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Mon. Not. R. Astron. Soc. 000, 000­000 (0000)

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Possible detection of two giant extrasolar planets orbiting the eclipsing p olar UZ Fornacis
Stephen B. Potter1 , Encarni Romero­Colmenero1, Gavin Ramsay2,6, Steven Crawford1, Amanda Gulbis1, Sudhanshu Barway1, Ewald Zietsman1,4, Marissa Kotze1,5, David A. H. Buckley1, Darragh O'Donoghue1, O. H. W. Siegmund3, J. McPhate3, B. Y. Welsh3 and John Vallerga3
1 2 3 4 5 6

arXiv:1106.1404v1 [astro-ph.SR] 7 Jun 2011

South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape Town, South Africa Armagh Observatory, Col lege Hil l, Armagh BT61 9DG Experimental Astrophysics Group, Space Sciences Laboratory, University of California Berkeley, CA 94720, USA Department of Mathematical Sciences, The University of South Africa, PO Box 392, UNISA, 0003, South Africa Astronomy Department, Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, Rondebosch 7701, South Africa Mul lard Space Science Laboratory, University Col lege London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

ABSTRACT

We present new high-speed, multi-observatory, multi-instrument photometry of the eclipsing polar UZ For in order to measure precise mid-eclipse times with the aim of detecting any orbital period variations. When combined with published eclipse times and archival data spanning 27 years, we detect departures from a linear and quadratic trend of 60 s. The departures are strongly suggestive of two cyclic variations of 16(3) and 5.25(25) years. The two favoured mechanisms to drive the periodicities are either two giant extrasolar planets as companions to the binary (with minimum masses of 6.3(1.5)MJ up and 7.7(1.2)MJ up ) or a magnetic cycle mechanism (e.g. Applegate's mechanism) of the secondary star. Applegate's mechanism would require the entire radiant energy output of the secondary and would therefore seem to be the least likely of the two, barring any further refinements in the effect of magnetic fields (e.g. those of Lanza et al.). The two planet model can provide realistic solutions but it does not quite capture all of the eclipse times measurements. A highly eccentric orbit for the outer planet would fit the data nicely, but we find that such a solution would be unstable. It is also possible that the periodicities are driven by some combination of both mechanisms. Further observations of this system are encouraged. Key words: accretion, accretion discs ­ methods: analytical ­ binaries: close ­ novae, cataclysmic variables ­ X­rays: stars, planetary systems.

1

INTRODUCTION

Approximately 20% of the known cataclysmic variables (CVs, see the catalogue of Ritter & Kolb 2003) are p olars, where the primary white dwarf has a sufficiently strong magnetic field to lock the system into synchronous rotation with the red dwarf secondary and to prevent completely the formation of an accretion disc. The material from the secondary overflowing the Roche

Based on observations made with the Southern African Large Telescope (SALT) sbp@saao.ac.za c 0000 RAS

lob e initially falls towards the white dwarf following a ballistic tra jectory until, at some distance from the white dwarf, the magnetic pressure overwhelms the ram pressure of the ballistic stream. From this p oint on the accretion flow is confined to follow the magnetic field lines of the white dwarf. The now sup ersonic accreting material suddenly b ecomes sub-sonic at a shock region, which forms at some height ab ove the white dwarf surface. The shock-heated material reaches temp eratures of 10 - 50 keV and is therefore ionised. The hot plasma cools by X-ray cooling, in the form of bremsstrahlung radiation. With sufficiently strong magnetic fields we find also cyclotron cooling, in the form of optical/infrared cyclotron radiation (e.g. ST LMi: Imamura,


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that adding these newer data to timing from the literature gives a baseline of 27 years.

Steiman-Cameron & Wolff, 2000, and Campb ell, Harrison, Mason, Howell & Schwop e, 2008). See e.g. Warner (1995) for a review of CVs and Cropp er (1990) and Patterson (1994) for reviews of magnetic CVs. UZ For is one of 15 known eclipsing p olars and was discovered with EXOSAT (EXO 033319-2554.2) as a serendipitous X-ray source (Giommi et al. 1987; Osb orne et al. 1988). Extensive followup observations at multi-wavelengths established a 126.5-min orbital p eriod, one or two accretion sp ots dep ending on accretion state, with magnetic fields of 53 MG and 48 MG and a white dwarf mass of 0.7M (Beuermann, Thomas & Schwop e 1988; Berriman & Smith 1988; Ferrario et al. 1989; Bailey & Cropp er 1991). The eclipses of the accretion sp ots in UZ For are particularly rapid at 1-3 s and can only b e resolved with high sp eed photometry. Bailey & Cropp er (1991) were able to resolve the eclipse of the white dwarf photosphere during a low state and Perryman et al. (2001) were able to resolve two accretion sp ots during a higher accretion state. These distinct rapid photometric transitions are ideal for making accurate timing measurements and therefore searching for any long term p eriod variations in UZ For. Some of the ab ovementioned authors have combined their observations with previous eclipse measurements in order to obtain accurate eclipse ephemerides. In general, significant residuals were seen in the O-Cs (Observed - Calculated) of the orbital p eriod, but no overall trend had b een detected (e.g. Perryman et al. 2001). More recently, Dai et al. (2010) claim the existence of a third b ody orbiting UZ For in order to explain the O-C. However, their singular new eclipse measurement and subsequent derived orbital parameters are grossly incompatible with all of our new observations spanning 10 years. Nevertheless, recent results of long term studies of some CV related ob jects are b eginning to show trends. Parsons et al. (2010) presented high-sp eed ULTRACAM photometry of 8 p ost-common-envelop e-binaries. They detect significant departures from linearity in some of these systems and suggest magnetic braking or a third b ody as p ossible mechanisms to drive the O-Cs. High precision eclipse measurements of the p ost-common envelop e binary NN Ser (Beuermann et al. 2010a) shows strong evidence for two additional b odies sup erp osed on the binary's linear ephemeris. Significant and complicated departures from a linear ephemeris have also b een seen in the eclipsing p olar HU Aqr (Schwarz et al. 2009). They find that neither a sinusoidal nor a quadratic ephemeris are sufficient to describ e their O-C departures, thus more eclipse observations over the next few years will b e needed in order to refine the ephemerides. Qian et al. (2010) discovered that the O-C curve of the eclipsing p olar DP Leo shows a cyclic variation with a p eriod of 23.8 years. They claim that this is as a result of a giant extrasolar planet orbiting DP Leo, recently refined by Beuermann et al (2010b). Here we present new high-sp eed HIPPO, BVIT, SALTICAM and UCTPOL photometry of UZ For, spanning 10 years, and use these observations to determine accurate mid-eclipse times of the main accretion sp ot in UZ For. We combine these with previous mid-eclipse times, that we either measure from archival data or extract from the literature, and analyse for any p eriod variations in UZ For. Note

