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L147
The Astrophysical Journal, 551:L147--L150, 2001 April 20
# 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A BLACK HOLE GREATER THAN 6 M, IN THE X­RAY NOVA XTE J1118#480 1
J. E. McClintock, 2 M. R. Garcia, 2 N. Caldwell, 3 E. E. Falco, 3 P. M. Garnavich, 4 and P. Zhao 2
Received 2001 January 24; accepted 2001 March 8; published 2001 April 6
ABSTRACT
Observations of the quiescent X­ray nova XTE J1118#480 with the new 6.5 m Multiple Mirror Telescope
have revealed that the velocity amplitude of the dwarf secondary is km s #1 and the orbital period of
698 # 14
the system is days. The implied value of the mass function, ,
0.17013 # 0.00010 f (M) p 6.00 # 0.36 M,
provides a hard lower limit on the mass of the compact primary that greatly exceeds the maximum allowed mass
of a neutron star (#3 ). Thus, we conclude that the compact primary is a black hole. Among the 11 dynamically
M,
established black hole X­ray novae, the large mass function of XTE J1118#480 is rivaled only by that of V404
Cyg. We estimate that the secondary supplies of the total light at 5900 A š and that its spectral type
34% # 8%
is in the range from K5 V to M1 V. A double­humped I­band light curve is probably due to ellipsoidal modulation,
although this interpretation is not entirely secure because of an unusual 12 minute offset between the spectroscopic
and photometric ephemerides. Assuming that the light curve is ellipsoidal, we present a provisional analysis that
indicates that the inclination of the system is high and the mass of the black hole is correspondingly modest
( ). The broad Balmer emission lines ( km s #1 ) also suggest a high inclination.
M # 10 M FWHM p 2300--2900
1 ,
For the range of spectral types given above, we estimate a distance of kpc.
1.8 # 0.6
Subject headings: accretion, accretion disks --- binaries: close --- stars: individual (XTE J1118#480) ---
X­rays: stars
1. INTRODUCTION
The X­ray nova XTE J1118#480 was discovered with the
Rossi X­Ray Timing Explorer All­Sky Monitor on 2000 March
29 (Remillard et al. 2000). In outburst the optical counterpart
brightened by about 6 mag to (Uemura et al. 2000).
V # 13
Extensive optical data in outburst reveal that the orbital period
is #4.1 hr (Patterson 2000; Uemura et al. 2000; Garcia et al.
2000; Dubus et al. 2001). XTE J1118#480 has one truly ex­
ceptional attribute: its low reddening, E(B#V mag
) # 0.013
( cm #2 ; Hynes et al. 2000). It is the least red­
20
N # 1.0 # 10
H
dened of all known X­ray binaries.
Including XTE J1118#480, very strong evidence now exists
for black hole primaries in 11 X­ray novae (McClintock 1998;
Filippenko et al. 1999; Orosz et al. 2001). Since XTE
J1118#480 was known to be optically bright in quiescence
( ; Uemura et al. 2000), the source appeared to be a
R # 18.8
good prospect to become the 11th black hole X­ray nova. Thus,
we monitored the brightness of the optical counterpart closely
when it first appeared in the night sky in late October, and we
found that it had returned to its preoutburst brightness (e.g.,
on 2000 October 29.48 UT). In early December,
V p 19.0
using the new 6.5 m Multiple Mirror Telescope (MMT), we
obtained the spectroscopic observations detailed herein.
2. OBSERVATIONS AND ANALYSIS
Spectroscopic observations of XTE J1118#480 were ob­
tained with the new 6.5 m MMT at the F. L. Whipple Obser­
1 Observations reported here were obtained at the Multiple Mirror Telescope
Observatory, a facility operated jointly by the University of Arizona and the
Smithsonian Institution.
2 Harvard­Smithsonian Center for Astrophysics, 60 Garden Street, Cam­
bridge, MA 02138; jem@cfa.harvard.edu, mgarcia@cfa.harvard.edu, pzhao@
cfa.harvard.edu.
3 Smithsonian Institution, F. L. Whipple Observatory, P.O. Box 97, 670
Mount Hopkins Road, Amado, AZ 85645; caldwell@flwo99.sao.arizona.edu,
falco@cfa.harvard.edu.
4 Physics Department, University of Notre Dame, Notre Dame, IN 46556;
pgarnavi@nd.edu.
vatory (FLWO) on the nights of 2000 December 1 and 4 (UT).
