Revisiting LS I +61 303 with VLBI astrometry
Y. W. Wu, G. Torricelli-Ciamponi, M. Massi, M. J. Reid, B. Zhang, L. Shao, X. W. Zheng
MMNRAS , 1– ?? (2017) Preprint 29 September 2018 Compiled using MNRAS L A TEX style file v3.0
Revisiting LS I + ◦
303 with VLBI astrometry
Y. W. Wu , (cid:63) , G. Torricelli-Ciamponi M. Massi † ,M. J. Reid , B. Zhang , L. Shao , X. W. Zheng National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan National Time Service Center, Key Laboratory of Precise Positioning and Timing Technology, Chinese Academy of Sciences, Xi’an 710600, China INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, Firenze, Italy Max-Planck-Institut für Radioastronomie, Auf demHügel 69, 53121 Bonn, Germany Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Shanghai Astronomical Observatory, 80 Nandan Road, Shanghai 20030, China Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, D-14476 Potsdam-Golm, Germany School of Astronomy and Space Sciences of Nanjing University, Nanjing 210093, China
Last updated 2017 April 15
ABSTRACT
We conducted multi-epoch VLBA phase reference observations of LS I + ◦
303 in orderto study its precessing radio jet. Compared to similar observations in 2006, we find that theobserved elliptical trajectory of emission at 8.4 GHz repeats after the 9-year gap. The ac-curate alignment of the emission patterns yields a precession period of 26.926 ± + ◦
303 absolute proper motion to be − . ± − east-ward and − ± − northward. Removing Galactic rotation, this reveals asmall, <
20 km s − , non-circular motion, which indicates a very low kick velocity when theblack hole was formed. Key words: radio continuum: stars – Stars: jet – X-rays: binaries – X-rays: individuals:LS I + ◦
303 — gamma rays: star — astrometry
CONTENTS + ◦ (cid:63) [email protected] † [email protected] LS I + ◦
303 is an unusual high-mass x-ray binary (HMXB). Itwas discovered as a periodic radio source by Gregory & Taylor(1978) and later periodic variations in X-ray (Paredes et al. 1997;Eikenberry et al. 2001) and γ -ray (Albert et al. 2009) were ob-served. The origin of its γ -ray, X-ray, optical / infrared and radioemission has been debated for decades (Taylor et al. 1992; Marti &Paredes 1995; Bosch-Ramon et al. 2006; Romero et al. 2007; Massiet al. 2013). The X-ray characteristics of LS I + ◦
303 fit those ofaccreting black holes at moderate luminosity (Massi et al. 2017)that would make this source along with MWC 656, the only sys-tems where a black hole accretes from the wind of a Be companionstar. Kaufman Bernadó et al. (2002) suggested LS I + ◦
303 is aprecessing microblazar, a kind of microquasars where precessionperiodically brings the approaching jet close to the line of sight andDoppler boosting its emission. Very Long Baseline Array (VLBA)astrometry in 2006 provided the first estimate of the precessionperiod. In order to study the properties of the precessing jet, weconducted a second set of multi-epoch VLBA phase-reference ob-servations in 2015. Section 2 summarizes previous radio observa-tions of LS I + ◦
303 and the precessing scenario. We describe thenew observations and data reduction in Section 3. In Section 4 we c (cid:13) a r X i v : . [ a s t r o - ph . GA ] N ov Y. W. Wu present a joint analysis of 2006 and 2015 VLBA datasets, whichindicates a very stable precession of LS I + ◦
303 and allows us todetermine an accurate precession period. In Section 5 we presentour theoretical astrometry model. In Section 6, we discuss the mea-sured 3-dimensional motion of LS I + ◦
303 . Section 7 presentsour conclusions. + ◦ A Lomb-Scargle timing analysis of 36.8-yr radio observations(Massi & Torricelli-Ciamponi 2016) confirmed previous discov-eries (e.g., Massi et al. 2015) of two characteristic periods, P = . ± .
013 d and P = . ± .
