15.6 THE SPIN-UP OF NEUTRON STARS BY ACCRETION

1. 15.6 THE SPIN-UP OF NEUTRON STARS BY ACCRETION The angular momentum comes from the inner point of the accretion disk. This inner point may be defined as the point where the ram pressure of the infalling gas just balances the magnetic field pressure of the neutron star : The Alfen Radius. The ram pressure is the rate at which momentum is transported inwards per unit area For a dipole field of intensity BS at the surface of the neutron star (radius R) the magnetic pressure is where rA is the Alfen radius Since the accretion rate and By substitution we can obtain an expression for the Alfen radius Thus for the innermost region of the accretion disk at the Alfen radius, we have The rate of angular momentum transfer by accretion is Since it is this which causes the neutron star to spin up then PHYS3010 - STELLAR EVOLUTION

2. . Log (- P/P) Now since where P is the period and the luminosity due to accretion is we can obtain by substitution for rA and dm/dt in equation (1). I = 2/5 MR2 is the moment of inertia of the neutron star The adjacent figure demonstrates that the theoretical model provides a good representation of the spin-up process, in which the spin-up rate is related to the luminosity of the source. i.e. that the accretion of matter provides the spin-up. L30 is the luminosity measured in units of 1030 J s-1 . Log (PL306/7) PHYS3010 - STELLAR EVOLUTION

3. 15.7 MILLISECOND PULSARS Millisecond radio pulsars have been discovered, many of which are members of a binary system. They are found to be slowing in the same way as ordinary radio pulsars at a rate which is consistent with the neutron stars having weak (105 T) magnetic fields. The most likely scenario is that these objects were spun-up by accretion in the past as an X-ray binary source, and now the accretion process has stopped leaving the neutron star to radiate as a radio pulsar. Substitution of expression for rA Now since we see that a higher accretion rate leads to a shorter period, and also that the stronger the magnetic field BS the longer this eventual period will be. If we assume the accretion to take place at the maximum level possible, i.e. the Eddington level then for a M = M0 and R = 104 m neutron star we can estimate the minimum attainable period Pmin so that, if the surface magnetic field is 105 Tesla, then we can just spin-up a neutron star to become a 2 ms pulsar. Note that it is not possible, on the basis of this theory, to generate millisecond pulsars from neutron stars with the strong (108 T) magnetic fields which are found to be associated with ordinary radio pulsars. PHYS3010 - STELLAR EVOLUTION

4. 15.8 ERRATICALLY VARIABLE X/g EMISSION FROM XRB SOURCES The above X-ray signal from Cygnus X-1 shows that it is extremely variable on just about all timescales down to milliseconds, and with no measurable periodicity. An optical search of the sky region at the location of the X-ray source revealed the existence of a 5.6 day spectroscopic binary HDE 226868 which is a supergiant star which has a mass of around 20 M0. Velocity km s-1 Orbital Phase The optical spectroscopy revealed that it had a large projected radial velocity of at least 50 km s-1 and no visible binary companion. If the x-ray object is the companion then its mass would be somewhere in the region of 15 M0, much too high to be a neutron star. Cyg X-1 is the archetypal black hole candidate. • NOTE :some caution as to the exact mass value must be considered since : • With a luminous X/g emitter so close is it really an OB type? • Cyg X-1 is not an eclipsing binary and hence the inclination is not sure PHYS3010 - STELLAR EVOLUTION

5. 103 102 1 Flux (Crab units) 10-1 10-2 10-3 50 100 150 200 250 Time (days after outburst) 15.9 OBSERVATIONAL CHARACTERISTICS OF BLACK HOLE CANDIDATES One of the key goals in the studies associated with black hole physics is to find a set of observational criteria which can be used to identify and define the existence of black holes in binary systems. So far, apart from the dynamic mass function, this has not been conclusive and the process is on-going. Let us briefly review some of these aspects. • The Dynamic Mass Function. This is currently the crucial factor, but as noted above has some problems. However for objects in e.g. the galactic centre the obscuration due to gas and dust makes it impossible to study any optical companion. • Rapid Variability of the X/g Signal. To do this well requires a bright source in order to get good statistics. However some NS binaries also exhibit the same characteristic. However Quasi Periodic Oscillation (QPO) characteristics have been observed in both BH and NS systems • Transient Emission. Most of the black hole candidate sources exhibit dramatic changes in intensity. This transient nature of their emission appears to be a strong clue as to the existence of a black hole in a close binary system. The adjacent figure illustrates the observed characteristics of a typical transient outburst from black hole candidate sources. The emission rises many orders of magnitude in intensity over a very short time period (< day) to a level which is consistent with the Eddington limit for a mass of typically 1 - 10 M0. The emission subsequently dies away over some day to months, often exhibiting secondary smaller outbursts PHYS3010 - STELLAR EVOLUTION

6. X/g-ray Emission Spectra. The emission spectra demonstrate a number of factors which appear to be largely restricted to BH binary systems. Broad red shifted 511 annihilation line? Fe Line In the so-called high state the spectrum is dominated by an intense soft X-ray excess, thought to be emission from the hot accretion disk. Soft X-ray excess Log IX/g In the so-called low state (transient HE outburst) the emission becomes dominated by g-rays in the 100 keV to 1 MeV range. Often visible is a broad line, thought to be due to electron-positron annihilation close to the black hole. There is also evidence for Compton backscatter peaks. Backscatter? 1 10 101 102 103 Photon Energy keV This bimodal nature of the high energy spectral emission seems to be a characteristic of black hole binary systems. The ~ 6 keV iron line spectral structure has been interpreted as due to the spiral motion of the material as it funnels down the potential well in the accretion disk. Likewise the backscatter peaks are thought to be related to related to 511 keV g-rays which interact with the surrounding accretion and are Compton scattered in the direction of the earth. Red shifted 511 keV e+e-annihilation line ~170 keV Compton backscattered g-rays Accretion disk Source PHYS3010 - STELLAR EVOLUTION

7. Time of g-ray transient event Distance of radio cloud from object Time • Relativistic Jets - Galactic Micro-Quasars Radio images of the transient g-ray sources have discovered vast radio jets which emerge from the object and extend several light years into the surrounding interstellar medium. Just like quasars there is a forward and 1800 backward jet, they are also superluminal. The adjacent picture shows the 6 cm radio jets associated with the g-ray transient source 1E 1740.7 which is situated close to the galactic centre. Site of the g-ray source { Expanding superluminal radio blob The g-ray transient events appear to be correlated with the production of the superluminal radio emitting blobs. The amount of energy associated with the bulk motion of the radio clouds is quite phenomenal. The mass of the clouds are typically >1022 kg, and the associated kinetic energy Where g is the Lorenz factor associated with the bulk motion. It is interesting to note that if the actual ejection took place within a timescale of about one minute then these objects become as powerful as an AGN during this short time. PHYS3010 - STELLAR EVOLUTION