## Discovery of Orbital Dips and Superhumps in the Optical Counterpart of the X-Ray Transient GRO J0422+32 (=V518 Per)

(T. Kato, S. Mineshige, R. Hirata 1995, PASJ 47, 31)

## Abstract

We report on the first detection of a period of 0.21211 +/- 0.00002 d (=5.0906 +/- 0.0005 hr) during decline, and a significantly different period of 0.2157 +/- 0.0010 d (=5.18 +/- 0.02 hr) during outburst in a newly discovered ultrasoft X-ray transient GRO J0422+32. We interpret these as being the orbital and superhump periods; using the relation between the mass ratio of the binary and the superhump period excess, we succeeded for the first time to estimate the mass ratio of the underlying binary of GRO J0422+32 as being between 5.4 and 20.5, which corresponds to the mass of a compact object between 3.0 and 11.5 solar masses with the assumption of a Roche lobe-filling main-sequence secondary. This fact strongly supports the idea that all ultrasoft X-ray transients contain black holes. The new findings that superhumps appeared only in the X-ray minimum (~100 days after the peak) suggests that it takes a longer time before superhumps appear in X-ray transients than in cataclysmic variables (a few days after the peak). A possible scenario to produce peculiar optical and X-ray light curves of ultrasoft X-ray transients is briefly discussed in connection to the tidal instability of the accretion disk.

## 1. Introduction

Besides popular black-hole candiates like Cyg X-1, there have recently arisen more potential black-hole candidates, in the so-called X-ray transients (X-ray novae). X-ray transients are transient sources which have a particularly large X-ray-to-optical flux ratio Lx/Lopt, and outbursts of X-ray transients are widely believed to represent intermittent mass-accreting processes to compact objects in close binaries containing either neutron stars or black holes (Priedhorsky, Holt 1987; Tanaka 1989, 1992).

X-ray transients have generally been classified into two classes, "hard" and "soft", based on their X-ray spectra (Cominsky et al. 1978; White et al. 1984). Hard X-ray transients are high-mass X-ray binaries containing neutron stars. Soft X-ray transients are usually subdivided into two classes: (real) soft X-ray transients (which seem to contain neutron stars), such as Aql X-1 and Cen X-4, and the so-called ultrasoft X-ray transients (hereafter called USXTs).

USXTs are characterized by: (1) the deficiency of a black-body spectral component with kT = 2 keV, usually observed in X-ray binaries containing neutron stars; (2) the absence of periodic pulses due to the rotation of magnetized neutron stars; and (3) the presence of a high-energy (above 100 keV) tail, which is usually absent from X-ray binaries containing neutron stars (e.g. Tanaka 1992).

These features have come to be understood in the scheme that USXTs phenomena do not originate from accretion to neutron stars, but to black holes (Tanaka 1989, 1992). The absence of a boundary layer of the accretion disk with the surface of the neutron star would explain the deficiency of a black-body component of the X-ray emission (1); the absence of magnetism of the compact object would explain the absence of periodic pulses (2); and the absence of copious soft photons emitted from a solid surface of a neutron star, which may be responsible for effective Compton cooling of the disk material, would explain the high-energy tail (3).

Besides these phenomenological features, which support the existence of objects without solid surfaces, there have been great observational advances in determining the mass of the central compact objects. Among previously discovered and well observed USXTs, A0620-00 (V616 Mon), and GS 1124-68 (Nova Mus 1991) have been shown to contain compact objects exceeding 3 solar masses (McClintock, Remillard 1986; Remillard et al. 1992), which is the generally believed to be the upper limit of the masses of stable neutron stars, using dynamical mass estimates from a radial-velocity study of the binary motion. A similar conclusion was derived for another type of transient black-hole candidates, GS 2023+338 = V404 Cyg (Casares et al. 1992), which is sometimes classified as an USXT, though exhibiting only hard spectra.

