超致密X射线双星引力波辐射
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摘要
超简并X射线源由中子星和充满洛希瓣的白矮星双星组成,该类双星系统轨道周期极短(约小于80 min).对此类双星系统的数值计算表明其在演化过程中可以产生强引力波辐射.以目前观测到的最短轨道周期超简并X射线源4U 1820-30为例,我们模拟了该双星系统的轨道和质量演化,发现物质交流稳定性判据建议该系统曾经经历过非稳定的物质交流,该系统的引力波辐射频率变化在10~(-5) a~(-1)的量级.通过比较不同质量双星的轨道周期和引力波频率随时间的演化,我们提出可以通过测量引力波频率变化的方法来研究此类双星星族的演化过程,也可以通过该方法来搜寻较大质量短轨道周期黑洞白矮星等双星系统.
The ultracompact X-ray sources are believed to be binaries consisting of neutron stars and Roche lobe filling white dwarfs. Using this binary model, we numerically calculated the gravitational waves(GW) radiated from ultracompact X-ray sources. Our results indicate that S/N of the shortest orbital period X-ray source 4U 1820-30 can reach ～3 by GW detectors with LISA-like sensitivity curves, and its GW frequency change is about 10~(-5) a~(-1). The mass transfer stability criteria suggests that this binary system has experienced unstable mass transfer. Measuring the first-order time derivative of GW frequency(i.e. orbital period) of these binaries may allow us to study the evolution the binary population, and search for binaries with high masses and short orbital periods, e.g. black hole white dwarf binaries.
The ultracompact X-ray sources are believed to be binaries consisting of neutron stars and Roche lobe filling white dwarfs. Using this binary model, we numerically calculated the gravitational waves(GW) radiated from ultracompact X-ray sources. Our results indicate that S/N of the shortest orbital period X-ray source 4U 1820-30 can reach ～3 by GW detectors with LISA-like sensitivity curves, and its GW frequency change is about 10~(-5) a~(-1). The mass transfer stability criteria suggests that this binary system has experienced unstable mass transfer. Measuring the first-order time derivative of GW frequency(i.e. orbital period) of these binaries may allow us to study the evolution the binary population, and search for binaries with high masses and short orbital periods, e.g. black hole white dwarf binaries.
引文
1 Nelemans G.The Galactic gravitational wave foreground.Class Quantum Grav,2009,26:094030
2 Nelemans G,Jonker P G.Ultra-compact(X-ray)binaries.New Astron Rev,2010,54:87-92
3 Stella L,White N E,Priedhorsky W.The discovery of a 685 second orbital period from the X-ray source 4U 1820-30 in the globular cluster NGC6624.Astrophys J,1987,312:L17-L21
4 Verbunt F.The formation of ultra-short period binaries in globular clusters.Astrophys J,1987,312:L23-L25
5 van der Klis M,Hasinger G,Dotani T,et al.Simultaneous ROSAT/Ginga observations of 4U 1820-30.Mon Not R Astron Soc,1993,260:686-692
6 Grindlay J,Gursky H,Schnopper H,et al.Discovery of intense X-ray bursts from the globular cluster NGC 6624.Astrophys J,1976,205:L127-L130
7 Kuulkers E,den Hartog P R,in’t Zand J J M,et al.Photospheric radius expansion X-ray bursts as standard candles.Astron Astrophys,2003,399:663-680
8 Valenti E,Ferraro F R,Origlia L.Near-infrared properties of 24 globular clusters in the galactic bulge.Astrophys J,2007,133:1287-1301
9 Gver T,Wroblewski P,Camarota L,et al.The mass and radius of the neutron star in 4U 1820-30.Astrophys J,2010,719:1807-1812
10 Geldzahler B J.Radio frequency observations of galactic X-ray sources.Astrophys J,1983,264:L49-L53
11 Grindlay J E,Seaquist E R.Radio observations of galactic bulge and globular cluster X-ray sources.Astrophys J,1986,310:172-175
12 Biggs J D,Bailes M,Lyne A G,et al.Two radio pulsars in the globular cluster NGC 6624.Mon Not R Astron Soc,1994,267:125-128
13 King I R,Stanford S A,Albrecht R,et al.Detection of an ultraviolet and visible counterpart of the NGC 6624 X-ray burster.Astrophys J,1993,413:L117-L120
