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M. Colpi

Publications and source records attributed to M. Colpi.

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Isolated Neutron Stars in the Galaxy

In this article we briefly review our recent results on evolution and properties of isolated neutron stars (INSs) in the Galaxy. As the first step we calculate a {\it census} of INSs in our Galaxy. We infer a lower bound for the mean kick velocity of NSs, $ \sim $(200-300) ${\rm km s^{-1}}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and for a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. These results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to $\sim$few percents. Then we show that the range of minimum value of magnetic moment, $μ_b$: $\sim 10^{29.5}\ge μ_b \ge 10^{28} {\rm G} {\rm cm}^3$, and the characteristic decay time, $t_d$: $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$, can be excluded assuming the standard initial magnetic momentum, $μ_0=10^{30} {\rm G} {\rm cm}^3$, if accreting INSs are observed. For these parameters an INS would never reach the stage of accretion from the interstellar medium even for a low space velocity of the star and high density of the ambient plasma. The range of excluded parameters increases for lower values of $μ_0$. It is shown that old accreting INSs become more abundant than young cooling INSs at X-ray fluxes below $\sim 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. We can predict that about one accreting INS per square degree should be observed at the {\it Chandra} and {\it Newton} flux limits of $\sim 10^{-16}$ erg cm$^{-2}$ s$^{-1}.$ The weak {\it ROSAT} sources, associated with INSs, can be young cooling objects, if the NSs birth rate in the solar vicinity during the last $\sim 10^6$ yr was much higher than inferred from radiopulsar observations.

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Magneto-rotational and thermal evolution of magnetars with crustal magnetic fields

Soft Gamma-ray Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are interpreted as young highly magnetized neutron stars (NSs). Their X-ray luminosity in quiescence, exceeding 10^{35} erg s^{-1} cannot be explained as due to cooling of a highly magnetized NS, but requires as an extra heat source the decay of its magnetic field (MF). We study numerically the coupled evolution of the MF, temperature and spin period under the assumption that the currents maintaining the field are confined in the crust of the star. The decay of the field depends on the field strength itself (Hall-drift), on the temperature and injects heat into the star, but is controlled by neutrino emission. Finally we consider the spin down from magnetic dipole braking with this decaying field to track the long term evolution. We find reasonable initial conditions for the MF strength and structure to explain their current observational values both of their rotational period, its time derivative and the X-ray luminosity of AXPs and SGRs.the X-ray luminosity of AXPs and SGRs.

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Population synthesis of old neutron stars in the Galaxy

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin-down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $ < V>\ga 200-300$ ${\rm km s^{-1}}$. The same conclusion is reached for both a constant ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to $\la 1%$.

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The Neutron Stars Census

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $ < V>\gtrsim 200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion $σ_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Such high velocities are consistent with those derived from radio pulsar observations. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to less than 1%.

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The Neutron Stars of Soft X-Ray Transients

Soft X-ray Transients (SXRTs) have long been suspected to contain old, weakly magnetic neutron stars that have been spun up by accretion torques. After reviewing their observational properties, we analyse the different regimes that likely characterise the neutron stars in these systems across the very large range of mass inflow rates, from the peak of the outbursts to the quiescent emission. While it is clear that close to the outburst maxima accretion onto the neutron star surface takes place, as the mass inflow rate decreases, accretion might stop at the magnetospheric boundary because of the centrifugal barrier provided by the neutron star. For low enough mass inflow rates (and sufficiently short rotation periods), the radio pulsar mechanism might turn on and sweep the inflowing matter away. The origin of the quiescent emission, observed in a number of SXRTs at a level of ~10^(32)-10^(33) erg/s, plays a crucial role in constraining the neutron star magnetic field and spin period. Accretion onto the neutron star surface is an unlikely mechanism for the quiescent emission of SXRTs, as it requires very low magnetic fields and/or long spin periods. Thermal radiation from a cooling neutron star surface in between the outbursts can be ruled out as the only cause of the quiescent emission. We find that accretion onto the neutron star magnetosphere and shock emission powered by an enshrouded radio pulsar provide far more plausible models. In the latter case the range of allowed neutron star spin periods and magnetic fields is consistent with the values recently inferred from the properties of kHz QPO in LMXRBs. If quiescent SXRTs contain enshrouded radio pulsars, they provide a missing link between X-ray binaries and millisecond pulsars.

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Aquila X-1 from outburst to quiescence: the onset of the propeller effect and signs of a turned-on rotation-powered pulsar

We report on the March-April 1997 BeppoSAX observations of Aql X-1, the first to monitor the evolution of the spectral and time variability properties of a neutron star soft X-ray transient from the outburst decay to quiescence. We observed a fast X-ray flux decay, which brought the source luminosity from ~10^36 to ~10^{33} erg/s in less than 10 days. The X-ray spectrum showed a power law high energy tail with photon index Gamma~2 which hardened to Gamma~1-1.5 as the source reached quiescence. These observations, together with the detection by RossiXTE of a periodicity of a few milliseconds during an X-ray burst, likely indicate that the rapid flux decay is caused by the onset of the propeller effect arising from the very fast rotation of the neutron star magnetosphere. The X-ray luminosity and hard spectrum that characterise the quiescent emission can be consistently interpreted as shock emission by a turned-on rotation-powered pulsar.

