In this paper we will give an overview of the past and present status of Gravitational Wave (GW) research associated with pulsars, taking into account the target sensitivity achieved from interferometric laser GW antennas such as Tama, Geo, Ligo and Virgo. We will see that the upper limits obtained with searches for periodic GW begin to be astrophysically interesting by imposing non-trivial constraints on the structure and evolution of the neutron stars. We will give prospects for the future detection of pulsar GW signals, with Advanced Ligo and Advanced Virgo and future enhanced detectors, e.g. the Einstein Telescope

Calloni, E.

De Laurentis, M.

De Rosa, R.

Di Fiore, L.

Garufi, F.

Milano, L.

English

L. Milano

E. Calloni

R. De Rosa

M. De Laurentis

L. Di Fiore

F. Garufi

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Acta Polytechnica

THE PAST AND THE FUTURE OF DIRECT SEARCH OF GW FROM PULSARS IN THE ERA OF GW ANTENNAS

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

doi:10.14311/AP.2013.53.0742Acta Polytechnica 53(Supplement):742–745, 2013 © Czech Technical University in Prague, 2013available online at http://ojs.cvut.cz/ojs/index.php/apTHE PAST AND THE FUTURE OF DIRECT SEARCH OF GWFROM PULSARS IN THE ERA OF GW ANTENNASL. Milanoa,b,∗, E. Callonia,b, R. De Rosaa,b, M. De Laurentisa,b,L. Di Fioreb, F. Garufia,ba Dipartimento di ‘Scienze Fisiche’ Università Federico II di Napoli, Complesso Universitario di MonteS. Angelo, Via Cinthia, I 80125, Napoli, Italyb Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia I 80125, Napoli, Italy∗ corresponding author: milano@na.infn.itAbstract. In this paper we will give an overview of the past and present status of GravitationalWave (GW) research associated with pulsars, taking into account the target sensitivity achieved frominterferometric laser GW antennas such as Tama, Geo, Ligo and Virgo. We will see that the upperlimits obtained with searches for periodic GW begin to be astrophysically interesting by imposingnon-trivial constraints on the structure and evolution of the neutron stars. We will give prospectsfor the future detection of pulsar GW signals, with Advanced Ligo and Advanced Virgo and futureenhanced detectors, e.g. the Einstein Telescope.Keywords: gravitational waves, pulsar, neutron star.1. IntroductionEfforts to detect gravitational waves started about fiftyyears ago with Joe Weber’s bar detectors [1]. Theyopened the way to the present day interferometric de-tectors with useful bandwidths of thousands of hertz,namely 10Hz÷ 10 kHz for Virgo [2], 40Hz÷ 10 kHzfor Ligo [3], 50Hz ÷ 1.5 kHz for GEO600 [4] and10Hz ÷ 10 kHz for the Japanese TAMA [5]. In thispaper we will give an overview of the past and presentstatus of research on Gravitational Waves from pul-sars. Taking into account all interferometric laser GWantennas Tama, GEO600, LIGO and Virgo, we mustnote that no direct detection of a GW credited signalhas yet been announced, although target sensitivityhas been reached for both VIRGO and LIGO (seeFig. 1). Searches for GWs from pulsars did not beginwith LIGO and VIRGO. After the discovery of theCrab pulsar optical pulsations at ∼ 30Hz [6] therewere a series of pioneering searches for GW emission:• 1972: Levine and Stebbins [7] used a 30m laserinterferometer (single arm Fabry–Pérot cavity);• 1978: Hirakawa et al. [8, 9]) searched for theCrab GW emission using a ∼ 1000 kg aluminumquadrupole antenna with resonant frequency at60.2Hz;• 1983: Hereld [10] at Caltech used a 40m interfer-ometer;• 1983: Hough et al, in Glasgow used a split bardetector [11];• 1993: Niebauer [12] searched for GWs from apossible Neutron Star (NS) remnant of SN1987Ausing a Garching 30m interferometer (100 hrs ofdata from 1989; searching around 2 and 4 kHz):h0 < 9× 10−21;• 1986–1995: Tokyo group Crab pulsar searchusing a 74 kg torsion-type antenna (cooled at4.2K) Owa et al. [13, 14], Suzuki [15] using acooled (4.2K) 1200 kg antenna: h0 < 2 × 10−22(∼ 140× spin-down limit);• 2008: CLIO search for GWs from Vela [16]:h0 < 5.3× 10−20 at 99.4% CL;• 2010: Tokyo prototype low-frequency mag-lev tor-sional bar antenna search for slowest pulsar (PSRJ2144-3933 at νrot ∼ 0.1Hz) [17]: h0 < 8.4× 10−10(Bayesian 95% UL with 10% calibration errors);• Various narrow-band all-sky, and galactic centre,blind searches have been performed using EX-PLORER and AURIGA bar detectors [18, 19,35]; for a review see [36]) h0 < 2 × 10−22(∼ 140× spin-down limit).We will divide our paper as follows: Section 2 offersa basic introduction to GW emission from pulsars,then results from past and present research are givenin Section 3. Future work is outlined in Section 4,conclusions and open questions are dealt with in Sec-tion 5.2. Basics of GW emission bypulsarsGW emission is a non-axisimmetric process, sinceGWs are emitted through a quadrupolar mechanism.Possible processes for this kind of asymmetry, involv-ing neutron stars, are: