BG Tri an example of a low inclination RW Sex-type novalike
M. S. Hernandez, G. Tovmassian, S. Zharikov, B. T. Gaensicke, D. Steeghs, A. Aungwerojwit, P. Rodriguez-Gil
aa r X i v : . [ a s t r o - ph . S R ] J a n MNRAS , 1– ?? (2018) Preprint 2 February 2021 Compiled using MNRAS L A TEX style file v3.0
BG Tri an example of a low inclination RW Sex-type novalike
M. S. Hernández ★ , G. Tovmassian , S. Zharikov , , B. T. Gänsicke , , D. Steeghs , ,A. Aungwerojwit , P. Rodríguez-Gil , . Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111 Valparaíso, Chile Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada, Baja California, C.P. 22830, Mexico Al-Farabi Kazakh National University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan University of Warwick, Department of Physics, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom. Centre for Exoplanets and Habitability, University of Warwick, Coventry CV4 7AL, UK. Department of Physics, Astronomy and Astrophysics group, University of Warwick, CV4 7AL, Coventry, UK. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA. Department of Physics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand. Instituto de Astrofísica de Canarias, Vía Láctea s/n, E-38205, La Laguna, Tenerife, Spain. Departamento de Astrofísica, Universidad de La Laguna, E-38206, La Laguna, Tenerife, Spain.
Accepted 2021 January 28. Received 2021 January 27; in original form 2020 October 16
ABSTRACT
We analyse a wealth of optical spectroscopic and photometric observations of the bright ( 𝑉 = .
9) cataclysmic variable BG Tri.The
Gaia
DR2 parallax gives a distance 𝑑 = ( ) pc to the source, making the object one of the intrinsically brightest nova-likevariables seen under a low orbital inclination angle. Time-resolved spectroscopic observations revealed the orbital period of 𝑃 orb = . h ( ) . Its spectroscopic characteristics resemble RW Sex and similar nova-like variables. We disentangled the H 𝛼 emission line into two components, and show that one component forms on the irradiated face of the secondary star. We suggestthat the other one originates at a disc outflow area adjacent to the L point. Key words: cataclysmic variables, dwarf novae, white dwarf, stars: individual: BG Tri
Cataclysmic variables (CVs) are close binary systems comprised ofa white dwarf (WD) and a low-mass star losing matter in a Roche-lobe overflow regime, usually creating an accretion disc around theaccreting WD (Warner 1995). CVs show diverse observational char-acteristics depending on fundamental physical properties, includingtheir orbital period, mass transfer rate; and strength of the magneticfield of the WD. Their diversity is also in part due to the viewingangle (Howell & Mason 2018). In non- or weakly-magnetic systems,the accretion flow takes place in a fully-developed accretion disc. Athigh mass transfer rates ( ≥ − M ⊙ yr − ), these are hot, steady-state discs (Baptista et al. 1996). Therefore, the disc thermal insta-bility that triggers dwarf nova outbursts is prevented (Shafter et al.1986; Shafter 1992; Lasota 2001). These high mass transfer ratesystems are known as nova-like variables (NLs), because it was ini-tially argued that they might potentially exhibit or have undergoneundetected nova eruptions (Vorontsov-Velyaminov 1934). No knownNL has ever been seen to erupt as a nova. However, some NLs mayresemble nova when the nova returns to a quiescent state after theeruption (Warner 1995). They constitute a small fraction of the entireCV population ( ∼
15 percent in Ritter & Kolb 2003a,b), which mightbe result of an observational bias. The vast majority of NLs have ★ e–mail: [email protected] orbital periods above the so-called "period gap" (Rappaport et al.1983; Kolb et al. 1998; Zorotovic et al. 2016; Abril et al. 2020). Weexclude CVs with moderately or highly magnetic WDs, which his-torically were also accounted for as NLs.There is a visible differentiation between NLs and dwarf novaein terms of their orbital periods and colours (Abril et al. 2020). It isnoticeable that NLs dominate the orbital period range 3-4h, wherevery few dwarf novae are observed (Knigge et al. 2011). However, inabsolute numbers, the amount and the distribution of NLs and dwarfnovae right above the period gap are comparable (Knigge et al. 2011).There is no good understanding why the two populations of NL anddwarf novae overlap in some period ranges, but not in others. NLshave accretion rates that are higher than "normal" CVs both at longerand shorter periods. They are intrinsically very bright, and their WDstend to be hotter (Townsley & Gänsicke 2009).The spectra of some NL variables display persistent broad Balmerabsorption lines, indicative of optically thick discs. However, NLsthemselves come in different flavours. A fraction of NLs, knownas VY Scl stars, show occasional states of low mass transfer rates,i.e. they become significantly fainter for prolonged periods of time(months to years, Warner & van Citters 1974; Rodríguez-Gil et al.2020). However, the physical cause of these low mass transfer statesis still uncertain (Livio & Pringle 1994; King & Cannizzo 1998;Schmidtobreick et al. 2018).SW Sex stars form a class of NL variables with distinctive spectro- © Hernández, Tovmassian, Zharikov et al.
Table 1.
