Near-Infrared Spectra of the Black Hole X-ray Binary A0620-00
Cynthia S. Froning1
cfroning@casa.colorado.edu
Center for Astrophysics and Space Astronomy, University of Colorado,
593 UCB, Boulder, CO 80309-0593
Edward L. Robinson
elr@astro.as.utexas.edu
Department of Astronomy, University of Texas at Austin, Austin, TX 78712
Martin A. Bitner
mbitner@astro.as.utexas.edu
Department of Astronomy, University of Texas at Austin, Austin, TX 78712
ABSTRACT
We present broadband NIR spectra of A0620-00 obtained with SpeX on the
IRTF. The spectrum is characterized by a blue continuum on which are super-
imposed broad emission lines of H I and He II and a host of narrower absorption
lines of neutral metals and molecules. Spectral type standard star spectra scaled
to the dereddened spectrum of A0620-00 in K exceed the A0620-00 spectrum in J
and H for all stars of spectral type K7V or earlier, demonstrating that the donor
star, unless later than K7V, cannot be the sole NIR flux source in A0620-00. In
addition, the atomic absorption lines in the K3V spectrum are too weak with
respect to those of A0620-00 even at 100% donor star contribution, restricting
the spectral type of the donor star in A0620-00 to later than K3V. Comparison
of the A0620-00 spectrum to scaled K star spectra indicates that the CO ab-
sorption features are significantly weaker in A0620-00 than in field dwarf stars.
Fits of scaled model spectra of a Roche lobe-filling donor star to the spectrum of
A0620-00 show that the best match to the CO absorption lines is obtained when
the C abundance is reduced to [C/H] = -1.5. The donor star contribution in the
H waveband is determined to be 82 ± 2%. Combined with previous published
results from Froning & Robinson (2001) and Marsh et al. (1994), this gives a
precise mass for the black hole in A0620-00 of M1 = 9.7± 0.6 M⊙.
http://arxiv.org/abs/0704.0267v1
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Subject headings: binaries: close — infrared: stars — stars: individual (A0620–
00) — stars: variables: other
1. Introduction
Among X-ray binary systems (XRBs), 18 or more have been identified as containing
probable black hole (BH) accretors (McClintock & Remillard 2005). The BH masses mea-
sured to date appear to fall into a limited range. From a Bayesian analysis of the observa-
tional parameters of several low-mass XRBs, Bailyn et al. (1998) concluded that 6 of the 7
systems measured had BH masses clustered around 7 M⊙and that the overall population was
heavily biased away from low BH masses (3 – 5 M⊙). Since that study, at least one system,
J0422+32, has been found to have a measured mass of about 4 M⊙(Gelino & Harrison 2003),
but the overall trend toward higher BH masses persists.
This result is in conflict with theoretical evolutionary models of the formation of BH
XRBs, which predict a continuous distribution of BH masses from neutron star masses up to
10–15 M⊙ (Fryer & Kalogera 2001). Confirmation or elimination of the low-mass BH “gap”
would provide important constraints on the role of massive star evolution, supernova ener-
getics, and subsequent binary evolution in BH formation (Fryer & Kalogera 2001). Further
analysis of the mass distribution of BHs in compact binary systems is currently hampered
by the generally poor precision of existing mass estimates (e.g., see Table 4.2 in McClintock
& Remillard 2005). In this manuscript, we address this limitation by analyzing near-infrared
(NIR) spectra to obtain a precise BH mass for one XRB, A0620-00.
A0620-00 was discovered in 1975 when it erupted in an X-ray nova (Elvis et al. 1975).
After its return to quiescence, A0620-00 was revealed as an interacting binary system with a
K star donating mass via an accretion disk to a compact object (Oke 1977; McClintock et al.
1983). Later, the orbital period of the binary and the radial velocity amplitude of the donor
star were measured and yielded a mass function, f(M) = 3.17 M⊙, which established A0620-
00 as a likely BH XRB (McClintock & Remillard 1986). Further observations established the
binary mass ratio and determined the masses of the stars to within one unknown, the binary
orbital inclination: M1 = (3.09±0.09) sin
3 i M⊙ and M2 = (0.21±0.09) sin
3 i M⊙, where M1
and M2 are the BH and donor star masses, respectively (Marsh, Robinson & Wood 1994;
1Visiting Astronomer at the Infrared Telescope Facility, which is operated by the University of Hawaii
under Cooperative Agreement no. NCC 5-538 with the National Aeronautics and Space Administration,
Science Mission Directorate, Planetary Astronomy Program.
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Orosz et al. 1994). Several groups have determined values for the inclination, with the num-
bers ranging from 38◦ ≤ i ≤ 75◦. As a result, estimates of the BH mass in A0620-00 vary from
3.3 to 13.6 M⊙(Haswell et al. 1993; Shahbaz, Naylor & Charles 1994; Froning & Robinson
2001; Gelino et al. 2001).
The broad range of derived inclinations and BH masses for A0620-00 result from long-
term variability in the system and from uncertain determinations of the amount of veiling,
or dilution, by sources other than the donor star. The inclination is determined by modeling
the amplitude of the ellipsoidal variations in the donor star light curve, so both of these
effects will alter the derived BH mass. In particular, an additional source will dilute the
amplitude of the ellipsoidal variation, leading to an underestimate of the inclination and a
corresponding overestimate of the BH mass if not taken into account.
The best way to determine the true donor star contribution in A0620-00 is to model
its spectrum, particularly in the NIR, where the late type donor star is expected to domi-
nate. Shahbaz, Bandyopadhyay & Charles (1999) modeled a low S/N, K-band spectrum of
A0620-00, from which they concluded that the accretion disk contributes at most 27% of the
continuum in the NIR. They fit only the 12CO bandhead at 2.29 µm, however, which is sen-
sitive to both temperature and luminosity of the donor star and may be prone to metallicity
effects in compact binary systems (Froning & Robinson 2001). Harrison et al. (2007) also
recently published a K-band spectrum of A0620-00 in which they confirmed that the 12CO
absorption lines are anomalously weak. What is needed to settle the debate over the con-
tribution of the accretion disk to the NIR spectrum of A0620-00 are higher S/N, broadband
spectra. To this end, we have obtained and present here 0.8 – 2.4 µm spectroscopy of A0620-
00 obtained with SpeX at the NASA InfraRed Telescope Facility (IRTF). This manuscript is
organized as follows: § 2 summarizes the data reduction and calibration steps; § 3 presents
the data analysis and modeling of the donor star spectrum; and § 4 gives discussion and
conclusions.
2. Observations and Data Reduction
We observed A0620-00 on 2004 January 8 – 10 using SpeX on the IRTF (Rayner et al.
2003). The weather was clear with good seeing conditions (. 0.7′′) throughout the run. We
observed A0620-00 using the ShortXD mode, which has a cross-dispersed echelle configu-
ration and covers 0.8 – 2.5 µm simultaneously in 6 orders. All observations were obtained
through the 0.′′5 slit, resulting in a spectral resolution in the center of each order of R = 1200
(250 km s−1). A nearby A0V star was observed hourly to sample the atmospheric absorption
spectrum. We also observed several spectral type calibration stars in the same configuration
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used for A0620-00 (supplemented with similar data from a previous SpeX observing run).
The observations are summarized in Table 1.
All data reduction, calibration, and spectral extraction steps were performed using
Spextool, an IDL-based package developed by the IRTF (Cushing, Vacca, & Rayner 2004;
Vacca, Cushing, & Rayner 2003). The calibration processing steps included flat-fielding,
sky subtraction, optimal spectral extraction, and wavelength calibration. Each A0620-00
exposure was extracted individually to preserve the full 300 sec time resolution. The spectra
were corrected for telluric absorption and flux-calibrated using the A0V stellar spectra as
described by Vacca, Cushing, & Rayner (2003). Finally, the orders were merged for each
exposure to create single spectra covering the full wavelength range. The S/N per resolution
element was ∼4 in the individual spectra. The slit was kept aligned to the parallactic angle
during data acquisition, so the relative fluxes along the full 0.8 – 2.4 µm range are accurate to
≤ 2% (where the upper limit is the uncertainty at 0.9 µm when guiding at 2.4 µm; Cushing
et al. 2004). In addition, stable observing conditions resulted in absolute flux calibrations
of comparable quality. We have not quantified this number as our analysis does not depend
on the absolute flux of the spectrum, but we note for completeness that a rough comparison
of our mean in-band colors to those of Froning & Robinson (2001) and Gelino et al. (2001)
yielded JHK colors within 0.1 mag of their results, well within the level of variability observed
in A0620-00 over long time periods.
For the time-averaged spectrum of A0620-00, we shifted each 300 sec spectrum to
the rest frame of the donor star before median combining, using the orbital ephemeris of
McClintock & Remillard (1986) and the donor star radial velocity amplitude fromMarsh, Robinson & Wood
(1994). The error bars were determined by calculating the median absolute deviation of each
pixel and then propagated through the smoothing and de-reddening steps. We did not cor-
rect for the effects of orbital smearing within an exposure time, but we note that this is
a negligible effect (≤30 km s−1) at our 250 km s−1 spectral resolution. The time-averaged
spectrum is shown in Figure 1. The spectrum has been boxcar-smoothed by 3 pixels, equiva-
lent to one resolution element. Based on the scatter around linear fits to (relatively) line-free
spectral regions, we find that the S/N in the time-averaged spectrum is ∼55 in H and K and
∼45 in J (> 1µm, ∼30 at shorter wavelengths).
Also shown in Figure 1 is the dereddened spectrum of A0620-00, calculated assuming a
reddening along the line of sight of E(B–V) = 0.39 (Wu et al. 1976). Figures 2 – 4 show ex-
panded views of the J,H, and K bands of the spectrum, with prominent spectral absorption
and emission features labeled. Line identifications were made using multiple sources, in-
cluding Wallace et al. (2000), Meyer et al. (1998), Kleinmann & Hall (1986), Harrison et al.
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(2004), and the Atomic Line List2.
3. Analysis
The broadband NIR spectrum of A0620-00 shown in Figures 1 – 4 is characterized by a
blue continuum on which are superposed broad (full width at zero intensities ≥4000 km s−1)
emission lines of H I and He II and narrow (full width at half minima ≃ 250 – 400 km s−1)
absorption lines of neutral metals, including transitions of Na I, Mg I, Al I, Si I, K I, Ca I,
Ti I, and Fe I. The emission lines are believed to originate in the accretion disk, while the
absorption features originate in the photosphere of the donor star. The absorption spectrum
is similar to that of a K star, with previous estimates of the spectral type ranging from K3V
to K7V (Oke 1977; González Hernández et al. 2004).