a rotating tri-axial ellipsoid(i.e. an NS with a bump), precessing NS (wobbling an-gle), oscillating NS, and accreting NS in an inspirallingbinary system.742vol. 53 supplement/2013 The Past and the Future of Direct Search of GW from PulsarsWe will focus on the first three items, since theygive rise to continuous GW emission, while accretingNS gives rise to a chirping GW emission in the verylast stage of life of the system.GW amplitude can be decomposed into two polar-izations: “+” and “×”, according to the effect theyhave on a circle of free falling masses orthogonal tothe propagation direction. The functional form isdescribed by [21]h+ = h0 1+cos2 ι2 cos 2Ω(t− dc)h× = h0 cos ι sin 2Ω(t− dc)(1)being Ω = 2piν the rotational angular velocity andh0 =16pi2Gc4Izzν2d (2)where ι is the angle between the rotation plane andthe observer, Izz is the momentum of inertia of NSwith respect to the rotation axis, d is the distancefrom the observation point, and  = (Ixx − Iyy)/(Izz)is quadrupole ellipticity. From a large set of Equationsof State (EoS), describing NS matter at supra-nucleardensities one gets: Izz = (1÷3)×1038 kgm2 dependingon the EoS and on the rotation velocity. So the scaleparameter of GW amplitude can be expressed in morephysical units ash0 = 4× 10−25( 10−6)( I1038 kgm2)(100 pcd)( ν100Hz)2. (3)GWs can also be emitted by an axisimmetric rotat-ing star, when the symmetry and the rotation axesare misaligned by “wobble” angle α.The maximum sustainable quadrupole deformation for an NS depends on the physics of the crust andthe EoS of matter at super-nuclear density. We canset a limit in  by looking at the maximum strainsustainable by the crust without breaking. Modelingof crustal strains indicates that [21] < kubreakBrLimwhere ubreak is the crustal limit strain, and k andBrLim depend on the star model. From moleculardynamics simulations, one obtains: k = 2× 10−5 andubreak ' BrLim = 0.1. This means that a NS breaksfor deformations larger than 20 cm.According to various models for solid quark stars,we can have BrLim = 10−2 and k = 6×10−4÷6×10−3.For strong initial magnetic fields (1016G), the star canemit intense GWs, due to the deformation induced bythe magnetic field.In brief, we have many estimates for the ellipticity,but few certainties. Something can be gathered bylooking at the data from GW experiments. How canLIGO and Virgo and astronomical data be useful forconstraining the EoS of NS using the upper limits on and the momentum of inertia I? Let us start fromwhat we know from astrophysical observations andgravitational observatory data.In our galaxy we can estimate a number of NSof about 108, 2000 of which are radio pulsars. Dis-tance d and rotation frequency ν can be evaluatedfrom radio and optical observations (GW emissionhas a frequency given by 2ν). If the variation of therotational period is such that ν˙ < 0, there is a mech-anism that makes the pulsar lose its energy. It canbe: electromagnetic (EM) dipole radiation, particleacceleration and GW emission. Since ν˙ = kνn, onecan derive the breaking index n from the rotationalfrequency and its derivatives,n = νν¨ν˙2.It has been evaluated that for pure magnetic dipoleradiation, the breaking index is n = 3, while for pureGW radiation n = 5.For the few objects that have been observed withsufficient accuracy to determine the breaking index,there is n < 3, thus some other mechanism or a com-bination must be invoked (see [20] for an interestingphenomnological analysis of the problem).Now let us try to derive some upper limit on GWemission. We start with the strong hypothesis that allthe energy is lost by GW emission. Thus the spindownGW amplitude is given byhSD ∼(52GIzz|ν˙|c3d2ν)1/2or, expressed in a more convenient set of units,hSD ∼2.5×−25(Izz1038 kgm2)( |ν˙|10−11Hz s−1)(100Hzν)(1 kpcd)from which we can get an upper limit for Izz combiningEM and GW observations.3. GW from pulsars, and resultsfrom the past until nowIn recent years, since ground-based GW interferomet-ric detectors have come into operation, several studieshave been carried out to detect GW signals from con-tinuous sources, both by single interferometers and bycoherent searches using two or more detectors, but asof June 2012, the results of these searches have onlyinvolved the upper limits on the rate and breakingstrain threshold.The search for periodic sources (or ContinuousWaves – CW), benefits from long integration times andcoincident analysis between different detectors. Thiswas the first to be started in Scientific Run 1 (S1) ofthe LIGO detector, using time and frequency domain743L. Milano, E. Calloni, R. De Rosa, M. De Laurentis, L. Di Fiore, F. Garufi Acta Polytechnica100 101 102 103 10410−3010−2810−2610−2410−22GW Frequency (Hz)StrainVirgo VSR2VirgoDesignLigoDesignCrab PulsarLigo S6AdVirgoDesignVela PulsarETDesignAdLigoDesignFigure 1. The figure shows the upper bounds on GW amplitude from known pulsars, assuming 