The blue channel spectrograph was used with the Loral CCD
( ) detector and the 500 groove mm #1 grating. This
3072 # 1024
configuration yielded #3.6 A š resolution (FWHM) for a slit
width of 1#.0, which approximately matched the seeing on the
two observing nights. The sky conditions were clear. Two ex­
posures of XTE J1118#480 (900 s each) were obtained on
December 1, and six additional exposures (900--1200 s each)
were obtained on December 4. Immediately before and after
each observation of the object, an exposure was obtained of a
wavelength calibration lamp (He­Ne­Ar). We also observed
BD #12447, an M2 dwarf with a well­determined systemic
velocity, and the flux standard Feige 34. In our data analysis,
we also made use of spectra of six additional dwarf stars, which
were obtained with precisely the same focal­plane instrumen­
tation in earlier MMT observing runs. The wavelength cali­
brations were interpolated dispersion solutions scaled according
to the time of an observation relative to the time of the lamp
exposures. Cross correlations between the flux­calibrated spec­
tra of XTE J1118#480 and the template spectra of the G/M
dwarfs were computed for the range 4900--6500 A š . The spectral
reductions and cross­correlation analysis were performed using
the software package IRAF. 5
Photometric monitoring observations were performed using
the 1.8 m Vatican Advanced Technology Telescope (VATT) lo­
cated at the Mount Graham International Observatory on the
nights of 2000 November 30 and December 1 (UT). These ob­
servations were conducted using the VATT CCD camera and
Loral CCD detector ( pixels) and a Harris I filter
2048 # 2048
( A š ; A š ). The CCD was binned at
l p 8105 FWHM p 1624
0
pixels providing a scale of 0#.4 pixel #1 . Ninety­six con­
2 # 2
secutive images were obtained on November 30, and an addi­
tional 53 images were obtained on December 1. The typical
integration time was 120 s, and the time between consecutive
5 IRAF (Image Reduction and Analysis Facility) is distributed by the Na­
tional Optical Astronomy Observatories, which are operated by the Association
of Universities for Research in Astronomy, Inc., under contract with the Na­
tional Science Foundation.

L148 BLACK HOLE IN X­RAY NOVA XTE J1118#480 Vol. 551
Fig. 1.---Spectroscopic and photometric data folded on the orbital period
and the ephemeris given in Table 1. (a) Radial velocity measurements of the
secondary star. The smooth curve is a fit to a circular orbit based on the
velocity amplitude and phase given in Table 1. (b) The residual differences
between the data and the fitted curve. Open and filled symbols are for December
1 and 4, respectively. (c) The top trace is the I­band light curve of XTE
J1118#480 with a superposed ellipsoidal model. Filled and open symbols are
for November 30 and December 1, respectively. The bottom trace shows the
intensity of a nearby comparison star of magnitude ; the trace is shown
I p 17.0
here offset by 0.75 mag for convenience of display. The rms variation in the
star's intensity is 0.015 mag.
TABLE 1
Spectroscopic Orbital Parameters
Parameter Value
T 0 (UT) a . . . . . . . . . . . . . . . 2000 Dec 1.6476 # 0.0010
T 0 (heliocentric) a . . . . . . JD 2,451,880.1485 # 0.0010
V 0 (km s #1 ) . . . . . . . . . . . 26 # 17
K 2 (km s #1 ) . . . . . . . . . . . 698 # 14
P (days) . . . . . . . . . . . . . . . 0.17013 # 0.00010
( ) b . . . . . . . . . .
a sin i R
2 , 2.35 # 0.05
f (M/ ) . . . . . . . . . . . . . .
M, 6.00 # 0.36
a Time of maximum redshift.
b Projected orbital radius of the secondary.
observations was typically 3 minutes. On both nights, seeing
was 2# at the start of the observations due to high air mass but
quickly improved to 1# thereafter. There was light cirrus on the
first night, and the second night was clear. Images were processed
to eliminate the electronic bias, correct for pixel­to­pixel sen­
sitivity variations, and remove significant interference fringes in
the images. The relative intensities of XTE J1118#480 and se­
lected field stars were computed using DAOPHOT photometry.
The photometric calibration was performed using Landolt stan­
dard stars.
3. SPECTROSCOPIC RESULTS
We used the spectra of the velocity standards as cross­
correlation templates to derive a radial velocity curve for the
secondary star. The eight individual spectra of XTE J1118#480
were cross­correlated against each of our seven template stars,
which ranged in spectral type from G8 V to M2 V. Comparable
velocity curves were obtained with each template spectrum.