2

OBSERVATIONS

All of the eclipse times extracted from the literature were published as Heliocentric Julian Dates (HJD). We have assumed that the Coordinated Universal Time (UTC) system was used in all cases as this was not explicitly stated in any of the publications. We re-corrected all times for the light travel time to the barycenter of the solar system, converted to the barycentric dynamical time system (TDB) and the times are listed (table 1) as Barycentric Julian Date (BJD; see Eastman, Siverd & Gaudi 2010 for achieving accurate absolute times and time standards). By doing this we have removed any timing systematics, particularly due to the unpredictable accumulation of leap seconds with UTC, and effects due to the influence of primarily Jupiter and Saturn when heliocentric corrections only are applied. We either calculate or re-calculate appropriate errors dep ending on the S/N and time resolution at the time of the sp ot ingress and egress. Table 1 also lists the eclipse width of the accretion sp ot and the observatory/instrument used. All of our new observations were also converted to BJD. We note that our new ground based instruments were synchronised to GPS to b etter than a milli-second. Given the high-sp eed nature of these instruments, their timing accuracies have b een verified through simultaneous multiinstrument observations. The remaining space observatories have documented rep orts on the p erformance of their onb oard clocks.

2.1

Eclipse times from the literature

The earliest UZ For eclipse measurements were made using EXOSAT and published by Osb orne et al. (1998). The data are of p oor time resolution but are at a sufficiently early ep och to provide constraints for model fitting. Beuermann et al. (1988) and Ferrario et al. (1989) observed multiple eclipses sp ectrophotometrically. These are also of very low time resolution, however the combination of multiple eclipses provides usable data. Allen et al. (1989) presented the first high sp eed photometry that could resolve the accretion sp ot. A typ ographical error in the eclipse time was corrected by Ramsay (1994). This was soon followed with more high quality optical low-state photometry by Bailey & Cropp er (1991) and high-state photometry by Imamura & Steiman-Cameron (1998) and EUVE light curves by Warren et al. (1995). An additional high quality STJ eclipse was also published by de Bruijne (2002) and three more, with the same instrument by Perryman et al. (2001). From the latter data we were able to obtain the raw observations and re-measure and confirm the eclipse times.

2.2

ROSAT (1991)

Observations were retrieved from the HEASARC archive and events were extracted using an ap erture centered on the source and also a background region. The resulting light curves were subtracted after appropriate scaling from the
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Possible detection of two giant extrasolar planets orbiting the eclipsing polar UZ Fornacis
differing areas. The observations spanned tiple eclipses were covered. The reduced and folded on the orbital p eriod in order t eclipse light curve from which the eclipse 1 day and muldata were binned o produce a single was measured. 2.7 SWIFT 2005

3

2.3

HST FOS (1992)

UZ For was observed by HST with FOS on 11th June 1992 in two consecutive, RAPID mode observations consisting of 925 sp ectra each with 1.64s exp osure times. This data set was originally published in Stockman & Schmidt (1996), but their mid-eclipse times were not quoted. Therefore the HST data products from this observation were downloaded from the HST archive at the MAST. The flux- and wavelengthcalibrated individual sp ectra were extracted and the flux summed-up b etween 1255 and 1518°(far UV) to create a A lightcurve. The far UV part of the sp ectrum was chosen as this seems to have the least contribution from the accretion stream. The end-times for each sp ectra were obtained from the observation header keywords and the group-delay-time subtracted in order to obtain times of start of each exp osure. Two consecutive eclipses were observed and folded and binned into a single eclipse from which measurements were made.

Observations were made in event mode using the SWIFT UV Optical Telescop e (Roming et al 2005) b etween Feb 2 and Feb 6 2005. There were a numb er p ointings, some lasting a few 100 sec and others a few 1000 sec. The U filter (center wavelength 3450°, FWHM 875°) and the V filter were A A used. Light curves were extracted using ap ertures centered on the source (radius 3 ) and also a source free background region with much larger ap erture radius. The light curve was generated by suitably scaling the size of the ap ertures. Two eclipses were observed in full, one of which was simultaneous with the UCTPOL observations.

