Initial Spin Period Research Articles

Spin Axis Precession of LARES Measured by Satellite Laser Ranging

Satellite laser ranging (SLR) is an efficient technique to measure spin parameters of the fully passive satellite LARES. Analysis of the laser range measurements gives information about the spin rate of the spacecraft and the orientation of its spin axis. A frequency analysis applied to the SLR data indicates an exponential increase of the satellite's spin period: T = 11.7612 ·exp(0.00293327 ·D) , RMS = 0.115 s, where D is in days since launch. The initial spin period of LARES is calculated from the spin observations during the first 30 days after launch and is equal to T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 11.7131, RMS = 0.073 s. The spin axis of the satellite is precessing around the initial coordinates of right ascension RA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">initial</sub> = 186.5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , RMS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RA</sub> = 3.1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , and Declination Decinitial = - 73.0 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , RMS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dec</sub> = 0.7 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> (J2000 inertial reference frame), with a period of 211.7 days. The precession of the spin axis may be responsible for the observed oscillation of the slowing down rate: the spin half-life period (the time after which the spin period has doubled) varies between 209 and 267 days. The measured spin parameters of LARES are compared-and show good agreement-with the theoretical predictions given by the satellite spin model. Information about the spin parameters of LARES is necessary for the accurate modeling of the forces and torques that are affecting the orbital motion of the satellite.

Unifying neutron stars getting to GUNS

AbstractThe variety of the observational appearance of young isolated neutron stars must find an explanation in the framework of some unifying approach. Nowadays it is believed that such scenario must include magnetic field decay, the possibility of magnetic field emergence on a time scale of ≲104–105 yr, significant contribution of non‐dipolar fields, and appropriate initial parameter distributions. We present our results on the initial spin period distribution, and suggest that inconsistencies between distributions derived by different methods for samples with different average ages can uncover field decay or/and emerging field. We describe a new method to probe the magnetic field decay in normal pulsars. The method is a modified pulsar current approach, where we study pulsar flow along the line of increasing characteristic age for constant field. Our calculations, performed with this method, can be fitted with an exponential decay for ages in the range of 8×104– 3.5×105 yr with a time scale of ∼5×105 yr. We discuss several issues related to the unifying scenario. At first, we note that the dichotomy, among local thermally emitting neutron stars, between normal pulsars and the Magnificent Seven remains unexplained. Then we discuss the role of high‐mass X‐ray binaries in the unification of neutron star evolution. We note, that such systems allow to check evolutionary effects on a time scale longer than what can be probed with normal pulsars alone. We conclude with a brief discussion of the importance of discovering old neutron stars accreting from the interstellar medium. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Spin parameters of Low Earth Orbiting satellites Larets and Stella determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) measurements contain information about the spin parameters of the fully passive, geodetic satellites. In this paper we spectrally analyze the SLR data of 5 geodetic satellites placed on the Low Earth Orbits: GFZ-1, WESTPAC, Larets, Starlette, Stella, and successfully retrieve the frequency signal from Larets and Stella only. The obtained signals indicate an exponential increase of the spin period of Larets: T=0.860499·exp(0.0197066·D) [s], and Stella: T=13.5582·exp(0.00431232·D) [s], where D is in days since launch. The initial spin periods calculated from the first month of the SLR observations are: Larets: Tinitial=0.8239s, Stella: Tinitial=13.2048s. Analysis of the apparent effects indicates the counter-clockwise spin direction of the satellites. The twice more heavy Stella lost its rotational energy more than four times slower than Larets. Fitting the spin model to the observed spin trends allows determination of the spin axis orientation evolution for Larets and Stella before their rotational period becomes equal to the orbital period.