Another independent method for providing an estimate of the mass of the compact object has been developed using the condition of the tidal instability of the accretion disk caused by the gravitational force of the secondary star (Mineshige et al. 1992). This method has an advantage in that it is unaffected by the binary inclination, which is generally the chief cause of uncertainty in a dynamical mass determination using the radial velocity motion. This method is very useful, especially when companion stars are so faint that binary motion is not detected optically.

The tidal instability is believed to give rise to an eccentric deformation of the accretion disk, which is then observed as flux modulation, called (a href=..DNe/superhump.html>"superhumps" in SU UMa-type cataclysmic variables, another class of interacting close binaries which possess accreting white dwarfs instead of black holes (Warner 1985; Whitehurst 1988; Osaki 1989). In addition to this instability criterion, the precession of eccentric orbits due to the gravitational force of the secondary star is exerted on particles orbiting the accretion disk. The photometric period (the superhump period) represents the synodic period between the orbital rotation of the secondary star and the axis rotation of the accretion disk caused by precession (Osaki 1985). The superhump period is thus a few percent longer than the orbital one; this difference provides another clue for determining the mass of the compact object. The same phenomenon is very likely to be also present in X-ray transients, since the condition for the tidal instability does not depend on the nature of the compact object. These methods have been applied to optical light variations found in two USXTs, GS 2000+25 (Charles et al. 1991) and GS 1124-68 (Bailyn 1992), during optical outbursts associated with X-ray eruptions, and have yielded independent and consistent mass estimates of compact objects; this supports the idea that all of the previously discovered USXTs are the most promising sites of stellar-mass black holes (Mineshige et al. 1992).

## 2. GRO J0422+32 as an Ultrasoft X-ray Transient

The fifth optically identified USXT, GRO J0422+32, was discovered on 1992 August 5, by the X-ray monitor of the GRO (Gamma Ray Observatory) satellite (Paciesas et al. 1992). The new source was subsequently identified with an optical counterpart, which showed a dramatic simultaneous optical flux increase of more than seven magnitudes (Castro-Tirado et al. 1992, 1993).

The source has been reported to have the following characteristics.

(1) In spite of intense X-ray flux reaching 2.9 Crab (40---150 keV) (Panciesas et al. 1992), the optical counterpart was a faint object of V=12.6 mag (Castro-Tirado et al. 1992, 1993). An examination of the Palomar Sky Survey Plate could not reveal any object down to 20th magnitude prior to the outburst (Mueller 1992). This fact precludes the existence of a luminous secondary star like O--B type stars, which are usually associated with hard X-ray transients.

(2) A high-energy tail reaching at least to 600 keV was observed (Harmon et al. 1992; Cameron et al. 1992; Sunyaev et al. 1992; Goldwurm et al. 1992).

(3) No periodic pulses of the sort seen in pulsars have been detected in any energy regions (Cameron et al. 1992).

(4) In the X-ray region, an exponential decay of the X-ray flux with an e-folding time of 40 or 44 days has been observed (Vikhlinin et al. 1992; Harmon, Fishman 1992). Exponential decays with $e$-folding times longer than 30 days are characteristic of black-hole-candidate X-ray transients, and are never observed in those containing neutron stars (Kitamoto et al. 1992).

(5) Emission lines from highly excited ions such as N V, C IV and He II in early ultraviolet spectroscopy using IUE satellite (Shrader et al. 1992) and emission lines from He II and N III in the optical region have been observed (Wagner et al. 1992).

(6) Radio emission similar to that from GS2023+338 was detected (Han et al. 1992).

Since these features share striking similarities with previously discovered USXTs, searches for a black hole in GRO J0422+32 should be fruitful. We therefore embarked on a systematic program of optical photometry, which has yielded evidence for two distinct periodicies. We have interpreted these two periods in terms of a tidal instability and a precessing-disk model, and in the context of this model have determined the underlying mass ratio of the system.