Log of spectroscopic observationsDate JD ∗ Range No. of Exp. time Comments(Å) Spectra (s)2002 Aug. 21 2507 3341-7546 2 200 INT2002 Aug. 23 2510 3341-7546 24 340 INT2002 Aug. 25 2512 3341-7546 15 120 INT2002 Aug. 31 2518 3341-7546 8 120 INT2002 Sep. 02 2520 3341-7546 4 120 INT2002 Sep. 03 2521 3341-7546 6 120 INT2003 Oct 19 2932 3784-9063 2 60 ISIS B&R2003 Dec. 13 2987 4257-8318 4 120 CA2003 Dec. 14 2988 4257-8318 9 60 CA2003 Dec. 15 2989 4257-8318 2 60 CA2003 Dec. 16 2990 4257-8318 10 60 CA2003 Dec. 17 2991 4257-8318 10 60, 120 CA2003 Dec. 17 2991 3775-6840 7 120 NOT2003 Dec. 23 2997 4257-8318 6 60 CA2003 Dec. 24 2998 4257-8318 6 60 CA2003 Dec. 25 2999 4257-8318 2 60 CA2003 Dec. 26 3000 4257-8318 4 60 CA2003 Dec. 27 3001 4257-8318 2 60 CA2004 Aug. 09 3226 4257-8318 2 180 CA2004 Aug. 10 3227 4257-8318 2 180 CA2004 Aug. 11 3228 4257-8318 2 180 CA2004 Aug. 12 3229 4257-8318 2 180 CA2004 Oct. 21 3300 4257-8318 2 120 CA2004 Oct. 23 3302 4257-8318 2 120 CA2004 Oct. 24 3303 4257-8318 2 120 CA2004 Oct. 26 3305 4257-8318 2 120 CA2004 Sep. 10 3623 4257-8318 2 120 CA2004 Nov. 04 3314 3775-6840 2 120 NOT2005 Jan. 01 3372 3784-9063 2 200 ISIS B&R2005 Jan. 04 3375 3784-9063 2 200 ISIS B&R2005 Jan. 05 3376 3784-9063 2 200 ISIS B&R2005 Jan. 06 3377 3784-9063 2 200 ISIS B&R2005 Jan. 07 3378 3784-9063 2 200 ISIS B&R2005 Sep. 10 3623 4257-8318 2 120 CA2017 Oct. 27 8053 3600–7300 3 1200 Echelle2017 Oct. 28 8054 3600–7300 3 1200 Echelle2017 Oct. 29 8055 3600–7300 3 1200 Echelle2018 Jan. 11 8129 3600–7300 13 1200 Echelle2018 Jan. 12 8130 3600–7300 12 1200 Echelle2018 Jan. 13 8131 3600–7300 3 1200 Echelle2018 Jan. 14 8132 3600–7300 10 1200 Echelle ∗ scopic behaviour (Thorstensen et al. 1991). They mostly cluster in the3-4 h orbital period range (Rodríguez-Gil et al. 2007b). Baptista et al.(1996), Dhillon et al. (2013), and Tovmassian et al. (2014) proposedan extended hot spot as the predominant source of emission linesfrom the optically and physically thick disc. However, such interpre-tation is challenged by Rodríguez-Gil et al. (2007, 2015). A search fornon-eclipsing SW Sex in the 3-4 h period range revealed systems withtwo-component emission lines (Rodríguez-Gil et al. 2007a), but theywere inconclusive whether these are low-inclination SW Sex objects.Conversely, two-component emission lines recently have been ob-served, in a couple of the UX UMa-type NLs (which are the primaryconcern of this paper). For example, Hernandez et al. (2017), basedon high-resolution spectroscopy, demonstrated that NLs RW Sex andRXS J064434.5+334451 show at least two components in the pro-files of the Balmer emission lines. The narrow component with a lowradial-velocity amplitude originates from the irradiated surface of the secondary facing the disc. The wide component is formed in anextended, low-velocity region in the outskirts of the opposite side ofthe accretion disc, with respect to the collision point of the accretionstream and the disc. Recently, Subebekova et al. (2020) claim, thatthis property is observed in RW Tri. They compiled a current list ofsimilar NLs with orbital periods ≥ 𝛼 emission closely resemble those seen in RW Sex.Other interpretations of line provenance (including absorption fea-tures frequently flanking emission lines) in such NL systems havebeen put forward. Notably, the disc overflow model by Hellier (1996)and disc wind interpretations and models (e.g. Patterson et al. 1996;Murray & Chiang 1996) are worth mentioning.BG Tri is a bright object reported by Woźniak et al. (2004);Khruslov (2008) to show an irregular, low-amplitude variabilityand tentatively identified as a CV, citing ROTSE1, TYC2 and ROSAT detections. Accordingly, the object is also catalogued asTYC 2298 01538 and 1RXS J014448.4+323320. Makarov (2017)confirms its NL identification based on a distance estimate by
Gaia (Gaia Collaboration et al. 2018) in combination with Galaxy Evolu-tion Explorer (GALEX) UV magnitudes (Martin et al. 2003). How-ever, BG Tri has not been studied in detail until now. We report theresults of the spectroscopic study of the object on the backdrop of thelong term photometry collected by the Catalina Real-time TransientSurvey and the All Sky Automated Surveys (ASAS). We present an extensive set of multi-wavelength observations ofBG Tri obtained by us as well as a variety of data collected in surveys.
The data from the Catalina Real-Time Transient Survey (CRTS)(Drake et al. 2009) and the All-Sky Automated Survey for Super-novae (ASAS SN) (Shappee et al. 2014; Kochanek et al. 2017) wereused to produce the light curve (Figure 1) of the object. The data wereobtained in 𝑉 - and 𝑔 -bands. The difference between filters 𝑔 and 𝑉 is not significant and the average colour index was 𝑔 − 𝑉 ≈ . ≈
12 mag, one of the brightestCVs in apparent magnitude) and nearly constant with non-regular,small amplitude variability. The average magnitude in a time stretchHJD 2456524.01 to HJD 2457668.08 is 𝑉 = .
91, with a devia-tion of ≈ ∼ . 𝑉 ≈ . ≈ − . Following a stand-still at thatmagnitude that last one month, the brightness briefly falls further(on HJD 2458373), reaching 𝑉 = . − . Thislow state episode, detailed in the upper panel of Figure 1, is fairlycommon among NLs, classifying BG Tri as a VY Scl star. There isalso an episode of a sudden jump of brightness detected betweenHJD 2457669.88 and HJD 2457797.72 before the anti-dwarf novaepisode when the average brightness of the object reaches 𝑉 ≈ . 𝑑 = . ± .
65 pc according to the revised estimate Bailer-Jones et al.(2018)MNRAS , 1– ?? (2018) G Tri: a low inclination RW Sex-type nova-like Figure 1.
Long-term light curve of BG Tri obtained by the sky patrol ASASSN and CRTS surveys. The dark green and orange points are ASAS data in 𝑉 and 𝑔 filters respectively, the light green points are CRTS 𝑉 -band data.In the lower panel, the entire data set is presented, while the upper showsexpanded segment of the same during and around the low state. The magentamarkers indicate moments of spectroscopic observations at the bottom of thelight curve. A large number of low-resolution spectra were obtained with a varietyof instruments listed in Table 1. At the 2.5-m Isaac Newton Telescope(INT), we used the Intermediate Dispersion Spectrograph (IDS) withthe R632V grating, the 2048 × . ′′ ∼ ∼ × ∼ . 𝜆 . ′′ 𝜆 ∼ . × iraf , while wavelength calibration and most of the subse-quent analyses made use of Tom Marsh’s molly package.No flux calibration is available for the low-resolution spectra,hence we present in Figure 2 normalized spectrum obtained by com-bining data at different epochs with different telescopes/instruments.The low-resolution spectra failed to reveal significant radial velocity(RV) variation.The overall spectral behaviour of BG Tri does not change sig-nificantly from epoch to epoch. The spectra indicate a steep bluecontinuum with Balmer lines showing emission features embeddedin broader absorption lines. The higher members of the Balmer se-ries appear to have more intense absorption, while towards the lowestnumbers the emission component dominates. Helium lines are alsopresent in the spectrum. The neutral helium lines have complex pro-files, especially at He i 𝜆 ii and Ca ii lines.The spectra are typical of NL variables with an optically thick discand low inclination. The high-resolution observations were obtained with the echelle RE-OSC spectrograph (Levine & Chakarabarty 1995), attached to the2.1m Telescope of the Observatorio Astronómico Nacional at SanPedro Mártir, during several nights of 2017 and 2018. The CCD2048 × ∼
18 000. All observations were carried out with the 300 l mm − cross–dispersor, which has a blaze angle at around 5500 Å. Thespectral coverage was about 3600–7300 Å. The exposure time foreach spectrum was 1200 s. Th-Ar lamp was used for wavelengthcalibration. The spectra were reduced using the echelle package in iraf . Standard procedures, including bias subtraction, cosmic-rayremoval, and wavelength calibration, were carried out. No flat-fieldcorrection and flux calibration was attempted; instead, the normalisedspectra were used for measurements and visualisation. The log of allspectroscopic observations is shown in Table 1. Khruslov (2008) in a discovery note, points out that BG Tri is a vari-able star, probably a CV. Presented here, the long term light curve andspectra leave no doubt that the first assessment was correct. However,CVs comprised of a WD and a late red or brown dwarf secondarystar come in different flavours depending on their orbital periods (orseparation), mass accretion rate, and strength of the magnetic fieldof the WD. Absence of nova or dwarf nova outbursts in a period oftime over 5000 days indicates that this is an NL variable. Moreover,an anti-dwarf nova occurrence registered in the light curve is anothercharacteristic of bright NLs, which occasionally undergo a fall inbrightness by more than one magnitude (Warner 1995).Low-resolution spectra confirm the CV identification of BG Tri,which exhibits a standard set of hydrogen and helium lines, with IRAF is distributed by the National Optical Astronomy Observatories,which are operated by the Association of Universities for Research in Astron-omy, Inc., under cooperative agreement with the National Science Foundation. molly is available at Tom Marsh’ web page:http://deneb.astro.warwick.ac.uk/phsaap/software/MNRAS , 1– ????
