gamma-rays

(0.01-102 s; Lx~1039-1047erg s-1)

  • faint infrared/optical emission
  • transient radio emission (in 4 cases)

Kaspi et al. 2003

Magnetars

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Bright X-ray pulsars with 0.5- 10keV spectra modelled by a thermal plus a non-thermal component

Soft Gamma Repeaters Anomalous X-ray Pulsars

Bright X-ray transients!

Transients magnetars

Short X/gamma-ray bursts (at the beginning thought to be GRBs)

How do we discover new magnetars?

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Magnetars

  • magnetars have highly twisted and complex

magnetic field morphologies, both inside and outside the star.

  • magnetar

magnetospheres are filled by charged particles trapped in the twisted field lines, interacting with the surface thermal emission through resonant cyclotron scattering.

  • twisted magnetic fields might locally (or

globally) stress the crust (either from the inside or from the outside). Plastic motions and/or returning currents convert into crustal heating causing large outbursts.

Magnetars

Normal Pulsars

(Rea & Esposito 2011; Kaspi & Beloborodov 2017)

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Magnetars' flaring activity

NR et al. 2009 Israel et al. 2008 Palmer et al. 2005

(Coti Zelati, Rea, Pons, Campana & Esposito 2017)

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(Mandea & Balasis 2006, Geophysical Journal)

(Palmer et al. 2005)

Magnetar giant flares: the Earth perspective

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VLGRB

SNe

(adapted from Smartt 2015)

Comparison with other energetic transients Typical Galactic sources….

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

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CCOs XDINs High-B Pulsars

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

Magnetars

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Other Magnetar-like sources

  • 2. Two X-ray Dim Isolated NSs show evidence of strong

magnetic structures

(Borghese et al. 2015, 2017)

  • 4. Two young rotational powered pulsars showed magnetar

activity.

(Gavriil et al. 2008; Kumar & Safi-Harb, 2008; Archibald et al. 2016, Gogus et al. 2016)

  • 1. Magnetars were discovered having also low dipolar

B-fiels and strong magnetic structures.

(Rea et al. 2010, 2012, 2014, Tiengo et al. 2013)

  • 3. A central compact object (CCO) with a 6.4hr period

showed magnetar-like activity.

(Rea et al. 2016; D’Ai et al. 2016)

  • utburst

quiescence

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We need to solve the thermal and magnetic evolution of a neutron star over > Myr timescales…

(Aguilera et al. 2008; Pons et al. 2009; Vigano', NR, Pons, Perna, Aguilera & Miralles 2013)

Thermal evolution: energy balance equation Magnetic evolution: Hall induction equation

Specific heat Thermal conductivity Neutrino emissivity Electrical resistivity: strongly depends on T Hall induction

Magnetic field evolution in neutron stars

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28 Very Magnetic Pulsar Initial conditions: Bdip~1014 G (white lines) Bint~ 1015 G (colors) Relatively Magnetic Pulsar Intial conditions: Bdip~1013 G (white lines) Bint~ 1014 G (colors) Extremely Magnetic Pulsar Intial conditions: Bdip~1015 G (white lines) Bint~ 1016 G (colors)

Strong non-dipolar fields are expected in all NSs

(Vigano’, Rea, Pons, Perna, & Miralles 2013; Elfritz, Pons, Rea & Glampedakis 2017)

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

Accreting pulsars

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Accreting neutron stars Transitional systems

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Pulsar accretion phases

Roughly speaking, X-rays arise from the release of gravitational potential energy as the accreting gas falls into the deep gravitational potential of the NS. e.g. A proton dropped radially onto a NS with M=1.4M¤ and R=10km, loses potential energy equal to: The energy released by the gas infalling onto the NS surface goes in part to heat the stellar surface, and in part is re-emitted in the X-ray band.

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Pulsar accretion phases Neutron Star

Magnetic pressure: repulsive Gravitational force: attractive Centrifugal force: repulsive Ram pressure: Depends on the density of the matter falling down onto the neutron star

Infalling matter

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Pulsar accretion phases

Light cylinder radius: The magnetic field lines break because the tangential velocity become greater than c: Magnetospheric radius: The magnetic pressure of the neutron star equals the ram pressure of the infalling material: Corotation radius: At this radius the matter corotates with the star in keplerian motion: inside win the gravitational force and outside win the centrifugal repulsion:

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Pulsar accretion phases

R(m)<R(cor)<R(lc)

spin axis

X-rays B

Part of the X-ray emission is modulated by the spin period: lighthouse effect magnetosphere

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Pulsar accretion phases

R(cor)<R(m)<R(lc)

magnetosphere

Accretion L=GMM/R

Propeller L=GMM/rm ∝M 9/7

Centrifugal gap

. . .