14 Chou Y,Grindlay J E.Binary and long-term(Triple?)modulations of 4U 1820-30 in NGC 6624.Astrophys J,2001,563:934-940
15 van der Klis M,Hasinger G,Verbunt F,et al.Further ROSAT measurements of the period of 4U 1820-30.Astron Astrophys,1993,279:L21-L24
16 Tan J,Morgan E,Lewin W H G,et al.Changes in the 11 minute period of 4U 1820-30.Astrophys J,1991,374:291-297
17 Morgan E H,Remillard R A,Garcia M R.SAS 3 and Einstein observations of the 11 minute orbital period of the globular cluster X-ray source 4U1820-30.Astrophys J,1988,324:851-858
18 Rappaport S,Ma C P,Joss P C,et al.The evolutionary status of 4U 1820-30.Astrophys J,1987,322:842-851
19 Prodan S,Murray N.On the dynamics of ultra compact X-ray binaries:4U 1850-087,4U 0513-40,and M15 X-2.Astrophys J,2015,798:117
20 Wang Z,Chakrabarty D.The orbital period of the ultracompact low-mass X-ray binary 4U 1543-624.Astrophys J,2004,616:L139-L142
21 Dieball A,Knigge C,Zurek D R,et al.An ultracompact X-ray binary in the globular cluster M15(NGC 7078).Astrophys J,2005,634:L105-L108
22 Deloye C J,Bildsten L.White dwarf donors in ultracompact binaries:The stellar structure of finite-entropy objects.Astrophys J,2003,598:1217-1228
23 in’t Zand J J M,Jonker P G,Markwardt C B.Six new candidate ultracompact X-ray binaries.Astron Astrophys,2007,465:953-963
24 Deutsch E W,Margon B,Anderson S F.Ultracompact X-ray binaries in globular clusters:Variability of the optical counterpart of X1832-330 in NGC 6652.Astrophys J,2000,530:L21-L24
25 Shahbaz T,Watson C A,Zurita C,et al.Time-resolved optical photometry of the ultracompact binary 4U 0614+091.Publ Astron Soc Pac,2008,120:848-851
26 Peters P C,Mathews J.Gravitational radiation from point masses in a Keplerian orbit.Phys Rev,1963,131:435-440
27 Lubow S H,Shu F H.Gas dynamics of semidetached binaries.Astrophys J,1975,198:383-405
28 Nelemans G,Portegies Zwart S F,Verbunt F,et al.Population synthesis for double white dwarfs.II.Semi-detached systems:AM CVn stars.Astron Astrophys,2001,368:939-949
29 Verbunt F,Rappaport S.Mass transfer instabilities due to angular momentum flows in close binaries.Astrophys J,1988,332:193-198
30 Marsh T R,Nelemans G,Steeghs D.Mass transfer between double white dwarfs.Mon Not R Astron Soc,2004,350:113-128
31 Zahn J.Tidal friction in close binary stars.Astron Astrophys,1977,57:383-394
32 Campbell C G.Tidal effects in twin-degenerate binaries.Mon Not R Astron Soc,1984,207:433-443
33 Eggleton P P,Kiseleva L G,Hut P.The equilibrium tide model for tidal friction.Astrophys J,1998,499:853-870
34 Campbell C G.Magnetic coupling in AM Herculis binaries.Mon Not R Astron Soc,1983,205:1031-1052
35 Kippenhahn R,Weigert A.Stellar Structure and Evolution.Berlin,Heidelberg:Springer,1990
36 Eggleton P P.Approximations to the radii of Roche lobes.Astrophys J,1983,268:368
37 Kopal Z.Close Binary Systems.In:The International Astrophysics Series.London:Chapman&Hall,1959
38 Landau L D,Lifshitz E M.The classical theory of fields.4th ed.In:Course of Theoretical Physics-Pergamon International Library of Science,Technology,Engineering and Social Studies.Oxford:Pergamon Press,1975,
39 Nelemans G,Yungelson L R,Portegies Zwart S F.The gravitational wave signal from the Galactic disk population of binaries containing two compact objects.Astron Astrophys,2001,375:890-898
40 Huerta E A,McWilliams S T,Gair J R,et al.Detection of eccentric supermassive black hole binaries with pulsar timing arrays:Signal-to-noise ratio calculations.Phys Rev D,2015,92:063010
41 Hughes S A.Gravitational waves from merging compact binaries.Annu Rev Astron Astrophys,2009,47:107-157
42 Moore C J,Cole R H,Berry C P L.Gravitational-wave sensitivity curves.Class Quantum Grav,2015,32:015014