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Population synthesis of millisecond and submillisecond pulsars

Known millisecond pulsars have periods longer than 1.558 ms. Recycled in binary systems, neutron stars can attain very short spin periods. In this paper we investigate the expected properties of the millisecond pulsar distribution by simulating synthetic populations under different assumptions for the neutron star equation of state and decay of the magnetic field. We find evidence that a tail in the distribution of millisecond pulsars may exist at periods shorter than those observed.

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Neutron stars accreting the ISM: Are they fast or slow objects ?

Old neutron stars (ONSs) which have radiated away their internal and rotational energy may still shine if accreting the interstellar medium. Rather stringent limits from the analysis of ROSAT surveys indicate that most optimistic predictions on ONSs observability are in excess of a factor as large as $\sim 100$. Here we explore two possible evolutionary scenarios that may account for the paucity of ONSs. In the first it is assumed that the ONS population is not too fast ($V<100 km s^{-1}$) and that magnetic field decay guides the evolution. In the second, NSs move with high speed ($V>100$ km s$^{-1}$) and preserve their magnetic field at birth. We find that according to the former scenario most ONSs are now in the propeller phase, while in the latter nearly all ONSs are silent, dead pulsars.

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The elusiveness of old neutron stars

Old neutron stars (ONSs) which have radiated away their internal and rotational energy may still shine if accreting the interstellar medium. Despite their large number, only two promising candidates have been detected so far and rather stringent limits on their observability follow from the analysis of ROSAT surveys. This contrasts with optimistic theoretical estimates that predicted a large number of sources in ROSAT fields. We have reconsidered the issue of ONSs observability, accounting for the spin and magnetic field evolution over the neutron star lifetime. In the framework of a spin-induced field decay model, we show that the total number of ONSs which are, at present, in the accretion stage is reduced by a factor ~5 over previous figures if the characteristic timescale for crustal current dissipation is ~ 10^8 - 10^9 yr. This brings theoretical predictions much closer to observational limits. Most ONSs should be at present in the propeller phase and, if subject to episodic flaring, they could be observable.

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Drag on a satellite moving across a spherical galaxy. I. Tidal and frictional forces in shortlived encounters

We derive a formalism, within the theory of linear response, for the analysis of the interaction of a satellite (the perturber) with a spherical galaxy whose equilibrium is described by a one-particle distribution function. We compute the formal expression of the force on the satellite including the self-gravity of the stars and the shift of the stellar center of mass. We apply the perturbative technique to the case of a satellite moving at high speed across a stellar system and find a natural decomposition of the force into a global component resulting from the tidal interaction and a component that is related to dynamical friction. When the satellite orbits outside the galaxy, we derive the force in the impulse approximation. In penetrating shortlived encounters, the wake excited in the density field is responsible for most of the deceleration. We find that dynamical friction rises from a memory effect involving only those stars perturbed along the path. The force can be written in terms of an effective Coulomb logarithm which now depends on the dynamical history. It is derived for two simple equilibrium density distributions. In the case of a homogeneous cloud, we compute the total energy loss: Tides excited by the satellite in the galaxy reduce the value of the energy loss by friction.

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Accretion of a satellite onto a spherical galaxy. II. Binary evolution and orbital decay

We study the dynamical evolution of a satellite orbiting outside of a companion spherical galaxy. The satellite is subject to a back-reaction force resulting from the density fluctuations excited in the primary stellar system. We evaluate this force using the linear response theory developed in Colpi and Pallavicini (1997). The force is computed in the reference frame comoving with the primary galaxy and is expanded in multipoles. To capture the relevant features of the physical process determining the evolution of the detached binary, we introduce in the Hamiltonian the harmonic potential as interaction potential among stars. The dynamics of the satellite is computed self-consistently. We determine the conditions for tidal capture of a satellite from an asymptotic free state. If the binary comes to existence as a bound pair, stability against orbital decay is lost near resonance. The time scale of binary coalescence is computed as a function of the eccentricity and mass ratio. In a comparison with Weinberg's perturbative technique we demonstrate that pinning the center of mass of the galaxy would induce a much larger torque on the satellite.

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X-ray variability in the quiescent state of Cen X-4

We report on a ROSAT-HRI observation of the soft X-ray transient Cen X-4 during quiescence. We discover a variation in the flux by a factor of 3 in less than four days. This relatively fast variation, the first observed from a quiescent soft X-ray transient, rules out some of the emission mechanisms that have been proposed for the quiescent flux. Accretion either onto the neutron star surface or onto the magnetospheric boundary is clearly favored.