013 d, inthe emission from LS I + ◦
303 (see Fig. 1). The period P corre-sponds to orbital periodicity (Gregory 2002). Several authors (Tay-lor et al. 1992; Marti & Paredes 1995; Bosch-Ramon et al. 2006;Romero et al. 2007; Jaron et al. 2016) have shown that because ofthe high eccentricity ( e = + ◦
303 : one close to peri-astron and a second one shifted towards apastron. Near periastronthe ejected relativistic particles encounter the strong stellar radi-ation field of the B0 star and su ff er strong inverse-Compton (IC)losses and, thus, do not produce a radio outburst. However, for thesecond accretion peak near apastron, the IC losses are smaller andsynchrotron emission in the radio band is observed (Taylor et al.1992; Marti & Paredes 1995; Bosch-Ramon et al. 2006; Romeroet al. 2007; Jaron et al. 2016).The second feature in the spectrum of Fig. 1, at P = . ± .
013 d, was more challenging to understand.The simplest explanation is that the observed flux density from arelativistic jet (Mirabel & Rodríguez 1999) is the product of an in-trinsically variable jet and Doppler boosting toward the observer: S observed = S intrinsic ( f ( P )) × DB , where DB is the Doppler boost-ing factor. Massi & Torricelli-Ciamponi (2014) suggested that the DB factor could be a function of P .The observations indeed support a variation of the jet an-gle. European VLBI Network (EVN), MERLIN and VLBA imagesshow not only a jet at di ff erent position angles, but in addition thejet is sometimes double-sided (Massi et al. 2012, and referencestherein, but see Dhawan et al. (2006) for interpretations with pulsarwind model). One-sided jet structures are seen in blazars, becauseof their small angle with respect to the line of sight, counter-jetemission is de-boosted below detection sensitivity. The switch inLS I + ◦
303 between a two-sided and a one-sided structure indi-cates that precession bringing the jet to small angles with respectto the line of sight. The radio images confirm therefore a variationof the angle between jet and line of sight and indicate that rathersmall jet to line-of-sight angles are reached. Information on peri-odicity came from 2006 astrometry (Dhawan et al. 2006). Massiet al. (2012) showed as the peak of the images, associated with thejet core, described an ellipse path on the sky over 27-28 d, i.e.,close to P . In the following sections we present new observationsand we compare the astrometry data from 2006 and 2015 with thepredictions of a precessing jet model. We conducted 10-epochs of phase-referenced observations with theVLBA from 2015 July 24 to August 23, spanning one orbital cycleof the binary with roughly 3-d intervals. At each epoch observations
Power
Period (d)P P LSI+61303
Lomb-Scargle periodogram of 37 yr of radio data
Power
Period (d) P P Figure 1.
Lomb-Scargle periodogram of LSI + P and P . spanned 4 hours. The angular separation between LS I + ◦ + ◦ . The antenna switch time,i.e., one phase-referencing cycle of the calibrator J0244 + + ◦
303 is 3 min. The total on-source times for LS I + ◦ + + × ◦ (East of North) for all epochs,except for epoch D for which the MK and NL antennas were un-available and the synthesized beam was 2.4 × ◦ . We used identical frequency setups as were used forthe 2006 VLBA observations: continuum emission at 8.4 GHz, wasrecorded with four adjacent dual circular polarization intermediatefreqency (IF) bands of 16 MHz and correlated with 64 channels perIFs. The 2006 and 2015 datasets were calibrated using Astronom-ical Image Processing System (AIPS) together with scripts writ-ten in ParselTongue, a python interface to AIPS and Obit (Ketteniset al. 2006). We first corrected the data for residual delays fromEarth orientation parameters (EOP) and ionosphere (TECOR); am-plitudes were adjusted for digital sampling corrections (ACCOR),system temperatures and antenna gains; manual phase-calibrationwas applied to correct for delay o ff sets between sub-bands. Afterthese procedures, the phase-reference source, J0244 + + + + ◦
303 and J0239 + + ◦
303 , which is neither Gaussian-like nor sym-metric, were determined from the brightest pixels (of size 0.05mas × + AIPS is a NRAO software package to reduce radio interferometric datathat can be available from http: // , 1– ????
303 , which is neither Gaussian-like nor sym-metric, were determined from the brightest pixels (of size 0.05mas × + AIPS is a NRAO software package to reduce radio interferometric datathat can be available from http: // , 1– ???? (2017) evisiting LS I + ◦
303 with VLBI astrometry −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20R.A. offset (mas)−0.20−0.15−0.10−0.050.000.050.100.150.20 D E C . o ff s e t ( m a s ) A BCD E FG HIJ
Figure 2.