2.8

SALTICAM 2007

UZ For was observed with SALTICAM (O'Donoghue et al. 2006) on SALT on 12 Novemb er 2007. SALTICAM was in slot-mode configuration, allowing a time resolution of 1s with no deadtime. The data were reduced using the SALT slottools data reduction package (Crawford et al. 2010). One eclipse of high time resolution and signal to noise was observed from which measurements were made.

2.9 2.4 EUVE 1993 and 1995

BVIT 2009

UZ For was observed with EUVE on the 18th Novemb er 1993 and on the 15th Jan 1995 for 102ks and 76ks resp ectively. These data were retrieved from the STScI archive and reduced following the recip e from http://archive.stsci.edu/euve/. Lightcurves were produced using the xray.xtiming package in IRAF with a 1s time resolution. For each observation, multiple eclipses were covered which were folded and binned into two single eclipses from which measurements were made.

BVIT (Berkeley Visible Imaging Tub e: Siegmund et al. 2008) is a visible photon counting detector designed as a guest facility on the SALT to provide very high time resolution (<25 nanoseconds) and high signal to noise, full imaging photometry. UZ For was observed during a BVIT commissioning run on 25th January 2009 simultaneous with the HIPPO on the 1.9m telescop e of the South African Astronomical Observatory. The data were extracted making use of the IDL data reduction software develop ed by the instrument team and binned into 0.5s bins. One eclipse of high time resolution and s/n was observed from which measurements were made.

2.5

UCTPOL 2002 and 2005 2.10 HIPPO January 2009, September 2010, October 2010 and November 2010

One unfiltered and two BG39 filtered eclipses were obtained in 2002 with the University of Cap e Town photo-p olarimeter (UCTPOL) at 10 second time resolution. Two eclipse times were extracted: one from the unfiltered and the second from the folded BG39 filtered eclipses. Three unfiltered eclipses were obtained in 2005 at 10 and 1 second time resolution. Two eclipse times were extracted. On b oth occasions, simultaneous linear and circular p olarimetric observations were also made and reduced as in Cropp er (1985).

Unfiltered photo-p olarimetric observations were made with the HIPPO (HI sp eed Photo-POlarimeter: Potter et al. 2010) on four separate occasions and reduced as in Potter et al. (2010). The single eclipse in January 2009 was observed simultaneously with the BVIT observations. Multiple eclipses were observed on the other occasions which were folded and binned from which measurements were made.

2.6

XMMOM 2002 3 3.1 RESULTS The eclipses

Observations were made in fast-mode using the XMMNewton Optical Monitor (Mason et al 2001) b etween Aug 7 and Aug 8 2002; two orbits after UCTPOL observations. The UVW1 filter was used (center wavelength 2910 °, FWHM A 500°) and the data were reduced using omfchain running A under SAS v9.0. Although three consecutive eclipses were observed, two had incomplete coverage. Nevertheless, up on folding and binning, a high signal-to-noise eclipse profile was obtained and eclipse measurements taken.
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A sample of our new and archival eclipse data is shown in Fig 1 phased on our new ephemeris (see b elow and table 2). The eclipse profiles are of varying quality and at multiple wavelengths. All of the eclipses can b e understood in the framework of the standard p olar model and from the general literature on UZ For (see section 1). UZ For undergoes


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Figure 1. A sample of our new eclipse observations phased on our new ephemeris (section 4.2) Vertical grey bars indicate ingress and egress of the main accretion spot. Solid vertical bars indicate times of white dwarf ingress and egress assuming a duration of 40s.

p eriods of either one (e.g. Bailey & Cropp er 1991) or twop ole (e.g. Perryman et al. 2001) accretion states, which has b een most clearly captured by our SALTICAM (2007) and BVIT (2009) observations resp ectively. During b oth accretion states the rapid fall and rise in flux at phases -0.031

and 0.031 corresp ond to the ingress and egress of the main accretion region. During the two-p ole accretion state a second accretion region is additionally present, seen as the fall and rise in flux at phases -0.027 and 0.027. The remaining gradual fall and rise during phases -0.031 to -0.025
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Possible detection of two giant extrasolar planets orbiting the eclipsing polar UZ Fornacis

5

Table 1. Mid-eclipse times of the main accretion spot of UZ For. BJDT D B is the Barycentric Julian Date in the barycentric dynamical time system. Times have also been barycentrically corrected. 1 de Bruijne et al. (2002), 2 Perryman et al. (2001), 3 Imamura & SteimanCameron (1998), 4 Warren et al. (1995), 5 Ramsay (1994), 6 Bailey & Cropper (1991), 7 Allen et al. (1989), 8 Ferrario (1989), 9 Beuermann et al. (1988), 10 Osborne et al (1988).

Cycle 23913 23595 23277 16526 16526 11518 34 23 0 -11.0 10362 10365 10376 18023 21360 21361 21429 38508 38543 41537 41538 41560 41571 41790 46605 46988 52587 56024 63462 63474 63476 67915 71248 71451 71452 71786 71821 71857 71868 71889 79193 89206

BJD

T DB

+2400000

BJD 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

T DB

Width(sec) 468(2) 468(2) 467(2) 469(2) 469(1) 468(1) 469(1) 469(2) 469(3) 467(4) 479(8) 469(3) 469(6) 467(2) 468(2) 468(2) 468(2)