43 Roelofs G H A,Rau A,Marsh T R,et al.Spectroscopic evidence for a 5.4 minute orbital period in HM cancri.Astrophys J,2010,711:L138-L142
44 Barros S C C,Marsh T R,Groot P,et al.Geometrical constraints upon the unipolar model of V407 Vul and RXJ0806.3+1527.Mon Not R Astron Soc,2005,357:1306-1312
45 Barros S C C,Marsh T R,Dhillon V S,et al.ULTRACAM photometry of the ultracompact binaries V407 Vul and HM Cnc.Mon Not R Astron Soc,2007,374:1334-1346
46 Steeghs D,Marsh T R,Barros S C C,et al.GEMINI spectroscopy of the ultracompact binary candidate V407 vulpeculae.Astrophys J,2006,649:382-388
47 Chan C,Mller B,Heger A,et al.Black hole formation and fallback during the supernova explosion of a 40MP Star.Astrophys J,2018,852:L19
48 Roelofs G H A,Groot P J,Benedict G F,et al.Hubble space telescope parallaxes of AM CVn stars and astrophysical consequences.Astrophys J,2007,666:1174-1188
49 Roelofs G H A,Groot P J,Marsh T R,et al.SDSS J124058.03-015919.2:A new AM CVn star with a 37-min orbital period.Mon Not R Astron Soc,2005,361:487-494
50 Brown W R,Kilic M,Hermes J J,et al.A 12 minute orbital period detached white dwarf eclipsing binary.Astrophys J,2011,737:L23
51 Hermes J J,Kilic M,Brown W R,et al.Rapid orbital decay in the 12.75-minute binary white dwarf J0651+2844.Astrophys J,2012,757:L21
52 Kilic M,Brown W R,Allende P C,et al.The ELM survey.IV.24 white dwarf merger systems.Astrophys J,2012,751:141
53 Kilic M,Brown W R,Gianninas A,et al.A new gravitational wave verification source.Mon Not R Astron Soc-Lett,2014,444:L1-L5
54 Brown W R,Kilic M,Prieto C A,et al.The ELM Survey.I.A complete sample of extremely low-mass white dwarfs.Astrophys J,2010,723:1072-1081
55 Webbink R F,Han Z.Gravitational radiation from close double white dwarfs.In:Folkner W M,ed.Laser Interferometer Space Antenna,Second International LISA Symposium on the Detection and Observation of Gravitational Waves in Space.Pasadena,1998.61-67
56 Liu J.Gravitational wave radiation from close double white dwarfs in the Galaxy.Mon Not R Astron Soc,2009,400:1850-1858
57 Yu S,Jeffery C S.The gravitational wave signal from diverse populations of double white dwarf binaries in the Galaxy.Astron Astrophys,2010,521:A85
58 Ruiter A J,Belczynski K,Benacquista M,et al.The LISA gravitational wave foreground:A study of double white dwarfs.Astrophys J,2010,717:1006-1021
59 Nissanke S,Vallisneri M,Nelemans G,et al.Gravitational-wave emission from compact galactic binaries.Astrophys J,2012,758:131
60 Yu S,Jeffery C S.The gravitational-wave signal generated by a galactic population of double neutron-star binaries.Mon Not R Astron Soc,2015,448:1078-1098
61 Kremer K,Breivik K,Larson S L,et al.Accreting double white dwarf binaries:Implications for LISA.Astrophys J,2017,846:95
62 Goldreich P,Soter S.Q in the solar system.Icarus,1966,5:375-389
2 Nelemans G,Jonker P G.Ultra-compact(X-ray)binaries.New Astron Rev,2010,54:87-92
3 Stella L,White N E,Priedhorsky W.The discovery of a 685 second orbital period from the X-ray source 4U 1820-30 in the globular cluster NGC6624.Astrophys J,1987,312:L17-L21
4 Verbunt F.The formation of ultra-short period binaries in globular clusters.Astrophys J,1987,312:L23-L25
5 van der Klis M,Hasinger G,Dotani T,et al.Simultaneous ROSAT/Ginga observations of 4U 1820-30.Mon Not R Astron Soc,1993,260:686-692
6 Grindlay J,Gursky H,Schnopper H,et al.Discovery of intense X-ray bursts from the globular cluster NGC 6624.Astrophys J,1976,205:L127-L130
7 Kuulkers E,den Hartog P R,in’t Zand J J M,et al.Photospheric radius expansion X-ray bursts as standard candles.Astron Astrophys,2003,399:663-680