18 000. All observations were carried out with the 300 l mm − cross–dispersor, which has a blaze angle at around 5500 Å. Thespectral coverage was about 3600–7300 Å. The exposure time foreach spectrum was 1200 s. Th-Ar lamp was used for wavelengthcalibration. The spectra were reduced using the echelle package in iraf . Standard procedures, including bias subtraction, cosmic-rayremoval, and wavelength calibration, were carried out. No flat-fieldcorrection and flux calibration was attempted; instead, the normalisedspectra were used for measurements and visualisation. The log of allspectroscopic observations is shown in Table 1. Khruslov (2008) in a discovery note, points out that BG Tri is a vari-able star, probably a CV. Presented here, the long term light curve andspectra leave no doubt that the first assessment was correct. However,CVs comprised of a WD and a late red or brown dwarf secondarystar come in different flavours depending on their orbital periods (orseparation), mass accretion rate, and strength of the magnetic fieldof the WD. Absence of nova or dwarf nova outbursts in a period oftime over 5000 days indicates that this is an NL variable. Moreover,an anti-dwarf nova occurrence registered in the light curve is anothercharacteristic of bright NLs, which occasionally undergo a fall inbrightness by more than one magnitude (Warner 1995).Low-resolution spectra confirm the CV identification of BG Tri,which exhibits a standard set of hydrogen and helium lines, with IRAF is distributed by the National Optical Astronomy Observatories,which are operated by the Association of Universities for Research in Astron-omy, Inc., under cooperative agreement with the National Science Foundation. molly is available at Tom Marsh’ web page:http://deneb.astro.warwick.ac.uk/phsaap/software/MNRAS , 1– ???? (2018) Hernández, Tovmassian, Zharikov et al.
Figure 2.
The combined and averaged low-resolution spectrum of BG Tri obtained at different epochs with different instruments. Major lines identified in thespectrum are marked on top, while atmospheric oxygen lines are marked at the bottom. Mg i triplet is also marked, although we are not sure if it is real. Figure 3.
The profiles of important lines in the spectrum of BG Tri from the echelle spectra. The lines are marked in upper corners of each panels. The blackline is the median of all high-resolution spectra, whether the low resolution spectrum from Figure 2 are presented in the background. higher numbers of the Balmer series showing wide adsorptions withembedded, relatively narrow emissions. In Figure 2, an averaged andcombined spectrum obtained at different epochs is plotted. All sig-nificant spectral features are marked. A combination of emission andabsorption features of Balmer lines usually occurs either in dwarfnovae near period minimum where the WD becomes dominant, or,in NLs with optically thick discs. Using the
Gaia distance d= 334(8) pc to BG Tri, we calculate theabsolute magnitude of the object M 𝑉 = .
26. Such high luminosityenlists BG Tri among the brightest CVs, making it only the secondafter the infamous RW Sex (Hewitt et al. 2020). The derived absolutemagnitude is consistent with the low inclination angle (Warner 1986,1987). We will detail spectral energy distribution (SED) and lumi-nosity of the accretion disc further in the paper. Nevertheless, based
MNRAS , 1– ?? (2018) G Tri: a low inclination RW Sex-type nova-like Figure 4.
The power spectra of BG Tri calculated for the radial velocitycurves of different lines and components. In the upper panel the red and bluelines are the power of the HVC and the LVC after the decomposition of H 𝛼 line. In the inset a zoom on the small range of frequencies around the derivedperiod are presented. The bottom panel shows the power of H 𝛽 measuredwith a single Gaussian. only on the derived absolute magnitude, we can state that this objectis not a low accretion rate WZ Sge type, near the period minimum.In NLs, the bulk of the accretion disc is optically thick (hot anddense), producing absorption lines. The emission lines are formed ei-ther in the separate parts of the disc or by the gas in its vicinity (Warner1976; Beuermann et al. 1992). Figure 3 displays a set of H i and He i line profiles from averaged, and normalised high-resolution echellespectra (with low-resolution profiles in the background), illustratingthe composition of lines. In the averaged spectra, the emission pro-file of the Balmer lines is rather symmetric. The absorption is muchwider, visually slightly blue-shifted in regard to the emission peak.Measuring this shift in spectra not corrected for the instrumentalsensitivity is complicated since the continuum is not well defined.H 𝛼 looks like it has a P Cyg profile with a blue-shifted absorptionfrom a material rapidly expanding in the direction of the observer.However, it is just a contrast effect, particularly in the case of thelow-resolution spectra. The emission feature is the strongest amongthe Balmer lines, hence the symmetry of the underlying absorptionline is visually distorted. However, the composition of the line issimilar to the rest of the Balmer lines; an emission peak is embeddedin a wider absorption line. Helium lines show a more complicatedstructure comparison with Balmer lines, discussed below.In general, BG Tri’s spectrum looks like a replica ofRW Sex (Hernandez et al. 2017) or IPHASX J210204.7+471015(Guerrero et al. 2018). Hence, our approach to interpreting BG Tribuilds on the assumption that it is a low inclination NL system. Low-resolution spectra did not provide information on the orbital mo-tion of emission lines. This supports our assumption of a low orbitalinclination. Hence, we obtained higher resolution echelle spectra toreveal the orbital period of the object. Fitting H 𝛼 emission with asingle Gaussian produced a large scatter but no definite periodicpattern. However, measuring H 𝛽 with a single Gaussian produced atime series which allowed us to determine a possible period and itsclosest one-day alias. The power spectrum calculated using a discreteFourier transformation provided by Period 04 (Lenz & Breger 2014,2005) indicated that the orbital frequency was either ∼ ∼ 𝛼 line is the strongestfeature. It is also the least affected by the absorption accompanyingall H emission lines. In general, it looks like a one peak line, butwith variable wings. We applied line de-blending splot -procedure in iraf to separate the line into components. We fit the profile with twoGaussians with unrestricted parameters. The details of the methodare provided in Tovmassian et al. (2018).We seek a periodic sinusoidal pattern in the RV/time-space by eye,and assign measurements of RVs to one or more component(s), inall cases when they are clearly distinct. Sometimes just one com-ponent stands out. We determine a more accurate orbital period bysubjecting the first emerging periodic pattern to the Fourier analy-sis. Period 04 was used to determine the best choice of the orbitalperiod. We refine RVs by fitting a 𝑠𝑖𝑛 -curve to the measurementsof the better-defined component and perform another round of de-blending, by fixing the central wavelength of this component. Asa result, we improve the determination of the second component,which can be used to measure the orbital period. The difference invalues