Observatory/Instrument 1.9m/HIPPO 1.9m/HIPPO 1.9m/HIPPO 1.9m/HIPPO SALT/BVIT SALT/SALTICAM 1.9m/UCTPOL 1.9m/UCTPOL 1.9m/UCTPOL SWIFT X M M OM 1.9m/UCTPOL 1.9m/UCTPOL WHT/SCAM 20001 WHT/SCAM 19992 WHT/SCAM 19992 WHT/SCAM 19992 CTIO 1m/Photometer3 CTIO 1m/Photometer3 CTIO 1m/Photometer3 CTIO 1m/Photometer3 CTIO 1m/Photometer3 CTIO 1m/Photometer3 EU V E EU V E E U V E4 HST ROSAT5 AAT6 AAT6 AAT6 2.3m Steward Obs.7,5 AAT8 AAT8 AAT8 ESO/MPI 2.2m9 ESO/MPI 2.2m9 ESO/MPI 2.2m9 ESO/MPI 2.2m9 ESO/MPI 2.2m9 EXOSAT10 EXOSAT10

-

55506. 55478. 55450. 54857. 54857. 54417. 53408. 53407. 53405. 53404. 52494. 52494. 52493. 51821. 51528. 51528. 51522. 50021. 50018. 49755. 49755. 49753. 49752. 49733. 49310. 49276. 48784. 48482. 47829. 47828. 47827. 47437. 47145. 47127. 47127. 47097. 47094. 47091. 47090. 47088. 46446. 45567.

42703435 48583116 54462082 36480850 36480517 33472170 28808581 32157438 30066303 33404192 83919610 57562568 60905802 70239393 49543399 40757990 43272958 779388 704108 634978 547148 614028 647568 40501704 33259382 680055 72141928 72808573 18486375 130520 954780 919920 064339 227739 139439 792559 717359 554239 587789 742549 973809 177597

00001 00001 00001 00001 0000086 0000086 0000086 00001 000035 00006 000087 000035 00007 00001 00002 00002 00002 00005 00005 00005 00005 00005 00005 00004 00003 00004 00003 0001 00003 00003 00003 00003 0002 0002 0002 0002 0002 0002 0002 0002 00016 00016

467(4) 471(4) 463(4) 477(5)

466.5(2.5)

and 0.025 to 0.031 is attributed to the ingress and egress resp ectively of the white dwarf photosphere and takes ab out 40s each.

3.2

The O-C

In table 1 we list all of our new mid-eclipse times as well as those we have measured from archival data or extracted from the literature. The orbital p eriod calculation of Perryman et al. (2001) was used to calculate the cycle numb er for each eclipse. The p eriod is sufficiently accurate to unambiguously assign cycle counts to the entire 27 years of eclipses. The eclipse observed in our 2005 UCTPOL photometry was used
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to define the ep och (cycle 0). This p eriod and ep och were next used as the starting p oint to p erform a least-square quadratic fit with appropriate weighting set by the eclipse error measurements. The resulting fit gives a reduced 2 > 95 with p eak-to-p eak residuals of 60 - 80s. Note that we have not included the eclipses of Dai et al. (2010) in our analysis as their O-Cs are over 300s compared to our quadratic ephemeris. We b elieve either their measurement and/or time standard conversion to b e in error. It is partures p ears to from a d immediately apparent that there are significant defrom the quadratic ephemeris with a trend that apb e p eriodic (see top plot of fig 2 for residuals, alb eit ifferent quadratic fit: see b elow).


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main accretion solution (Fig 3) pace of possible M3,4,f nc is the spot of UZ For and corresponding planet model parameters. Ephemeris paand are rounded off to the 1 sigma errors. The planet parameter errors were solutions and not the smaller 1 sigma errors of any one fit. Minimum planet mass function. The combined mass of the primary and secondary stars are

Table 2. Mid-eclipse ephemerides of the rameters correspond to the representative calculated using the range in parameter s masses are listed assuming coplanearity. assumed to be 0.84M . Quadratic term:

T0 = 2453405.30086(3) d Pbin = 0.087865425(2) d A = -7(2)10-14 3 = (E+T3 )f3 T3 = 60383(416) (binary cycle) f3 = 0.000098(3) (cycles/binary cycle) 3 = 0.85(5) Kbin,(3) = 0.00025(2) d e = 0.04(5) 4 = (E+T4 )f4 T4 = 4833(215) (binary cycle) f4 = 0.000288(2) (cycles/binary cycle) 4 = 1.20(6) Kbin,(4) = 0.000141(6) d e = 0.05(5)

Planet Parameters: M3,f nc = 2.9(1.1)10-7 M M3,J up = 6.3(1.5) P3 = 16(3) years a3 = 5.9(1.4) AU a1,2 = 0.042(1) AU M4,f nc = 5.3(5) 10-7 M M4,J up = 7.7(1.2) P4 = 5.25(25) years a4 = 2.8(5) AU a1,2 = 0.025(1) AU


1st Elliptical term:

2nd Elliptical term:



Figure 2. The O-C after successive subtraction of the three terms comprising our new eclipse ephemeris. Top: O-C after subtraction of the quadratic term with the first elliptical term overplotted (dashed curve). Middle: O-C after subtraction of the first elliptical term with the second elliptical term overplotted (dashed curve). Bottom: The final O-C residuals after subtraction of the second elliptical term. Diamonds are our new data or data that we have reduced from archives. Crosses are eclipse times from the literature and converted (by us) to BJDT D B .