## 3. Optical Observation of GRO J0422+32

The observations were performed with a CCD camera (Thomson TH 7882 chip, 576 x 384 pixels) attached to the 0.6-m reflector at Ouda Station, Kyoto University during five consecutive nights from 1992 November 21 to 25, and 36 nights between 1992 November 29 and 1993 April 7. The on-chip summation of 2 x 2 pixels was adopted in order to minimize the readout time and noise. The interference filter, which is designed to reproduce the Johnson V-band (Ohtani et al. 1992), was adopted, and the exposure was set to between 30 and 300 s, depending the brightness of the object and the sky background. The readout dead times between exposures were 8 to 10 s, and the bias frames for zero corrections were taken every five to ten frames. Some additional V-band observations were also made with the CCD camera (Hamamatsu, 1024 x 1024 pixels) attached to the 0.6-m telescope at Ogawa Observatory, Nagano Japan. The total number of useful frames was 5636.

A summary of the observation is listed in table 1. The CCD frames were, after standard de-biasing and flat-fielding, analyzed using an automatic microcomupter-based aperture photometry package developed by the author (T.K.). The magnitudes of the object were determined relatively using two local standard stars [C1: 04h 21m 37s.7 +32o 53' 41" (J2000.0) V=13.9 mag and C2: 04h 21m 40s.0 +32o 55' 43" (J2000.0) V=14.4 mag; positions and magnitudes are taken from the Guide Star Catalog] in the same field. During the course of the observations we independently measured the magnitude of C1 to be V=14.25 by absolute photometry using Johnson standard stars (Landolt 1983). We thusdopted the value of V=14.25 in the present study. The aperture size was 18" in diameter and the local sky levels were determined from pixels located between at 24" and 48" from the individual objects. The constancy of the comparisons was confirmed to be within 0.01 mag through the comparisons of C1, C2, and brighter standards in the same field. Heliocentric corrections were made for all of the observed times before an analysis.

## 4. Photometric Behavior of GRO J0422+32 during an Outburst

### 4.1. Detection of a 0.2157-Day Periodicity in 1992 November

The resulting light curve of the observations since 1992 November is displayed in figure 1. The object showed a gradual decline by the end of 1993 March (about 210 days after the outburst). Superimposed with this fade, recurring hump-like features with an amplitude of 0.10 mag were evident in November runs (figure 2). Secondary maxima were not detected. A period analysis using the Phase Dispersion Minimization (PDM) Method (Stellingwerf 1978) implemented in the IRAF package (IRAF is distributed by the National Optical Astronomy Observatories, U.S.A.) after removing the trends of steady decline has revealed a firm period of 0.2157 +/- 0.0010 d (=5.18 +/- 0.02 hr). The variance statistic (theta) of Stellingwerf (1978) was calculated against trial periods (figure 3). A sharp minimum at a frequency of 4.64 day^-1 represents the detected period.

Here, the errors in the period were derived as follows: We first identified the observed time of each maximum by an eye-estimate, and then fit it by a linear least-squares method with respect to equi-distant time sequences with the time interval being a fitting parameter. The derived period is in good agreement with the above-mentioned value. We were thus able to calculate the deviation in the observed time from the expected time for each maximum, finally deriving a one-sigma error for the period. We repeated the same procedure for the minimum of the light curves, finding consistent results.

The folded light curve of 1992 November, that was averaged over every 0.02 phase bin, is shown in figure 4. The phase was calculated using the best period of 0.2157 d; since the phase zero can be taken arbitrarily, we defined the zero phase to be at HJD 2448948.997. The error bar represents the standard error (expected 1-sigma error) in each phase bin. A light variation with an amplitude of 0.10 mag, showing a steeper rise and a slower decline, is clearly seen. This is quite reminiscent of superhumps in SU UMa stars (Warner 1985). The period and the amplitude together with the light-curve profiles are strikingly distinct from those previously reported by Chevalier and Ilovaisky (1992); that is, they show rather smooth light fluctuations with low amplitudes of 0.04 mag. These hump features must have developed fully after their observations in 1992 September and October. The light curve of GRO J0422+32 during this stage resembles those of dwarf novae more than those of X-ray binaries.

