Acta Polytechnica doi:10.14311/AP.2013.53.0742 Acta Polytechnica 53(Supplement):742–745, 2013 © Czech Technical University in Prague, 2013 available online at http://ojs.cvut.cz/ojs/index.php/ap THE PAST AND THE FUTURE OF DIRECT SEARCH OF GW FROM PULSARS IN THE ERA OF GW ANTENNAS L. Milanoa,b,∗, E. Callonia,b, R. De Rosaa,b, M. De Laurentisa,b, L. Di Fioreb, F. Garufia,b a Dipartimento di ‘Scienze Fisiche’ Università Federico II di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, I 80125, Napoli, Italy b Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia I 80125, Napoli, Italy ∗ corresponding author: milano@na.infn.it Abstract. 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. Keywords: gravitational waves, pulsar, neutron star. 1. Introduction Efforts to detect gravitational waves started about fifty years ago with Joe Weber’s bar detectors [1]. They opened the way to the present day interferometric de- tectors with useful bandwidths of thousands of hertz, namely 10 Hz ÷ 10 kHz for Virgo [2], 40 Hz ÷ 10 kHz for Ligo [3], 50 Hz ÷ 1.5 kHz for GEO600 [4] and 10 Hz ÷ 10 kHz for the Japanese TAMA [5]. In this paper we will give an overview of the past and present status of research on Gravitational Waves from pul- sars. Taking into account all interferometric laser GW antennas Tama, GEO600, LIGO and Virgo, we must note that no direct detection of a GW credited signal has yet been announced, although target sensitivity has been reached for both VIRGO and LIGO (see Fig. 1). Searches for GWs from pulsars did not begin with LIGO and VIRGO. After the discovery of the Crab pulsar optical pulsations at ∼ 30 Hz [6] there were a series of pioneering searches for GW emission: • 1972: Levine and Stebbins [7] used a 30 m laser interferometer (single arm Fabry–Pérot cavity); • 1978: Hirakawa et al. [8, 9]) searched for the Crab GW emission using a ∼ 1000 kg aluminum quadrupole antenna with resonant frequency at 60.2 Hz; • 1983: Hereld [10] at Caltech used a 40 m interfer- ometer; • 1983: Hough et al, in Glasgow used a split bar detector [11]; • 1993: Niebauer [12] searched for GWs from a possible Neutron Star (NS) remnant of SN1987A using a Garching 30 m interferometer (100 hrs of data from 1989; searching around 2 and 4 kHz): h0 < 9 × 10−21; • 1986–1995: Tokyo group Crab pulsar search using a 74 kg torsion-type antenna (cooled at 4.2 K) Owa et al. [13, 14], Suzuki [15] using a cooled (4.2 K) 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 (PSR J2144-3933 at νrot ∼ 0.1 Hz) [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 offers a basic introduction to GW emission from pulsars, then results from past and present research are given in 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 by pulsars GW emission is a non-axisimmetric process, since GWs 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 inspiralling binary system. 742 http://dx.doi.org/10.14311/AP.2013.53.0742 http://ojs.cvut.cz/ojs/index.php/ap vol. 53 supplement/2013 The Past and the Future of Direct Search of GW from Pulsars We will focus on the first three items, since they give rise to continuous GW emission, while accreting NS gives rise to a chirping GW emission in the very last stage of life of the system. GW amplitude can be decomposed into two polar- izations: “+” and “×”, according to the effect they have on a circle of free falling masses orthogonal to the propagation direction. The functional form is described by [21] h+ = h0 1+cos 2 ι 2 cos 2Ω ( t− d c ) h× = h0 cos ι sin 2Ω ( t− d c ) (1) being Ω = 2πν the rotational angular velocity and h0 = 16π2G c4 Izzν 2 d � (2) where ι is the angle between the rotation plane and the observer, Izz is the momentum of inertia of NS with respect to the rotation axis, d is the distance from the observation point, and � = (Ixx − Iyy)/(Izz) is quadrupole ellipticity. From a large set of Equations of State (EoS), describing NS matter at supra-nuclear densities one gets: Izz = (1÷3)×1038 kg m2 depending on the EoS and on the rotation velocity. So the scale parameter of GW amplitude can be expressed in more physical units as h0 = 4 × 10−25 ( � 10−6 ) ( I 1038 kg m2 ) ( 100 pc d ) ( ν 100 Hz )2 . (3) GWs can also be emitted by an axisimmetric rotat- ing star, when the symmetry and the rotation axes are misaligned by “wobble” angle α. The maximum sustainable quadrupole deformation � for an NS depends on the physics of the crust and the EoS of matter at super-nuclear density. We can set a limit in � by looking at the maximum strain sustainable by the crust without breaking. Modeling of crustal strains indicates that [21] � < k ubreak BrLim where ubreak is the crustal limit strain, and k and BrLim depend on the star model. From molecular dynamics simulations, one obtains: k = 2 × 10−5 and ubreak ' BrLim = 0.1. This means that a NS breaks for 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 (1016 G), the star can emit intense GWs, due to the deformation induced by the magnetic field. In brief, we have many estimates for the ellipticity, but few certainties. Something can be gathered by looking at the data from GW experiments. How can LIGO and Virgo and astronomical data be useful for constraining the EoS of NS using the upper limits on � and the momentum of inertia I? Let us start from what we know from astrophysical observations and gravitational observatory data. In our galaxy we can estimate a number of NS of about 108, 2000 of which are radio pulsars. Dis- tance d and rotation frequency ν can be evaluated from radio and optical observations (GW emission has a frequency given by 2ν). If the variation of the rotational period is such that ν̇ < 0, there is a mech- anism that makes the pulsar lose its energy. It can be: electromagnetic (EM) dipole radiation, particle acceleration and GW emission. Since ν̇ = kνn, one can derive the breaking index n from the rotational frequency and its derivatives, n = νν̈ ν̇2 . It has been evaluated that for pure magnetic dipole radiation, the breaking index is n = 3, while for pure GW radiation n = 5. For the few objects that have been observed with sufficient 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 interesting phenomnological analysis of the problem). Now let us try to derive some upper limit on GW emission. We start with the strong hypothesis that all the energy is lost by GW emission. Thus the spindown GW amplitude is given by hSD ∼ ( 5 2 GIzz|ν̇| c3d2ν )1/2 or, expressed in a more convenient set of units, hSD ∼2.5 ×−25 ( Izz 1038 kg m2 ) ( |ν̇| 10−11 Hz s−1 ) ( 100 Hz ν ) ( 1 kpc d ) from which we can get an upper limit for Izz combining EM and GW observations. 