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Possible detection of two giant extrasolar planets orbiting the eclipsing polar UZ Fornacis
We next investigated the solutions resulting from models consisting of a quadratic plus an elliptical fit to the eclipse times. A b est reduced 2 of 6.2 was achieved. An F-test shows that it is the b etter model (compared to the quadratic ephemeris) with a confidence of > 99.999% even though the elliptical term adds 5 more parameters to the model. However significant residuals still remain, (10s) for some of the eclipse times (not shown). We next attempted a simultaneous quadratic plus two ellipticals fit to the eclipse times. The second elliptical term adds a further five parameters to the model, giving 13 in total. Therefore, given the large numb er of parameters, a grid of starting parameters for minimisation was required in order to explore the resulting degeneracy in the solutions. Approximately 107 minimisations were calculated. During minimisation all 13 parameters were free to vary. Predictably, the results have b etter reduced 2 but with degeneracy in many of the parameters. Formally the F-test confirms that adding a second elliptical term is the b etter model with a high level of confidence (> 99.9999%) for the solutions with reduced 2 = 1.0. Other solutions with reduced 2 = 4.0 and 3.0 are also significantly b etter with a 98% and 99.9995% confidence resp ectively. We explore the degeneracy in the multi-dimensional 2 space in section 4.2.

7

Figure 3. The reduced 2 parameter space for the two elliptical periods. Black crosses, dark grey triangles and light grey diamonds are the solutions with reduced 2 < 1.0, 1.0 < 2 < 2.5 and 1.0 < 2 < 2.5 respectively. The diamonds have the additional constraint of both eccentricities < 0.1. The large black cross represents the location of the solution shown in Fig 2 with parameters listed in table 2. From left to right, the diagonal lines represent contours of constant period ratios of 3.1, 3.0 and 2.9. Typical one sigma errors are shown in the top left and bottom right corners.

4 4.1

DISCUSSION The O-C

Our results suggest that the deviations in the eclipse O-C are b est describ ed by the combination of a quadratic term plus two elliptical terms. This is highly suggestive of b oth secular and cyclic p eriod variations. Period changes in binary systems are generally understood to b e due to gravitational radiation, magnetic braking, solar-typ e magnetic cycles in the secondary star (Applegate's mechanism) and/or the presence of a third b ody in an orbit around the binary. Applegate's mechanism and/or the presence of a third b ody would b e more consistent with cyclic variability. The latter would produce strictly p eriodic cycles while nonstrictly p eriodic cycles would b e exp ected from the former mechanism. Therefore, we next look at each of these mechanisms in turn.

4.2

Tertiary and quaternary components

We now explore the degeneracy in the multi-dimensional 2 space of the model fits containing one quadratic plus two elliptical terms in the context that the variations are due to the effect of third and fourth b odies in the system. Then the changes in the O-C arise b ecause of the light-time effect caused by the gravitational influence of the additional b odies. As a first step, we plot the distribution of the p eriod of the two elliptical orbits for those solutions which had reduced 2 < 2.5 (Fig 3). The starting grid, for minimisation, had p eriod values b etween 2 and 50 years and Fig 3 shows that the minimised solutions have clustered in the p eriod ranges 13 - 19 and 5 - 5.5 years. All of the solutions with reduced 2 1.0 (2 28,
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shown as the black crosses in Fig 3) show p eriods centered on approximately 5.3 and 15 years, giving a p eriod ratio of Rp 2.8 . The corresp onding predicted eccentricities of these solutions are >> 0.1 for b oth ellipses. We p erformed N-b ody simulations on a sample of these solutions. The Euler method was used with sufficiently small time steps to ensure accurate calculations. We tested the accuracy of our code by first applying it to single elliptical orbits comparable to the innermost high eccentricity orbit. Our code preserves the eccentricity and the semi-ma jor axis to b etter than 10%, and the p eriastron angle to < 0.1 radians over a time p eriod corresp onding to > 105 orbits of the outermost b ody. We then defined orbital solutions that have essentially the same two planet orbital elements to the starting conditions after > 105 orbits of the longer p eriod as stable. As exp ected, we found that they all are very unstable orbits and are therefore unrealistic solutions. We next looked at the solutions with reduced 2 in the range 1.0 < 2 < 2.5, which are shown as the dark grey triangles in Fig 3. They occupy a larger area of the plot which overlaps with the previous solutions. However most of these solutions still require the longer p eriod elliptical to have a large eccentricity (> 0.1 and typically 0.4). Nb ody simulations within this parameter range also revealed unstable orbits. We therefore identified those solutions which had orbital eccentricities < 0.1 for b oth planets and which had stable orbits according to our N-b ody simulations. These are represented as the light grey diamonds in Fig 3 which also overlap with the higher eccentric solutions presented ab ove. However, the b est of these solutions give 2 =58 (28 dof, giving 2 =2.06), which is a significantly p oorer fit com pared to our b est-fit highly eccentric orbital solutions and also gives a formally p oor fit to our data. We note that our models assume the two planets to b e


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co-planar. There may yet b e a set of realistic, more eccentric, solutions if the planets have inclined orbits with resp ect to each other. We have not investigated this additional parameter space as our data set is not of sufficient quality nor quantity to warrant it. Given these caveats, in order to calculate the implied two planet parameters, we selected the b est-fit low eccentric and stable solutions. Additionally we applied p eriod errors that encompass the whole range of solutions in Fig 3. We note that the two planet parameters calculated b elow are not sp ecific to this one b est-fit solution but are representative of all the solutions with reduced 2 < 2.5 shown in Fig 3. The calculations are indep endent of the eccentricities. This particular solution is marked as the large black cross in Fig 3, the two elliptical parameters are listed in table 2 and overplotted on the O-C in Fig 2. The amplitudes of the oscillations can b e used to calculate the pro jected distances asin(i) from the center of mass of the binary to the center of mass of each of the triple systems (0.042(1) and 0.025(1) AU for the long and short resp ectively). Setting the binary mass to b e 0.7M + 0.14M gives the corresp onding mass functions (f (m3,4 ) = 2.9 â 10-7 M , 5.3 â 10-7 M ). With the binary inclination at i = 80o the resp ective minimum masses for the third and fourth b odies (assuming they are in the plane of the binary) are 0.006(1) M and 0.007(1) M and would therefore qualify as extrasolar giant planets (6.3(1.5)MJ up and 7.7(1.2)MJ up ) for orbital inclinations i3 > 25o , i4 > 32o resp ectively. The quoted errors include the range in p eriods shown in Fig 3 and not the formal one sigma errors of one of the solutions. In addition, the quoted errors include the propagated uncertainties in the inclination and binary mass. These parameters are summarised in table 2. The equation for the times (T ) of mid-eclipse of the main accretion sp ot are then given by: T (B J DT ) = + + T0 + Pbin E + AE Kbin, Kbin,
(3) 2