8 Valenti E,Ferraro F R,Origlia L.Near-infrared properties of 24 globular clusters in the galactic bulge.Astrophys J,2007,133:1287-1301
9 Gver T,Wroblewski P,Camarota L,et al.The mass and radius of the neutron star in 4U 1820-30.Astrophys J,2010,719:1807-1812
10 Geldzahler B J.Radio frequency observations of galactic X-ray sources.Astrophys J,1983,264:L49-L53
11 Grindlay J E,Seaquist E R.Radio observations of galactic bulge and globular cluster X-ray sources.Astrophys J,1986,310:172-175
12 Biggs J D,Bailes M,Lyne A G,et al.Two radio pulsars in the globular cluster NGC 6624.Mon Not R Astron Soc,1994,267:125-128
13 King I R,Stanford S A,Albrecht R,et al.Detection of an ultraviolet and visible counterpart of the NGC 6624 X-ray burster.Astrophys J,1993,413:L117-L120
14 Chou Y,Grindlay J E.Binary and long-term(Triple?)modulations of 4U 1820-30 in NGC 6624.Astrophys J,2001,563:934-940
15 van der Klis M,Hasinger G,Verbunt F,et al.Further ROSAT measurements of the period of 4U 1820-30.Astron Astrophys,1993,279:L21-L24
16 Tan J,Morgan E,Lewin W H G,et al.Changes in the 11 minute period of 4U 1820-30.Astrophys J,1991,374:291-297
17 Morgan E H,Remillard R A,Garcia M R.SAS 3 and Einstein observations of the 11 minute orbital period of the globular cluster X-ray source 4U1820-30.Astrophys J,1988,324:851-858
18 Rappaport S,Ma C P,Joss P C,et al.The evolutionary status of 4U 1820-30.Astrophys J,1987,322:842-851
19 Prodan S,Murray N.On the dynamics of ultra compact X-ray binaries:4U 1850-087,4U 0513-40,and M15 X-2.Astrophys J,2015,798:117
20 Wang Z,Chakrabarty D.The orbital period of the ultracompact low-mass X-ray binary 4U 1543-624.Astrophys J,2004,616:L139-L142
21 Dieball A,Knigge C,Zurek D R,et al.An ultracompact X-ray binary in the globular cluster M15(NGC 7078).Astrophys J,2005,634:L105-L108
22 Deloye C J,Bildsten L.White dwarf donors in ultracompact binaries:The stellar structure of finite-entropy objects.Astrophys J,2003,598:1217-1228
23 in’t Zand J J M,Jonker P G,Markwardt C B.Six new candidate ultracompact X-ray binaries.Astron Astrophys,2007,465:953-963
24 Deutsch E W,Margon B,Anderson S F.Ultracompact X-ray binaries in globular clusters:Variability of the optical counterpart of X1832-330 in NGC 6652.Astrophys J,2000,530:L21-L24
25 Shahbaz T,Watson C A,Zurita C,et al.Time-resolved optical photometry of the ultracompact binary 4U 0614+091.Publ Astron Soc Pac,2008,120:848-851
26 Peters P C,Mathews J.Gravitational radiation from point masses in a Keplerian orbit.Phys Rev,1963,131:435-440
27 Lubow S H,Shu F H.Gas dynamics of semidetached binaries.Astrophys J,1975,198:383-405
28 Nelemans G,Portegies Zwart S F,Verbunt F,et al.Population synthesis for double white dwarfs.II.Semi-detached systems:AM CVn stars.Astron Astrophys,2001,368:939-949
29 Verbunt F,Rappaport S.Mass transfer instabilities due to angular momentum flows in close binaries.Astrophys J,1988,332:193-198
30 Marsh T R,Nelemans G,Steeghs D.Mass transfer between double white dwarfs.Mon Not R Astron Soc,2004,350:113-128
31 Zahn J.Tidal friction in close binary stars.Astron Astrophys,1977,57:383-394
32 Campbell C G.Tidal effects in twin-degenerate binaries.Mon Not R Astron Soc,1984,207:433-443
33 Eggleton P P,Kiseleva L G,Hut P.The equilibrium tide model for tidal friction.Astrophys J,1998,499:853-870
34 Campbell C G.Magnetic coupling in AM Herculis binaries.Mon Not R Astron Soc,1983,205:1031-1052
35 Kippenhahn R,Weigert A.Stellar Structure and Evolution.Berlin,Heidelberg:Springer,1990
36 Eggleton P P.Approximations to the radii of Roche lobes.Astrophys J,1983,268:368
37 Kopal Z.Close Binary Systems.In:The International Astrophysics Series.London:Chapman&Hall,1959
