PoS(GOLDEN 2017)008 https://pos.sissa.it/ ∗ [email protected] Speaker. The recent direct detection of gravitationalsources. waves has Some triggered sources the are interest potentially in observablethe gravitational only forthcoming wave with LISA space scheduled based for interferometers, launchwhose such after 2030. as emission Cataclysmic is variables are in binarygravitational the sources wave sensititivity emission band of of aboutsources five LISA. are hundreds The AM cataclysmic CVn paper variables. systems. presents The an most estimation promising of the ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). The Golden Age of Cataclysmic Variables11-16 and September, Related 2017 Objects IV Palermo, Italy Rosa Poggiani Università di Pisa and Istituto NazionaleE-mail: di Fisica Nucleare, Sezione di Pisa Cataclysmic variables as gravitational wave sources PoS(GOLDEN 2017)008 ] ]. 1 6 Rosa Poggiani ]. ] during run O2. Advanced Virgo joined O2 4 Hz, includes a stochastic background and the 40 5 and 0.1 Hz, includes the coalescence of massive − 1 5 − Hz, a region precluded to ground based instruments by Hz, and includes a large variety of astronomical sources 1 4 − ], GW170608 [ 3 to 10 ] and the first coalescence of a binary neutron star system [ 10 5 − Hz to 10 5 − The spectrum of gravitational waves, based on the tool at http://rhcole.com/apps/GWplotter/ ) that involve different detection techniques [ 1 The forthcoming space based laser interferometer LISA aims to detect gravitazional waves in The Very Low Frequency region, below 10 The direct detection of gravitational waves from the binary black hole merger GW150914 [ ]. The Low Frequency region, between 10 Figure 1: ] during run O1, and GW170104 [ 41 2 the presence of seismic noise. As mentionedlarge, above, including the the science reach coalescence of of theincluding low supermassive frequency black compact region holes, is objects, contact such binary systems as and white binaries dwarfs, neutron stars or black holes. Electromagnetic the frequency range from 10 binaries and of extreme mass ratio systemsbinaries; and it the emission can of be resolvable probed and by unresolvableHz, space galactic based is interferometers. the The High domain Frequencystellar of region, mass above ground black some holes, based of interferometers neutron starscore and and collapse of includes supernovae, the pulsars, the still stochastic undetected radiation background neutron of star/blackbinaries. by unresolved hole the black mergers, hole mergers and of neutron star radiation of supermassive binaries.[ The region can be accessed using pulsar timing techniques by the two Advanced LIGO interferometers duringin run astrophysics. O1 Additional has black opened hole a mergers new have[ observational been window detected by Advanced LIGO: GW151226 The signatures of black holespanning and the neutron frequency star region from mergers a inwaves few is ground Hz very based to extended, interferometers some from 10 hundreds are Hz. chirps The spectrum of gravitational (Fig. Cataclysmic variables as gravitational wave sources 1. Introduction in August 2017. Theblack network hole of merger Advanced GW170814 LIGO [ and Advanced Virgo has detected the binary PoS(GOLDEN 2017)008 Rosa Poggiani ]; the catalogue ]. The estimation 49 59 ], [ 48 ], [ ]. 19 19 ], [ ], who estimated the emission ], [ 32 38 32 20 ], [ 27 ], [ ]. 15 ], are of special interest. To date, more than 34 38 58 ], [ ], [ 18 28 2 10 Orbital period (hr) period Orbital ], [ 39 ]. The total number of galactic cataclysmic variables is 49 ], [ 5 ]. Their orbital periods range from minutes to hours, thus 53 ], [ 32 [ 48 6 0 0