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The Pulsed Soft X-Ray Emission from PSR 0656+14

We present the results of a spectral and timing analysis of PSR 0656+14 based on the complete set of ROSAT observations carried out with the PSPC instrument in 1991 and 1992. The present analysis confirms the thermal origin of the bulk of the emission in the soft X-ray band (Finley et al. 1992). In addition, we find strong evidence of a harder component, described equally well with a blackbody at T about 2x10^6 K, or with a steep power law with photon index Gamma about 4.5. This bimodal emission is also supported by an analysis of the light curve shape as a function of the energy. The 0.1--2.4 keV light curve of PSR 0656+14, with a pulsed fraction of about 9%, is interpreted with a simple model for the temperature distribution on the neutron star surface, coupled with the geometrical information derived from radio data. In this model, which includes the effects of relativistic light bending and gravitational redshift, the X--rays originate from two thermal components resulting from neutron star cooling and blackbody emission released in the hotter polar cap regions. The observed modulation can be reproduced only if PSR 0656+14 has a relatively high dipole inclination (about 30 deg) and (1+z) is less than about 1.15. The overall pulsed fraction cannot be significantly increased by including the polar cap contribution, if its temperature and intensity are to be consistent with the observed spectra.

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Was the propeller mechanism active during the periastron passage of PSR 1259--63?

Timing analisys of PSR 1259-63 during its recent periastron passage suggested that the pulsar was spinning-down due to the propeller mechanism (Manchester et al. 1995). This requires that the radio pulsar mechanism is temporarily quenched. On the basis of the Be equatorial disk model derived from the dispersion and rotation measures analysis (Melatos et al. 1995), we show that the mass inflow is sufficiently high to yield accretion down to the magnetospheric radius. In this case the X-ray spectrum might result from the propeller shock emission.

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Radio pulsar and accretion regimes of rapidly rotating magnetic neutron stars in early-type eccentric binaries

Rapidly rotating magnetic neutron stars in eccentric binary systems containing an early type star provide a unique opportunity to investigate the interplay between radio pulsar, stellar wind and accretion phenomena. We summarise the radio pulsar-dominated and the accretion-dominated regimes, discussing how the transition from one regime to another can take place as a result of the varying orbital distance and relative velocity along the orbit, as well as changes of the wind characteristics. We derive the conditions under which the two known B star/radio pulsar binaries (PSR 1259-63 and PSR J0045-7319) can undergo a transition to the accreting regime. A strong increase of the mass loss ouflow from the companion is required, just to cause the onset of accretion onto the magnetospheric boundary. We also show that the X--ray transient A0538-66 is likely to undergo transitions from the accreting neutron star regime, to the regime of accretion onto the magnetosphere. These two regimes might correspond to the high (> 10^{38} erg/s) and the low-luminosity (< 10^{38} erg/s) outbursts observed from this source. A radio pulsar might become detectable in the long quiescent states of A0538-66. A new model of the enigmatic high-energy binary LS I +61 303 involving accretion onto the magnetosphere is also presented.

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The fate of central black holes in merging galaxies

This paper presents results of a series of numerical N-body experiments that describe the merging of galaxy pairs containing a massive black hole in their core. The aim is to study the orbital evolution of the two black holes through the merger event. It is found that merging does NOT lead to the formation of a CLOSE black hole pair} at the center of the remnant when the two progenitor galaxies have (1) similar masses, (2) different central densities, and (3) relative orbit with non zero angular momentum. Under these conditions, the central black hole of the less dense galaxy settles into an wide orbit, i.e., at a distance from the center comparable to the half mass radius of the remnant, where the time scale for orbital decay by dynamical friction can be several Gyrs. The implications of this result are briefly discussed.

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Orbital Evolution of a Massive Black Hole Pair by Dynamical Friction

We investigate the evolution of a massive black hole pair under the action of dynamical friction (DF) by a uniform background of light stars with isotropic velocity distribution. In our scenario, the primary black hole $M_1$ sits, at rest, in the center of the spherical star distribution (with mass $M_c$) and the secondary less massive companion $M_2$ moves along bound orbits determined by the background gravitational field; it loses energy $E$ and angular momentum $J$ by DF. We investigate mostly analytically the secular evolution of the orbital parameters when the motion of $M_2$ is determined either by the mean field generated by the uniform stellar distribution or by the gravitational field of $M_1$. We find that $J$ and $E$ are lost so as to cause the increase of the eccentricity $e$ during the orbital decay of $M_2$. When $M_2$ enters the region where the gravitational field of $M_1$ dominates, the evolution depends on the ratio between the black hole velocity $v$ and the stellar dispersion velocity $σ.$ We explore both cases $v<σ$ and $v>σ$. Only for $v>σ$ the rise of $e$ would be severe but this transition occurs close to the cusp radius below which our description becomes invalid. Energy losses by gravitational wave emission become comparable to those by dynamical friction at a critical distance that depends sensitively on the ratio $M_1/M_c$. The braking index $n$ is calculated in this transition region.

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