Astrometric accuracy of J0239 + + J0244 + ∼ ∼ . Table 1 lists the jet-core positions of LS I + ◦ In Figure 3, we show the phase reference images of LS I + ◦
303 in2006 and 2015, with observation dates labeled. Changes of jet posi-tion angles can be clearly seen in both sessions. In most epochs, thejet appears one-sided; however, in epochs of 06JUL03, 06JUL24and 15JUL24, there are two-side morphologies. This phenomenoncan be explained by precession of the jet axis, as illustrated in Fig-ure 7 of Massi & Torricelli-Ciamponi (2014), especially when theangle between the line-of-sight and the jet axis is minimized andDoppler boosting is maximized.The apparent motions of the jet core can be attribute to fourcomponents: (1) orbital motion of ≈ . ≈ . ≈ ≈ . x , y , x , y , a , b , Θ ), where The R.A. o ff sets in the Figure are ∆ R.A. × cos(DEC). ( x , y ) and ( x , y ) are centers of two ellipses, a , b and Θ are thelong / short axes and the position angle of the long axis. (The bestfitting values of these parameters, respectively, are 0.87 ± ± ± ± ± ± ± r = a × b (cid:112) a sin ( θ − Θ ) + b cos ( θ − Θ ) (1)where the reference point is the elliptical center, the reference di-rection is the east direction, a , b and Θ are the long / short axes andthe position angle of the long axis. The polar coordinates r and θ can be converted to the Cartesian coordinates x and y using trigono-metric functionsIn Figure 5, we present θ , x and y vary with time, where ∆ t = t - t ref . We assume an identical precessing phase at the referencetime, t ref . For 2006 and 2015 sessions, we set t ref = t [2006-A] and t ref = t [2015-B]- ∆ T , respectively. Here the ∆ T is the parameter thatwe need to estimate.In the left panel of Figure 5, the dash line is an empirical re-lationship between ∆ t and θ , that is a monotonic polynomial fittedusing data of 2006 sessions. θ ( ∆ t ) = a + b × ∆ t + c × ∆ t + d × ∆ t (2)Here we used an odd order polynomial (i.e., with diagonal symme-try rather than mirror symmetry for an even order). The 5th orderpolynomial was adopted, as it produced much smaller scatter than a3rd order polymomial and a 7th order polynomial did not yield sig-nificant improvement. The dash lines in the middle and right panelsthen can be determined with equation (1)-(2).The best ∆ T , can be estimated as the maximum of the proba-bility density function (PDF), which is defined as Prob ∝ N (cid:89) i = σ √ π e − ∆ i / σ (3)where, ∆ i = ( x i [ obs ] − x i [ model ]) + ( y i [ obs ] − y i [ model ]) (4)are residuals (data minus model); σ was estimated from the post-fitresiduals from σ = N (cid:88) i = ∆ i N . (5)In Figure 6, we show the PDF for ∆ T , from which we estimate ∆ T = ± ∆ T = ± ± P long MNRAS , 1– ?? (2017) Y. W. Wu
A: 06JUN30 ◦ ′ ′′ ′′ ′′ ′′ ′′ D e c . ( . ) B: 06JUL03 C: 06JUL07 D: 06JUL11 E: 06JUL15F: 06JUL18 h m s s s R.A. (2000.0) ◦ ′ ′′ ′′ ′′ ′′ ′′ D e c . ( . ) G: 06JUL21 h m s s s R.A. (2000.0)
H: 06JUL24 h m s s s R.A. (2000.0)
I: 06JUL27 h m s s s R.A. (2000.0)
J: 06JUL30 h m s s s R.A. (2000.0)
A: 15JUL24 ◦ ′ ′′ ′′ ′′ ′′ ′′ D e c . ( . ) B: 15JUL26 C: 15JUL30 D: 15AUG03 E: 15AUG06F: 15AUG10 h m s s s s R.A. (2000.0) ◦ ′ ′′ ′′ ′′ ′′ ′′ D e c . ( . ) G: 15AUG13 h m s s s s R.A. (2000.0)
H: 15AUG19 h m s s s s R.A. (2000.0)
I: 15AUG21 h m s s s s R.A. (2000.0)
J: 15AUG23 h m s s s s R.A. (2000.0)
Figure 3.