100 300 500 600 200 400 N Distribution of the orbital periods of cataclysmic variables . The catalogue version 7.23 contains the main parameters of more than 1400 1 Figure 2: , that clearly shows the period gap between two and three hours. 2 http://wwwmpa.mpa-garching.mpg.de/RKcat/ The cataclysmic variables have been catalogued by Ritter and Kolb [ The gravitational wave emission of binary systems has been thoroughly investigated, making In the following, the estimation of the gravitational wave emission of about five hundreds The paper firstly presents a summary of the properties of cataclysmic variables relevant for 1 systems. The orbital periodreported is in Fig. known for most cataclysmic variables. The period distribution is 2. Cataclysmic variables: orbital periods and masses is available online them the better understood sources [ cataclysmic variables is presented. Following the approach by [ of gravitational emission of amasses binary of system the components requires and thewhite of knowledge dwarf the of is distance. accreting the material The orbital fromone cataclysmic period, another thousand variables, star of systems binary [ the are system known where [ a their gravitational emission, that occurs at twice the orbital period, is in the LISA frequency range. the gravitational wave emission. Thencussed. the The problem properties of and the thethe distance sensitivity gravitational to of wave cataclysmic emission the systems is LISA estimated is interferometerthan for dis- previous are abot estimations presented five reported later. hundred in systems, Finally, literatures a [ factor of three larger Cataclysmic variables as gravitational wave sources observations of binary systems areand often the orbital available, period providing of informationbackground the about from system. binary the systems Due sky is to position expected, thepairs expecially large of from number white galactic unresolved dwarfs of contact or binary binaries, neutron systems, stars an and astrophysical cataclysmic binaries [ estimated to be of the order of 10 for 160 systems, I have estimated the(distance, gravitational orbital wave period emission and for masses) systems are where known,the all complementing distance parameters them and with the the orbital systems period where only are known. PoS(GOLDEN 2017)008 (2.4) 3.5 ]. I have 45 3.0 Rosa Poggiani ], [ 44 2.5 ], [ 21 ) 2.0 , left and right. ⊙ 3 (M 2 M 1.5 ) 1.0 hr ( P 0.5 093 . 0 0.0 0 5

10 15 20 25

+ N in period gap (2.2) ]. Nine additional parallaxes have been measured

3 above period gap (2.3) below period gap (2.1) M 50 0084 2.0 .

0 78 ], [ . M M 0 31 85 ) = 76 = . .

], [ 0 1 0 M 1.5 M 30 = ( = 2 1 1 ], [ M M M 23 ) ⊙ ], [ (M 1.0 ]. I have fitted the mass versus orbital period for 146 systems with 1 M 22 52 ], [ 37 ]. The mass of the primary is estimated the unweigthed average of the systems 0.5 38 ], [ 36 ] for 26 cataclysmic variables. Parallax measurements with HST are available for 19 Distribution of the mass of the primary (left) and secondary (right) of cataclysmic variables ], [ 55 29 0.0