However, based on the Tonry & Davis (1979) R­value, which
is a measure of signal­to­noise ratio achieved in a cross­
correlation, we found that the K3 V, K5 V, and K5/8V templates
yielded the best correlations. The eight velocities derived using
the K5/8V template star, GJ 9698, are shown in Figure 1a. The
velocity data imply that the secondary star in XTE J1118#480
is orbiting a compact object with a velocity amplitude of ap­
proximately 700 km s #1 . The large velocities of the secondary
contrast sharply with the behavior of the night­sky lines, which
show an rms variation of less than 10 km s #1 .
Assuming a sine function, the velocities are well fitted by
the orbital parameters given in Table 1, where is the time
T 0
of maximum velocity, is the systemic velocity, is the
V K
0 2
velocity semiamplitude of the secondary, and P is the orbital
period. These four parameters were fitted simultaneously using
the interactive data language routine CURVEFIT. A prelimi­
nary account of these dynamical results (McClintock et al.
2000) and the consistent results obtained by a second group
(Wagner et al. 2000) appeared earlier in the IAU circulars. In
§ 4 we argue that the period given in Table 1 is the correct
orbital period, not an alias. In fitting the velocities, we have
assumed that the eight velocity errors are all the same because
the R­values are all comparably high (#7--12). We have ad­
justed this error to the value 24 km s #1 in order to give
. The orbital parameters in Table 1 define the velocity
2
x p 1.0
n
ephemeris, which is represented by the solid line in Figure 1a.
The postfit residuals are shown in Figure 1b. The mass function
may be derived from the above results:
3 3
(M sin i) PK
1 2
f (M) { p p 6.00 # 0.36 M .
,
2
(M #M ) 2pG
1 2
Since the mass of the compact primary necessarily exceeds the
value of the mass function, our results imply that the primary
is much too massive to be a neutron star within general rela­
tivity and is therefore a black hole (Rhoades & Ruffini 1974).
An average of the six spectra taken on December 4 in the
rest frame of the secondary star is shown in Figure 2a. Before
averaging the individual spectra, they were Doppler shifted to
zero velocity using the velocities predicted by the ephemeris
in Table 1. The spectrum of the template star, GJ 9698, is shown
in Figure 2b for comparison. Most of the stronger absorption
lines of GJ 9698 are evident in XTE J1118#480. The most
prominent features are the continuum discontinuity at Mg b
(#5175 A š ) and the Na i 5890--96 A š doublet. As noted above,
the cross­correlation analysis favors template stars of mid­K
spectral type over those with spectral types of M0 V or later.
However, an inspection of the rest­frame spectrum itself sug­
gests that it is somewhat later than mid­K. Given our limited
signal­to­noise ratio, we conclude that the spectral type of the
secondary is in the range K5--M1. Since the orbital period and
mass estimates imply a binary separation of #3 , the sec­
R ,
ondary is presumed to be luminosity class V.
Because of the very low column depth to the source (§ 1),
the Na i line is quite free of interstellar contamination. We there­
fore use its equivalent width to estimate the relative contributions
of the secondary star and the accretion disk to the total light at
5900 A š . For the spectrum of XTE J1118#480 (Fig. 2a) we find
A š . For five comparison stars with spectral
EW p 2.8 # 0.2
types ranging from K5 V to M1 V, we find A š .
EW p 6.6--10.8
From these results, we conclude that the K/M dwarf secondary

No. 2, 2001 McCLINTOCK ET AL. L149
Fig. 2.---(a) Spectrum of XTE J1118#480 in the rest frame of the secondary
star. The photospheric absorption features are most apparent in this frame;
however, the prominent Balmer emission lines are significantly distorted.
(b) The spectrum of GJ 9698, which was used as a velocity template for the
cross­correlation analysis.
contributes of the total light at 5900 A š , a result we
34% # 8%
use in § 4 to analyze the ellipsoidal light curve and we now use
to estimate the distance to the source.
We estimate the distance to XTE J1118#480 using ``meth­
od 2'' described in Barret, McClintock, & Grindlay (1996). For
the secondary, we compute an average density of r p 6.9
g cm #3 from the orbital period and assume ,
M p 0.4 M
2 ,
which is very probably correct to within a factor of 2 (e.g.,
van Paradijs & McClintock 1994). With these inputs we cal­
culate . We use the total magnitude of the optical
R p 0.45 R
2 ,
counterpart, (§ 1), and the fraction of the light con­
V p 19.0
tributed by the secondary, to estimate the magnitude of the
secondary: . Finally, for the range of spectral
V p 20.1 # 0.3
types in question, K5 V--M1 V, we obtain an estimate of the
distance: kpc. There are two nearly equal
d p 1.8 # 0.6
(#25%) contributions to the error: the uncertainty in the spectral
type of the secondary and the (assumed) factor of 2 uncertainty
in the mass of the secondary.