38 Landau L D,Lifshitz E M.The classical theory of fields.4th ed.In:Course of Theoretical Physics-Pergamon International Library of Science,Technology,Engineering and Social Studies.Oxford:Pergamon Press,1975,
39 Nelemans G,Yungelson L R,Portegies Zwart S F.The gravitational wave signal from the Galactic disk population of binaries containing two compact objects.Astron Astrophys,2001,375:890-898
40 Huerta E A,McWilliams S T,Gair J R,et al.Detection of eccentric supermassive black hole binaries with pulsar timing arrays:Signal-to-noise ratio calculations.Phys Rev D,2015,92:063010
41 Hughes S A.Gravitational waves from merging compact binaries.Annu Rev Astron Astrophys,2009,47:107-157
42 Moore C J,Cole R H,Berry C P L.Gravitational-wave sensitivity curves.Class Quantum Grav,2015,32:015014
43 Roelofs G H A,Rau A,Marsh T R,et al.Spectroscopic evidence for a 5.4 minute orbital period in HM cancri.Astrophys J,2010,711:L138-L142
44 Barros S C C,Marsh T R,Groot P,et al.Geometrical constraints upon the unipolar model of V407 Vul and RXJ0806.3+1527.Mon Not R Astron Soc,2005,357:1306-1312
45 Barros S C C,Marsh T R,Dhillon V S,et al.ULTRACAM photometry of the ultracompact binaries V407 Vul and HM Cnc.Mon Not R Astron Soc,2007,374:1334-1346
46 Steeghs D,Marsh T R,Barros S C C,et al.GEMINI spectroscopy of the ultracompact binary candidate V407 vulpeculae.Astrophys J,2006,649:382-388
47 Chan C,Mller B,Heger A,et al.Black hole formation and fallback during the supernova explosion of a 40MP Star.Astrophys J,2018,852:L19
48 Roelofs G H A,Groot P J,Benedict G F,et al.Hubble space telescope parallaxes of AM CVn stars and astrophysical consequences.Astrophys J,2007,666:1174-1188
49 Roelofs G H A,Groot P J,Marsh T R,et al.SDSS J124058.03-015919.2:A new AM CVn star with a 37-min orbital period.Mon Not R Astron Soc,2005,361:487-494
50 Brown W R,Kilic M,Hermes J J,et al.A 12 minute orbital period detached white dwarf eclipsing binary.Astrophys J,2011,737:L23
51 Hermes J J,Kilic M,Brown W R,et al.Rapid orbital decay in the 12.75-minute binary white dwarf J0651+2844.Astrophys J,2012,757:L21
52 Kilic M,Brown W R,Allende P C,et al.The ELM survey.IV.24 white dwarf merger systems.Astrophys J,2012,751:141
53 Kilic M,Brown W R,Gianninas A,et al.A new gravitational wave verification source.Mon Not R Astron Soc-Lett,2014,444:L1-L5
54 Brown W R,Kilic M,Prieto C A,et al.The ELM Survey.I.A complete sample of extremely low-mass white dwarfs.Astrophys J,2010,723:1072-1081
55 Webbink R F,Han Z.Gravitational radiation from close double white dwarfs.In:Folkner W M,ed.Laser Interferometer Space Antenna,Second International LISA Symposium on the Detection and Observation of Gravitational Waves in Space.Pasadena,1998.61-67
56 Liu J.Gravitational wave radiation from close double white dwarfs in the Galaxy.Mon Not R Astron Soc,2009,400:1850-1858
57 Yu S,Jeffery C S.The gravitational wave signal from diverse populations of double white dwarf binaries in the Galaxy.Astron Astrophys,2010,521:A85
58 Ruiter A J,Belczynski K,Benacquista M,et al.The LISA gravitational wave foreground:A study of double white dwarfs.Astrophys J,2010,717:1006-1021
59 Nissanke S,Vallisneri M,Nelemans G,et al.Gravitational-wave emission from compact galactic binaries.Astrophys J,2012,758:131
60 Yu S,Jeffery C S.The gravitational-wave signal generated by a galactic population of double neutron-star binaries.Mon Not R Astron Soc,2015,448:1078-1098
61 Kremer K,Breivik K,Larson S L,et al.Accreting double white dwarf binaries:Implications for LISA.Astrophys J,2017,846:95
62 Goldreich P,Soter S.Q in the solar system.Icarus,1966,5:375-389