Phase reference images of LS I + ◦
303 in 2006 and 2015 observations. The observational dates are labeled in the top left corner. The hatched greyareas in the bottom left corner denote the synthesized beams. All contour levels start from 5 σ , and increase with step of 5 σ (here σ is the rms noise level ofthe image, which typically was 0 . − ). = P × P / ( P - P ) holds (e.g., Massi & Torricelli-Ciamponi 2016),then we can calculate P long , once P and P are given. In upperand lower panels of Figure 7, we present P and P long estimatedvia Monte Carlo simulations, assuming there are 122, 123 and 124cycles over the time interval of 3311.9 ± / dashed lines indicate P = ± P long = ± P and P long values. With the value of 123 cycles, we determined an accu-rate P , P = (3311 . ± . / = . ± . d . (6) The emissions of LS I + ◦
303 from γ -rays, X-rays, opti-cal / infrared, and radio wavelengths have been modeled by severalauthors (Taylor et al. 1992; Marti & Paredes 1995; Bosch-Ramon et al. 2006; Romero et al. 2007; Massi & Torricelli-Ciamponi 2014)in the context of accretion onto a compact object along an eccen-tric orbit. Observational evidence, especially from measurementsof the radio spectral index (Massi & Kaufman Bernadó 2009) anda high energy double-peak light curve (Jaron et al. 2016) favors amicroquasar rather than a pulsar wind origin (Dhawan et al. 2006).Massi & Torricelli-Ciamponi (2014) developed a model of a pre-cessing conical jet which emits synchrotron radiation to explainthe radio light curve. In this section, we integrate their radiationtransfer model in order to simulate observations on the sky plane.For an optically thin jet, the maximum of the emission is at the jetbase, while for an optically thick jet the maximum will be displaceddown the jet where optical depth unity is achieved. The displace-ment of the observed radio peaks on the sky plane is due to theemitting plasma changing position owing to the orbital motion ofthe compact object around the primary star and to the jet preces-sion. In this section, we first examine the two e ff ects separately andthen we derive the full jet motion as it appears on the sky. MNRAS , 1– ????
303 from γ -rays, X-rays, opti-cal / infrared, and radio wavelengths have been modeled by severalauthors (Taylor et al. 1992; Marti & Paredes 1995; Bosch-Ramon et al. 2006; Romero et al. 2007; Massi & Torricelli-Ciamponi 2014)in the context of accretion onto a compact object along an eccen-tric orbit. Observational evidence, especially from measurementsof the radio spectral index (Massi & Kaufman Bernadó 2009) anda high energy double-peak light curve (Jaron et al. 2016) favors amicroquasar rather than a pulsar wind origin (Dhawan et al. 2006).Massi & Torricelli-Ciamponi (2014) developed a model of a pre-cessing conical jet which emits synchrotron radiation to explainthe radio light curve. In this section, we integrate their radiationtransfer model in order to simulate observations on the sky plane.For an optically thin jet, the maximum of the emission is at the jetbase, while for an optically thick jet the maximum will be displaceddown the jet where optical depth unity is achieved. The displace-ment of the observed radio peaks on the sky plane is due to theemitting plasma changing position owing to the orbital motion ofthe compact object around the primary star and to the jet preces-sion. In this section, we first examine the two e ff ects separately andthen we derive the full jet motion as it appears on the sky. MNRAS , 1– ???? (2017) evisiting LS I + ◦
303 with VLBI astrometry −2.0−1.5−1.0−0.50.00.51.01.52.0 R.A. offset (mas)−2.0−1.5−1.0−0.50.00.51.01.52.0 D E C . o ff s e t ( m a s ) A B C D EF GHI J AB C D E FGHIJ−4−3−2−10123 R.A. offset (mas)−4−3−2−1012 D E C . o ff s e t ( m a s ) A B C D EF GHI J ABC D E FGHIJ2006 JUL 2015 AUG
Figure 4.
Le f t panel : Astrometric results of 2006 and 2015 VLBA observations, with parallax motions removed. Blue characters denote jet peaks in 2006,and red characters denote jet peaks in 2015. The reference coordinate (zero point) is 02h40m31s.6645, 61d13m45s.594.