### 4.2. ~ Detection of a 0.21211-Day Periodicity and Dips in 1992 December --- 1993 January

GRO J0422+32, however, exhibited a distinct type of light variation during 1992 December (figure 5). (Note that the February data are not included because of poor statistics.) The light curve is charaterized by a roughly sinusoidal variation (averaged amplitude, 0.14 mag) and dips. By applying a least-squares fit to the epochs of the sinusoidal variation and dips, they are found to be excellently expressed by a single period of 0.21211 +/- 0.00002 d (=5.0906 +/- 0.0005 hr) from 1992 December through 1993 February. The variance statistic (theta) of Stellingwerf (1978) was calculated against trial periods (figure 6). A sharp minimum at a frequency of 4.71 day^-1 represents the detected period. The period is in excellent agreement with that reported by Chevalier and Ilovaisky (1993) for their 1993 January observations. This fact indicates that the stability of the periodicity lasted for at least 64 days since 1992 December 18.

The difference in dominant periods between 1992 November and December, is not only already significant from the estimated errors for the periods, but was also confirmed by comparing the expected maxima calculated from the better-defined period (i.e. 0.21211 d period in December and January) with the observed values in November. The expected times of the maxima extrapolated from the light curves in December using the 0.21211-day period are displayed by arrows in figure 2. Large differences in the expected phases from the maximum phases observed in November (~0.5) preclude the same origin as that of the humps observed in 1992 November. [The error in the derived period (delta P) does not affect this conclusion, since it was only delta P/P ~ 10^-4, so that the uncertainty in the phase amounts to 30(d)/P(d) x (delta P/P) ~ 1.5x10^-2 within one month.]

Concerning the profile of the light variation, our observations indicate the presence of recurring dips in addition to the findings by Chevalier and Ilovaisky (1993). The dips occur at an averaged phase of 0.36 after the minima of the sinusoidal variation, and have a typical duration of one hour and an amplitude of 0.1 mag; however, the amplitude increased from 0.05 mag on January 1.52 UT to 0.17 mag on January 12.58 UT.

A folded light curve for 1992 December and 1993 January is shown in figure 7. The phase was calculated using the best period of 0.21211 day; we took the zero-phase to be at HJD 2449000.076. The error bar represents the standard error in each phase bin. Although indiviudal dip features are somewhat smoothed in this folded light curve, a general light variation with an averaged amplitude of 0.14 mag is clearly seen. The light maximum is divided into two peaks by an averaged phase of 0.9. This profile is strikingly different from singly peaked hump features in previously observed USXTs (GS 2000+25: Charles et al. 1991; GS 1124-68: Bailyn 1992) during outbursts, and more resembles those of X-ray binaries in quiescence.

## 5. Discussion

### 5.1. The Dips and the Orbital Period

By analogy with X-ray dips in some X-ray binaries, it would be natural to believe that the period of the dips reflects the orbital motion. Furthermore, the sharp profile of the dips suggest that part of the accretion disk is partially eclipsed by the secondary, or the X-ray-irradiated secondary by the accretion disk. The fluctuations in the phases and the amplitudes of the dips can be understood, since the outermost region of the disk has a rather rugged, unstable structure due to substantial tidal effects and interactions between disk material and an incoming gas stream from the secondary (e.g., Hirose et al. 1991). The two possibilities would be settled by a radial-velocity study of the secondary during quiescence. The appearance of the dips in almost every cycle of sinusoidal variations precludes the possibility of a double period for the orbital period. It is usually thought that X-ray binaries in quiescence show ellipsoidal variations caused by tidal distortion of the secondary, and thus the light curves contain two minima of nearly equal amplitude. This, however, depends on the observed wavelengths. McClintock and Remillard (1986), for example, have reported a rather sharp primary minimum and broader and shallower secondary minimum for A0620-00 observed at short (550 nm) wavelength. At longer wavelength, in contrast, these two features become similar and produce the well-known "double wave" light curve. We thus propose that the orbital period of this binary system is 0.21211 +/- 0.00002 d, which is the shortest known period among USXTs. The proposed orbital period shows a significant difference from the photometric periodicity of 0.2157 d detected in the November observations. The latter is 1.7 +/- 0.5% longer than the orbital one, thus confirming the superhump nature of the transient periodicity observed in November.