0 8 6 2 4

12 10 14 16 N The Ritter and Kolb catalogue does not report the distances of the cataclysmic variables. Com- I have estimated the masses of the primary and secondary stars with missing values following The parallax is a primary method for measuring the distance of celestial objects and is used The mass of the secondary has been estimated with a mass-period relation, following the The masses of the primary and secondary stars are known only for a small fraction of all ] and [ Figure 3: 54 pilations of distances including a few tens systems have been presented by [ 3. Cataclysmic variables: distances systems [ periods smaller than ten hours: the approach by [ below the period gap, in the period gap and above the period gap: as a reference for otheravailable. methods. Distance In based the on following, parallax theavailable measurements parallax for using based ground about distance and fifty will space[ be systems. based used telescopes when are Ground based parallax measurements have been obtained by prepared a compilation of distances, combiningusing the different values methods. in the literature that have been obtained approach proposed by [ known cataclysmic variables, about 10%. Thesystems) distribution and of of the secondary masses stars of (about the 140 primary (about systems) 150 are reported in Fig. Cataclysmic variables as gravitational wave sources PoS(GOLDEN 2017)008 ], P 25 (3.1) ]. The ]. The ]: 8 35 16 magnitude ], [ 7 K Rosa Poggiani ]. In response 0 ) 10 s K ], [ − 11 H ( 380 . 7 ] has been updated with larger + 16 0 ) is a function of the orbital period J H colour index, a proxy of the effective M − K J ( − V 598 ]. An approach of distance estimation using . 2 24 4 ) + surface brightness [ ]. The surface brightness is calibrated as a function of days K ( 16 P , according to the Period-Luminosity-Relation [ 0 ) K ]. The absolute magnitude 721log . − 8 5 H ], [ ( − 7 ]). The features of the energy distribution of the cataclysmic variables , 0 ] to determine the separate contributions of the secondary star and of the ) 17 ]. Recently, the surface brightness of field dwarfs has been calibrated as 894 ]. The method of 56 . H ]. 0 47 color and the spectral type [ 20 − − 43 ]. Recently, a new method based on the position of red clump giants on colour- ]. The first data release of GAIA has provided parallaxes for 16 cataclysmic J ( K = ] relies on observations of shells around novae in the years or decades after the 57 26 J − ] and [ 51 ], [ M V ]. 21 ], [ 25 46 25 surface brightness parameter is related to the ]. Since the method of infrared magnitude generally does not provide distance values, but The initial concept of the LISA space based interferometer, a constellation of three spacecraft In the following, I will consider distances based on the parallax, the nova expansion parallax, A new calibration of absolute magnitude of cataclysmic variable based on 2MASS infrared The approach has produced an homogenous sample of more thanThe four distance of hundreds novae distances can be to measured by using different methods. The methods of expansion Limits to the distance of cataclysmic variables can be set by using the infrared K 33 ], providing the distance to 73 systems. The method has been calibrated against the parallax or ]. The approach must take into account the non isotropic mass ejection and the inclination of ]. The infrared light is produced by the red dwarf and by the accretion disk, but near infrared 43 51 20 [ design of LISA was later reshaped into eLISA, with a shorter arm length [ outburst. The angular expansion rate is combined with the measurement of the radial velocity [ expansion parallax [ in heliocentric orbit lagging Earth by 20 degrees, foresaw an arm length of 5 million km [ the system [ magnitude diagrams and reddening-distance relations towards galactic[ novae has been proposed by the Period-Luminosity-Colour relation, since they provide distance values and not limits. 4. The LISA interferometer only limits, it will not be used in the following. data has been proposed by [ cataclysmic variables. parallax [ of the secondary star, aseffective suggested temperature, by relying [ on theThe small sensitivity to the evolutionary level of the secondary. a function of and of the colours photometry cannot disentangle thefrom two the contributions, secondary allowing [ only to set limits to the fraction has been addressed by [ accretion disk. The origin of[ the infrared emission in cataclysmic variables has been discussed by variables [ Cataclysmic variables as gravitational wave sources with Hipparcos [ temperature, via a linear relation orsurface a brightness combination is of also linear related relationsof in to stellar different the regions radii angular [ (see diameter e.g. of the [ star, allowing to use compilations datasets by [ theoretical models for the secondary star,by that is [ assumed to fill the Roche lobe, has been presented PoS(GOLDEN 2017)008 r ]: (5.1) 53 ] and by 18 Rosa Poggiani 2 3  Hz 3 f − 10  ]. pc ]. LISA is scheduled for launching in r 14 9 100 ], [  Hz [ 13 2 3 1  −