of the orbital period from two components is rather small.The higher velocity amplitude component (HVC) power spectrumpeaks at 6.31114 c/d, while the lower velocity amplitude component(LVC) has a frequency of 6.33794 c/d. The spread of measurementsremains high. The residuals (RMS) of the fit of HVC are 36 km s − with the amplitude of variation 121 km s − . The LVC has an am-plitude of 78 km s − and RMS of 25 km s − . They reconcile betterat the period determined from the HVC, which we adopted as theorbital period of P orb = . ( ) h = 0.15845(10) d. The powerspectra obtained from RVs of H 𝛽 and two components of H 𝛼 are pre-sented in Figure 4. Obviously, the power of H 𝛽 as a whole is muchsmaller than the power of separate components of H 𝛼 , but they allare consistent with one another.The RV curves of H 𝛽 and H 𝛼 components along the measurementsfolded with the determined orbital period are presented in the twomiddle panels of Figure 5, respectively. We assigned phase zero atthe negative to positive crossing of the LVC. Plots are flanked bytrailed spectra of corresponding lines on both sides. In the upperpanel of Figure 6 Gaussian profiles of individual components, theirsum, and the observed line profiles in four different orbital phases arepresented to illustrate the result of the separation of the line into twocomponents. Residual spectra of individual components, as well asresiduals after subtraction of both components, are displayed in thebottom panel. H 𝛽 is probably also multi-component, but dismantlingit into components is rather difficult. There is a stronger absorption MNRAS , 1– ????
The power spectra of BG Tri calculated for the radial velocitycurves of different lines and components. In the upper panel the red and bluelines are the power of the HVC and the LVC after the decomposition of H 𝛼 line. In the inset a zoom on the small range of frequencies around the derivedperiod are presented. The bottom panel shows the power of H 𝛽 measuredwith a single Gaussian. only on the derived absolute magnitude, we can state that this objectis not a low accretion rate WZ Sge type, near the period minimum.In NLs, the bulk of the accretion disc is optically thick (hot anddense), producing absorption lines. The emission lines are formed ei-ther in the separate parts of the disc or by the gas in its vicinity (Warner1976; Beuermann et al. 1992). Figure 3 displays a set of H i and He i line profiles from averaged, and normalised high-resolution echellespectra (with low-resolution profiles in the background), illustratingthe composition of lines. In the averaged spectra, the emission pro-file of the Balmer lines is rather symmetric. The absorption is muchwider, visually slightly blue-shifted in regard to the emission peak.Measuring this shift in spectra not corrected for the instrumentalsensitivity is complicated since the continuum is not well defined.H 𝛼 looks like it has a P Cyg profile with a blue-shifted absorptionfrom a material rapidly expanding in the direction of the observer.However, it is just a contrast effect, particularly in the case of thelow-resolution spectra. The emission feature is the strongest amongthe Balmer lines, hence the symmetry of the underlying absorptionline is visually distorted. However, the composition of the line issimilar to the rest of the Balmer lines; an emission peak is embeddedin a wider absorption line. Helium lines show a more complicatedstructure comparison with Balmer lines, discussed below.In general, BG Tri’s spectrum looks like a replica ofRW Sex (Hernandez et al. 2017) or IPHASX J210204.7+471015(Guerrero et al. 2018). Hence, our approach to interpreting BG Tribuilds on the assumption that it is a low inclination NL system. Low-resolution spectra did not provide information on the orbital mo-tion of emission lines. This supports our assumption of a low orbitalinclination. Hence, we obtained higher resolution echelle spectra toreveal the orbital period of the object. Fitting H 𝛼 emission with asingle Gaussian produced a large scatter but no definite periodicpattern. However, measuring H 𝛽 with a single Gaussian produced atime series which allowed us to determine a possible period and itsclosest one-day alias. The power spectrum calculated using a discreteFourier transformation provided by Period 04 (Lenz & Breger 2014,2005) indicated that the orbital frequency was either ∼ ∼ 𝛼 line is the strongestfeature. It is also the least affected by the absorption accompanyingall H emission lines. In general, it looks like a one peak line, butwith variable wings. We applied line de-blending splot -procedure in iraf to separate the line into components. We fit the profile with twoGaussians with unrestricted parameters. The details of the methodare provided in Tovmassian et al. (2018).We seek a periodic sinusoidal pattern in the RV/time-space by eye,and assign measurements of RVs to one or more component(s), inall cases when they are clearly distinct. Sometimes just one com-ponent stands out. We determine a more accurate orbital period bysubjecting the first emerging periodic pattern to the Fourier analy-sis. Period 04 was used to determine the best choice of the orbitalperiod. We refine RVs by fitting a 𝑠𝑖𝑛 -curve to the measurementsof the better-defined component and perform another round of de-blending, by fixing the central wavelength of this component. Asa result, we improve the determination of the second component,which can be used to measure the orbital period. The difference invalues of the orbital period from two components is rather small.The higher velocity amplitude component (HVC) power spectrumpeaks at 6.31114 c/d, while the lower velocity amplitude component(LVC) has a frequency of 6.33794 c/d. The spread of measurementsremains high. The residuals (RMS) of the fit of HVC are 36 km s − with the amplitude of variation 121 km s − . The LVC has an am-plitude of 78 km s − and RMS of 25 km s − . They reconcile betterat the period determined from the HVC, which we adopted as theorbital period of P orb = . ( ) h = 0.15845(10) d. The powerspectra obtained from RVs of H 𝛽 and two components of H 𝛼 are pre-sented in Figure 4. Obviously, the power of H 𝛽 as a whole is muchsmaller than the power of separate components of H 𝛼 , but they allare consistent with one another.The RV curves of H 𝛽 and H 𝛼 components along the measurementsfolded with the determined orbital period are presented in the twomiddle panels of Figure 5, respectively. We assigned phase zero atthe negative to positive crossing of the LVC. Plots are flanked bytrailed spectra of corresponding lines on both sides. In the upperpanel of Figure 6 Gaussian profiles of individual components, theirsum, and the observed line profiles in four different orbital phases arepresented to illustrate the result of the separation of the line into twocomponents. Residual spectra of individual components, as well asresiduals after subtraction of both components, are displayed in thebottom panel. H 𝛽 is probably also multi-component, but dismantlingit into components is rather difficult. There is a stronger absorption MNRAS , 1– ???? (2018) Hernández, Tovmassian, Zharikov et al. -400 -200 0 200 400
V (km s -1 ) pha s e -100 0 100 V (km s -1 ) -200 -100 0 100 200 V (km s -1 ) -400 -200 0 200 400 V (km s -1 ) H β H α Figure 5.