In Figure 5, we show the dereddened spectrum of A0620-00 compared to that of a field
K5V star. The K star has been normalized to A0620-00 near 2.29 µm, just blueward of
the 12CO (2,0) bandhead. The comparison immediately shows that a K5V (or hotter) star
cannot be the only flux source in the NIR. If the K5 star is scaled to the flux of A0620-00
in the K band, it exceeds the dereddened flux by >20% at bluer wavelengths. Adopting the
K4V and K3V spectral types of Gelino et al. (2001) and González Hernández et al. (2004)
results in an even larger disparity between the expected and observed J- and H-band fluxes.
Even a spectral type as late at K7V exceeds the observed flux in A0620-00 by up to 10%
over most of the J and H bands when normalized to 100% contribution in K.
Modest increases in the assumed reddening along the line of sight do not reconcile the
spectrum of A0620-00 with that of a K5V star. Adopting a reddening of E(B–V) = 0.45
brings the 0.8 µm fluxes into agreement, but the template spectrum is still brighter than the
spectrum of A0620-00 at longer wavelengths, including most of the J and H bands. Because
the relative reddening values between H and K are small, the reddening must be increased to
E(B–V) > 1.0 to bring the spectrum of the normalized K5V template below the spectrum of
A0620-00 at all NIR wavelengths. It is extremely difficult to reconcile a reddening this high
with the observed depth of the interstellar absorption feature at 2200 Å in the spectrum of
A0620-00 (Wu et al. 1976). As a result, the fundamental conclusion remains: if the donor
star is the sole source of NIR emission in A0620-00, its spectral type must be later than that
of a K7V. Otherwise, some level of dilution must be present.
The absorption spectrum of A0620-00 resembles that of the K5V template, but there
2http://www.pa.uky.edu/p̃eter/atomic/
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is at least one important difference between them: the CO molecular absorption features in
A0620-00 are significantly weaker relative to the metal lines than in the template spectrum.
This difference can affect determinations of the donor star contribution to the NIR spectrum.
For example, the dilution analysis performed by Shahbaz, Bandyopadhyay & Charles (1999)
on the K-band spectrum of A0620-00 is unlikely to be a valid determination of the contribu-
tion of the donor star to the NIR spectrum, since they relied entirely on the relative strength
of the 12CO 2.29 µm feature. The weakness of the CO lines also suggests that other anomalies
may exist in the spectrum, necessitating that its decomposition be undertaken over a wide
wavelength range and using multiple line species and features. Accordingly, we compare the
line equivalent widths and line ratios in A0620-00 with those of field star populations and
model the spectrum using both spectral type standards and synthetic spectra.
3.1. Classification Based on Spectral Indices
Studies using equivalent widths (EWs) and EW ratios to determine the spectral type of
a star or stellar population have been pursued by several groups (e.g., Origlia, Moorwood,
& Oliva 1993; Ali et al. 1995; Förster Schreiber 2000; and sources therein). Of particular
interest to us is the work of Förster Schreiber (2000; hereafter FS), who examined H and
K-band absorption lines to find temperature and luminosity indices and indices sensitive to
dilution of the stellar spectrum by other sources. FS was primarily interested in spectral
trends in giant and supergiant stars as the dominant stellar source in extragalactic NIR
spectra, but his analysis includes some dwarf stars as well.
For comparison, we calculated the EWs of several prominent stellar absorption lines in
the time-averaged spectrum of A0620-00 to compare to the spectral indices in FS. Table 2
gives the measured EWs. The lines were chosen to correspond to those in Table 3 of FS
and were calculated using the same continuum normalization and integration limits. Where
applicable, we also applied the EW correction for spectral resolution from Equations 2 –
4 of FS. The error bars on the EWs are the standard deviation of the mean for several
measurements of each line with variable estimates of the continuum placement.
We first compared our EWs to the spectral indices given in Figure 5 of FS, which presents
temperature and luminosity indicators for stars with solar or near-solar abundances. With
the exception of Si I λ1.59 µm and Mg I λ2.28 µm, all of the lines under analysis show a
strong trend of increasing EWs with decreasing stellar temperature. The EWs in A0620-00
are on the low side of the distributions for these lines, indicating stellar temperatures of
≥5000 K.
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We also compared our EWs with those presented in Ali et al. (1995), who concentrated
on temperature indices for dwarf stars. Note that the EWs in Table 2 used to compare
to the Ali et al. (1995) indices are larger than those used for the FS indices because Ali
et al. used a wider wavelength interval for their measurements, which we mirrored. Using
their EW-temperature relationships, we obtain a temperature of 4600±300 K from Ca I and
5000±450 K from Na I. Therefore, if uncorrected for dilution, EWs in A0620-00 point to
a donor star of roughly type K3V star or earlier. However, stars of spectral type K7V or
earlier exceed the observed spectrum of A0620-00 in J and H when zero dilution is assumed
in K. Therefore, we conclude that a diluting continuum source must be present in the NIR
spectrum of A0620-00.
The amount of dilution of the stellar spectrum by another source is determined in FS
by comparing the line ratios of adjacent atomic and molecular features (their Table 8).
Unfortunately, their line ratios use the H and K band CO molecular absorption features,
which we have already seen are not normal in A0620-00. Indeed, a comparison of the 12CO
1.62 µm and 2.29 µm features in A0620-00 gives a result so disproportionately strong in the
1.62 µm line that the ratio doesn’t even appear on the FS spectral index plot. Similarly, a
comparison of the 2.29 µm feature to the nearby Na I and Ca I EWs indicates that the CO
feature is weaker in A0620-00 than in any of the dwarf stars analyzed by FS. These results
indicate that the CO features cannot be used to estimate the non-stellar dilution component
A0620-00.
3.2. Fitting Spectral Type Standard Stars to the Spectrum of A0620-00
In an effort to quantify the contribution of the donor star to the NIR spectrum of A0620-
00 and its dilution by other sources, we compared its spectrum to those of K3V, K5V, and
K7V spectral type standard stars. The standard stars (listed in Table 1) were observed
with the same instrument configuration and calibrated using the same procedures as for the
A0620-00 observations. Before comparing the A0620-00 and template spectra, both were
boxcar-smoothed over 3 pixels (one resolution element). The spectrum of A0620-00 was also
dereddened with E(B–V) = 0.39 (using the reddening curve of Cardelli, Clayton, & Mathis
(1989) and the standard star spectra were convolved with a Gaussian of 83 km s−1 FWHM to
mimic the rotational broadening of the donor star in A0620-00 (Marsh, Robinson & Wood
1994). Note, however, that the rotational broadening is smaller than the 250 km s−1 resolu-
tion of the spectra and has a minimal effect on the results.
We wrote an IDL program to fit scaled template spectra to the spectrum of A0620-00
using the following steps. First, we selected a small wavelength range (typically, 0.1 µm or
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smaller) and fit a spline function to the continuum. The continuum points were selected by
eye. After normalizing both the spectrum of A0620-00 and that of the template star and
placing both spectra on a common, linear dispersion, we multiplied the template spectrum
by a fraction, f , which represents the donor star contribution to the spectrum of A0620-00,
and subtracted the scaled donor star spectrum from that of A0620-00. We varied f from 0
to 1 in increments of 0.01 to find the fraction that minimized the rms of the residual in each
waveband. Finally, we repeated this analysis over several spectral lines and groups of lines
over the full NIR spectral range. The fit regions we examined are given in Table 3. The
resulting best values of f and the rms for each fit region and template spectrum is given in
Table 4.
There are few absorption lines in the J band that are both relatively strong and un-
contaminated by emission lines in the A0620-00 spectrum, so our fits were restricted to the
portion of the long J band between Pγ and Pβ (1.10 – 1.26 µm). This region contains a
blend of singly-ionized atomic species, including transitions of Mg I, Fe I, and Si I. The best
fit fractions range from 0.78 to 1.0. There is a disparity between the strongest line in this
range, Mg I λ1.183 µm and the other lines in this band: the Mg I line is best fit at f ∼0.9,
but the other lines are weaker in the template than in A0620-00 even at f = 1.
The situation is less ambiguous in the H band. The best fit to the full H band spectrum
using the K5V standard star is shown in Figure 6. The fit has f = 0.76 and an rms of
0.016. Although the χ2 statistics are relatively poor (χ2ν = 13.5), there is a good qualitative
correspondence between the morphologies of the observed and template spectra. Similar
results are obtained with the K3V and K7V templates. Many of the stronger transitions
(predominately Mg I and Si I lines) are too weak in the f = 0.76 template, however. If
we restrict the fits to narrower regions around these lines, we generally obtain higher f and
better fits (e.g., χ2ν = 5.2 for the 1.48 – 1.52 µm region fit by the K5V template).
The large χ2ν values for our fits indicate that our error bars are undersized relative to
the true uncertainty in the fits. This is unsurprising, given the systematic uncertainties
that affect modeling of NIR spectra in faint compact binaries, including the influence of
sky background and telluric absorption correction, uncertain placement of the continuum
level where no true continuum exists, and complex line blending wherein small temperature
and/or abundance variations between the template and target stars can affect fit results. As
a result, we have chosen to determine the mean value and uncertainty in the H-band donor
star contribution by using an average of fits to multiple lines and multiple templates over
the full waveband, rather than thorough the use of χ2 statistics, as we believe the scatter
between line fits provides a more rigorous sampling of uncertainties, particularly systematics.
We determined the best representative value for the H band donor star contribution by
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averaging the best-fit f values for the three narrowband H fit regions (1.48 – 1.52 µm, 1.56–
1.61 µm, and 1.70–1.72 µm) and the K5V and K7V templates. Averaging these values for
the K5V and K7V template stars gives a donor star fraction f = 0.82±0.02.
In K, we fit three regions: the spectrum shortward of He I λ2.058 µm, which is dominated
by Ca I absorption lines; the region between He I and Bγ, which includes transitions of
Mg I, Al I, and Si I; and the region longward of Bγ, which contains a rich blend of features,
including transitions of Na I, Ca I, Fe I, Ti I, Mg I, and CO. Note that we do not have any
fit results for the K3V template to the K-band spectrum, because the absorption lines in the
K3V template are too weak relative to those of A0620-00, even at f=1. We have already
shown from the comparison of the SEDs of A0620-00 and a K3V star that a star this hot
cannot be the sole emission source (i.e., have f = 1) in A0620-00 in K without exceeding
the observed spectrum at shorter wavelengths. Now we see that a K3V star also cannot be
reconciled to the spectrum of A0620-00 by decreasing its fractional contribution, because its
absorption lines are already too weak at f = 1 to match those observed in A0620-00. As a
result, we restrict our fits in K to K5V and K7V templates.