5 are the masses of the primary and secondary star, M M 2 M  , 1

µ M M , the gravitational wave frequency. 2  2 f M M Hz to above 10 21 + 1 1 5 − M ], launched in December 2015, has been the demonstrator of the M − 10 12 = × µ 7 . , 8 2 M = h + 1 M = M The gravitational wave emission of cataclysmic variables has been addressed by [ The constellation of three spacecrafts forming LISA will orbit the Sun in a triangular configu- LISA Pathfinder (LPF) [ where ], who investigated a sample of about 160 objects each. Cataclysmic variables, as other binary 38 5. Gravitational waves from cataclysmic variables the distance of the cataclysmic and systems, emit gravitational waves atof twice the the harmonics orbital is frequency generally andevolution. negligible, harmonics. The since The gravitational the wave contribution orbits characteristic amplitude are produced progressively by circularized a during binary the system is [ LISA concept and ofPathfinder key has placed technologies. two test masses Thethan in five test free times fall, better masses unperturbed than by were the other orginal at stray specifications forces a [ at distance a level of more 0.38 m. LISA ration, along heliocentric orbits that willwill avoid be the centered necessity of in orbit the corrections.angle ecliptic will The plane, be constellation trailing inclined the by Earth 60free by degrees falling with about test respect 20 masses to degrees. and the willing ecliptic. The controlled forces plane The to three on of be spececrafts constantly the the will centered tri- masses. contain oninside The the an drag masses, housing without free that apply- operation probes willthe the be spacecraft relative achieved thrusters. position by embedding of Each thegeodesic the test reference. test masses mass masses The and defines drag the free the spacecrafttest configuration end and mass will will side manages minimize be the for a effects 46 the of mmReference optical cube force Sensor made length gradients. of (GRS), and Each non operating magnetic acts with Au-Ptcontaining as alloy, a capacitive surrounded a Gravitational by sensing. Reference the Sensor Gravitational Each andMichelson spacecraft an interferometer embedded will free-falling configuration host test with two mass. direct units large The reflection standard distance cannot between be the used spacecrafts.beam in is The LISA, sent lasers due from will to one be spacecraft the beam to used and the sends in back other a a one, transponder replicated wherewith configuration: beam. the the The laser local a beam laser is received beam. phase by The locked theders procedure to original will the in spacecraft be incoming is each used compared in arm. alltechnique three arms of The of Time-Delay LISA, virtual Interferometry with (TDI). armlength two transpon- interferometer is built during post-processing with the 2034. [ Cataclysmic variables as gravitational wave sources to ESA call foron missions three for arms L3, with aformation, six new with laser proposal a links separation was exchanged of presented.sky, between 2.5 measuring three million both The identical km. polarisations new spacecrafts of The LISAband in LISA the extending will a interferometer gravitational from be triangular will waves below based monitor at 10 the the entire same time, with a sensitivity PoS(GOLDEN 2017)008 . The 2 ] 35 -1 Rosa Poggiani 10 . The better low 4 ] and short period 42 ]. For comparison, the 9 LISA noise Confusion LISA Original masses Known masses Estimated masses known Cvn, AM masses estimated Cvn, AM ], the dashed line is the binary -2 10 35 km, an acceleration noise based on 6 ]. An observation time of 2 years is 9 10 × -3 10 6 Frequency (Hz) Frequency ], as discussed by [ 19 ], [ -4 10 32 ], the dotted line of the original LISA [ ], with an arm length of 2.5 15 ˜ shane/sensitivity/ 15 for the sample of about 500 hundred systems investigated in the present paper is -5 ] . The strain of systems with known masses and of systems with estimated masses 9 h 10 4 -24 -21 -22 -23 -20