RV curves of H 𝛽 and components of H 𝛼 folded with the orbital period are in the left and right panels respectively. RV of H 𝛽 line was first measuredby fitting a single Gaussian, which enabled determination of the orbital period. H 𝛼 was separated into two components; by fitting two Gaussians (see the text forthe description). The RV measurements corresponding to the high-velocity component of H 𝛼 are marked by red symbols and the fit to them with 121 km s − semi-amplitude as a red line. Respectively, the low-velocity component is plotted in blue. The semi-amplitude of the best fit curve is 74 km s − . Figure 6.
The line profile phase-evolution of H 𝛼 . Four orbital phases (markedin the upper right corner of each panel) are displayed. In the upper panelsthe grey line are the observed spectra. Two Gaussians obtained as a resultof de-blending are plotted by red and blue curves. Their sum is plotted by ablack line as a fit to the observed profile. In the bottom panels by the red andblue lines the residuals of subtraction of the counterpart Gaussian are plotted,while the gray line is after subtraction of both Gaussians. undermining the wings of the emission components. One component(the HVC) dominates, as evident from Figure 5. The amplitude offitted 𝑠𝑖𝑛 -curve to single-Gaussian measurements of the line is only24 km s − , decreasing to 22 km s − if the adopted 0.15845 d periodis used to fit the data. The RMS is 16 km s − .Armed with a set of two components comprising H 𝛼 , we may try to figure out their origin. We compare our spectroscopic ob-servation with a small sample of similar objects published re-cently (Hernández Santisteban et al. 2017; Hernandez et al. 2017),which show similar two-component emission lines. RW Sex and1RXS J064434.5+334451 (Hernandez et al. 2017) and RW Tri(Subebekova et al. 2020) were all observed with the same instru-mental settings as BG Tri, so the measurements are uniform, and thecomparison is straightforward. All three objects show two distinctcomponents varying with the respective orbital periods in almostcounter-phase, relative to one another. One component is usuallywider. Another, the narrow one, is firmly linked to the irradiated faceof the secondary by two eclipsing objects in the sample, for which thezero phases were known precisely. The wide component is also regu-larly the higher velocity component in other NLs. In case of BG Tri,the difference in widths of components is insignificant, but still, theHVC is slightly broader than LVC (average FWHM = . ( ) Å vs5 . ( ) Å, respectively).Assuming that the secondary star emits the LVC, in analogy withthe above-mentioned NLs (Hernandez et al. 2017; Subebekova et al.2020), we determine the orbital phase zero ( φ =
0) of the systemas the moment when the RV of LVC changes sign from negative topositive, i.e. when the secondary star is in the inferior conjunction.In which case, the ephemeris of BG Tri can be expressed asHJD φ= = . ( ) + . d ( ) × E . (1)All phases used in this paper were calculated with this ephemeris. A customary way to illustrate the emission line behaviour is viatrailed spectra and Doppler tomography (Marsh & Horne 1988). Itis worth mentioning that the Doppler tomography works best if theemitting particles are in the orbital plane, and the inclination of thesystem’s orbital plane is high (Marsh 2005). In order to constructtrailed spectra and Doppler maps, we used the phase zero as definedabove, stemming from the assumption that the LVC is the com-ponent originating from the irradiated face of the secondary. Withthis premise, the Doppler tomograms presented in Figures 7 and 8
MNRAS , 1– ?? (2018) G Tri: a low inclination RW Sex-type nova-like -400 -200 0 200 400 V (km s -1 ) -400-2000200400 V ( k m s - ) -400 -200 0 200 400 V (km s -1 ) -400-2000200400 V ( k m s - ) -400 -200 0 200 400 V (km s -1 ) -400-2000200400 V ( k m s - ) -400 -200 0 200 400 V (km s -1 ) -400-2000200400 V ( k m s - ) -400 -200 0 200 400V (km s -1 )0.00.51.01.52.0 pha s e -400 -200 0 200 400V (km s -1 )0.00.51.01.52.0 -400 -200 0 200 400V (km s -1 )0.00.51.01.52.0 pha s e -400 -200 0 200 400V (km s -1 )0.00.51.01.52.0 HVC LVC
Figure 7.
The trailed observed and reconstructed spectra of H 𝛼 components along with the Doppler maps are presented here. In the left side the separated HVCtrailed spectrum and its reconstruction are plotted at the bottom, while the corresponding velocity map of the HVC is displayed above. Respectively, on the upperright side of the figure is the Doppler tomogram of the LVC with the separated observed and reconstructed trailed spectra at the bottom. The Keplerian velocityof the disc in the Doppler maps is located at 𝜐 disc sin ( 𝑖 ) ≥
220 km s − and the circle shows the disc external radius. The system parameters discussed in the text. were constructed (Spruit 1998). Echelle high-resolution spectra wereused for this purpose. The Doppler map of the H 𝛼 line without sep-aration into two components was calculated, but is not presentedhere because it is less informative. Tomograms of unaltered lineswere presented by Hernandez et al. (2017); Guerrero et al. (2018).Instead, we split the H 𝛼 line into components, as demonstrated in thebottom panel of Figure 6, and made a tomogram of each componentseparately.In the bottom panels of Figure 7 trailed spectra (and their recon-structed counterparts) of H 𝛼 ’s HVC and LVC are presented side byside. Together, they form the trailed spectra of H 𝛼 shown at the rightside of Figure 5. Meanwhile, in the upper panels, the velocity mapsresulting from the Doppler tomography are shown. Locations of thestellar components are marked by " × ", the centre of the masses by" + ". The Roche lobe of the secondary star and the ballistic trajectoryof mass transfer flow are over-plotted, as well as a ring correspondingto the outer radius of the disc. To calculate them, we selected the massof the WD, M WD = . ⊙ , and the mass ratio, 𝑞 = . orb = . 𝑖 = ◦ (see Section 5 for justification of these parameters).The LVC produces a spot converging with the position of thesecondary in the velocity map. Apparently, this is a result of ourphase allocation. Usually, when the irradiated secondary star formsthe emission, the line is narrower (3.8 Å in the eclipsing RW Tri(Subebekova et al. 2020) against 5.3 Å in BG Tri), and the compact spot is concentrated at the hemisphere facing the WD. The reason forsuch a diffuse spot is not clear, but a low orbital inclination of the sys-tem probably contributes to it. Meanwhile, the HVC produces anotherdiffuse and elongated concentration (upper left panel), at a regionwhich is clearly evading identification with either the stellar compo-nent of the binary, the accretion disc, or the mass transfer stream;including impact area of the stream with the disc. Detection of thisH 𝛼 component and its corresponding location in the velocity mapshas become common for RW Sex-type NLs. Among a few possibleexplanations cited by Hernandez et al. (2017) and Subebekova et al.(2020), we prefer the model in which the outflow from the disc takesplaces in the orbital plane, instead of the wind perpendicular to theplane direction. Three-dimensional numerical simulations of the gasdynamics show that such outflows are viable through the vicinity ofthe Lagrange L point (Sytov et al. 2007). BG Tri provides a good ar-gument in favour of this hypothesis: firstly, the object shows meagreemission from He ii line, even though we observe it almost face-on,hence it is difficult to argue that a disc wind is significant enough toproduce an intense enough emission spectrum (e.g. Matthews et al.2015) to overcome the bright accretion disc. Generally, P Cygni-likeprofiles for NLs are observed in UV, and quite successfully mod-elled for recombination emission (Long & Knigge 2002), where thelines of low inclination systems exhibit the characteristic imprint.However, reproducing it in the optical range is a challenging task;it produces some double-peaked emission line contribution only ina high inclination ( 𝑖 > ◦ ) systems. Matthews (2016) attempted to MNRAS , 1– ????