The spectrum of XTE J1118#480 shows strong Balmer
emission lines, which indicate the presence of an accretion disk.
In individual exposures, the Balmer lines are often double­
peaked and quite broad with widths in the range 2300--2900
km s #1 (FWHM).
4. PHOTOMETRY RESULTS
The I­band light curve of XTE J1118#480 folded on the
spectroscopic ephemeris is shown in Figure 1c; data for a com­
parison star of comparable magnitude are plotted just below.
The light curve shows two maxima and two minima per orbital
cycle. This behavior is the hallmark of an ellipsoidal light
curve, which is commonly observed for quiescent black hole
X­ray novae. However, the light curve deviates significantly
from an ideal ellipsoidal light curve, which is represented by
the solid line (see § 5), in several ways. For example, there is
extra light near phase 0.8, which may be due to the bright spot
(Warner 1995). A more problematic deviation from the ellip­
soidal model is the apparent phase lag of the light curve relative
to the spectroscopic ephemeris. Fitting the light curve to a
sinusoid gives a phase lag of , which corre­
0.050 # 0.008
sponds to a time delay of minutes. In contrast,
12.2 # 2.0
studies of other quiescent X­ray novae indicate good agreement
between the photometric and spectroscopic phases (e.g.,
McClintock & Remillard 1986; Shahbaz et al. 1994; Orosz &
Bailyn 1997). Consequently, this 12 minute phase lag calls into
question the ellipsoidal nature of the light curve. Possibly XTE
J1118#480 was not yet fully quiescent during our observa­
tions, even though our dynamical results (Table 1) are entirely
consistent with those obtained more than a month earlier by
Wagner et al. (2000). Possibly our light curve is dominated by
eclipse effects, which can effectively shift the phase of a light
curve. An example of this phenomenon is the set of light curves
observed for GRO J1655#40 as it approached quiescence in
early 1995 (see Fig. 1 in Bailyn et al. 1995). Future obser­
vations in deep quiescence can be expected to resolve these
issues. In the meantime, we assume below in § 5 that the light
curve is ellipsoidal.
Could this 12 minute phase difference be due to an error in
the data clock at either the VATT or the MMT? We believe
that the answer to this question is ``no,'' despite the fact that
the performance of these clocks was not rigorously checked at
the time of the observations. The time base for both obser­
vatories is Network Time Protocol (NTP) via SUN computers,
which routinely provides reliable and precise time to these
observatories. Moreover, both observatories also use their NTP
connection for the precise (#1#) pointing of their telescopes.
If the NTP­based time had been in error by even 10 s during
the observations, the telescope operator and observer would
have noted gross errors in the telescope pointing; none was
observed. Finally, independent and simultaneous photometry
of XTE J1118#480 was obtained by P. Groot using the FLWO
1.2 m telescope; the light curve derived from these data agrees
in phase with our VATT light curve to within 0.010 in phase
or 2.4 minutes in time. We conclude that a terrestrial origin of
the 12 minute phase offset appears very unlikely, and we be­
lieve that the offset is due to the source itself.
We searched the photometric data shown in Figure 1c for
periodicities by computing the variance statistic of Stellingwerf
(1978) for trial periods between 0.01 and 0.5 days. Deep minima
in the V­statistic occur only at days and
P p 0.170 # 0.006
phot
at half that period. The statistical uncertainty in the period de­
termination was estimated using a Monte Carlo method (Silber
et al. 1992). The adopted spectroscopic period is approximately
days (Table 1), and its two closest aliases
P p 0.1701 # 0.0001
are days and days. We now give four
P p 0.1610 P p 0.1803
# #
reasons for rejecting these alias periods and adopting P p
days as the orbital period: (1) The light curves obtained
0.1701
by folding the photometric data on and are complex and
P P
# #
much less compelling than the light curve shown in Figure 1c,
as expected since they differ from the best photometric period
by greater than 1.5 j. (2) A superhump modulation (Warner
1995) was repeatedly observed during outburst; its period
decreased from days (Patterson 2000) to
0.1708 # 0.0001
days (Uemura et al. 2000) over the course of
0.1703 # 0.0001
several weeks. These results argue very strongly in favor of
days and against the aliases (e.g., Bailyn
P p 0.1701 # 0.0001
1992; Kato, Mineshige, & Hirata 1995). (3) The given by
T 0
Wagner et al. (2000) agrees with our for
T P p 0.1701 #
0
days but disagrees if one adopts or . (4) Wagner et
0.0001 P P
# #

L150 BLACK HOLE IN X­RAY NOVA XTE J1118#480 Vol. 551
al. (2000) independently found days with
P p 0.1699 # 0.0001
spectroscopic observations separated by 10 nights. We therefore
conclude that days is the correct or­
P p 0.17013 # 0.00010
bital period.