Right panel : Same as left panel, butwith centers of the two ellipses overlaid. The solid ellipse in the top left corner indicates the scale of the orbit, with a semimajor axis of 0.22 mas (Massi et al.2012). −5 0 5 10 15 20 25 ∆t (day) −1000100200300400500 Θ ( ◦ ) A B C D E F G HI JA B C D E F GH I J −5 0 5 10 15 20 25 ∆t (day) −2.0−1.5−1.0−0.50.00.51.01.52.0 x ( m a s ) A B C D E F G HI JA B C D E F GH I J −5 0 5 10 15 20 25 ∆t (day) −2.0−1.5−1.0−0.50.00.51.01.52.0 y ( m a s ) A B C D E F G HI JA B C D E F GH I J
Figure 5.
Left, middle and right panels are the position angle θ , x = ∆ R.A. and y = ∆ Dec. of jet core versus time, respectively. Blue / red characters and dotswith error bars denote 2006 / In Massi & Torricelli-Ciamponi (2014) model, the base of the jetis anchored to the compact object and, hence, follows the compactobject along its orbit; this path is drawn as a green ellipse in Fig. 8.The orbit plane forms an angle ζ with respect to the plane perpen-dicular to the line-of-sight.The system of reference in the orbital plane is at the center ofmass of the system i.e. the point O . The y (cid:48) axis is defined by theintersection of the orbital plane and the plane perpendicular to theline-of-sight, with the x (cid:48) axis perpendicular to the y (cid:48) axis at O . Inthis way a rotation of the system [ x (cid:48) , y (cid:48) ] around [ y (cid:48) ] by an angle ζ defines the system of reference [ x (cid:48)(cid:48) , y (cid:48) ] in the plane perpendicular to the line-of-sight. In order to parameterize the orientation of theellipse in the orbital plane we introduce the angle ω , which definesthe ellipse rotation with respect to the Cartesian system [ x (cid:48) , y (cid:48) ] pre-viously defined. See Fig. 8 for angle definitions.The compact object moves at a distance ρ from the origin ofcoordinates. In the plane of motion, the vector radius can be ex-pressed in terms of the ellipse semi-major axis, a , ellipse eccentric-ity, e , and the angle θ (which is zero when the vector radius pointstoward apastron) as ρ ( θ ) = a (1 − e )1 − e cos θ (7) MNRAS , 1– ?? (2017) Y. W. Wu −3 −2 −1 0 1 2 3 4 5∆T (day)0.00.10.20.30.40.50.60.7 P r o b a b ili t y D e n s i t y ( d a y − ) ∆T = 0.98± 0.63 days Figure 6.
Probability density function for ∆ T . The PDF was calculated atsteps of 0.1 d, shown with black dots connected by the dashed line. The components of the vector radius in the [ x (cid:48) , y (cid:48) ] orbital plane, foran ellipse rotation of an angle ω , are ρ x (cid:48) = a (1 − e ) cos( θ + ω )1 − e cos( θ ) (8) ρ y (cid:48) = a (1 − e ) sin( θ + ω )1 − e cos( θ ) (9)In the plane perpendicular to the line-of-sight, owing to a ro-tation of an angle ζ around [ y (cid:48) ], these components become x (cid:48)(cid:48) = ρ x (cid:48) cos ζ y (cid:48) = ρ y (cid:48) . (10)and, in the system of reference [ x , y ], x orbit = x (cid:48)(cid:48) cos w − y (cid:48) sin w (11) y orbit = y (cid:48) cos w + x (cid:48)(cid:48) sin w (12)where w = ˆ MAW = ˆ MOW in Fig. 8 is a free angle, to bedetermined by the fit (see Sec. 5.3).