220 km s − and the circle shows the disc external radius. The system parameters discussed in the text. were constructed (Spruit 1998). Echelle high-resolution spectra wereused for this purpose. The Doppler map of the H 𝛼 line without sep-aration into two components was calculated, but is not presentedhere because it is less informative. Tomograms of unaltered lineswere presented by Hernandez et al. (2017); Guerrero et al. (2018).Instead, we split the H 𝛼 line into components, as demonstrated in thebottom panel of Figure 6, and made a tomogram of each componentseparately.In the bottom panels of Figure 7 trailed spectra (and their recon-structed counterparts) of H 𝛼 ’s HVC and LVC are presented side byside. Together, they form the trailed spectra of H 𝛼 shown at the rightside of Figure 5. Meanwhile, in the upper panels, the velocity mapsresulting from the Doppler tomography are shown. Locations of thestellar components are marked by " × ", the centre of the masses by" + ". The Roche lobe of the secondary star and the ballistic trajectoryof mass transfer flow are over-plotted, as well as a ring correspondingto the outer radius of the disc. To calculate them, we selected the massof the WD, M WD = . ⊙ , and the mass ratio, 𝑞 = . orb = . 𝑖 = ◦ (see Section 5 for justification of these parameters).The LVC produces a spot converging with the position of thesecondary in the velocity map. Apparently, this is a result of ourphase allocation. Usually, when the irradiated secondary star formsthe emission, the line is narrower (3.8 Å in the eclipsing RW Tri(Subebekova et al. 2020) against 5.3 Å in BG Tri), and the compact spot is concentrated at the hemisphere facing the WD. The reason forsuch a diffuse spot is not clear, but a low orbital inclination of the sys-tem probably contributes to it. Meanwhile, the HVC produces anotherdiffuse and elongated concentration (upper left panel), at a regionwhich is clearly evading identification with either the stellar compo-nent of the binary, the accretion disc, or the mass transfer stream;including impact area of the stream with the disc. Detection of thisH 𝛼 component and its corresponding location in the velocity mapshas become common for RW Sex-type NLs. Among a few possibleexplanations cited by Hernandez et al. (2017) and Subebekova et al.(2020), we prefer the model in which the outflow from the disc takesplaces in the orbital plane, instead of the wind perpendicular to theplane direction. Three-dimensional numerical simulations of the gasdynamics show that such outflows are viable through the vicinity ofthe Lagrange L point (Sytov et al. 2007). BG Tri provides a good ar-gument in favour of this hypothesis: firstly, the object shows meagreemission from He ii line, even though we observe it almost face-on,hence it is difficult to argue that a disc wind is significant enough toproduce an intense enough emission spectrum (e.g. Matthews et al.2015) to overcome the bright accretion disc. Generally, P Cygni-likeprofiles for NLs are observed in UV, and quite successfully mod-elled for recombination emission (Long & Knigge 2002), where thelines of low inclination systems exhibit the characteristic imprint.However, reproducing it in the optical range is a challenging task;it produces some double-peaked emission line contribution only ina high inclination ( 𝑖 > ◦ ) systems. Matthews (2016) attempted to MNRAS , 1– ???? (2018) Hernández, Tovmassian, Zharikov et al. -400 -200 0 200 400
V (km s -1 ) -400-2000200400 V ( k m s - ) -400 -200 0 200 400 V (km s -1 ) -400-2000200400 V ( k m s - ) -400 0 400V (km s -1 )0.00.51.01.52.0 pha s e -400 0 400V (km s -1 )0.00.51.01.52.0 He I Em
Figure 8.
The Doppler map of He I 𝜆 . 𝜐 disc sin ( 𝑖 ) ≥
220 km s − and the circle showsthe disc external radius. The system parameters discussed in the text. convert lines into the single peaked, requiring an extension of theline forming region to ∼
150 R WD , which again works only for highinclinations. As a result, Matthews (2016) succeeded to produce asuccessful model for RW Tri by comparing it to a low-resolutionspectrum of the object. But Subebekova et al. (2020) demonstratedthat the H 𝛼 in RW Tri is complex and at least partially formed atthe heated surface of the secondary star. Secondly, H 𝛼 emissionhas been disentangled already in four objects, including BG Tri,all of which have vastly different inclination angles. After correc-tion for the inclination angle 𝑖 = ◦ (see Section 5), the measured 𝜐 HVC / sin ( 𝑖 ) =
121 km s − of the HVC converts into 286 km s − .According to Hernandez et al. (2017) and Subebekova et al. (2020)the HVC (also called "the wide component" in these publications)in all studied objects is ≈
300 km s − , after the inclination angle isaccounted for. The fact that the HVC in all morphologically similarNL variables obtains the same value after correction for a variety ofinclination angles, is a good evidence that the source of HVC is in theorbital plane. One would expect that the wind will constitute itselfdifferently, depending on the viewing aspect. Notwithstanding, theHVC always appears on the Doppler maps at the same spot, adjacentto the outer edge of the accretion disc on the opposite side from thesecondary/hot-spot, regardless of the system inclination.Figure 3 demonstrates that He i acts somewhat differently with respect to the Balmer lines. It is also a common characteristic ofRW Sex-type NLs. Helium lines are fainter than H 𝛼 or H 𝛽 and arecomprised of equally intense emission and absorption. Nevertheless,we explored their phase evolution using illustrative trailed spectra andtheir respective tomograms. We concentrated on the He i 𝜆 . 𝛼 . The observed trailed spectrum is faint, but the program picksup the signal correctly, reflecting it in the reconstructed spectrum.The low-velocity component definitely dominates, and hence a com-pact spot materialises close to the L point, contrary to the diffuseappearance in the H 𝛼 case. The HVC is hardly traceable in the ob-served trailed spectra, but apparently some emission comes fromhere too. Hence, a coma-like extension in the velocity map. The average masses of WDs in CVs above the period gap isM wd (P orb > = . ( ) M ⊙ (Zorotovic et al. 2011). For sim-plicity, we adopted M WD = . ⊙ . Taking into account the semi-empiric relation of secondary type vs orbital period, we expect asecondary with a mass of M ≈ . ⊙ , and spectral type of M3V-M4V (Knigge 2006). The expected mass ratio and separations are 𝑞 ≡ M / M WD ≈ . 𝑎 = .