5. ON THE MASS OF THE BLACK HOLE
We now use the absence of X­ray eclipses and a preliminary
analysis of the light curve to further constrain the mass of the
black hole. Despite very extensive X­ray observations of XTE
J1118#480 in outburst, no X­ray eclipses have been reported.
We can use this result to place an upper limit on the inclination
angle, which boosts somewhat the 6.0 mass limit that is set
M,
by the mass function. We consider two models for the secondary:
(1) First is an 0.5 star with a radius of 0.5 that just fills
M R
, ,
its Roche lobe. In this case, we find that an absence of eclipses
implies and . (2) Second is a very low
i ! 79#.5 M 1 7.2 M
1 ,
mass secondary, , which we assume just fills its
M p 0.2 M
2 ,
Roche lobe radius of . In this case, we find and
0.35 R i ! 81#.8
,
. Here we have used the mean radius of the Roche
M 1 6.5 M
1 ,
lobe in calculating the eclipse condition.
We modeled the I­band light curve (Fig. 1c), which we assume
to be ellipsoidal (but see § 4), using a computer code written by
Avni (1978; see also Orosz & Bailyn 1997). We assumed a
K7 V stellar atmosphere, a limb­darkening coefficient of u p
(Al­Naimiy 1978), and a gravity­darkening exponent of
0.60
. We assumed that the star fills its Roche lobe and that
b p 0.08
its rotation period is the orbital period. We further assumed that
, although the light curve is very insensitive to the
M /M p 20
1 2
choice of this parameter for . The biggest uncer­
M /M # 10
1 2
tainty is the fraction of the light at 8100 A š that is nonstellar; we
call this component the ``disk fraction.'' For the purposes of this
approximate analysis, we assume that the disk fraction at
8100 A š is 66%, the same as the value we derived at 5900 A š in
§ 3. We computed a set of ellipsoidal models for the star for
to in steps of 5#. To each model, we added a
i p 40# i p 90#
constant component of the flux corresponding to the 66% con­
tribution of the accretion disk.
The model that best matches the folded light curve is shown
in Figure 1c. This model corresponds to a very high inclination,
, and a value for the mass of (for
i p 80# M p 7.2 M
1 ,
). This result is consistent, but just barely, with
M p 0.5 M
2 ,
the limits obtained above from the absence of X­ray eclipses.
There are several caveats on this preliminary analysis, the most
important of which concerns our use of the disk fraction at
5900 A š as a proxy for the unknown disk fraction at 8100 A š .
The available evidence indicates that the disk fraction decreases
with increasing wavelength (e.g., Oke 1977; Casares et al. 1993;
Marsh, Robinson, & Wood 1994). Consequently, we have very
likely added too much disk light to our models. As a hypothetical
example, consider the effect of adding a disk fraction of only
40% (instead of 66%) to our models. In this case we would have
found and (for ). A very
i p 52# M p 13.2 M M p 0.5 M
1 , 2 ,
strong upper limit on the mass is obtained by making the extreme
assumption that the disk contributes no light at all in the I band.
In this case we find and . Despite the over­
i 1 40# M ! 24 M
1 ,
riding uncertainty in the I­band disk fraction, our provisional
light curve results suggest that the orbital inclination is relatively
high, , and that the black hole mass is correspondingly
i # 55#
modest . The broad Balmer emission lines (§ 3)
M # 10 M
1 ,
also suggest a high inclination.
6. CONCLUSION
With XTE J1118#480, there are now 11 X­ray novae that
have been dynamically confirmed to contain black hole pri­
maries. For XTE J1118#480, we find an exceptionally large
mass function, , which is rivaled only by that
6.00 # 0.36 M,
of V404 Cyg (Casares, Charles, & Naylor 1992). XTE
J1118#480 is additionally distinguished by having the shortest
orbital period (4.08 hr) of the black hole binaries. Finally, the
extraordinarily low column depth ( cm #2 ) and
20
N # 1.3 # 10
H
modest distance (#1.8 kpc) of XTE J1118#480 make this sys­
tem central to the study of Galactic black holes.
We are grateful to Paul Groot for help in confirming the
photometric phase and to Mike Fitzpatrick and Frank Valdes
for IRAF support. This work was supported in part by NASA
through grant DD0­1003X and contract NAS8­39073.
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