POPULATION SYNTHESIS OF YOUNG ISOLATED NEUTRON STARS: THE EFFECT OF FALLBACK DISK ACCRETION AND MAGNETIC FIELD EVOLUTION

The spin evolution of isolated neutron stars (NSs) is dominatd by their magnetic fields. The measured braking indices of young NSs show that the spin-down mechanism due to magnetic dipole radiation with constant magnetic fields is inadequate. Assuming that the NS magnetic field is buried by supernova fallback matter and re-emerges after accretion stops, we carry out Monte-Carlo simulation of the evolution of young NSs, and show that most of the pulsars have the braking indices ranging from -1 to 3. The results are compatible with the observational data of NSs associated with supernova remnants. They also suggest that the initial spin periods of NSs might occupy a relatively wide range.

Neutron star's initial spin period distribution

We analyze different possibilities to explain the wide initial spin period distribution of radio pulsars presented by Noutsos et al. (2013). With a population synthesis modeling we demonstrate that magnetic field decay can be used to interpret the difference between the recent results by Noutsos et al. (2013) and those by Popov & Turolla (2012), where a much younger population of NSs associated with supernova remnants with known ages has been studied. In particular, an exponential field decay with tau_mag = 5Myrs can produce a "tail" in the reconstructed initial spin period distribution (as obtained by Noutsos et al. 2013) up to P_0 > 1 s starting with a standard gaussian with P_0 = 0.3 s and sigma_P = 0.15 s. Another option to explain the difference between initial spin period distributions from Noutsos et al. (2013) and Popov & Turolla (2012) -- the emerging magnetic field -- is also briefly discussed.

CHARACTERISTIC AGE AND TRUE AGE OF PULSARS

Age of a pulsar is a useful parameter, but it is difficult to get the age from observation. We can only derive the characteristic age from the observed parameters: spin period (P) and period derivative (Ṗ). In this paper, we discussed the relationship between characteristic age and magnetic field of a pulsar. Monte Carlo simulation is also used to support the idea: it is useless to study the magnetic field evolution using characteristic age. From some observation evidences we get that: the characteristic age cannot be used as true age, especially for millisecond pulsar (MSP). The difference between them is also discussed. From the studying of breaking index and MSP's initial spin period (P0), we get the conclusion that: the problem cannot be resolved using different radiation models.

Spectral Analysis of Borowiec SLR Data For Spin Determination Of Geodetic Satellite EGP

Borowiec 10 Hz Satellite Laser Ranging (SLR) station is capable to measure spin of the Japanese Experimental Geodetic Satellite (EGP). Spectral analysis of 391 passes measured from March 10, 1994 to November 27, 2009 gives frequency signal representing the 3 rd and the 6 th harmonics of the satellite spin rate. Analysis of this signal, corrected for the apparent effects, indicates en exponential slowing down of the satellite: the spin rate decreases according to the equation f = 671.115907 · exp(-4.08324 x 10 -5 · D) (mHz), where D is a day after launch. More than 15 years of the SLR measurements allowed investigating the initial spin rate of the satellite fini = 671.116, RMS = 0.203 (mHz) (initial spin period Tini = 1.49006, RMS = 0.0007 (s)).

RADIO TRANSIENTS FROM THE ACCRETION-INDUCED COLLAPSE OF WHITE DWARFS

It has long been expected that in some scenarios when a white dwarf (WD) grows to the Chandrasekhar limit, it can undergo an accretion induced collapse (AIC) to form a rapidly rotating neutron star. Nevertheless, the detection of such events has so far evaded discovery, likely because the optical, supernova-like emission is expected to be dim and short-lived. Here we propose a novel signature of AIC: a transient radio source lasting for a few months. Rapid rotation along with flux freezing and dynamo action can grow the WD's magnetic field to magnetar strengths during collapse. The spindown of this newly born magnetar generates a pulsar wind nebula (PWN) within the ~0.001-0.1Msun of ejecta surrounding it. Our calculations show that synchrotron emission from the PWN may be detectable in the radio, even if the magnetar has a rather modest magnetic field of ~2*10^14 G and an initial spin period of ~10 ms. An all-sky survey with a detection limit of 1 mJy at 1.4 GHz would see ~4(f/10^-2) above threshold at any given time, where f is the ratio of the AIC rate to Type Ia supernova rate. A similar scenario may result from binary neutron stars if some mergers produce massive neutron stars rather than black holes. We conclude with a discussion of the detectability of these types of radio sources in an era of facilities with high mapping speeds.