The Ca I lines from 1.90 – 2.02 µm could not be simultaneously fit by a single value for
f . The fit values given in Table 4 appear to the eye to be overdiluted as a result of spurious
features (residuals of the telluric absorption correction) driving the fits. The strongest lines
— 1.978 and 1.987 µm — are fit by f ∼ 0.5, but at this value the other lines in this region
are too weak. This spectral region may be contaminated by Bδ λ1.945 µm emission from
the accretion disk. Problems also beset the spectral fits in the 2.07 – 2.15 µm region. The
K5V and K7V stellar spectra have anomalous emission bumps at 2.14 µm that cause visibly
overdiluted fits over the full wavelength range. If the fits are restricted to 2.07 – 2.13 µm,
best fits are obtained for f ∼ 0.65, while fits to the strongest feature alone, Al I 2.117 µm,
gives f = 0.75 for both the template fits.
The final fit region was the long-K portion of the spectrum, 2.18 – 2.42 µm, which
includes numerous atomic species transitions and the CO bandheads. Figure 7 shows the
best fits for the K5V template over the full fit region and when the fit is restricted to
λ < 2.28 µm, excluding the region dominated by the CO lines. When long K is fit in
its entirety, the fits are driven to large dilutions of the donor star to match the weak CO
absorption in the A0620-00 spectrum. At these low donor fractions (f = 0.45 for the K5V
template and f = 0.37 for the K7V template), the atomic lines are too weak in the template
spectrum relative to those in A0620-00. If the fit is restricted to 2.18 – 2.28 µm, the donor
fractions rise to f = 0.81 (K5V) and f = 0.76 (K7V). At these values, the atomic absorption
spectrum of A0620-00 is well fit although there remain discrepencies between template and
target spectra, most notably in the red components of Na I λ2.209 and λ2.339 µm and in
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the Fe I lines from 2.226 – 2.247 µm, all of which are too weak in the template relative
to A0620-00. A single discrepancy in Fe I may explain these deviations, as there are Fe I
transitions coincident with both of the ”Na I” lines (see Figure 6 of FS for an illustration of
the complex line blending in this spectral region).
3.3. Fitting Model Spectra to the Spectrum of A0620-00
In addition to modeling A0620-00 with standard star spectra, we used the LinBrod
program to generate synthetic spectra for a Roche lobe-filling star in a compact binary
with the geometry of A0620-00 (Bitner & Robinson 2006). We adopted the following pa-
rameter values for the models: Porb = 0.323 d, q = 0.067, i = 41
◦, and K2 = 433 km s
(McClintock & Remillard 1986; Marsh, Robinson & Wood 1994; Gelino et al. 2001). We cre-
ated phase-resolved spectra for donor star temperatures of T = 4000, 4250, 4500, 4750, and
5000 K. Finally, we also created models at each temperature in which the carbon abundance
in the star was reduced to [C/H] = -0.5, -1.0, -1.5, and -2.0. To compare to the observed
spectrum of A0620-00, we averaged the model spectra over the binary orbit after removing
the donor star orbital motion and smoothed the spectra to the observed spectral resolution.
Because the SED and spectral type standard star fits to the A0620-00 spectrum point
to a donor star spectral type later than K3V, or T < 5000 K, we concentrated on the T =
4000, 4250, and 4500 K models. In an effort to characterize the carbon depletion required to
match the observed CO line depths, we also focused on the long-K portion of the spectrum
(2.18 – 2.42 µm) . Table 5 gives fit results for the LinBrod model fits. We first fit the solar
abundance models and then repeated the fits for the carbon-depleted spectra. Figure 8 shows
the normalized long K spectrum of A0620-00 with the solar abundance, T = 4000 K model
and with the T = 4000 K, [C/H] = -1.5 spectrum. The model spectra has been scaled by
f = 0.77, the best fit donor fraction for the 2.18 – 2.28 µm region. The [C/H] = -1.5 models
provided the best fit to the spectrum of A0620-00 for all three of the donor temperatures
examined (χ2ν = 4.0 for the T=4000 K, [C/H] = -1.5 model fit to 2.28 – 2.39 µm, versus
χ2ν = 5.9 and χ
ν = 5.2 for the [C/H] = -1.0 and -2.0 models, respectively). The -0.5 and
-1.0 models had CO lines that were still too strong relative to those of A0620-00, while the
CO features were virtually absent in the -2.0 models and too weak to match the observed
spectrum.
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4. Discussion and Conclusions
4.1. The Donor Star in A0620–00
4.1.1. The Donor Star Spectral Type and Fractional Contribution to the NIR Spectrum
Our analysis of the NIR spectrum of A0620-00 has demonstrated three principal results:
1) the donor star is not the only NIR flux source, with 18±2% of the H-band flux originating
in another component of the binary; 2) the donor star must be later than a K3V spectral
type; and 3) the CO absorption lines are anomalously weak, requiring a carbon abundance
of [C/H] = -1.5 in the donor star to match the observed line depths.
A comparison of the broadband NIR SED of A0620-00 with those of spectral type
standard star spectra shows that the donor star cannot be the sole source of NIR flux. If
the standard star spectra are normalized to the dereddened spectrum of A0620-00 in the
K-band, they exceed the observed flux in the J and H wavebands. This result is true for all
standard star spectra earlier than M0V. The discrepancy cannot be reconciled by changes
in the differential reddening correction because the relative reddening correction between K
and J and H is too small. Additionally, the K-band absorption lines in the K3V standard
star are too weak to match the line depths seen in the A0620-00 spectrum even at a 100%
donor star contribution. Decreasing the donor star contribution to f < 1 will only make the
template lines weaker, so a K3V spectral type for the donor star is ruled out.
The most precise measurement of the donor star temperature is by González Hernández et al.
(2004), who fit synthetic spectra created from model atmospheres to the visible spectrum of
A0620-00. They found that T2 = 4900 ± 100 K, which corresponds to a K2/K3V spectral
type. This result is not in agreement with our requirement that the donor star be later than
K3V. There are reasons to believe that the González Hernández et al. (2004) results may be
unreliable, however. To determine the stellar parameters they used 24 Fe I lines, to which
they fit models with five free parameters: stellar temperature, gravity, and metallicity, as
well as a normalization and slope to represent dilution from the accretion disk. The use of
Fe I lines alone to constrain all stellar parameters (plus the disk contribution) is uncommon
practice for stellar modeling, which typically relies on independent determinations of the
stellar temperature, as well as on both Fe I and Fe II transitions. González Hernández et al.
(2004) also determined that the abundances of the elements they fit were slightly above solar
values. The adoption of a cooler donor star temperature, as required by our results, will
reduce their derived abundances.
We conclude that the spectral type of the donor star is most likely between K5V to
K7V, but do not attempt to constrain the spectral type more precisely. The rms values
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for the dilution fits to various regions of the A0620-00 spectrum are comparable for both
spectral types and we cannot rely on the CO features to create more precise temperature
indices. We therefore averaged the dilution values from both spectral type fits for the three
narrow regions in the H-band to derive our H-band donor star fraction: f = 0.82 ± 0.02,
or an 82% donor star contribution in H. The donor fraction in long K (> 2.2µm) is 81%
for a K5V template or 76% for the K7V. Figure 9 shows the spectrum of A0620-00 with
a K5V template star scaled to 82% of the H-band flux and the A0620-00 spectrum after
the contribution of the donor star has been subtracted. While the spectrum of A0620-00 is
dominated by the K type donor, there is a significant second component consisting of a blue
continuum and strong H I and He II line emission.
Our results of a K5V to K7V donor star spectral type and 18% – 24% veiling in H
and K do not agree with those of Gelino et al. (2001), who found that the NIR SED of
A0620-00 matched that of a K4V (T = 4600 K) star with no dilution. As pointed out by
Hynes et al. (2005), however, there is a degeneracy between the spectral type of the star and
the amount and distribution of a veiling spectrum in an XRB: a cooler donor star plus a
diluting component can result in the same SED as a hotter donor star with no contamination.
Hynes et al. showed that even a 100 K overestimate of the temperature of the donor star
could result in a factor of two underestimate of the veiling. Because our data show, both
in the line EWs and the NIR SED, that a K type donor star cannot be the only NIR flux
source, we conclude that Gelino et al. (2001) overestimated the temperature of the donor
star and consequently underestimated the spectral dilution in the NIR.
Our results also disagree with the recent work of Harrison et al. (2007), who argue by
analogy with the IR spectrum of the cataclysmic variable SS Cygni that A0620-00 has <4%
dilution in the K-band. Their argument can be summarized as follows: a) A0620-00 and
SS Cyg have similar K-band spectral slopes, binary properties, and quiescent mass accretion
rates; b) SS Cyg also has a mid-IR excess; c) the NIR and MIR SEDs of SS Cyg can be
well fit by a K4V stellar spectrum plus free-free emission; d) because A0620-00 and SS Cyg
are similar, application of the star plus wind model can be extended from the latter to the
former to estimate a ∼4% limit on the contamination level of the NIR spectrum of A0620-00.
We have several concerns about this line of reasoning. First, as already discussed above,
the similarity of a SED to that of a field star does not preclude contaminating emission
from the disk. The data shown in Harrison et al. reinforce this: the JHK colors of SS Cyg
are consistent with that of an undiluted K4V star even as the ellipsoidal light curves show
clear evidence of contamination. In fact, Harrison el al. point out that the K-band spectrum
of A0620-00 has a different slope from those of the field stars, which provides fairly clear
evidence of contamination. Second, it is not known whether free-free emission is the correct
– 13 –
explanation for the excess MIR flux observed in SS Cyg. Another possibility discussed by
Dubus et al. (2004), who originally published the IR SED shown by Harrison et al., is that
circumbinary disk emission is responsible. Indeed, Muno & Mauerhan (2006) have found a
MIR component in A0620-00, which they fit with a ≃600 K blackbody component, consistent
with emission from circumbinary dust rather than free-free emission in a wind. The cool
blackbody component found by Muno & Mauerhan (2006) does not affect the NIR spectrum
of A0620-00, which suggests that the attempt to use MIR data from SS Cyg to estimate the
NIR contamination in A0620-00 is a red herring. Finally, we reiterate what our simultaneous,
JHK spectra of A0620-00 indicate directly about the donor star contamination in the system:
based on the shape and fluxes of the JHK continuum spectrum, the absolute EWs of the
atomic absorption lines, and dilution analyses using both field stars and a Roche-lobe filling
model spectrum, the donor star must be significantly diluted (∼20%), even in the K-band.
4.1.2. Weak CO Features in the Donor Star Spectrum
Although the atomic absorption line spectrum in A0620-00 is consistent with a K5V –
K7V spectral type, the molecular 12CO lines are significantly weaker in A0620-00 than in
a field star, corresponding to CO line strengths normally seen in early G stars. Using the
LinBrod model spectra of a Roche lobe-filling star, we found that reducing the C abundance
to [C/H] = -1.5 results in a better match to the CO lines in the spectrum than the [C/H] =
0, -1.0, and -2.0 models when the donor star fraction is fit to f = 0.77.