Figure 4. Solid curve shows the energy required to effect the period change observed in UZ For as a function of assumed shell mass, using Applegate's (1992) mechanism. The two horizontal lines represent the total radiant energy of the secondary (assuming 2880 < Tef f < 3020K) and hence the amount of energy available.

subtraction of the three terms comprising our new eclipse ephemeris with parameters listed in table 2. The top and middle plots show that the two elliptical terms describ e the time of eclipse variations very well. The lower plot shows the final O-C residuals after subtraction of the full ephemeris. Some residuals still remain which could b e reduced further if larger eccentricities were p ermitted, particularly for the outer planet. Such orbital solutions may exist, esp ecially given the p ossible indication that the planets could b e locked in a 3:1 ratio. However b etter sampled observations are required to further constrain the solutions. 4.3 The secular variability

DB

(1 - e23) ) ( sin(3 - 3 ) (1 + e(3) cos(3 ) sin(4 - 4 ) (1 - e (1 + e
(4) 2 (4)

)

(4)

cos(4 )

T0 , Pbin , A, E are the time of ep och, the binary orbital p eriod (days), the quadratic parameter (related to the rate of p eriod decrease by Pbin = 2A/Pbin ) and the binary cycle numb er which comprise the quadratic term of the ephemeris. In the context that the two elliptical terms are due to third and fourth b odies in the system, then the parameters of the elliptical terms are: Kbin,(3,4) are the amplitudes of the eclipse time variations as a result of the light-travel-time effect of the two b odies, (3,4) are the true anomalies of the two b odies, which progresses through 2 over the orbital p eriods (P(3,4) ) and are functions of E , the times of the p eriastron passages (T(3,4) ) and the orbital frequencies (in cycles p er binary orbital cycle) of the two b odies (f3,4 ). e(3,4) are the eccentricities and (3,4) are the longitudes of p eriastron passage measured from the ascending node in the plane of the sky. Similar elliptical variations have b een seen in NN Ser and DP Leo (Beuermann et al 2010a,b). Fig 2 shows the fit and the O-C residuals after successive

The secular variability amounts to a decrease in the orbital p eriod of Pbin = -1.56(5) 10-12 s s-1 . Of the 1416 solutions that comprise the `chosen' parameter space (light grey area in Fig 3) only one solution showed a Pbin consistent with 0. It has a reduced 2 = 2.6. The rest predict a minimum in the p eriod decrease rate of Pbin = -1.0 10-12 s s-1 . Formally an F-test shows that adding the quadratic parameter to the ephemeris is the b etter model with a 99.99% level of confidence (2 = 109, 86 for 30, 29 degrees of freedom for the two models resp ectively). Similar levels of p eriod decrease has b een detected in other similar short p eriod binaries e.g. DP Leo (Schwop e et al. 2002), NN Ser (Brinkworth et al. 2006) and HU Aqr (Schwarz et al. 2009) for which gravitational radiation and magnetic braking have b een shown to b e either insufficient or problematic in the framework of the standard CV evolutionary model. Future observations are needed to show if these variations are indeed secular or p eriodic. 4.4 Applegate mechanism that solar-like magnetic cycles the secondary, thus redistributwithin the star, changing its to a change in its quadrup ole

Applegate (1992) prop osed would drive shap e changes in ing the angular momentum oblateness. This then leads

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Possible detection of two giant extrasolar planets orbiting the eclipsing polar UZ Fornacis
moment and consequently a change in orbital p eriod at the exp ense of some energy. This has b een the preferred mechanism to explain such cyclic variations in CVs and other long p eriod close binaries (Algol, RS CVn and W UMa stars). Following the prescription of Applegate (1992), the energy required to generate a p eriod change is: E = dr J + J 2 2Ief f

9

The initial differential rotation dr J is set to zero in order to calculate the minimum energy required. The effective moment of inertia Ief f = IS I /(IS + I ) is calculated by assuming the star is separated into a shell IS and a core I . We exp erimented with a range of shell masses. J is the change in angular momentum and is given by J = -GM R
2