### 5.2. The "Plateau" Phase and its Connection with Superhumps

The orbital folded light curves obtained in 1992 December, and 1993 January, (figure 7), were subtracted from the original data. The residuals are exellently expressed by a single exponential decline of 0.0055 mag/day outside the dips; this rate can be traced back to November observations. We calculated the mean rate of decline between August 24 and November 21 by a least-squares fit to the observed light curve, and derived 0.0079 mag/day. Therefore, the period between 1992 November, and 1993 January, is likely to correspond to the "plateau" phase observed in A0620-00 (Lloyd et al. 1977; Whelan et al. 1977).

The nightly deviation from this linear decline was less than 0.02 mag. Therefore, there is no evidence of beat modulation in flux up to 2% between the orbital and superhump periods. Following this plateau phase, the star showed a precipitous decline similar to those observed during the terminal stage of superoutbursts of SU UMa-type dwarf novae (Warner 1985). The general features of the optical light curve is strikingly similar to that of A0620-00.

### 5.3. Mass Estimate of the Compact Object Using Superhumps

Since the appearance of superhumps indicates the tidal instability to be exerted on the accretion disk, we can apply the instability criterion that the mass of the primary star (compact object) must exceed four-times that of the secondary star (Whitehurst 1988; Hirose, Osaki 1990).

Based on the difference in the superhump period and the orbital one, we can put a more stringent limit on the mass ratio of the binary, $$\triangle P = {q\over 4 \sqrt{1+q}}\eta^{3/2}, \eqno(1)$$ where $\triangle P \equiv (\Psh-\Porb)/\Porb$, with $\Psh$ being a superhump period, $q \equiv M_2/M_1$, and $\eta$ a fitting parameter. Mineshige et al. (1992) found that all 13 SU UMa stars (whose mass ratios and superhump/orbital periods were known) are in the $0.6 \lsim \eta \lsim 0.8$ range. This empirical relation (1) puts the most probable range of the mass ratio of the binary between 5.4 and 20.5 within a one-sigma error. If we assume the Roche lobe-filling main sequence secondary star, this corresponds to 3.0 and 11.5 solar masses. A spectroscopic mass estimate of the secondary suggests that the relation by Mineshige et al. (1992) may be ~ 20% overestimated. Even if we reduce the above estimate by 20/120 ~ 16%, we still have the one-sigma lower limit of the mass of the compact object as 2.4 solar masses, which still exceeds 1.4 solar mass of the canonical neutron star.

Thus, the inclination-independent mass determination using superhumps puts forth GRO J0422+32 as a highly promising candidate for a stellar-mass black hole.

### 5.4. Possible Origin of the "Secondary" X-Ray Maximum --- a Clue to a Full Understanding of the Optical and X-Ray Light Curves of USXTs

Furthermore, it would be important to call attention to the fact that the transient periodicity attributable to superhumps was only observed during X-ray minima between the exponential decay and the "secondary" X-ray maximum (this term is not used here as in the usual sense, which corresponds to "reflares" or "notches" observed in other USXTs, but follows the notation in IAU Circulars to avoid confusion) observed in 1992 December (Harmon, Fishman 1992).

There are two conditions for superhump light variations to be observed (Whitehurst 1988; Hirose, Osaki 1990): (1) the excitation of a tidal instability due to the 3:1 resonance, and (2) dominance of tidal dissipation over other internal (viscous) or external (X-irradiation) heating. Of great importance is the fact that condition (1) does not depend on the nature of the compact object; a tidal instability is expected to take place if the mass-ratio is less than $M_2/M_1 \lsim 0.25$. Thus, it is no wonder that a tidal instability works in X-ray transients, if it is the real cause of the superhump phenomenon in SU UMa stars. The late appearance of superhumps suggests either that the development of the tidal instability is delayed in USXTs, or that the manifestation of the superhumps is somehow suppressed by the strong X-ray irradiation from the central source [cf. condition (2) above]. Although superhumps have been detected in other USXTs (Bailyn 1992; Charles et al. 1991), these photometric observations did not, unfortunately, sufficiently cover the full course of the optical outburst to confirm this finding and suggestion.