Gravitational wave background from rotating neutron stars

The background of gravitational waves produced by the ensemble of rotating neutron stars (which includes pulsars, magnetars and gravitars) is investigated. A formula for \Omega(f) (commonly used to quantify the background) is derived, properly taking into account the time evolution of the systems since their formation until the present day. Moreover, the formula allows one to distinguish the different parts of the background: the unresolvable (which forms a stochastic background) and the resolvable. Several estimations of the background are obtained, for different assumptions on the parameters that characterize neutron stars and their population. In particular, different initial spin period distributions lead to very different results. For one of the models, with slow initial spins, the detection of the background can be rejected. However, other models do predict the detection of the background by the future ground-based gravitational wave detector ET. A robust upper limit for the background of rotating neutron stars is obtained; it does not exceed the detection threshold of two cross-correlated Advanced LIGO interferometers. If gravitars exist and constitute more than a few percent of the neutron star population, then they produce an unresolvable background that could be detected by ET. Under the most reasonable assumptions on the parameters characterizing a neutron star, the background is too faint. Previous papers have suggested neutron star models in which large magnetic fields (like the ones that characterize magnetars) induce big deformations in the star, which produce a stronger emission of gravitational radiation. Considering the most optimistic (in terms of the detection of gravitational waves) of these models, an upper limit for the background produced by magnetars is obtained; it could be detected by ET, but not by BBO or DECIGO.

Initial spin periods of neutron stars in supernova remnants

We present estimates of initial spin periods, $P_0$, for radio pulsars associated with supernova remnants. By using the published data on 30 objects, we were able to derive a reliable estimate for the initial spin period, assuming standard magneto-dipole spin-down (braking index n=3), in many cases. Our set of estimates is still not sufficient to infer the exact shape of the initial period distribution. However, we show that a gaussian distribution with mean and deviation $\sim 0.1$ s is consistent with our results, while flat, wide distributions and very narrow ones are disfavored.

MULTI-ZONE MODELING OF THE PULSAR WIND NEBULA HESS J1825–137

The pulsar wind nebula associated with PSR J1826-1334, HESS J1825-137, is a bright very high energy source with an angular extent of ~1 degree and spatially-resolved spectroscopic TeV measurements. The gamma-ray spectral index is observed to soften with increasing distance from the pulsar, likely the result of cooling losses as electrons traverse the nebula. We describe analysis of X-ray data of the extended nebula, as well as 3-D time-dependent spectral energy distribution modeling, with emphasis on the spatial variations within HESS J1825-137. The multi-wavelength data places significant constraints on electron injection, transport, and cooling within the nebula. The large size and high nebular energy budget imply a relatively rapid initial pulsar spin period of 13 \pm 7 ms and an age of 40 \pm 9 kyr. The relative fluxes of each VHE zone can be explained by advective particle transport with a radially decreasing velocity profile with $v(r) \propto r^{-0.5}$. The evolution of the cooling break requires an evolving magnetic field which also decreases radially from the pulsar, $B(r,t) \propto r^{-0.7} \dot{E}(t)^{1/2}$. Detection of 10 TeV flux ~80 pc from the pulsar requires rapid diffusion of high energy particles with $\tau_{esc} \approx 90 (R / 10 pc)^2 (E_e/100 TeV)^{-1}$ year, contrary to the common assumption of toroidal magnetic fields with strong magnetic confinement. The model predicts a rather uniform Fermi LAT surface brightness out to ~1 degree from the pulsar, in good agreement with the recently discovered LAT source centered 0.5 degree southwest of PSR J1826-1334 with extension 0.6 \pm 0.1 degree.