The weakness of the 12CO lines in A0620-00 has already been noted by Harrison et al.
(2007), who determine that the 12C abundance must be decreased 50% to match the depth
of the 12CO bandheads. The 50% reduction in 12C abundance ([12C/H] = -0.3) found by
Harrison et al. is significantly smaller than the 97% drop we claim. Again, however, we
have several concerns about the method by which Harrison et al. obtained their results.
First, they started with the line list included in the spectral synthesis program SPECTRUM
(Gray & Corbally 1994), but when they were unable to match the spectra of standard spec-
tral type field stars using this line list (and Kurucz atmospheres) due to the presence of
strong absorption features in the model but not the observed spectra, they abandoned it
and constructed one consisting only of Na I, Mg I, and CO transitions. When they found
that the lines in their new models were too weak to match those of field stars at the correct
temperature, they globally increased the log(gf) values of every line in their new line list
to match up with observations. They then applied this revised model to the spectrum of
A0620-00, adjusting the C isotopic abundances until the best fit by eye was achieved.
We are not confident in the quantitative reliability of spectral model fits in which spectral
– 14 –
lines have been dropped and oscillator strengths altered in order to achieve even a rough fit
to a K5V field star. We note in contrast that our LinBrod models give fits to the spectrum
of A0620-00 of comparable quality of those using template field stars with no deletions or
alterations to the spectral synthesis line lists required. Our other concern with the Harrison
et al. fits is the placement of the continuum and evaluation of the best model fit. They
determined the best-fit model by eye. To our eyes, however, the fits they show in their
Figure 3 do not properly take into account the actual data quality: their pseudo-continuum
levels appear too high and their CO line minima are too low in their preferred model. A
rough comparison of their observed spectrum to ours shows that the 12CO normalized line
depths are similar in both data sets, suggesting that a statistical model fit to their spectrum
would result in a 12C abundance similar to the one we obtain.
Finally, Harrison et al. contend that in addition to a low 12C abundance in A0620-00, the
13C abundance is enhanced, such that 13C/12C = 1. They base their identification of 13CO
on the presence of a feature coinciding with the 13CO(3,1) 2.374 µm bandhead. However,
they also note that the 13CO(2,0) 2.345 µm is not seen in their spectrum, despite being the
stronger feature of the two. Given the poor atmospheric conditions at the time their data
was taken and the increasing amount of telluric H20 absorption at these wavelengths, we
do not believe that their data provide a clear detection of 13CO and certainly not of 13C at
equal abundance with 12C. In our spectrum of A0620-00, there is a feature at the location of
the 13CO(2,0) 2.345 µm bandhead, but no feature coinciding with 13CO(3,1) 2.374 µm. We
have marked the locations of the first two 13CO bandheads in our Figure 4. Dhillon et al.
(2002) point out, however, that a Ti I feature is coincident with the 13CO(2,0) 2.345 µm
bandhead and is a much more likely explanation of the feature we see. As a result, we do
not believe that an unambiguous detection of 13CO can be made in our spectrum and we
find no evidence of any enhancement of this species in A0620-00.
Anomalously weak CO absorption features have been seen in other compact binary sys-
tems. The NIR spectra of several cataclysmic variables show weak or absent 12CO absorption
(Harrison et al. 2000, 2004). In the dwarf nova U Gem, the NIR CO absorption lines are sig-
nificantly weaker than in the M3V standard star spectrum that provides a good match to the
atomic lines. Model fits to the FUV spectrum of the metal-enriched white dwarf in U Gem
show that the C abundance on the WD surface is [C/H] = -1.0, while the N abundance
is highly super-solar, [N/H] = 0.7 (Sion et al. 1998; Long & Gilliland 1999; Froning et al.
2001). Similarly, in the UV spectrum of the BH XRB XTE J1118+480 in outburst, typically
strong emission lines of C IV and O V are undetectable, while the N V λ1240 Å appears
enhanced (Haswell et al. 2002). The UV line ratios are inconsistent with photoionization
models, leading Haswell et al. to conclude that the emission spectrum is indicative of the
accretion of C-depleted material from the donor star. As a result, A0620-00 can be added
– 15 –
to the ever-increasing list of cataclysmic variables and XRBs that show depleted C (and, in
some cases, enhanced N), pointing to a common history of nuclear processing of C to N in
compact binary systems.
4.2. The Mass of the Black Hole in A0620–00
Based on previous work, the mass of the BH in A0620-00 is known to the value of
one unknown, the binary inclination: M1 = (3.09± 0.09) sin
−3 i (Marsh, Robinson & Wood
1994). The orbital inclination can be obtained by modeling the light curve of the donor star.
The donor star fills its Roche lobe and is distorted in shape, which leads to a double-humped
ellipsoidal variation in the light curve, the amplitude of which is dependent on inclination. If
a source besides the donor star contributes to the light curve, the amplitude of the ellipsoidal
variation will be diluted, leading to an underestimate of the inclination and a corresponding
overestimate of the BH mass if the contaminating source is not taken into account.
The most precise inclination results to date were reported by Gelino et al. (2001), who
modeled JHK light curves of A0620-00. Based on good agreement between the target SED
and that of a dereddened K4 star, they concluded that the donor star is the only NIR
continuum source in A0620-00. Using this assumption, they modeled the ellipsoidal light
curve and found i = 40.◦75± 3◦ and M1 = 11.0± 1.9 M⊙. As discussed above, however, the
NIR SED alone is insufficient to resolve the degeneracy between donor star temperature and
veiling by another flux source in the system. Our results indicate that the donor star cannot
be the only NIR flux source in A0620-00 and that consequently, the Gelino et al. results
overestimate the BH mass in A0620-00.
We previously modeled the H-band light curve in A0620-00 with a donor star plus accre-
tion disk model and determined 38◦ ≤ i ≤ 75◦, or 3.3 ≤ M1 ≤ 13.6M⊙ (Froning & Robinson
2001). The broad range of values was caused by a degeneracy between the inclination
and the fractional contribution of the accretion disk to the H-band light. Table 5 of
Froning & Robinson (2001) gives the inclination in A0620-00 as a function of the fractional
contribution of diluting sources in the H-band. In § 3.2 of this paper, we determined that
the donor star contributes 82±2% of the H-band flux in A0620-00. This result, a diluting
fraction of 18±2%, combined with Table 5 in Froning & Robinson (2001) gives a binary
inclination for A0620-00 of i = 43± 1◦.
Based on this inclination, we obtain the mass of the BH accretor in A0620-00: M1 =
9.7±0.6M⊙. This result is comparable to previous estimates of the BH mass in the literature.
Shahbaz, Naylor & Charles (1994) found a BH mass of 10 M⊙, while Gelino et al. (2001)
– 16 –
found M1 = 11.0±1.9 M⊙. The inclination we derive is within the error interval of Gelino
et al. The difference in BH masses between the two results comes from the slightly higher
inclination we adopt as a result of our determination that the donor star cannot be the sole
NIR emission source.
The error bar on our derived BH mass represents the propagated statistical errors in
the result. A potential source of systematic uncertainty is our assumption that the atomic
absorption spectrum of A0620-00 can be modeled by template spectra with solar abundances.
The fact that the C abundance in A0620-00 has to be decreased significantly to match the
CO lines suggests the need for caution in this regard. However, the relative line ratios of
the atomic transitions largely agree with each other in the derived fractional donor star
contributions. These lines are also strong transitions that lie on the flat portion of the curve
of growth and will not be sensitive to small abundance variations. Finally, we note that while
González Hernández et al. (2004) derived slightly super-solar abundances for the metal lines
in A0620-00, they used a stellar temperature that is too hot to be consistent with the NIR
SED. The adoption of a cooler temperature for the donor star will cause the metal line
abundances required to fit the optical spectrum to decrease.
Another potential source of systematic error is the large time interval (8 years) between
acquisition of the NIR light curve and the spectra. Our analysis assumed that the donor star
diluting fraction found by analyzing the spectra applies equally well to the light curve data.
This assumption is valid, we believe, because while A0620-00 is variable, its NIR colors typi-
cally don’t vary by more than 0.2 mag, and six observations of the H-band light curve spaced
over days to years had mean colors that agreed to within 0.04 mag (Froning & Robinson 2001;
Gelino et al. 2001). Our rough estimate of the absolute calibration of our time-averaged
spectrum was also consistent with the previous measurements. We can estimate the uncer-
tainty in the non-donor star contribution by assuming that it could vary by ±4%, consistent
with the previous measurements. This would cause the donor star fraction to range from
79 ≤ f ≤ 86, which results in i = 43± 1◦, consistent with our statistical uncertainties.
We thank Nathaniel Cunningham for assistance in observing A0620-00, and the staff at
the IRTF for their support. We also thank Chris Sneden and Niall Gaffney for their help in
calculating the LinBrod donor star spectra and for useful discussions.
Facilities: IRTF(SpeX)
– 17 –
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This preprint was prepared with the AAS LATEX macros v5.2.
– 20 –
– 21 –
Table 1. SpeX Observations
Object Date (UT) Instrument Texp (min) Φ
A0620-00 2004 Jan 8 SpeX 290 0.59 – 1.47
A0620-00 2004 Jan 9 SpeX 280 0.69 – 1.49
A0620-00 2004 Jan 10 SpeX 250 0.92 – 1.61
HD42606 (K2.5 III) 2004 Jan 18 SpeX 1.2 · · ·
HD 3765 (K2 V) 2004 Jan 18 SpeX 2 · · ·
HD16160 (K3 V) 2004 Jan 19 SpeX 1.8 · · ·
61 Cyg A (K5 V) 2000 Sept 15 SpeX 0.5 · · ·
61 Cyg B (K7 V) 2000 Sept 15 SpeX 0.5 · · ·
aOrbital phase coverage of A0620–00 for each night’s observations, based
on the ephemeris of McClintock & Remillard (1986).
– 22 –
Table 2. Equivalent Widths of Selected Absorption Lines
Feature EWa (Å) EWb (Å)
Si I 1.5892 1.52±0.04 · · ·
12CO (6,3) 1.6187 0.86±0.07 · · ·
Na I 2.2076 0.94±0.06 2.18±0.04
Fe I 2.2263 0.36±0.05 · · ·
Fe I 2.2387 0.40± · · ·
Ca I 2.2636 1.06±0.06 3.21±0.03
Mg I 2.2814 0.43±0.04 0.68±0.06
12CO (2,0) 2.2935 0.38±0.06 2.26±0.08
12CO (3,1) 2.3227 0.22±0.02 · · ·
13CO (2,0) 2.3448 0.64±0.04 · · ·
aEWs calculated using the integration lim-
its of Förster Schreiber 2000.
bEWs calculated using the integration lim-
its of Ali et al. (1995).