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Pulsar accretion phases

R(cor)<R(lc)<R(m)

magnetosphere

The centrifugal barrier is closed. The matter cannot reach the NS surface. Pulsations might appear in Radio due to particles emission, not due anymore to the shock caused by the matter falling onto the magnetic poles.

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Pulsar accretion phases

Centrifugal gap Accretion L=GMM/R Propeller L=GMM/rm ∝M 9/7 Radio pulsar regime L ~ ε Lsd

. . .

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Pulsar Bestiary

Spin Period derivative (s/s)

Spin Period (s)

Binary millisecond pulsars

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Double neutron stars Neutron star plus a low mass companion star

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Binary millisecond pulsars

The discovery of the binary pulsar PSR B1913+16 with a period of 59ms and an orbit of 7hr (Hulse & Taylor 1979)

tPSR-BARY = Tpsr + ΔR + ΔE + ΔS + ΔA

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Triple System: PSR J0337+1715

(Ransom et al. 2014, Nature)

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Binary millisecond pulsars and GR tests

Th The modification in the shape of the orbit pe periastron pr precession

  • r
  • rbital decay

Th The modification in the shape of the orbit Th The modification in the time of arrival of th the pulses gr gravitational reds dshift an and time dilat ation Th The modification in the time of arrival of the pu pulses Sha Shapiro del elay

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Periastron precession Time dilation & gravitational redshift Shapiro delay (amplitude) Shapiro delay (shape) Orbital period decay

GR tests! Binary millisecond pulsars and GR tests

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Shapiro delay in the data of a binary pulsar

( )

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

− + Δ ψ φ sin sin 1 cos 1

ln

i e c R t

g Shap

[ Lyne, Burgay, Kramer, Possenti et al. 2004]

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GR verified at 0.2% level

Binary millisecond pulsars and GR tests

PSR B1913+16 PSR J0737-3039

(Weisberg et al. 2010) (Kramer et al. in prep)

GR tested at 0.2% GR tested at 0.05%

Nobel Prize 1993 to Hulse & Taylor!

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The masses of the double pulsar PSR J0737-3039

(Burgay et al. 2003; Lyne et al. 2004)

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MB=1.249(1)M¤ MA=1.338(1)M¤

4 independent tests of GR!

(Kramer et al 2006; Stairs et al. 2010)

The masses of the double pulsar PSR J0737-3039

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The International Pulsar Timing Array

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The International Pulsar Timing Array

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EPTA: Effelsberg, Nancay, Jodrell, Westerborg: 42 millisecond pulsar for 7-18 years (Desvignes et al. 2016)

The International Pulsar Timing Array

(PPTA, EPTA, NanoGRAV) PPTA : Parkes: 24 millisecond pulsar for 8-25 years (Reardon et

  • al. 2016)

NanoGRAV : Arecibo, GBT, VLA: 59 millisecond pulsar for 9 years (Arzoumanian et al. 2016) Na Nanda nda Rea ea - In

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Pulsars as deep space GPS

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NASA's Voyager 1, launched 35 years ago with various messages from the Earth, is

  • n the verge of moving into interstellar
  • space. It has a Golden Record on-boad in

case it will intercepted by extraterrestrial life

Pulsars GPS idea already flying…

The Pioneer plaques are a pair

  • f aluminium plaques which were

placed on board the 1972 Pioneer 10, 1973 Pioneer 11 spacecrefts, featuring a pictoral image in case either Pioneer 10 or 11 is intercepted by extraterrestrial life.

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On January 2018 the first test of this pulsar GPS system has been successfully performed using the SEXTANT instrument onboard NICER, hosted by the International Space Station that orbits around Earth at slightly more than 17,500

  • mph. Within eight hours of starting the X-ray pulsar timing experiment, via

timing 14 X-ray millisecond pulsars, the algorithm converged on a location with an error of 10 miles.

Pulsars as deep space GPS

(NICER collaboration, Nature 2018)

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Pulsars are Cosmic gifts.

Taking their beats we can probe:

  • Dense matter within the neutron stars
  • The most extreme magnetic fields
  • The electron density in the Galaxy
  • Plasma studies at high densities and gravity in accreting systems
  • General Relativity and test alternative theories
  • Use them as Gravitational Wave Detectors
  • Use them as GPS for deep space travels

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