Thermal evolution of Pluto and implications for surface tectonics and a subsurface ocean

Determining whether or not Pluto possesses, or once possessed, a subsurface ocean is crucial to understanding its astrobiological potential. In this study we use a 3D convection model to investigate Pluto’s thermal and spin evolution, and the present-day observational consequences of different evolutionary pathways. We test the sensitivity of our model results to different initial temperature profiles, initial spin periods, silicate potassium concentrations and ice reference viscosities. The ice reference viscosity is the primary factor controlling whether or not an ocean develops and whether that ocean survives to the present day. In most of our models present-day Pluto consists of a convective ice shell without an ocean. However if the reference viscosity is higher than 5×1015Pas, the shell will be conductive and an ocean should be present. For the nominal potassium concentration the present-day ocean and conductive shell thickness are both about 165km; in conductive cases an ocean will be present unless the potassium content of the silicate mantle is less than 10% of its nominal value. If Pluto never developed an ocean, predominantly extensional surface tectonics should result, and a fossil rotational bulge will be present. For the cases which possess, or once possessed, an ocean, no fossil bulge should exist. A present-day ocean implies that compressional surface stresses should dominate, perhaps with minor recent extension. An ocean that formed and then re-froze should result in a roughly equal balance between (older) compressional and (younger) extensional features. These predictions may be tested by the New Horizons mission.

Spin period evolution of a recycled pulsar in an accreting binary

We investigate the spin-period evolutions of recycled pulsars in binary accreting systems. Taking both the accretion induced field decay and spin-up into consideration, we calculate their spin-period evolutions influenced by the initial magnetic-field strengths, initial spin-periods and accretion rates, respectively. The results indicate that the minimum spin-period (or maximum spin frequency) of millisecond pulsar (MSP) is independent of the initial conditions and accretion rate when the neutron star (NS) accretes $\sim> 0.2\ms$. The accretion torque with the fastness parameter and gravitational wave (GW) radiation torque may be responsible for the formation of the minimum spin-period (maximum spin frequency). The fastest spin frequency (716 Hz) of MSP can be inferred to associate with a critical fastness parameter about $\omega_{c}=0.55$. Furthermore, the comparisons with the observational data are presented in the field-period ($B-P$) diagram.

Isolated pulsar spin evolution on the diagram

We look at two contrasting spin-down models for isolated radio pulsars and, accounting for selection effects, synthesize observable populations. While our goal is to reproduce all of the observable characteristics, in this paper we pay particular attention to the form of the spin period vs. period derivative (P-Pdot) diagram and its dependence on various pulsar properties. We analyse the initial spin period, the braking index, the magnetic field, various beaming models, as well as the pulsar's luminosity. In addition to considering the standard magnetic dipole model for pulsar spin-down, we also consider the recent hybrid model proposed by Contopoulos & Spitkovsky. The magnetic dipole model, however, does a better job of reproducing the observed pulsar population. We conclude that random alignment angles and period dependent luminosity distributions are essential to reproduce the observed P-Pdot diagram. We also consider the time decay of alignment angles, and attempt to reconcile various models currently being studied. We conclude that, in order to account for recent evidence for the alignment found by Weltevrede & Johnston, the braking torque on a neutron star should not depend strongly on the inclination. Our simulation code is publically available and includes a web-based interface to examine the results and make predictions for yields of current and future surveys.