– 23 –
Table 3. Wavelength Ranges for Spectral Fits
Waveband λ Range (mum) Description
J 1.10 – 1.26 Long J
1.175 – 1.215 Blend incl. Mg I, Fe I, Si I
H 1.4 – 1.8 Full H band
1.48 – 1.52 Mg1 lines.
1.56 – 1.61 Blend incl. Mg I, Si I
1.70 – 1.72 Mg1
K 1.90 – 2.02 Several Ca I lines.
2.07 – 2.15 Short K incl. Mg I, Si I, Al I.
2.18 – 2.42 Long K incl. CO bandhead.
2.18 – 2.28 No CO, lines incl. Na I, Fe I, Ca I, Mg I.
– 24 –
Table 4. Template Star Fits to A0620–00 Spectrum
Template Wavelength Range Template Fraction rms
Spectral Type (µm) (f)
K3V 1.10–1.26 0.78 0.012
1.175 – 1.215 0.82 0.010
1.4–1.8 0.76 0.016
1.48 – 1.52 0.71 0.011
1.56 – 1.61 0.81 0.011
1.70 – 1.72 0.91 0.009
K5V 1.10 – 1.26 0.90 0.013
1.175 – 1.215 1.0 0.010
1.4 – 1.8 0.78 0.016
1.48 – 1.52 0.82 0.010
1.56 – 1.61 0.88 0.015
1.70 – 1.72 0.78 0.010
1.90 – 2.02 0.37 0.02
2.07 – 2.15 0.52 0.01
2.18 – 2.42 0.45 0.012
2.18 – 2.28 0.81 0.009
K7V 1.10 – 1.26 0.87 0.013
1.175 – 1.215 0.99 0.011
1.4 – 1.8 0.76 0.017
1.48 – 1.52 0.82 0.010
1.56 – 1.61 0.85 0.015
1.70 – 1.72 0.77 0.009
1.90 – 2.02 0.39a 0.021
2.07 – 2.15 · · · b · · ·
2.18 – 2.42 0.37 0.014
2.18 – 2.28 0.76 0.009
– 25 –
aFits too diluted due to noise in spectra.
bFits compromised by spurious feature in template.
– 26 –
Table 5. LinBrod Fits to A0620–00 Spectrum
Model Temperature Model C Abundance Wavelength Range Template Fraction rms
(K) (log[C/H]/[C/H]⊙) (µm) (f)
4000 0.0 2.18 – 2.28 0.72 0.011
4250 0.0 2.18 – 2.28 0.76 0.011
4500 0.0 2.18 – 2.28 0.99 0.011
Full Long K Region Including CO Lines
4000 0.0 2.18 – 2.38 0.14 0.015
4000 -0.5 2.18 – 2.38 0.28 0.014
4000 -1.0 2.18 – 2.38 0.54 0.012
4000 -1.5 2.18 – 2.38 0.78 0.011
4000 -2.0 2.18 – 2.38 0.74 0.012
4250 0.0 2.18 – 2.38 0.14 0.015
4250 -0.5 2.18 – 2.38 0.28 0.014
4250 -1.0 2.18 – 2.38 0.56 0.013
4250 -1.5 2.18 – 2.38 0.82 0.012
4250 -2.0 2.18 – 2.38 0.81 0.012
4500 0.0 2.18 – 2.38 0.17 0.015
4500 -0.5 2.18 – 2.38 0.35 0.014
4500 -1.0 2.18 – 2.38 0.71 0.013
4500 -1.5 2.18 – 2.38 0.96 0.012
4500 -2.0 2.18 – 2.38 0.93 0.013
Longward of the 2.29 µm Bandhead Onlya
4000 -0.5 2.28 – 2.38 0.77 0.025
4000 -1.0 2.28 – 2.38 0.77 0.014
4000 -1.5 2.28 – 2.38 0.77 0.012
4000 -2.0 2.28 – 2.38 0.77 0.013
4250 -0.5 2.28 – 2.38 0.77 0.024
– 27 –
Table 5—Continued
Model Temperature Model C Abundance Wavelength Range Template Fraction rms
(K) (log[C/H]/[C/H]⊙) (µm) (f)
4250 -1.0 2.28 – 2.38 0.77 0.014
4250 -1.5 2.28 – 2.38 0.77 0.012
4250 -2.0 2.28 – 2.38 0.77 0.013
4500 -0.5 2.28 – 2.38 0.77 0.020
4500 -1.0 2.28 – 2.38 0.77 0.014
4500 -1.5 2.28 – 2.38 0.77 0.013
4500 -2.0 2.28 – 2.38 0.77 0.014
aDonor star fraction fixed in these models to the best-fit value to the nearby atomic lines
from the template star fits.
– 28 –
Fig. 1.— The NIR spectrum of A0620–00, obtained in 2004 January. The solid line shows
the time-averaged spectrum of A0620. Individual exposures were shifted to remove the
orbital motion of the donor star before averaging. The dotted line shows the spectrum after
dereddening, assuming E(B–V) = 0.39 (Wu et al. 1976).
Fig. 2.— The spectrum of A0620-00 in J. Prominent spectral features are labeled. An error
bar representative of the statistical uncertainty per resolution element is plotted on the far
right of the plot. Also shown at the bottom of the figure is the spectrum of HD45137, the
A0V star used for telluric correction of the A0620–00 spectra. The spectrum retains the
throughput profile of each spectral order but is not shown with absolute flux calibration.
The H I lines intrinsic to the A0V spectrum have been fitted and removed using the xtellcor
program developed by the IRTF.
Fig. 3.— The spectrum of A0620-00 in H. Prominent spectral features are labeled. A
representative error bar for a resolution element is plotted on the far right. The telluric
spectrum is also shown at the bottom of the figure.
Fig. 4.— The spectrum of A0620-00 in K. Prominent spectral features are labeled. A
representative error bar for a resolution element is plotted on the far right. The telluric
spectrum is also shown.
Fig. 5.— Shown in black is the dereddened spectrum of A0620-00. Shown in gray is the
spectrum of 61 Cyg A, a K5V spectral type star. The spectrum of 61 Cyg A has been
normalized to the flux of A0620 just blueward of the 12CO 2.29 µm bandhead.
Fig. 6.— The normalized H-band spectrum of A0620–00 with a scaled spectral type standard
star fit. The standard star, shown in red, is 61 Cyg A, a K5V star. It has been scaled by
f = 0.76.
Fig. 7.— The normalized K-band spectrum of A0620–00 with a scaled spectral type standard
star fit. The template star is 61 Cyg A, a K5V star. The solid red spectrum shows the
template scaled by f = 0.45, the best fit over the full 2.18 – 2.42 µm range. The dashed red
spectrum shows the template scaled by f = 0.81, the best fit to the 2.18 – 2.28 µm region.
Fig. 8.— The normalized K-band spectrum of A0620–00 with scaled LinBrod T = 4000 K
model spectra fits. The solid red line shows the LinBrod model with [C/H] = -1.5, while the
dashed red line shows the solar abundance model. To avoid confusion, the latter is shown
only for λ > 2.288 µm. The models are scaled by f = 0.77.
Fig. 9.— The top panel shows the dereddened spectrum of A0620-00 in black and the
spectrum of 61 Cyg A, a K5V star, in gray. The spectrum of the K5V template has been
– 29 –
scaled to 82% of the A0620-00 flux at the center of the H band, 1.6 µm. The lower panel shows
the NIR spectrum of the accretion disk in A0620-00, created by subtracting the template
spectrum from that of A0620-00.
– 30 –
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	Introduction
	Observations and Data Reduction
	Analysis
	Classification Based on Spectral Indices
	Fitting Spectral Type Standard Stars to the Spectrum of A0620-00
	Fitting Model Spectra to the Spectrum of A0620-00
	Discussion and Conclusions
	The Donor Star in A0620–00
	The Donor Star Spectral Type and Fractional Contribution to the NIR Spectrum
	Weak CO Features in the Donor Star Spectrum
	The Mass of the Black Hole in A0620–00

  We present broadband NIR spectra of A0620-00 obtained with SpeX on the IRTF.
The spectrum is characterized by a blue continuum on which are superimposed
broad emission lines of HI and HeII and a host of narrower absorption lines of
neutral metals and molecules. Spectral type standard star spectra scaled to the
dereddened spectrum of A0620-00 in K exceed the A0620-00 spectrum in J and H
for all stars of spectral type K7V or earlier, demonstrating that the donor
star, unless later than K7V, cannot be the sole NIR flux source in A0620-00. In
addition, the atomic absorption lines in the K3V spectrum are too weak with
respect to those of A0620-00 even at 100% donor star contribution, restricting
the spectral type of the donor star in A0620-00 to later than K3V. Comparison
of the A0620-00 spectrum to scaled K star spectra indicates that the CO
absorption features are significantly weaker in A0620-00 than in field dwarf
stars. Fits of scaled model spectra of a Roche lobe-filling donor star to the
spectrum of A0620-00 show that the best match to the CO absorption lines is
obtained when the C abundance is reduced to [C/H] = -1.5. The donor star
contribution in the H waveband is determined to be 82+-2%. Combined with
previous published results from Froning & Robinson (2001) and Marsh et al.
(1994), this gives a precise mass for the black hole in A0620-00 of M_BH =
9.7+-0.6 M_solar.

Introduction
Among X-ray binary systems (XRBs), 18 or more have been identified as containing
probable black hole (BH) accretors (McClintock & Remillard 2005). The BH masses mea-
sured to date appear to fall into a limited range. From a Bayesian analysis of the observa-
tional parameters of several low-mass XRBs, Bailyn et al. (1998) concluded that 6 of the 7
systems measured had BH masses clustered around 7 M⊙and that the overall population was
heavily biased away from low BH masses (3 – 5 M⊙). Since that study, at least one system,
J0422+32, has been found to have a measured mass of about 4 M⊙(Gelino & Harrison 2003),
but the overall trend toward higher BH masses persists.
This result is in conflict with theoretical evolutionary models of the formation of BH
XRBs, which predict a continuous distribution of BH masses from neutron star masses up to
10–15 M⊙ (Fryer & Kalogera 2001). Confirmation or elimination of the low-mass BH “gap”
would provide important constraints on the role of massive star evolution, supernova ener-
getics, and subsequent binary evolution in BH formation (Fryer & Kalogera 2001). Further
analysis of the mass distribution of BHs in compact binary systems is currently hampered
by the generally poor precision of existing mass estimates (e.g., see Table 4.2 in McClintock
& Remillard 2005). In this manuscript, we address this limitation by analyzing near-infrared
(NIR) spectra to obtain a precise BH mass for one XRB, A0620-00.