100% conversionof spindown energy into GWs. An integration time of one year is assumed. The (green) diamonds represent apulsar with a spindown outside the detection band for both AdV and Advanced LIGO; the (cyan) squares are in thepotential detection band for at least one of the advanced detectors. The red circles represent Crab and Vela pulsars.analyses [22] on a single pulsar of known frequency.In S2–S5, it evolved into a broadband search [23, 24],using various techniques, e.g. the Hough transforms,the short Fourier transforms and excess power. Re-cently, the S5/VSR1 (VSR1 is the first Virgo ScientificRun) search on pulsars of known period and spindownusing ephemerides given by radio-telescopes and X-raysatellites [25], has set lower limits on GW radiationfrom targets, on the assumption that it is locked toEM emission. A further analysis was performed onjoint data from S6 and the VSR2 run and resultsinteresting for physics were obtained from the upperlimit in GW emission from the Crab pulsar [25] andthe Vela pulsar (Abadie et al. 2011) as shown by thered circles in Fig. 1.Figure 1 shows that the great majority of knownpulsars (green diamonds) are below the present sen-sitivity curves of the LIGO and Virgo GW anten-nas, and only a few of them (shown in cyan) fallin the range of sensitivity of either Advanced LIGOor Advanced Virgo or in the range of the EinsteinTelescope [32]. The upper limits obtained by theanalysis of the sources that can be studied by thepresent interferometers, provide interesting astrophys-ical information, since they give non-trivial constraintson the structure and the evolution of NS. Two high-light results have come from pulsars GW data anal-ysis [26, Abadie et al. 2011]: for the Crab pulsarthe hSD ' 1.4 × 10−24 limit was beaten, findingh0 < 2.4 × 10−25 i.e. ≈ hSD/6. This implies thatless than 2% of the rotational energy is lost in GWand also constrains the ellipticity to  < 1.3 × 10−4.For the Vela pulsar the hSD ' 3.29× 10−24 limit wasbeaten, by finding h0 < 2.4×10−24 implying that lessthan 35% of the rotational energy is lost in GW andconstraining the ellipticity to  < 1.1× 10−3. Theseresults also impose stringent limits on the EoS of anNS [21].4. The near future: the newproposalsThe ground-based GW detector network has been run-ning with improved sensitivity (the Virgo VSR3 runin 2010 July and the S6b Ligo run), major upgrades,e.g. Advanced LIGO [27] and Advanced Virgo [28],are aimed at achieving one order of magnitude bettersensitivity than the current instruments (Fig. 1 blueand red curves). These detectors come into opera-tion in 2014 or 2015, and, unless something in GRtheory is wrong, we can foresee regular detections ofbinary inspirals with very good prospects of detectingvarious other signals. The proposals for other large in-terferometric detectors, LCGT in Japan [29] (approvalreceived in June 2010) and AIGO in Australia [30],will significantly improve the capabilities of the cur-rent detector network. We will have good chances ofdetecting low-frequency signals with pulsar timing ar-rays on about the same time scale (Hobbs et al. 2010),while space-based detectors such as LISA/NGO [33],aimed to detect GW in the range 10−4÷ 10−1Hz andDecigo [34], are anticipated years later to open upthe intermediate frequency band. Third generationconceptual designs for the Einstein Telescope (ET)(Fig .1) [32] will be at future opportunity for GWdetection since this telescope should attain greatersensitivity by a factor of 100 more in sensitivity thanfirst generation Virgo and LIGO interferometers.5. Conclusions and open questionsIn this paper we have given an overview of the past andpresent status of Gravitational Wave (GW) researchassociated with pulsars. Many questions remain open,e.g.: What are the upper limits for pulsars: Whenthere will be a direct detection? What fraction ofpulsars energy is emitted in the form of gravitational744vol. 53 supplement/2013 The Past and the Future of Direct Search of GW from Pulsarswaves? Can we have direct inferences on pulsar pa-rameters from gravitational waves to constrain theEoS of an NS? What will be the model of NS or quarkstars?With interferometric GW antennas (LIGO,GEO600, Tama, Virgo), we have as yet only succeededin setting interesting upper limits, but the cherishedbelief is that the first direct detection will be possiblewith the new generation of interferometers, and as aresult answers may be found to some open questions.AcknowledgementsThis work was supported by INFN grant 2011.References[1] Shawhan P.S.: 2010 Class. Quantum Grav. 27 084017[2] Accadia T. et al.: 2012 Journal of Instrumentation 7P03012[3] Abbott B P et al.: 2009 Rep. Prog. Phys. 72 076901[4] Grote H. et al.: 2008 Class. 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THE PAST AND THE FUTURE OF DIRECT SEARCH OF GW FROM PULSARS IN THE ERA OF GW ANTENNAS

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