THE ROLE OF NEWLY BORN MAGNETARS IN GAMMA-RAY BURST X-RAY AFTERGLOW EMISSION: ENERGY INJECTION AND INTERNAL EMISSION

Swift observations suggest that the central compact objects of some gamma-ray bursts (GRBs) could be newly born millisecond magnetars. Therefore, considering the spin evolution of the magnetars against r-mode instability, we investigate the role of magnetars in GRB X-ray afterglow emission. Besides modifying the conventional energy injection model, we pay particular attention to the internal X-ray afterglow emission, whose luminosity is assumed to track the magnetic dipole luminosity of the magnetars with a certain fraction. Following a comparison between the model and some selected observational samples, we suggest that some so-called canonical X-ray afterglows including the shallow decay, normal decay, and steeper-than-normal decay phases could be internally produced by the magnetars (possibly through some internal dissipations of the magnetar winds), while the (energized) external shocks are associated with another type of X-ray afterglows. If this is true, then from those internal X-ray afterglows we can further determine the magnetic field strengths and the initial spin periods of the corresponding magnetars.

Coupling of thermal evolution and despinning of early Iapetus

The Cassini mission revealed two spectacular characteristics of Iapetus: (1) a geologically old and high equatorial ridge, which is unique in the Solar System and (2) a large flattening of 35 km consistent with the equilibrium figure for a hydrostatic body rotating with a period of 16 h, whereas the current spin period is 79.33 days. This study describes three-dimensional simulations of solid-state convection within an undifferentiated Iapetus. It investigates the implications for the evolution of the interior thermal structure and its spin rate and global shape using radially layered viscoelastic models. The role of the concentration in the short-lived radiogenic element [ 26Al], just after accretion is completed, is specifically addressed. The first result is to show that whatever the [ 26Al] value, convection occurs. As suggested by Castillo-Rogez et al. [Castillo-Rogez, J., Matson, D., Sotin, C., Johnson, T., Lunine, J., Thomas, P. [2007] Icarus, 190, 179–202], convection reduces the warming of the interior compared to the conductive evolution and therefore limits the conditions for despinning. In our calculations, two conceptual linear viscoelastic models are used. When considering a Maxwell rheology, the interior temperature (viscosity) never reaches a value high (low) enough to induce despinning. In order to promote dissipation at low temperature, a Burgers rheology, which includes an additional dissipation peak, is introduced. For favorable parameter values, this latter rheology leads to despinning. However, only models associated with large amounts of short-lived radiogenic elements ( [ 26 Al ] ⩾ 25 ppb ) lead to the observed flattening. This suggests that the accretion process needs to be completed shortly after the formation of CAIs (Calcium–Aluminum-rich Inclusions) (⩽4 Myr). For [ 26Al] varying between 72 and 46 ppb, the observed flattening is obtained only for a limited range of initial spin period, between 9.5 and 10.2 h. For [ 26Al] ranging between 30 and 15 ppb, initial spin rates smaller than 8.5 h are required. For smaller values of [ 26Al], the body is too cold and viscous to acquire a significant flattening even if a rotation period close to the body disruption limit is considered. Even with a thin lithosphere during the early stage, our simulations show that Iapetus never reaches the equilibrium figure for a hydrostatic body due to the non-zero rigidity of the lithosphere. The 35 km value of the flattening is the result of the partial relaxation of an ancient larger flattening ranging between 45 and 80 km, depending on the evolution of the lithosphere thickness mainly controlled by the radiogenic content. A thin lithosphere is consistent with an early building of the equatorial ridge. The lithosphere thickening due to interior cooling can explain the preservation of the ridge throughout the remaining evolution of Iapetus.

The formation of submillisecond pulsars and the possibility of detection

Pulsars have been recognized to be normal neutron stars, but sometimes have been argued to be quark stars. Submillisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. We focus on the formation of such submillisecond pulsars in this paper. A new approach to the formation of a submillisecond pulsar (quark star) by means of the accretion-induced collapse (AIC) of a white dwarf is investigated. Under this AIC process, we found that: (i) almost all newborn quark stars could have an initial spin period of ∼0.1 ms; (ii) nascent quark stars (even with a low mass) have a sufficiently high spin-down luminosity and satisfy the conditions for pair production and sparking process and appear as submillisecond radio pulsars; (iii) in most cases, the times of newborn quark stars in the phase with spin period < 1( or<0.5) ms are long enough for the stars to be detected. As a comparison, an accretion spin-up process (for both neutron and quark stars) is also investigated. It is found that quark stars formed through the AIC process can have shorter periods (≤0.5 ms), whereas the periods of neutron stars formed in accretion spin-up processes must be longer than 0.5 ms. Thus, if a pulsar with a period shorter than 0.5 ms is identified in the future, it could be a quark star.