A0620-00 was discovered in 1975 when it erupted in an X-ray nova (Elvis et al. 1975).
After its return to quiescence, A0620-00 was revealed as an interacting binary system with a
K star donating mass via an accretion disk to a compact object (Oke 1977; McClintock et al.
1983). Later, the orbital period of the binary and the radial velocity amplitude of the donor
star were measured and yielded a mass function, f(M) = 3.17 M⊙, which established A0620-
00 as a likely BH XRB (McClintock & Remillard 1986). Further observations established the
binary mass ratio and determined the masses of the stars to within one unknown, the binary
orbital inclination: M1 = (3.09±0.09) sin
3 i M⊙ and M2 = (0.21±0.09) sin
3 i M⊙, where M1
and M2 are the BH and donor star masses, respectively (Marsh, Robinson & Wood 1994;
1Visiting Astronomer at the Infrared Telescope Facility, which is operated by the University of Hawaii
under Cooperative Agreement no. NCC 5-538 with the National Aeronautics and Space Administration,
Science Mission Directorate, Planetary Astronomy Program.
– 3 –
Orosz et al. 1994). Several groups have determined values for the inclination, with the num-
bers ranging from 38◦ ≤ i ≤ 75◦. As a result, estimates of the BH mass in A0620-00 vary from
3.3 to 13.6 M⊙(Haswell et al. 1993; Shahbaz, Naylor & Charles 1994; Froning & Robinson
2001; Gelino et al. 2001).
The broad range of derived inclinations and BH masses for A0620-00 result from long-
term variability in the system and from uncertain determinations of the amount of veiling,
or dilution, by sources other than the donor star. The inclination is determined by modeling
the amplitude of the ellipsoidal variations in the donor star light curve, so both of these
effects will alter the derived BH mass. In particular, an additional source will dilute the
amplitude of the ellipsoidal variation, leading to an underestimate of the inclination and a
corresponding overestimate of the BH mass if not taken into account.
The best way to determine the true donor star contribution in A0620-00 is to model
its spectrum, particularly in the NIR, where the late type donor star is expected to domi-
nate. Shahbaz, Bandyopadhyay & Charles (1999) modeled a low S/N, K-band spectrum of
A0620-00, from which they concluded that the accretion disk contributes at most 27% of the
continuum in the NIR. They fit only the 12CO bandhead at 2.29 µm, however, which is sen-
sitive to both temperature and luminosity of the donor star and may be prone to metallicity
effects in compact binary systems (Froning & Robinson 2001). Harrison et al. (2007) also
recently published a K-band spectrum of A0620-00 in which they confirmed that the 12CO
absorption lines are anomalously weak. What is needed to settle the debate over the con-
tribution of the accretion disk to the NIR spectrum of A0620-00 are higher S/N, broadband
spectra. To this end, we have obtained and present here 0.8 – 2.4 µm spectroscopy of A0620-
00 obtained with SpeX at the NASA InfraRed Telescope Facility (IRTF). This manuscript is
organized as follows: § 2 summarizes the data reduction and calibration steps; § 3 presents
the data analysis and modeling of the donor star spectrum; and § 4 gives discussion and
conclusions.
2. Observations and Data Reduction
We observed A0620-00 on 2004 January 8 – 10 using SpeX on the IRTF (Rayner et al.
2003). The weather was clear with good seeing conditions (. 0.7′′) throughout the run. We
observed A0620-00 using the ShortXD mode, which has a cross-dispersed echelle configu-
ration and covers 0.8 – 2.5 µm simultaneously in 6 orders. All observations were obtained
through the 0.′′5 slit, resulting in a spectral resolution in the center of each order of R = 1200
(250 km s−1). A nearby A0V star was observed hourly to sample the atmospheric absorption
spectrum. We also observed several spectral type calibration stars in the same configuration
– 4 –
used for A0620-00 (supplemented with similar data from a previous SpeX observing run).
The observations are summarized in Table 1.
All data reduction, calibration, and spectral extraction steps were performed using
Spextool, an IDL-based package developed by the IRTF (Cushing, Vacca, & Rayner 2004;
Vacca, Cushing, & Rayner 2003). The calibration processing steps included flat-fielding,
sky subtraction, optimal spectral extraction, and wavelength calibration. Each A0620-00
exposure was extracted individually to preserve the full 300 sec time resolution. The spectra
were corrected for telluric absorption and flux-calibrated using the A0V stellar spectra as
described by Vacca, Cushing, & Rayner (2003). Finally, the orders were merged for each
exposure to create single spectra covering the full wavelength range. The S/N per resolution
element was ∼4 in the individual spectra. The slit was kept aligned to the parallactic angle
during data acquisition, so the relative fluxes along the full 0.8 – 2.4 µm range are accurate to
≤ 2% (where the upper limit is the uncertainty at 0.9 µm when guiding at 2.4 µm; Cushing
et al. 2004). In addition, stable observing conditions resulted in absolute flux calibrations
of comparable quality. We have not quantified this number as our analysis does not depend
on the absolute flux of the spectrum, but we note for completeness that a rough comparison
of our mean in-band colors to those of Froning & Robinson (2001) and Gelino et al. (2001)
yielded JHK colors within 0.1 mag of their results, well within the level of variability observed
in A0620-00 over long time periods.
For the time-averaged spectrum of A0620-00, we shifted each 300 sec spectrum to
the rest frame of the donor star before median combining, using the orbital ephemeris of
McClintock & Remillard (1986) and the donor star radial velocity amplitude fromMarsh, Robinson & Wood
(1994). The error bars were determined by calculating the median absolute deviation of each
pixel and then propagated through the smoothing and de-reddening steps. We did not cor-
rect for the effects of orbital smearing within an exposure time, but we note that this is
a negligible effect (≤30 km s−1) at our 250 km s−1 spectral resolution. The time-averaged
spectrum is shown in Figure 1. The spectrum has been boxcar-smoothed by 3 pixels, equiva-
lent to one resolution element. Based on the scatter around linear fits to (relatively) line-free
spectral regions, we find that the S/N in the time-averaged spectrum is ∼55 in H and K and
∼45 in J (> 1µm, ∼30 at shorter wavelengths).
Also shown in Figure 1 is the dereddened spectrum of A0620-00, calculated assuming a
reddening along the line of sight of E(B–V) = 0.39 (Wu et al. 1976). Figures 2 – 4 show ex-
panded views of the J,H, and K bands of the spectrum, with prominent spectral absorption
and emission features labeled. Line identifications were made using multiple sources, in-
cluding Wallace et al. (2000), Meyer et al. (1998), Kleinmann & Hall (1986), Harrison et al.
– 5 –
(2004), and the Atomic Line List2.
3. Analysis
The broadband NIR spectrum of A0620-00 shown in Figures 1 – 4 is characterized by a
blue continuum on which are superposed broad (full width at zero intensities ≥4000 km s−1)
emission lines of H I and He II and narrow (full width at half minima ≃ 250 – 400 km s−1)
absorption lines of neutral metals, including transitions of Na I, Mg I, Al I, Si I, K I, Ca I,
Ti I, and Fe I. The emission lines are believed to originate in the accretion disk, while the
absorption features originate in the photosphere of the donor star. The absorption spectrum
is similar to that of a K star, with previous estimates of the spectral type ranging from K3V
to K7V (Oke 1977; González Hernández et al. 2004).
In Figure 5, we show the dereddened spectrum of A0620-00 compared to that of a field
K5V star. The K star has been normalized to A0620-00 near 2.29 µm, just blueward of
the 12CO (2,0) bandhead. The comparison immediately shows that a K5V (or hotter) star
cannot be the only flux source in the NIR. If the K5 star is scaled to the flux of A0620-00
in the K band, it exceeds the dereddened flux by >20% at bluer wavelengths. Adopting the
K4V and K3V spectral types of Gelino et al. (2001) and González Hernández et al. (2004)
results in an even larger disparity between the expected and observed J- and H-band fluxes.
Even a spectral type as late at K7V exceeds the observed flux in A0620-00 by up to 10%
over most of the J and H bands when normalized to 100% contribution in K.
Modest increases in the assumed reddening along the line of sight do not reconcile the
spectrum of A0620-00 with that of a K5V star. Adopting a reddening of E(B–V) = 0.45
brings the 0.8 µm fluxes into agreement, but the template spectrum is still brighter than the
spectrum of A0620-00 at longer wavelengths, including most of the J and H bands. Because
the relative reddening values between H and K are small, the reddening must be increased to
E(B–V) > 1.0 to bring the spectrum of the normalized K5V template below the spectrum of
A0620-00 at all NIR wavelengths. It is extremely difficult to reconcile a reddening this high
with the observed depth of the interstellar absorption feature at 2200 Å in the spectrum of
A0620-00 (Wu et al. 1976). As a result, the fundamental conclusion remains: if the donor
star is the sole source of NIR emission in A0620-00, its spectral type must be later than that
of a K7V. Otherwise, some level of dilution must be present.
The absorption spectrum of A0620-00 resembles that of the K5V template, but there
2http://www.pa.uky.edu/p̃eter/atomic/
– 6 –
is at least one important difference between them: the CO molecular absorption features in
A0620-00 are significantly weaker relative to the metal lines than in the template spectrum.
This difference can affect determinations of the donor star contribution to the NIR spectrum.
For example, the dilution analysis performed by Shahbaz, Bandyopadhyay & Charles (1999)
on the K-band spectrum of A0620-00 is unlikely to be a valid determination of the contribu-
tion of the donor star to the NIR spectrum, since they relied entirely on the relative strength
of the 12CO 2.29 µm feature. The weakness of the CO lines also suggests that other anomalies
may exist in the spectrum, necessitating that its decomposition be undertaken over a wide
wavelength range and using multiple line species and features. Accordingly, we compare the
line equivalent widths and line ratios in A0620-00 with those of field star populations and
model the spectrum using both spectral type standards and synthetic spectra.
3.1. Classification Based on Spectral Indices
Studies using equivalent widths (EWs) and EW ratios to determine the spectral type of
a star or stellar population have been pursued by several groups (e.g., Origlia, Moorwood,
& Oliva 1993; Ali et al. 1995; Förster Schreiber 2000; and sources therein). Of particular
interest to us is the work of Förster Schreiber (2000; hereafter FS), who examined H and
K-band absorption lines to find temperature and luminosity indices and indices sensitive to
dilution of the stellar spectrum by other sources. FS was primarily interested in spectral
trends in giant and supergiant stars as the dominant stellar source in extragalactic NIR
spectra, but his analysis includes some dwarf stars as well.