One may explain that the tidal deformation of the disk can be present even when superhumps are not observed, but the superhump light variation was not visible because the optical disk luminosity due to X-ray irradiation surpassed that due to the intrinsic viscous heating. We, however, disagree with this point of view, because at the peak the object was brighter only by one magnitude than during the epoch when superhumps were observed, indicating that superhumps should have been detected even at the peak, if there were light variations with a similar amplitude of ~ 0.1 mag.

Chen et al. (1993) proposed a senario to produce the "secondary" X-ray maximum (named the third maximum or the final minioutburst in their paper) by a mass-transfer instability from the heated secondary. However, when taking the present new findings of superhumps into account, another attractive senario arises, which may at the same time explain the universal feature of the "secondary" X-ray maxmimum following exponential X-ray decay observed in all USXTs (Tanaka 1989, 1992). The growth rate of the tidal instability is strongly affected by the binary mass ratio (Lubow 1991a,b), which may lead to the delayed development of the tidal instability if the binary mass ratio of GRO J0422+32 is sufficiently high, as suggested from the present observation. When its effect becomes prominent, the superhumps appear, and the mass accretion is greatly enhanced via tidal dissipation, which may first become prominent as an excess amount of flux ("plateau"), finally leading to an enhanced mass supply to the compact object to produce a "secondary" X-ray maximum (Ichikawa et al. 1994). Such a condition of tidal instability would be hard to achieve in X-ray binaries containing neutron stars with lower masses than those of black holes. This condition of the mass ratios may lead to a natural explanation of distinct X-ray light curves of X-ray transients containing black holes from those containing neutron stars.

## 6. Conclusion

(1) The optical light curve of GRO J0422+32 showed an initial rather steep decline followed by a plateau phase of slower decline lasting for ~ 100 days, and a precipitous decline 210 days after the X-ray maximum. The general behavior of the light curve closely resembles that of A0620-00, prototypical USXT.

(2) Superimposed with this fade, a periodic variation with a period of 0.2157 +/- 0.0010 day and an amplitude of 0.10 mag was observed in 1992 November. The profile of the variation resembles that of superhumps observed in SU UMa-type cataclysmic variables.

(3) Another distinct type of variation with a period of 0.21211 +/- 0.00002 d developed in 1992 December, and persisted for at least 64 days. The profile of the variation consists of a nearly constant sinusoidal component and slightly variable dips just prior to the maximum of the sinusoidal variation.

(4) The orbital period of GRO J0422+32 was determined to be 0.21211 +/- 0.00002 d from the existence of the dips. The 0.2157-day periodicity observed in 1992 November, is 1.7 +/- 0.5% longer than the orbital period, and is attributed to superhumps.

(5) From the empirical relation based on the theory of a tidal instability, we first estimate the mass ratio of the binary to be between 5.4 and 20.5, corresponding to the compact object mass in GRO J0422+32 to be between 3.0 and 11.5 solar masses. This fact strongly supports the idea that all ultrasoft X-ray transients contain black holes

(6) Superhumps were observed only in the X-ray minimum between the primary and "secondary" X-ray maximum. The delayed appearance of superhumps in the light curve may reflect a slow growth rate of the tidal instability expected from the high binary mass ratio of USXTs.

Finally, the present unprecedented discovery of orbital dips among USXTs provides not only a rare opportunity for a long-awaited unique determination of the binary inclination, which subsequently allows a unique determination of the mass of the compact object by a radial-velocity study during X-ray quiescence, but also the opportunity of spatially resolving the geometry of a black-hole accretion disk by using recently developed photometric and spectroscopic eclipse mapping techniques. The observations are continuing.

The authors are grateful to the staff of Ogawa Observatory for helping the observations. This research has been partly supported by Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists (T.K.) and by a Scientific Research Grant of the Ministry of Education, Science and Culture, Japan (No. 05242213, 05836017, 06233101; S.M.).

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