23 R ⊙ , respectively. The accretiondisc truncation radius is 𝑟 outdisc = .
52 R ⊙ . Corresponding primary,secondary, and L orbital velocities are 117 km s − , 292 km s − , and129 km s − , respectively (see Figure 9).There are numerous flux measurements of BG Tri available inthe public domain. We fetched all available data from VizieR (Ochsenbein et al. 2000). We revised the available data, since somemeasurements are erroneous (e.g. the SDSS data are not correct be-cause the object is too bright), and compiled those which passedthe scrutiny in Table 2. Selected data are plotted using circles in thebottom panel of Figure 10, after the interstellar reddening correctionof E( 𝐵 − 𝑉 )=0.03 (Green et al. 2015). Using the Gaia distance of 𝑑 = ( ) pc, we can calculate the luminosity of different compo-nents. In particular, even a hot 50 kK white dwarf will have a neg-ligible contribution to the optical flux. A secondary M3-4 V Rochelobe filling star has some insignificant influence in the IR. The com-parison of the observed fluxes with those expected from differentcomponents confirms that the flux in the entire wavelength range isformed mostly by the accretion disc. The dashed lines in the bottompanel of Figure 10 indicate a simple accretion disc spectrum as acomposition of multiple black-bodies; from concentric rings with acorresponding distribution of temperatures throughout the stationary,optically thick disc (La Dous 1989). Since the observed flux woulddepend on the aspect of the disc, we fitted the observed SED as afunction of the mass transfer rate ¤ 𝑀 , and the system inclination.The UV points were excluded from consideration because it iswell known that accretion disc models do not reproduce the ob-served spectrum shape of CVs in the wide range including the UV(Puebla et al. 2007).For the fit’s robustness, we added a spectrum of M3V-type starsfrom the empirical template library of the Sloan Digital Sky Survey equation 2.61 from Warner (1995) http://vizier.unistra.fr/vizier/sed/MNRAS , 1– ?? (2018) G Tri: a low inclination RW Sex-type nova-like !" ! " $ ! $ %$ $$ %" $ & ’( ! ) * ’ ( ! ) +
117 km s −
129 km s −
292 km s − ✂✂✂✂✂✂✂✂✂✂✂✌❄❆❆❆❆❆❆❯ outflow zone ✻ ⋆L L Figure 9.
The geometric model of BG Tri. The center of mass (x) and Lagrangian corresponding points are marked. Velocities of the L point, the disc outflowarea (green), and the WD are denoted. LVC which is emitted from the irradiated hemisphere of the secondary star has a velocity exceeding that of the L pointand less than the orbital velocity of the star. stellar spectra (Kesseli et al. 2017), which was extended to the IRrange using spectral templates from Rayner et al. (2009). The starspectrum was scaled to the object’s distance. For each band listedin Table 2 (except 𝐹𝑈𝑉 and
𝑁𝑈𝑉 ) the flux 𝑚 𝑐𝑎𝑙𝑐 was calculated asa sum of the disc model and the secondary. The result of the bestfit of function 𝜒 = Σ (( 𝑚 𝑜𝑏𝑠 − 𝑚 𝑐𝑎𝑙𝑐 )/ Δ 𝑚 𝑜𝑏𝑠 ) is presented as along dashed line in the lower panel of Figure 10. In the upper panelof Figure 10, the goodness-of-fit is presented as an intensity scalediagram. Following the assumption that the LVC is emitted from theheated hemisphere of the companion star, the expected LVC veloc-ity is located in the range of 𝜐 LVC ∈ [130 sin ( 𝑖 ) ,
290 sin ( 𝑖 ) km s − ](see Figure 9), which allow us to estimate limits on the orbit incli-nation from the dynamical constrains. The observed value of LVC is78 km s − , which defines the limits marked by the vertical dashedlines in Figure 10, top. The line at the right side of the plot indicatesthe observed LVC, which is consistent with the L point, and an-other corresponds to the center of mass of the secondary (at the leftside). In other words, the inclination angle and mass accretion ratewould be highest if the LVC is emitted just from the L point, andaccordingly, lowest if the entire surface of the secondary is heated. Ofcourse, neither assumption is correct, so we introduced some param-eter which reflects the increasing cross-section of the secondary, withdecreasing temperature. According to which, the best fit is achievedat 𝑖 = ( ) degree and ¤ 𝑀 =8 . ( . ) × − M ⊙ year − .Given all uncertainties of adopted assumptions, the fit is remark-ably good. The values of mass accretion rate are within the range ofestimates for a number of other NLs (e.g. Figure 2 of Hameury 2019). The mass transfer ¤ 𝑀 dependends slightly on the mass of the WD. Fora 0.6 M ⊙ WD, the mass transfer rate increases to 10 − M ⊙ year − .On the down side, ¤ 𝑀 is ∼ . × − M ⊙ year − for a massive ≥ . ⊙ WD.The LVC velocity corrected for a system inclination of 𝑖 = ◦ is 𝜐 LVC =
185 km s − . As we showed earlier, the corrected HVCvelocity is ≈
300 km s − , it corresponds to the orbital velocity atthe edge of the disc on the opposing side of the system relative tothe secondary. The location of the HVC on Doppler maps of allsimilar NLs is related to the Lagrangean L point. According tosome hydrodynamic models (Sytov et al. 2007; Lukin et al. 2017) anoutflow of matter from the disc in to the orbital plane takes placefrom this area (marked green area in Figure 9). The concentration ofgas in that area might be responsible for HVC or wide component ofemission lines in these objects. We studied BG Tri, one of the brightest CVs at 𝑉 = .