For comparison, we calculated the EWs of several prominent stellar absorption lines in
the time-averaged spectrum of A0620-00 to compare to the spectral indices in FS. Table 2
gives the measured EWs. The lines were chosen to correspond to those in Table 3 of FS
and were calculated using the same continuum normalization and integration limits. Where
applicable, we also applied the EW correction for spectral resolution from Equations 2 –
4 of FS. The error bars on the EWs are the standard deviation of the mean for several
measurements of each line with variable estimates of the continuum placement.
We first compared our EWs to the spectral indices given in Figure 5 of FS, which presents
temperature and luminosity indicators for stars with solar or near-solar abundances. With
the exception of Si I λ1.59 µm and Mg I λ2.28 µm, all of the lines under analysis show a
strong trend of increasing EWs with decreasing stellar temperature. The EWs in A0620-00
are on the low side of the distributions for these lines, indicating stellar temperatures of
≥5000 K.
– 7 –
We also compared our EWs with those presented in Ali et al. (1995), who concentrated
on temperature indices for dwarf stars. Note that the EWs in Table 2 used to compare
to the Ali et al. (1995) indices are larger than those used for the FS indices because Ali
et al. used a wider wavelength interval for their measurements, which we mirrored. Using
their EW-temperature relationships, we obtain a temperature of 4600±300 K from Ca I and
5000±450 K from Na I. Therefore, if uncorrected for dilution, EWs in A0620-00 point to
a donor star of roughly type K3V star or earlier. However, stars of spectral type K7V or
earlier exceed the observed spectrum of A0620-00 in J and H when zero dilution is assumed
in K. Therefore, we conclude that a diluting continuum source must be present in the NIR
spectrum of A0620-00.
The amount of dilution of the stellar spectrum by another source is determined in FS
by comparing the line ratios of adjacent atomic and molecular features (their Table 8).
Unfortunately, their line ratios use the H and K band CO molecular absorption features,
which we have already seen are not normal in A0620-00. Indeed, a comparison of the 12CO
1.62 µm and 2.29 µm features in A0620-00 gives a result so disproportionately strong in the
1.62 µm line that the ratio doesn’t even appear on the FS spectral index plot. Similarly, a
comparison of the 2.29 µm feature to the nearby Na I and Ca I EWs indicates that the CO
feature is weaker in A0620-00 than in any of the dwarf stars analyzed by FS. These results
indicate that the CO features cannot be used to estimate the non-stellar dilution component
A0620-00.
3.2. Fitting Spectral Type Standard Stars to the Spectrum of A0620-00
In an effort to quantify the contribution of the donor star to the NIR spectrum of A0620-
00 and its dilution by other sources, we compared its spectrum to those of K3V, K5V, and
K7V spectral type standard stars. The standard stars (listed in Table 1) were observed
with the same instrument configuration and calibrated using the same procedures as for the
A0620-00 observations. Before comparing the A0620-00 and template spectra, both were
boxcar-smoothed over 3 pixels (one resolution element). The spectrum of A0620-00 was also
dereddened with E(B–V) = 0.39 (using the reddening curve of Cardelli, Clayton, & Mathis
(1989) and the standard star spectra were convolved with a Gaussian of 83 km s−1 FWHM to
mimic the rotational broadening of the donor star in A0620-00 (Marsh, Robinson & Wood
1994). Note, however, that the rotational broadening is smaller than the 250 km s−1 resolu-
tion of the spectra and has a minimal effect on the results.
We wrote an IDL program to fit scaled template spectra to the spectrum of A0620-00
using the following steps. First, we selected a small wavelength range (typically, 0.1 µm or
– 8 –
smaller) and fit a spline function to the continuum. The continuum points were selected by
eye. After normalizing both the spectrum of A0620-00 and that of the template star and
placing both spectra on a common, linear dispersion, we multiplied the template spectrum
by a fraction, f , which represents the donor star contribution to the spectrum of A0620-00,
and subtracted the scaled donor star spectrum from that of A0620-00. We varied f from 0
to 1 in increments of 0.01 to find the fraction that minimized the rms of the residual in each
waveband. Finally, we repeated this analysis over several spectral lines and groups of lines
over the full NIR spectral range. The fit regions we examined are given in Table 3. The
resulting best values of f and the rms for each fit region and template spectrum is given in
Table 4.
There are few absorption lines in the J band that are both relatively strong and un-
contaminated by emission lines in the A0620-00 spectrum, so our fits were restricted to the
portion of the long J band between Pγ and Pβ (1.10 – 1.26 µm). This region contains a
blend of singly-ionized atomic species, including transitions of Mg I, Fe I, and Si I. The best
fit fractions range from 0.78 to 1.0. There is a disparity between the strongest line in this
range, Mg I λ1.183 µm and the other lines in this band: the Mg I line is best fit at f ∼0.9,
but the other lines are weaker in the template than in A0620-00 even at f = 1.
The situation is less ambiguous in the H band. The best fit to the full H band spectrum
using the K5V standard star is shown in Figure 6. The fit has f = 0.76 and an rms of
0.016. Although the χ2 statistics are relatively poor (χ2ν = 13.5), there is a good qualitative
correspondence between the morphologies of the observed and template spectra. Similar
results are obtained with the K3V and K7V templates. Many of the stronger transitions
(predominately Mg I and Si I lines) are too weak in the f = 0.76 template, however. If
we restrict the fits to narrower regions around these lines, we generally obtain higher f and
better fits (e.g., χ2ν = 5.2 for the 1.48 – 1.52 µm region fit by the K5V template).
The large χ2ν values for our fits indicate that our error bars are undersized relative to
the true uncertainty in the fits. This is unsurprising, given the systematic uncertainties
that affect modeling of NIR spectra in faint compact binaries, including the influence of
sky background and telluric absorption correction, uncertain placement of the continuum
level where no true continuum exists, and complex line blending wherein small temperature
and/or abundance variations between the template and target stars can affect fit results. As
a result, we have chosen to determine the mean value and uncertainty in the H-band donor
star contribution by using an average of fits to multiple lines and multiple templates over
the full waveband, rather than thorough the use of χ2 statistics, as we believe the scatter
between line fits provides a more rigorous sampling of uncertainties, particularly systematics.
We determined the best representative value for the H band donor star contribution by
– 9 –
averaging the best-fit f values for the three narrowband H fit regions (1.48 – 1.52 µm, 1.56–
1.61 µm, and 1.70–1.72 µm) and the K5V and K7V templates. Averaging these values for
the K5V and K7V template stars gives a donor star fraction f = 0.82±0.02.
In K, we fit three regions: the spectrum shortward of He I λ2.058 µm, which is dominated
by Ca I absorption lines; the region between He I and Bγ, which includes transitions of
Mg I, Al I, and Si I; and the region longward of Bγ, which contains a rich blend of features,
including transitions of Na I, Ca I, Fe I, Ti I, Mg I, and CO. Note that we do not have any
fit results for the K3V template to the K-band spectrum, because the absorption lines in the
K3V template are too weak relative to those of A0620-00, even at f=1. We have already
shown from the comparison of the SEDs of A0620-00 and a K3V star that a star this hot
cannot be the sole emission source (i.e., have f = 1) in A0620-00 in K without exceeding
the observed spectrum at shorter wavelengths. Now we see that a K3V star also cannot be
reconciled to the spectrum of A0620-00 by decreasing its fractional contribution, because its
absorption lines are already too weak at f = 1 to match those observed in A0620-00. As a
result, we restrict our fits in K to K5V and K7V templates.
The Ca I lines from 1.90 – 2.02 µm could not be simultaneously fit by a single value for
f . The fit values given in Table 4 appear to the eye to be overdiluted as a result of spurious
features (residuals of the telluric absorption correction) driving the fits. The strongest lines
— 1.978 and 1.987 µm — are fit by f ∼ 0.5, but at this value the other lines in this region
are too weak. This spectral region may be contaminated by Bδ λ1.945 µm emission from
the accretion disk. Problems also beset the spectral fits in the 2.07 – 2.15 µm region. The
K5V and K7V stellar spectra have anomalous emission bumps at 2.14 µm that cause visibly
overdiluted fits over the full wavelength range. If the fits are restricted to 2.07 – 2.13 µm,
best fits are obtained for f ∼ 0.65, while fits to the strongest feature alone, Al I 2.117 µm,
gives f = 0.75 for both the template fits.
The final fit region was the long-K portion of the spectrum, 2.18 – 2.42 µm, which
includes numerous atomic species transitions and the CO bandheads. Figure 7 shows the
best fits for the K5V template over the full fit region and when the fit is restricted to
λ < 2.28 µm, excluding the region dominated by the CO lines. When long K is fit in
its entirety, the fits are driven to large dilutions of the donor star to match the weak CO
absorption in the A0620-00 spectrum. At these low donor fractions (f = 0.45 for the K5V
template and f = 0.37 for the K7V template), the atomic lines are too weak in the template
spectrum relative to those in A0620-00. If the fit is restricted to 2.18 – 2.28 µm, the donor
fractions rise to f = 0.81 (K5V) and f = 0.76 (K7V). At these values, the atomic absorption
spectrum of A0620-00 is well fit although there remain discrepencies between template and
target spectra, most notably in the red components of Na I λ2.209 and λ2.339 µm and in
– 10 –
the Fe I lines from 2.226 – 2.247 µm, all of which are too weak in the template relative
to A0620-00. A single discrepancy in Fe I may explain these deviations, as there are Fe I
transitions coincident with both of the ”Na I” lines (see Figure 6 of FS for an illustration of
the complex line blending in this spectral region).
3.3. Fitting Model Spectra to the Spectrum of A0620-00
In addition to modeling A0620-00 with standard star spectra, we used the LinBrod
program to generate synthetic spectra for a Roche lobe-filling star in a compact binary
with the geometry of A0620-00 (Bitner & Robinson 2006). We adopted the following pa-
rameter values for the models: Porb = 0.323 d, q = 0.067, i = 41
◦, and K2 = 433 km s
(McClintock & Remillard 1986; Marsh, Robinson & Wood 1994; Gelino et al. 2001). We cre-
ated phase-resolved spectra for donor star temperatures of T = 4000, 4250, 4500, 4750, and
5000 K. Finally, we also created models at each temperature in which the carbon abundance
in the star was reduced to [C/H] = -0.5, -1.0, -1.5, and -2.0. To compare to the observed
spectrum of A0620-00, we averaged the model spectra over the binary orbit after removing
the donor star orbital motion and smoothed the spectra to the observed spectral resolution.