a R

2

P 6

We used the secondary star mass from Bailey & Cropp er (1991) namely M = 0.14M and the corresp onding radius R = 0.177R following Patterson (1984). a = 5.5 â 108 m is the binary separation using a = 3.53 â 1010 (M1 /M )1/3 (1 + 2/3 q )1/3 Porb (h) (Warner 1995, equation 2.1b). P can b e obtained from equation (38) of Applegate (1992) relating the amplitude of orbital p eriod modulation and the amplitude of the O-C oscillation: P O-C = 2 P Pmod where P and Pmod are the orbital and modulation p eriod resp ectively (using P3 listed in table 2). The solid curve in Fig. 4 shows the minimum energy required to drive the maximum observed p eriod change in UZ For, as a function of assumed secondary shell mass. The two horizontal lines represent the total radiant energy of the secondary L = 4 R2 T 4 over the modulation p eriod, assuming 2880 < Tef f < 3020K, which app ears to b e more than sufficient to drive the Applegate mechanism. The situation is not so clear cut if one instead integrates over shells and allows for the quadrup ole moment of the core (using the calculations of Brinkworth et al. 2006). This raises the minimum energy by ab out an order of magnitude, which makes it comparable, at minimum, to the energy of the star. We should add that Lanza et al. (1998) prop ose a prescription that is more energy efficient than the Applegate mechanism, p erhaps by a factor of two. Therefore, with further refinements, magnetic fields may yet b e shown to able to drive the p eriod changes seen here.

4.5

Spot motion

The eclipse times are derived from the observed ingress and egress times of the accretion sp ot and not the center of the white dwarf itself. Therefore the observed O-Cs could b e as a result of motion of the sp ot on the white dwarf. In addition, the egress and ingress of the white dwarf photosphere has b een observed to take ab out 40 seconds (seen unambiguously in the low state observations of Bailey & Cropp er (1991) and confirmed in our low state SALTICAM 2007 observations) and therefore could accommodate a 40 - 60s of sp ot motion.
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To assess this p ossibility we investigated the actual morphologies of the eclipse profiles in order to measure the relative phases of the white dwarf photosphere ingresses and egresses to that of the main accretion sp ot. Accordingly, we display a sample of our eclipse observations in Fig. 1 phase folded and binned on our new ephemeris. The upp er two eclipse profiles are the HIPPO 2010 and the BVIT 2009 observations resp ectively. These corresp ond to the two newest data p oints in Fig. 2 which show a O-C shift of 30s with resp ect to each other on the quadratic subtracted O-C plot (upp er plot Fig. 2). Therefore if the sp ot did indeed change locations, on the surface of the white dwarf, b etween these two observations then we should observe a corresp onding relative phase shift b etween sp ot ingress/egress to that of the white dwarf photosphere ingress/egress. However one can see that the b eginning of the white dwarf photosphere egress (solid vertical line at phase 0.026) is consistently 40s (0.005 phase) ahead of the sp ot egress (vertical grey bars) b etween these two observations. Thus, one would have exp ected the relative time difference b etween the white dwarf photosphere and sp ot to b e shorter by 30s b etween the two observations and not approximately equal as observed. Therefore we conclude that the sp ot has not moved on the surface of the white dwarf during these observations, at least within our measurable errors of ab out 1-5s. The same relative phase difference (sp ot, white dwarf photosphere) is also apparent in the other eclipse profiles in which the sp ot and white dwarf photosphere are resolved (see the next five plots in Fig. 1 corresp onding to the SALTICAM 2007, UCTPOL 2005, SWIFT 2002, UCTPOL 2002 and SCAM 1999 observations). Furthermore, the same unchanging relative time differences are seen in the ingresses, although the white dwarf photosphere ingress emission may b e complicated by an additional contribution from the accretion stream. The stream is not visible during the white dwarf photosphere egress, which can b e understood from simple eclipse geometrical arguments, and confirmed through HST UV sp ectroscopy (Stockman & Schmidt 1996). We note, however, that the longitude of the accretion sp ot should b e exp ected to change during different accretion states. For example, Schwop e et al. (2001) calculated a change in sp ot longitude of 10o b etween high and intermediate accretion states in the eclipsing p olar HU Aqr. This would translate to ab out a shift of 2 - 3s in the O-C values (Schwarz et al. 2009) which therefore cannot account for the observed O-C values. This implies that if there was a similar sp ot motion in UZ For during different accretion states, it cannot account for the large shift seen in the measured O-C values. Additionally there was not any measurable movement of the sp ot in latitude during our observations. This is apparent from table 1 where the eclipse width measurements agree within errors: a change in sp ot latitude would have resulted in a corresp onding change in eclipse length.

5

SUMMARY AND CONCLUSION

We have detected departures in the eclipse times of UZ For from a simple quadratic ephemeris of up to 60s. The departures are suggestive of two p eriodicities of 16 and 5.25 years. The two favoured mechanisms to drive the p eriodic-