9, whichsomehow escaped attention until now. We determined its orbital pe-riod to be 0.15845 d or 3.8028 h. We show that it is a NL system,identified by its characteristic blue spectrum containing a set of H i and He i lines, comprised of wide absorption features containingstrong emission peaks. The orbital period and the spectrum, com-bined with the SED, indicate the presence of a bright accretion discin a high density and temperature state, proper to NLs. The long term MNRAS , 1– ????
9, whichsomehow escaped attention until now. We determined its orbital pe-riod to be 0.15845 d or 3.8028 h. We show that it is a NL system,identified by its characteristic blue spectrum containing a set of H i and He i lines, comprised of wide absorption features containingstrong emission peaks. The orbital period and the spectrum, com-bined with the SED, indicate the presence of a bright accretion discin a high density and temperature state, proper to NLs. The long term MNRAS , 1– ???? (2018) Hernández, Tovmassian, Zharikov et al. !" ) * + , !$ ! " * ! - ./ ! $ !$ !$ !% !$ !& !$ ! : ; < + =- ! + " >1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Figure 10.
The plot of spectral energy distribution of BG Tri in the bottompanel. Circles represent the fluxes from Table 2. They were corrected for theinterstellar extinction E( 𝐵 − 𝑉 )=0.03. The dashed line through the observeddata in the optical-IR range represents the spectrum of accretion disc. The redpoints represent a spectrum of a M3V star scaled to a 337 pc distance. Thesolid line is a combination of fluxes from the accretion disc and the secondary.The outermost left two points correspond to UV data. In the upper panel thebest fit parameters (mass accretion rate vs. inclination angle) of the accretiondisc model to the data are presented in the form of intensity map. The extremeboundaries of 𝑖 corresponding to the secondary mass center and L point aremarked by vertical lines. Preferred values of ¤ 𝑀 and 𝑖 (blue strip) are alsofunction of increasing surface and decreasing temperature along latitude. Table 2.
VizieR photometric data of BG Tri 𝜆 Flux 1 𝜎 Flux Band Source Ref.( 𝜇 m) ( × − Jy) × − 𝐹𝑈𝑉
GALEX
𝑁𝑈𝑉
GALEX 𝑔 PAN-STARRS 30.482 64.6 9.3 𝑔 ′ AAVSO 20.505 65.7 0.9
𝐺𝑏 𝑝
GAIA2 𝑉 AAVSO 20.613 63.2 𝑟 PAN-STARRS 30.623 58.9 0.3 𝐺 GAIA2 𝑟 ′ AAVSO 20.748 51.6 𝑖 PAN-STARRS 30.763 51.5 7.6 𝑖 ′ AAVSO 20.772 49.6 0.7
𝐺𝑟 𝑝
GAIA2 𝑧 PAN-STARRS 30.960 36.5 0.8 𝑦 PAN-STARRS: 31.24 29.9 0.6 𝐽 𝐻 𝐾 𝑠 𝑊 WISE 𝑊 WISE 𝑊 WISE
61 - Bianchi et al. (2017)2 - Henden et al. (2015)3 - Chambers et al. (2016)4 - Gaia Collaboration et al. (2018)5 - Cutri et al. (2003)6 - Cutri & et al. (2012) light curve of BG Tri, obtained by ASAS SN and CRTS sky surveys,shows the absence of dwarf novae style outbursts, but reveals an in-stance of low luminosity state often detected in NLs, also known asthe VY Scl phenomenon.Absorption lines originate from the optically thick accretion disc,while emission forms elsewhere. We demonstrate that the Balmeremission lines are complex and we are able to separate H 𝛼 intotwo components. We identify the LVC with the heated surface ofthe secondary star facing the luminous disc. We associate the HVCwith the disc outflow region situated on the opposite from the sec-ondary and the hot-spot, side of the disc. A similar occurrence isalso common for mentioned NLs, which we may call RW Sex typesystems, all of which are concentrated in a 3-6 h range of orbital pe-riods (Subebekova et al. 2020). An HVC velocity, corrected for theinclination angle, of ∼
300 km sec − , is very definite in all studiedobjects, regardless of their orientation. That, in our opinion, arguesagainst the disc wind origin of the HVC component. However, it is notevidence of the absence of wind, just a rationalisation that emissionlines in the optical range are not formed in the wind.The SED of BG Tri confirms that stellar components contributionis negligible and that most of the flux from UV to near-IR is emittedby the disc. The energy balance favours that we observe the systemnearly face-on, and the deduced inclination angle validates the valuefetched from the dynamical considerations. ACKNOWLEDGEMENTS
We are grateful to the anonymous referee for the valuable commentswhich helped to improve this paper. This work is based upon observa-tions carried out at the OAN SPM, Baja California, México. We thankthe daytime and night support staff at the OAN-SPM for facilitatingand helping obtain our observations. This research has made use ofthe VizieR catalogue access tool, CDS, Strasbourg, France (DOI:10.26093/cds/vizier). The original description of the VizieR servicewas published in A&AS 143, 23. GT and SZ acknowledge PAPIIT-DGAPA-UNAM (grants IN108316, IN102120 and IN110619) andCONACyT grant 166376. MSH acknowledges the Fellowship forNational PhD from ANID, grant number 21170070. MSH and GTare thankful to SIMA project 687 of UNAM. This research has beenwas funded in a part by the Science Committee of the Ministry ofEducation and Science of the Republic of Kazakhstan (Grant No.AP08856419). BTG was supported by a Leverhulme Research Fel-lowship and the UK STFC grant ST/T000406/1. AA received sup-port from Thailand Science Research and Innovation (TSRI) grantFRB640025 contract no. R2564B006.
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
REFERENCES
Abril J., Schmidtobreick L., Ederoclite A. r., López-Sanjuan C., 2020,MNRAS, 492, L40Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Mantelet G., Andrae R.,2018, AJ, 156, 58Baptista R., Steiner J. E., Horne K., 1996, MNRAS, 282, 99Beuermann K., Stasiewski U., Schwope A. D., 1992, A&A, 256, 433Bianchi L., Shiao B., Thilker D., 2017, ApJS, 230, 24MNRAS , 1– ?? (2018) G Tri: a low inclination RW Sex-type nova-like Chambers K. C., et al., 2016, arXiv e-prints, p. arXiv:1612.05560Cutri R. M., et al. 2012, VizieR Online Data Catalog, p. II/311Cutri R. M., et al., 2003, VizieR Online Data Catalog, p. II/246Dhillon V. S., Smith D. A., Marsh T. R., 2013, MNRAS, 428, 3559Drake A. J., et al., 2009, ApJ, 696, 870Gaia Collaboration et al., 2018, A&A, 616, A1Green G. M., et al., 2015, ApJ, 810, 25Guerrero M. A., et al., 2018, ApJ, 857, 80Hameury J.-M., 2019, arXiv e-prints, p. arXiv:1910.01852Hellier C., 1996, ApJ, 471, 949Henden A. A., Levine S., Terrell D., Welch D. L., 2015, in American Astro-nomical Society Meeting Abstracts , 1– ????