We assume the jet geometry and properties as described inMassi & Torricelli-Ciamponi (2014). In Fig. 9 the base of thejet is at point C . The jet base will be projected at a distance BF = BC sin η = x sin η , where η is the angle the jet makeswith the line-of-sight and x (i.e., BC in Fig.9) is the position of thejet base. Hence, for a thin jet,the components of the emitting regionwith respect to the plane perpendicular to the line of sight are x j = x sin η cos( δ + w ) y j = x sin η sin( δ + w ) , (13) where the angle δ can be derived from the spherical triangle ACG (see Fig.9) assin δ sin η = sin Ω sin ψ (14)cos δ sin η = cos ψ − cos η cos ζ sin ζ , (15)and the angle Ω , which changes because of precession, is definedas Ω = π t / P . (16) Since the jet is anchored to the accretion disk of the compact object,the generic coordinate of the jet emitting plasma with respect to theassumed center of coordinates of Fig.8 will be X = l x j + x orbit Y = l y j + y orbit (17)where l specifies the position along the jet of the peak radio flux;For an optically thin jet l =
1, while for an optically thick jet l is theposition of optical depth unity. The value of l needs to be computedat each orbital phase in order to derive the correct coordinates ( x , y )of the radio emission.The resulting positions for the model astrometry are shown inFig. 10. We use a physical model, i.e., the number of relativisticelectrons injected every period P in a conical jet at a particular or-bital phase, as found by Massi & Torricelli-Ciamponi (2014), whofitted 6.7 yr of Green Bank Interferometer radio data. With astro-metric position, we can now better constrain the geometrical pa-rameters of the model; i.e., ψ , the jet angle to its precession axisand ξ , the jet opening angle. The angle ζ is set to 25 degrees, whichis the measured angle of the rotation axis of the Be star (Nagaeet al. 2006), assuming the star spin axis is parallel to the orbitalaxis. The parameter w , that translates and rotates the trajectory inspace without changing its shape is w =
230 degrees. The modelfor the astrometric data shown in Fig. 10 result in a jet angle to itsprecession axis of ψ =
21 degrees and a jet opening angle ξ = + ◦
303 are similarto those of the well-studied precessing jet system SS 433; SS 433has a half precessing cone angle of 20 deg and a jet opening angleof 5 deg (Margon et al. 1979; Paragi et al. 1999).Since our physical model assumes a steady jet, any transientemission, e.g., observation E in 2006 (Massi et al. 2012), cannotbe used in the fits. For all other observations in 2006 the data andmodel overlap to within ± σ . The same occurs for 2015, exceptfor observation A. The model is able to reproduce the main fea-ture of the observed ellipse, i.e. the non-uniform motion of the corewith time, as seen in the middle panels of Fig. 10. For the 2006observations, which were taken regularly every 3–4 d, the jet base(large squares) follows a regular path. The positions of the core (at τ =
1) for A, H, I and G are displaced by the jet base and justoverlap with the edge of their related squares. The same occurs inthe 2016 session, where the predicted core positions for A, B, H,and I are o ff set from the observed peaks. As shown in the bottompanels of Fig. 10, for these observations the angle between jet andthe line of sight is small, below 21 degrees. Possibly the longer pathof the radiation within the jet causes the higher optical depth (seeFig. A1 in Massi & Torricelli-Ciamponi 2014) MNRAS , 1– ????
1) for A, H, I and G are displaced by the jet base and justoverlap with the edge of their related squares. The same occurs inthe 2016 session, where the predicted core positions for A, B, H,and I are o ff set from the observed peaks. As shown in the bottompanels of Fig. 10, for these observations the angle between jet andthe line of sight is small, below 21 degrees. Possibly the longer pathof the radiation within the jet causes the higher optical depth (seeFig. A1 in Massi & Torricelli-Ciamponi 2014) MNRAS , 1– ???? (2017) evisiting LS I + ◦
303 with VLBI astrometry (day)0100200300400500600700800 N u m b e r o f t r a il s P = 27.147 ± 0.005 dayscycle number = 1221000 1233 1467 1700P long (day)0100200300400500600700800 N u m b e r o f t r a il s P long = 1105 ± 78 dayscycle number = 122 26.9 26.9 26.9 27.0P (day)0200400600800 N u m b e r o f t r a il s P = 26.926 ± 0.005 dayscycle number = 1231400 1567 1733 1900P long (day)0200400600800 N u m b e r o f t r a il s P long = 1659 ± 184 dayscycle number = 123 26.7 26.8 26.9 27.0 27.1P (day)0200400600800 N u m b e r o f t r a il s P = 26.709 ± 0.005 dayscycle number = 1241500 2500 3500 4500P long (day)0200400600800 N u m b e r o f t r a il s P long = 3335 ± 768 dayscycle number = 124 Figure 7.
Top panels : Histograms of P estimated via Monte Carlo simulation, by adopting ∆ T = ± = σ error of P . Bottom panels : Histograms of P long estimated withrelationship of P long = P × P / ( P - P ), by adopting P = ± P values from top panel estimations.Red solid and dashed vertical lines in top and bottom panels denote values and 1 σ errors of P and P long estimated by Massi & Torricelli-Ciamponi (2016)and Gregory (2002) with Lomb-Sargle method, respectively. Figure 8.