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Stephen B. Potter et al.
REFERENCES
Alexander M. E., Chau W. Y., & Henriksen R. N. 1976, ApJ, 204, 879 Allen R. G., Berriman G., Smith P. S. & Schmidt G. D., 1989, 347, 426 Applegate J. H., 1992, ApJ, 385, 621 Bailey J. A. & Cropper M., 1991, MNRAS, 253, 27 Brinkworth C. S., Marsh T. R., Dhillon V. S., & Knigge C., 2006, MNRAS, 365, 287 Berriman G. & Smith P. S., 1988, ApJ, 329, L97 Beuermann K. et al. 2010a, A&A, 521, L60 Beuermann K. et al. 2010b, A&A, 526, A53 Beuermann K., Thomas H.-C. & Schwope A. D., 1988, A&A, 195, L15 de Bruijne J. H. J., Reynolds A. P., Perryman M. A. C., Favata F. & Peacock A., 2002, SPIE, Optical Engineering 41(06), 1158 Campbell R. K., Harrison T. E., Mason E, Howell S. & Schwope A. D., 2008, ApJ, 678, 1304 Crawford S. M., et al. 2010, spie, 7737, 54 Cropper M. S., 1985, MNRAS, 212, 709 Cropper M. S., 1990, Space Sci. Rev. 54, 195 Dai Z. -B., Qian S.-B., Fernandez La jus E. & Baume G. L., 2010, arXiv:1007.4070v1 Eastman J., Siverd R. & Scott Gaudi B., 2010, arXiv:1005.4415v2 Ferrario L., Wickramasinghe Dayal T., Bailey J. A., Tuohy I. R. & Hough J. H., 1989, ApJ, 337, 832 Giommi P., Angelini L., Osborne J., Stella L., Tagliaferri G., Beuermann K., & Thomas H.-C., 1987, IAU Circ. No. 4486 Holman M. J. & Wiegert P. A. 1999, AJ, 117, 621 Imamura J. N. & Steiman-Cameron T. Y., 1998, ApJ, 501, 830 Imamura J. N., Steiman-Cameron T. Y. & Wolff M. T., 2000, PASP, 112, 18 Lanza A. F., Rodon´ M., Rosner R., 1998, MNRAS, 296, 893 o Mason K. O., et al 2001, A&A, 365, L36 O'Donoghue D., et al., 2006, MNRAS, 372, 151 Osborne J.P., Giommi P., Angelini L., Tagliaferri G. & Stella L. 1988, ApJ, L45 Parsons S. G. et al., 2010, MNRAS, 407, 2362 Patterson J., 1984, ApJS, 54, 443 Patterson J., 1994, PASP, 106, 209 Perets H. B. 2010, arZiv:1001.0581 Perryman M. A. C. et al. 2001, MNRAS, 324, 899 Potter S. B. et al 2010, MNRAS, 402, 1161 Qian S. -B., Liao W. -P., Zhu L.-Y. & Dai Z.-B. 2010, ApJ, 708, L66 Qian S. -B. et al 2011, MNRAS, in press Ramsay G., 1994, IBVS, No. 4075 Rappaport S., Verbunt F. & Joss P. C., 1983, ApJ, 275, 731 Roming P. W. A., 2005, SSRv, 120, 95 Ritter H., Kolb U., 2003, A&A, 404, 301 (update RKcat7.9) Schwarz R. et al. 2009, A&A, 496, 833 Siegmund O. H. W., McPhate J., Tremsin A., Vallerga J. V., Welsh B. Y. & Wheatley J. M., 2008, AIPC, 984, 103 Schwarz R., et al. 2009, A&A, 496, 833 Schwope A. D., Schwarz R., Sirk M. & Howell S. B., 2001, A&A, 375, 419 Schwope A. D., Hambaryan V., Schwarz R., Kanbach G. & G¨nsicke B. T., 2002, A&A, 392, 541 a Stockman H. S. & Schmidt G. D., 1996, ApJ, 468, 883 Warner B. 1995, Cataclysmic Variable Stars, Cambridge Astrophysics Series 28, Cambridge University Press Warren J. K., Sirk M. M. & Vallerga J. V., 1995, 445, 909

ities are either two giant extrasolar planets as companions to the binary or a magnetic cycle mechanism (e.g. Applegate's mechanism) of the secondary star. However, Applegate's mechanism would require the entire radiant energy output of the secondary and therefore would seem to b e the least likely of the two, barring any further refinements in the effect of magnetic fields (e.g. Lanza 1998). A two planet model is also problematic given the quality of the data in that a high eccentric orbit, for at least one of the planets, seems to b e required to fully capture all of the eclipse times. If it can b e confirmed that the residuals are due to a third and a fourth b ody, then the planets either formed in a pre-common envelop e circumbinary protoplanetary disc (first generation) or in a disc that resulted from the common envelop e (CE) phase (second generation: Perets 2010). The separation of the progenitor binary is of the order of a few AU, comparable to that of the planets, which implies that only second generation planets could have formed at the orbits suggested here. However, Beuermann et al (2010a) suggested for the planets around NN Ser, a slowly expanding CE could provide the dynamical force to drag inwards planets formed further out, which would have otherwise b een lost to the system due to the decrease in mass of the central binary (Alexander et al. 1976). In either case, we note that the semi-ma jor axis of even the shortest p eriod ob ject p oses no problem for orbit stability (Holman & Wiegert 1999). It is intriguing that Qian et al (2011) prop ose a very similar two elliptical model fit for the p olar HU Aqr, also using eclipse timing results. In particular they also find that the larger ellipse requires a high eccentricity (0.51) to correctly capture all of the data. Therefore, their two planet model for HU Aqr seems to have a similar problem with orbit instabilities that we have found for UZ For. As yet there is insufficient data on UZ For to identify conclusively the mechanism resp onsible for the p eriodic changes in its eclipse times, and indeed more than one mechanism could b e present. Further good signal/noise, high time resolved observations of UZ For and other similarly eclipsing systems are encouraged.

6

ACKNOWLEDGMENTS

We thank for referee for an insightful rep ort that has significantly improved the pap er. This material is based up on work supp orted financially by the National Research Foundation. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and therefore the NRF does not accept any liability in regard thereto. Some of the observations rep orted in this pap er were obtained with the Southern African Large Telescop e (SALT). Some of the data presented in this pap er were obtained from the Multi-mission Archive at the Space Telescop e Science Institute (MAST). STScI is op erated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Supp ort for MAST for nonHST data is provided by the NASA Office of Space Science via grant NAG5-7584 and by other grants and contracts. We would also like to thank Drs. Jean Dupuis, Phil Hodge and Damian J. Christian for their invaluable help when reducing EUVE and HST archival data.

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