22 Years of AJISAI spin period determination from standard SLR and kHz SLR data

Satellite Laser Ranging (SLR) is a powerful and efficient technique to measure spin parameters of satellites equipped with corner cube reflectors. We obtained spin period determination of the satellite AJISAI from SLR data only: 17246 pass-by-pass estimates from standard 1–15 Hz SLR data (14/Aug/1986–30/Dec/2008) and 1444 pass-by-pass estimates (9/Oct/2003–30/Dec/2008) from data of the first 2 kHz SLR system from Graz, Austria. A continuous history of the slowing down of AJISAI spin is derived from frequency analysis, and corrected for the apparent effects. The apparent corrections, elaborated here, allowed very accurate determination of AJISAI initial spin period: 1.4855 ± 0.0007 [s]. The paper identifies also non-gravitational effects as a source of the periodical changes in the rate of slowing down of the satellite.

10 Years of LAGEOS-1 and 15 years of LAGEOS-2 spin period determination from SLR data

Satellite Laser Ranging (SLR) stations measure distance to the satellites equipped with Corner Cube Reflectors (CCRs). These range measurements contain information about spin parameters of the spacecraft. In this paper we present results of spin period determination of two passive satellites from SLR data only: 10 years of LAGEOS-1 (10426 values), and 15 years of LAGEOS-2 (15580 values). The measurements have been made by standard 10 Hz SLR systems and the first 2 kHz SLR system from Graz (Austria). The obtained data allowed calculation of the initial spin period of the satellites: 0.61 s for LAGEOS-1 and 0.906 s for LAGEOS-2. Long time series of the spin period values show that the satellite’s slowing down rate is not constant but is oscillating with a period of 846 days for LAGEOS-1 and 578 days for LAGEOS-2. The results presented here definitely prove that the SLR is a very efficient technique able to measure spin period of the geodetic satellites.

Simulations of Magnetically Driven Supernova and Hypernova Explosions in the Context of Rapid Rotation

We present here the first 2D rotating, multi-group, radiation magnetohydrodynamics (RMHD) simulations of supernova core collapse, bounce, and explosion. In the context of rapid rotation, we focus on the dynamical effects of magnetic stresses and the creation and propagation of MHD jets. We find that a quasi-steady state can be quickly established after bounce, during which a well-collimated MHD jet is maintained by continuous pumping of power from the differentially rotating core. If the initial spin period of the progenitor core is $\sles$ 2 seconds, the free energy reservoir in the secularly evolving protoneutron star is adequate to power a supernova explosion, and may be enough for a hypernova. The jets are well collimated by the infalling material and magnetic hoop stresses, and maintain a small opening angle. We see evidence of sausage instabilities in the emerging jet stream. Neutrino heating is sub-dominant in the rapidly rotating models we explore, but can contribute 10$-$25% to the final explosion energy. Our simulations suggest that even in the case of modest or slow rotation, a supernova explosion might be followed by a secondary, weak MHD jet explosion, which, because of its weakness may to date have gone unnoticed in supernova debris. Furthermore, we suggest that the generation of a non-relativistic MHD precursor jet during the early protoneutron star/supernova phase is implicit in both the collapsar and "millisecond magnetar" models of GRBs. The multi-D, multi-group, rapidly rotating RMHD simulations we describe here are a start along the path towards more realistic simulations of the possible role of magnetic fields in some of Nature's most dramatic events.