Geometry of the orbit. The real orbital plane is in green; the greyplane is perpendicular to the observer. The center of mass of the system islocated at O ; ˆ WOL = ζ is the angle between the orbital plane and the planeperpendicular to the line of sight; ω = o − ˆ POH and ˆ
MOW = w . Our observations also provide an accurate proper motion forLS I + ◦
303 as is evident in Figure 4. We find eastwardand northward motions of µ α = − ± − , µ δ = − ± − , base on a time span of 3311 d be- Figure 9.
Geometry of the precessing radio jet. BC is the distance of thejet base ( x ) from the compact object (located in B ); BF is the projectionof BC on the plane perpendicular to the line of sight; CA = η ; CG = ψ ; AG = ζ ; ˆ CGA = Ω ; ˆ
FBD = ˆ CAG = δ ; ˆ DAW = ˆ DBW = w free angle to bedetermined. tween the 2006 and 2015 observations. For comparison, the propermotions of LS I + ◦
303 measured by
Hipparcos (Hoogerwerf& Blaauw 2000) and
GAIA (Data Release 1, Arenou et al. 2017)are [0.62 ± ± − and [-0.354 ± ± − , respectively. Boboltz et al. (2003) mea- MNRAS , 1– ?? (2017) Y. W. Wu -2.5-2-1.5-1-0.5 0 0.5 1 1.5 2 -7-6-5-4-3-2-1 0 1 2 m a s mas "A""B""C""D""F""G""H""I""J" -2.5-2-1.5-1-0.5 0 0.5 1 1.5 2 -7-6-5-4-3-2-1 0 1 2 m a s mas "A""B""C""D""E""F""G""H""I" -2.5-2-1.5-1-0.5 0 0.5 1 1.5 2 -7-6-5-4-3-2-1 0 1 2 m a s mas "A""B""C""D""E""F""G""H""I""J" -2.5-2-1.5-1-0.5 0 0.5 1 1.5 2 -7-6-5-4-3-2-1 0 1 2 m a s mas "A""B""C""D""E""F""G""H""I""J" A ng l e be t w een j e t and l . o . s ( deg r ee ) VLBA run number (1=A)
A B C D E F G H I J A ng l e be t w een j e t and l . o . s ( deg ) VLBA run number (1=A)
A B C D E F G H I J
Figure 10.
Top-panels: Model-data comparisons. The blue and red points are from VLBA astrometry in 2006 and 2015, respectively. The same symbols inblack are used for the model data. Middle panels: Comparison of positions of the jet base (squares) and jet peak. Bottom panel: angle between the jet and theline of sight (see Section 5.3). MNRAS , 1– ????
Top-panels: Model-data comparisons. The blue and red points are from VLBA astrometry in 2006 and 2015, respectively. The same symbols inblack are used for the model data. Middle panels: Comparison of positions of the jet base (squares) and jet peak. Bottom panel: angle between the jet and theline of sight (see Section 5.3). MNRAS , 1– ???? (2017) evisiting LS I + ◦
303 with VLBI astrometry sured the proper motions of [0.97 ± ± − with Very Large Array (VLA) data. Except for the Boboltz et alvalues, previous estimates are consistent with our results. But, ofcourse, our measurements have orders of magntitude better accu-racy.Assuming a distance of 2.0 ± V LSR = ± − (Aragona et al. 2009), we can estimate the full spacevelocity of the system. Adopting the distance to the Galac-tic center of 8.34 ± ± − , and solar motion components of U (cid:12) = ± V (cid:12) = ± − and W (cid:12) = ± − from Reid et al.(2014b), we find peculiar (non-circular) of motion components forLS I + ◦
303 of U = ± − , V = − ± − , W = ± − . This translates to a speed of only 16 km s − .Recent analysis of swi f t X-ray data suggest that LS I + ◦ ff erent channels, i.e, with or with-out natal kicks and with or without supernovae (SN) explosion. Forexample, GRO J1655-40, is a runaway black hole system with apeculiar speed of 112 ±
18 km s − (Mirabel et al. 2002). It may beformed after an SN explosion created a neutron star, followed byfall-back of ejected envelope and a secondary collapse (Israelianet al. 1999; Mirabel et al. 2002; Mirabel & Rodrigues 2003). Al-ternatively, the black hole may be formed directly with a largenatal kick (Repetto et al. 2012). In contrast, the peculiar motionsof the well studied black hole X-ray binaries, Cygnus X-1 andGRS 1915 + ≈
20 km s − (Reidet al. 2011, 2014a). Cygnus X-1 is believed to have been formedthrough direct collapse of a massive star (Fryer & Kalogera 2001;Mirabel & Rodrigues 2003). The similarly low peculiar motion(16 km s − ) of LS I + ◦
303 measured here suggest that it mayalso contain a black hole formed through direct collapse of a mas-sive star.