10 10 10 10 10 h Gravitational wave emission of cataclysmic variables with known masses (red circles) and with http://www.srl.caltech.edu/ The majority of potentially detectable systems are AM CVn objects [ The present estimation of gravitational wave emission from cataclysmic variables includes The strain 2 confusion noise [ Figure 4: estimated masses (blue squares); the AM CVNby systems with green known masses circles and and estimated masses greendesign are squares, marked LISA respectively; interferometer the [ solid curve is the instrumental sensitivity of the new about five hundreds systems, a factor three larger than the previous estimations. The strongest dotted curve is the sensitivity of thedashed LISA curve original design is with the 5 millionby contribution km unresolved of arm binary length the [ systems confusion [ noise, the astrophysical background produced systems in general. The AMfrequency CVn sensitivity objects of are marked the by originalnoise. green LISA symbols design in is Fig. however made uneffective by the confusion 6. Conclusions shown in Fig. Cataclysmic variables as gravitational wave sources are reported with differentLISA symbols. design reported The by solid [ curve is the sky averaged sensitivity of the new assumed. the LISA Pathfinder performances and the confusion noise estimated by [ PoS(GOLDEN 2017)008 Rosa Poggiani 7 (2000) 2007. (1996) 489. 120 (1967) 1071. 174 (2013) 4. AJ 18 6 (1997) 1439. (2012) 124016. (1985) 327. 14 (2003) 821. (2004) 291. PRL (1987) 41. MNRAS 29 (1991). (1999) L93. (2013) 7. (2012) 124014. (2004) 460. (2016) 061102. (2016) 241103. (2017) 221101. (2017) 141101. (2017) 161101. (2017) L35. 217 (2016) 231101. (2018) 061101. (1987) 129. 68 412 419 (2006) 783. CQG 29 515 767 (1992) 323. (2017) 103012. 4731 127 CQG GW Notes 116 116 118 119 119 851 116 120 323 (1981) 31. 24 (2007) 446. (2008) 133. 460 A&A A&A 95 ApJ AJ ApJ CQG MNRAS A&ASS PRL PRL PRL ApJ PRL PRL 12 13 ApJ IBVS 197 PRL PRL GRG A&A PRD NewA NewA MNRAS [1] B. P. Abbott et al., [2] B. P. Abbott et al., [3] B. P. Abbott et al., [4] B. P. Abbott et al., [5] B. P. Abbott et al., [6] B. P. Abbott et al., [7] T. Ak et al., [8] T. Ak et al., [9] P. Amaro-Seoane et al., arXiv:1702.00786. [26] H. W. Duerebeck, [27] C. R. Evans et al., [28] R. L. Forward and D. Berman, [29] T. E. Harrison et al., [30] T. E. Harrison et al., [31] T. E. Harrison et al., [23] K. Beuermann et al., [24] K. Beuermann, [25] R. A. Downes and H. W. Duerbeck, [21] G. Berriman et al., [22] K. Beuermann et al., [12] F. Antonucci et al., [13] M. Armano et al., [14] M. Armano et al., [15] S. Babak et al., [18] F. Barone et al., [19] P. L. Bender and D. Hils, [20] G. Berriman et al., [16] J. Bailey, [11] P. Amaro-Seoane et al., [17] T. G. Barnes and D. S. Evans, Cataclysmic variables as gravitational wave sources sources are AM CVn and short period systems. References [10] P. Amaro-Seoane et al., PoS(GOLDEN 2017)008 (1998) Rosa Poggiani Publication MPQ-233 , (1987) 330, Cambridge University Press, (2015) 21. 2 8 (1998) 767. 301 (1995), Cambridge University Press, Cambridge (2016) 1177. (2004) 181. (2003) 301. (2007) 1174. (2008) 2107. (1999) L59. (2001) 907. (1995) 353. (1987) L1. MNRAS (2000) 417. (1987) 653. (2000) 614. 461 349 404 666 LISA Pre-Phase A Report. 2nd Edition (2017) A107. (2015) 015014. (2015) 055004. 136 520 560 276 176 (2003) 3017. 358 (2011) 2695. (1966) 752. 314 112 (1994) 243. (2006) 484. 32 32 AJ 9 ApJ 604 (1990) 65. A&A Acta Polytech. CTU Proc. ApJ ApJ 126 (1984) 443. 411 A&A ApJ 425 MNRAS A&A 372 MNRAS PASP SvA (1982) 1558. AJ 360 CQG CQG 54 MNRAS A%A Three Hundreds Years of Gravitation 87 ApJ ApJ AJ ApJS MNRAS MNRAS Cataclysmic Variable Stars Max-Plank Institute for Quantum Optics, Garching. Cambridge, eds. S. Hawking and W. Israel. [34] V. M. Lipunov et al., Cataclysmic variables as gravitational wave sources [32] D. Hils et al., [35] LISA Study Team, 1998, in [33] C. Knigge, [36] B. E. McArthur et al., [37] B. E. McArthur et al., [38] M. T. Meliani et al., [39] V. N. Mironovskii, [40] C. J. Moore et al., [41] C. J. Moore et al., [42] G. Nelemans et al., [56] R. A. Wade, [57] R. A. Wade eta al., [58] B. Warner, [59] R. F. Webbink et al., [54] J. R. Thorstensen, [55] J. R. Thorstensen et al., [43] A. Özdönmez et al., [53] K. S. Thorne, in [46] G. Ramsay et al., [44] J. Patterson, [45] J. Patterson, [47] T. F. Ramseyer, [49] H. Ritter and U. Kolb, [52] D. A. Smith and V. S. Dhillon, [48] H. Ritter and U. Kolb, [50] G. H. A. Roelofs et al., [51] A. J. Slavin et al.,