3. GW from pulsars, and results from the past until now In recent years, since ground-based GW interferomet- ric detectors have come into operation, several studies have been carried out to detect GW signals from con- tinuous sources, both by single interferometers and by coherent searches using two or more detectors, but as of June 2012, the results of these searches have only involved the upper limits on the rate and breaking strain threshold. The search for periodic sources (or Continuous Waves – CW), benefits from long integration times and coincident analysis between different detectors. This was the first to be started in Scientific Run 1 (S1) of the LIGO detector, using time and frequency domain 743 L. Milano, E. Calloni, R. De Rosa, M. De Laurentis, L. Di Fiore, F. Garufi Acta Polytechnica 10 0 10 1 10 2 10 3 10 4 10 −30 10 −28 10 −26 10 −24 10 −22 GW Frequency (Hz) S tr a in Virgo VSR2 Virgo Design Ligo Design Crab Pulsar Ligo S6 AdVirgo Design Vela Pulsar ET Design AdLigo Design Figure 1. The figure shows the upper bounds on GW amplitude from known pulsars, assuming 100 % conversion of spindown energy into GWs. An integration time of one year is assumed. The (green) diamonds represent a pulsar with a spindown outside the detection band for both AdV and Advanced LIGO; the (cyan) squares are in the potential 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 Scientific Run) search on pulsars of known period and spindown using ephemerides given by radio-telescopes and X-ray satellites [25], has set lower limits on GW radiation from targets, on the assumption that it is locked to EM emission. A further analysis was performed on joint data from S6 and the VSR2 run and results interesting for physics were obtained from the upper limit in GW emission from the Crab pulsar [25] and the Vela pulsar (Abadie et al. 2011) as shown by the red circles in Fig. 1. Figure 1 shows that the great majority of known pulsars (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) fall in the range of sensitivity of either Advanced LIGO or Advanced Virgo or in the range of the Einstein Telescope [32]. The upper limits obtained by the analysis of the sources that can be studied by the present interferometers, provide interesting astrophys- ical information, since they give non-trivial constraints on 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 pulsar the hSD ' 1.4 × 10−24 limit was beaten, finding h0 < 2.4 × 10−25 i.e. ≈ hSD/6. This implies that less than 2 % of the rotational energy is lost in GW and also constrains the ellipticity to � < 1.3 × 10−4. For the Vela pulsar the hSD ' 3.29 × 10−24 limit was beaten, by finding h0 < 2.4×10−24 implying that less than 35 % of the rotational energy is lost in GW and constraining the ellipticity to � < 1.1 × 10−3. These results also impose stringent limits on the EoS of an NS [21]. 4. The near future: the new proposals The ground-based GW detector network has been run- ning with improved sensitivity (the Virgo VSR3 run in 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 better sensitivity than the current instruments (Fig. 1 blue and red curves). These detectors come into opera- tion in 2014 or 2015, and, unless something in GR theory is wrong, we can foresee regular detections of binary inspirals with very good prospects of detecting various other signals. The proposals for other large in- terferometric detectors, LCGT in Japan [29] (approval received in June 2010) and AIGO in Australia [30], will significantly improve the capabilities of the cur- rent detector network. We will have good chances of detecting 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 ÷10−1 Hz and Decigo [34], are anticipated years later to open up the intermediate frequency band. Third generation conceptual designs for the Einstein Telescope (ET) (Fig .1) [32] will be at future opportunity for GW detection since this telescope should attain greater sensitivity by a factor of 100 more in sensitivity than first generation Virgo and LIGO interferometers. 5. Conclusions and open questions In this paper we have given an overview of the past and present status of Gravitational Wave (GW) research associated with pulsars. Many questions remain open, e.g.: What are the upper limits for pulsars: When there will be a direct detection? What fraction of pulsars energy is emitted in the form of gravitational 744 vol. 53 supplement/2013 The Past and the Future of Direct Search of GW from Pulsars waves? Can we have direct inferences on pulsar pa- rameters from gravitational waves to constrain the EoS of an NS? What will be the model of NS or quark stars? With interferometric GW antennas (LIGO, GEO600, Tama, Virgo), we have as yet only succeeded in setting interesting upper limits, but the cherished belief is that the first direct detection will be possible with the new generation of interferometers, and as a result answers may be found to some open questions. Acknowledgements This 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 7 P03012 [3] Abbott B P et al.: 2009 Rep. Prog. Phys. 72 076901 [4] Grote H. et al.: 2008 Class. Quantum Grav. 25 114043 [5] Takahashi R.: 2004 CQG 21 S403-8 [6] Cocke W. 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Aguiar : 2010 arXiv:1009.1138v1 745 Acta Polytechnica 53(Supplement):742–745, 2013 1 Introduction 2 Basics of GW emission by pulsars 3 GW from pulsars, and results from the past until now 4 The near future: the new proposals 5 Conclusions and open questions Acknowledgements References