Using multi-epoch VLBA observations of LS I + ◦
303 in 2015,we were able to map the elliptical trajectory its radio emission. Theagreement between these maps and those from previous observa-tions in 2006 suggests that the radio jet is stable over the nine yearinterval. We then aligned the precessing phase and estimated theprecession period to P = . ± . d , with a physical modelthat takes into account orbital motion, jet precessing and radiativetransfer. In addition, the long time span between observations al-low us to determine an accurate proper motion and, then, the fullspace motion of LS I + ◦
303 . We find a small peculiar motion of16 km s − for the system, which favors a black hole formation bydirect collapse instead of a supernova explosion. ACKNOWLEDGEMENTS
This work has made use of data from the European SpaceAgency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and Analy-sis Consortium (DPAC, ). Funding for the DPAC has been pro-vided by national institutions, in particular the institutions partici-pating in the
Gaia
Multilateral Agreement. We would like to thankProf. X.D. Li from the Nanjing University for useful discussions. We would like to thank the referee, Dr Benito Marcote, who car-fully read the original draft and share valuable comments and sug-gestions that greatly imporve the quality of this paper.
Facilities:
VLBA
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Table 1.
Jet core positions and estimated orbital, precessing and beating phases for 2006 and 2015 sessionsEpoch date ∆ R.A. × cos(Dec) ∆ DEC. JD Φ ( P ) Φ ( P ) Φ ( P long )year-mn-dy-hr-mm (mas) (mas) (day)A 2006-06-30-15-26 2.40 -0.60 2453917.143056 0.187 0.822 0.352B 2006-07-03-15-13 1.60 -0.60 2453920.134028 0.300 0.934 0.354C 2006-07-07-14-58 1.40 -0.40 2453924.123611 0.451 0.082 0.356D 2006-07-11-13-42 1.00 -0.20 2453928.070833 0.600 0.228 0.358E 2006-07-15-14-27 -0.20 -0.60 2453932.102083 0.752 0.378 0.361F 2006-07-18-14-15 0.60 0.40 2453935.093750 0.865 0.489 0.363G 2006-07-21-14-03 0.20 1.00 2453938.085417 0.978 0.600 0.364H 2006-07-24-13-51 1.40 1.00 2453941.077083 0.091 0.711 0.366I 2006-07-27-13-39 2.40 -0.40 2453944.068750 0.203 0.822 0.368J 2006-07-30-13-28 1.80 -0.60 2453947.061111 0.316 0.934 0.370A 2015-07-24-13-34 -7.45 -3.10 2457228.065278 0.147 0.784 0.345B 2015-07-26-13-27 -5.55 -4.80 2457230.060417 0.222 0.858 0.346C 2015-07-30-13-11 -5.70 -5.05 2457234.049306 0.372 0.007 0.349D 2015-08-03-09-25 -6.70 -4.50 2457237.892361 0.517 0.149 0.351E 2015-08-06-12-43 -6.95 -4.35 2457241.029861 0.636 0.266 0.353F 2015-08-10-12-28 -7.15 -3.90 2457245.019444 0.786 0.414 0.355G 2015-08-13-12-15 -7.15 -3.85 2457248.010417 0.899 0.525 0.357H 2015-08-19-11-52 -5.70 -4.90 2457253.994444 0.125 0.747 0.361I 2015-08-21-11-44 -5.30 -4.85 2457255.988889 0.200 0.821 0.362J 2015-08-23-11-36 -4.85 -5.50 2457257.983333 0.276 0.895 0.363 Note : Orbital, precessing and long beating phases (turns) are estimated with formula φ = [( t − t ) mod P ] / P , by using P = P = P long = is JD 2 443 366.775 (Gregory 2002). MNRAS , 1– ????