Because the SED and spectral type standard star fits to the A0620-00 spectrum point
to a donor star spectral type later than K3V, or T < 5000 K, we concentrated on the T =
4000, 4250, and 4500 K models. In an effort to characterize the carbon depletion required to
match the observed CO line depths, we also focused on the long-K portion of the spectrum
(2.18 – 2.42 µm) . Table 5 gives fit results for the LinBrod model fits. We first fit the solar
abundance models and then repeated the fits for the carbon-depleted spectra. Figure 8 shows
the normalized long K spectrum of A0620-00 with the solar abundance, T = 4000 K model
and with the T = 4000 K, [C/H] = -1.5 spectrum. The model spectra has been scaled by
f = 0.77, the best fit donor fraction for the 2.18 – 2.28 µm region. The [C/H] = -1.5 models
provided the best fit to the spectrum of A0620-00 for all three of the donor temperatures
examined (χ2ν = 4.0 for the T=4000 K, [C/H] = -1.5 model fit to 2.28 – 2.39 µm, versus
χ2ν = 5.9 and χ
ν = 5.2 for the [C/H] = -1.0 and -2.0 models, respectively). The -0.5 and
-1.0 models had CO lines that were still too strong relative to those of A0620-00, while the
CO features were virtually absent in the -2.0 models and too weak to match the observed
spectrum.
– 11 –
4. Discussion and Conclusions
4.1. The Donor Star in A0620–00
4.1.1. The Donor Star Spectral Type and Fractional Contribution to the NIR Spectrum
Our analysis of the NIR spectrum of A0620-00 has demonstrated three principal results:
1) the donor star is not the only NIR flux source, with 18±2% of the H-band flux originating
in another component of the binary; 2) the donor star must be later than a K3V spectral
type; and 3) the CO absorption lines are anomalously weak, requiring a carbon abundance
of [C/H] = -1.5 in the donor star to match the observed line depths.
A comparison of the broadband NIR SED of A0620-00 with those of spectral type
standard star spectra shows that the donor star cannot be the sole source of NIR flux. If
the standard star spectra are normalized to the dereddened spectrum of A0620-00 in the
K-band, they exceed the observed flux in the J and H wavebands. This result is true for all
standard star spectra earlier than M0V. The discrepancy cannot be reconciled by changes
in the differential reddening correction because the relative reddening correction between K
and J and H is too small. Additionally, the K-band absorption lines in the K3V standard
star are too weak to match the line depths seen in the A0620-00 spectrum even at a 100%
donor star contribution. Decreasing the donor star contribution to f < 1 will only make the
template lines weaker, so a K3V spectral type for the donor star is ruled out.
The most precise measurement of the donor star temperature is by González Hernández et al.
(2004), who fit synthetic spectra created from model atmospheres to the visible spectrum of
A0620-00. They found that T2 = 4900 ± 100 K, which corresponds to a K2/K3V spectral
type. This result is not in agreement with our requirement that the donor star be later than
K3V. There are reasons to believe that the González Hernández et al. (2004) results may be
unreliable, however. To determine the stellar parameters they used 24 Fe I lines, to which
they fit models with five free parameters: stellar temperature, gravity, and metallicity, as
well as a normalization and slope to represent dilution from the accretion disk. The use of
Fe I lines alone to constrain all stellar parameters (plus the disk contribution) is uncommon
practice for stellar modeling, which typically relies on independent determinations of the
stellar temperature, as well as on both Fe I and Fe II transitions. González Hernández et al.
(2004) also determined that the abundances of the elements they fit were slightly above solar
values. The adoption of a cooler donor star temperature, as required by our results, will
reduce their derived abundances.
We conclude that the spectral type of the donor star is most likely between K5V to
K7V, but do not attempt to constrain the spectral type more precisely. The rms values
– 12 –
for the dilution fits to various regions of the A0620-00 spectrum are comparable for both
spectral types and we cannot rely on the CO features to create more precise temperature
indices. We therefore averaged the dilution values from both spectral type fits for the three
narrow regions in the H-band to derive our H-band donor star fraction: f = 0.82 ± 0.02,
or an 82% donor star contribution in H. The donor fraction in long K (> 2.2µm) is 81%
for a K5V template or 76% for the K7V. Figure 9 shows the spectrum of A0620-00 with
a K5V template star scaled to 82% of the H-band flux and the A0620-00 spectrum after
the contribution of the donor star has been subtracted. While the spectrum of A0620-00 is
dominated by the K type donor, there is a significant second component consisting of a blue
continuum and strong H I and He II line emission.
Our results of a K5V to K7V donor star spectral type and 18% – 24% veiling in H
and K do not agree with those of Gelino et al. (2001), who found that the NIR SED of
A0620-00 matched that of a K4V (T = 4600 K) star with no dilution. As pointed out by
Hynes et al. (2005), however, there is a degeneracy between the spectral type of the star and
the amount and distribution of a veiling spectrum in an XRB: a cooler donor star plus a
diluting component can result in the same SED as a hotter donor star with no contamination.
Hynes et al. showed that even a 100 K overestimate of the temperature of the donor star
could result in a factor of two underestimate of the veiling. Because our data show, both
in the line EWs and the NIR SED, that a K type donor star cannot be the only NIR flux
source, we conclude that Gelino et al. (2001) overestimated the temperature of the donor
star and consequently underestimated the spectral dilution in the NIR.
Our results also disagree with the recent work of Harrison et al. (2007), who argue by
analogy with the IR spectrum of the cataclysmic variable SS Cygni that A0620-00 has <4%
dilution in the K-band. Their argument can be summarized as follows: a) A0620-00 and
SS Cyg have similar K-band spectral slopes, binary properties, and quiescent mass accretion
rates; b) SS Cyg also has a mid-IR excess; c) the NIR and MIR SEDs of SS Cyg can be
well fit by a K4V stellar spectrum plus free-free emission; d) because A0620-00 and SS Cyg
are similar, application of the star plus wind model can be extended from the latter to the
former to estimate a ∼4% limit on the contamination level of the NIR spectrum of A0620-00.
We have several concerns about this line of reasoning. First, as already discussed above,
the similarity of a SED to that of a field star does not preclude contaminating emission
from the disk. The data shown in Harrison et al. reinforce this: the JHK colors of SS Cyg
are consistent with that of an undiluted K4V star even as the ellipsoidal light curves show
clear evidence of contamination. In fact, Harrison el al. point out that the K-band spectrum
of A0620-00 has a different slope from those of the field stars, which provides fairly clear
evidence of contamination. Second, it is not known whether free-free emission is the correct
– 13 –
explanation for the excess MIR flux observed in SS Cyg. Another possibility discussed by
Dubus et al. (2004), who originally published the IR SED shown by Harrison et al., is that
circumbinary disk emission is responsible. Indeed, Muno & Mauerhan (2006) have found a
MIR component in A0620-00, which they fit with a ≃600 K blackbody component, consistent
with emission from circumbinary dust rather than free-free emission in a wind. The cool
blackbody component found by Muno & Mauerhan (2006) does not affect the NIR spectrum
of A0620-00, which suggests that the attempt to use MIR data from SS Cyg to estimate the
NIR contamination in A0620-00 is a red herring. Finally, we reiterate what our simultaneous,
JHK spectra of A0620-00 indicate directly about the donor star contamination in the system:
based on the shape and fluxes of the JHK continuum spectrum, the absolute EWs of the
atomic absorption lines, and dilution analyses using both field stars and a Roche-lobe filling
model spectrum, the donor star must be significantly diluted (∼20%), even in the K-band.
4.1.2. Weak CO Features in the Donor Star Spectrum
Although the atomic absorption line spectrum in A0620-00 is consistent with a K5V –
K7V spectral type, the molecular 12CO lines are significantly weaker in A0620-00 than in
a field star, corresponding to CO line strengths normally seen in early G stars. Using the
LinBrod model spectra of a Roche lobe-filling star, we found that reducing the C abundance
to [C/H] = -1.5 results in a better match to the CO lines in the spectrum than the [C/H] =
0, -1.0, and -2.0 models when the donor star fraction is fit to f = 0.77.
The weakness of the 12CO lines in A0620-00 has already been noted by Harrison et al.
(2007), who determine that the 12C abundance must be decreased 50% to match the depth
of the 12CO bandheads. The 50% reduction in 12C abundance ([12C/H] = -0.3) found by
Harrison et al. is significantly smaller than the 97% drop we claim. Again, however, we
have several concerns about the method by which Harrison et al. obtained their results.
First, they started with the line list included in the spectral synthesis program SPECTRUM
(Gray & Corbally 1994), but when they were unable to match the spectra of standard spec-
tral type field stars using this line list (and Kurucz atmospheres) due to the presence of
strong absorption features in the model but not the observed spectra, they abandoned it
and constructed one consisting only of Na I, Mg I, and CO transitions. When they found
that the lines in their new models were too weak to match those of field stars at the correct
temperature, they globally increased the log(gf) values of every line in their new line list
to match up with observations. They then applied this revised model to the spectrum of
A0620-00, adjusting the C isotopic abundances until the best fit by eye was achieved.
We are not confident in the quantitative reliability of spectral model fits in which spectral
– 14 –
lines have been dropped and oscillator strengths altered in order to achieve even a rough fit
to a K5V field star. We note in contrast that our LinBrod models give fits to the spectrum
of A0620-00 of comparable quality of those using template field stars with no deletions or
alterations to the spectral synthesis line lists required. Our other concern with the Harrison
et al. fits is the placement of the continuum and evaluation of the best model fit. They
determined the best-fit model by eye. To our eyes, however, the fits they show in their
Figure 3 do not properly take into account the actual data quality: their pseudo-continuum
levels appear too high and their CO line minima are too low in their preferred model. A
rough comparison of their observed spectrum to ours shows that the 12CO normalized line
depths are similar in both data sets, suggesting that a statistical model fit to their spectrum
would result in a 12C abundance similar to the one we obtain.
Finally, Harrison et al. contend that in addition to a low 12C abundance in A0620-00, the
13C abundance is enhanced, such that 13C/12C = 1. They base their identification of 13CO
on the presence of a feature coinciding with the 13CO(3,1) 2.374 µm bandhead. However,
they also note that the 13CO(2,0) 2.345 µm is not seen in their spectrum, despite being the
stronger feature of the two. Given the poor atmospheric conditions at the time their data
was taken and the increasing amount of telluric H20 absorption at these wavelengths, we
do not believe that their data provide a clear detection of 13CO and certainly not of 13C at
equal abundance with 12C. In our spectrum of A0620-00, there is a feature at the location of
the 13CO(2,0) 2.345 µm bandhead, but no feature coinciding with 13CO(3,1) 2.374 µm. We
have marked the locations of the first two 13CO bandheads in our Figure 4. Dhillon et al.
(2002) point out, however, that a Ti I feature is coincident with the 13CO(2,0) 2.345 µm
bandhead and is a much more likely explanation of the feature we see. As a result, we do
not believe that an unambiguous detection of 13CO can be made in our spectrum and we
find no evidence of any enhancement of this species in A0620-00.
Anomalously weak CO absorption features have been seen in other compact binary sys-
tems. The NIR spectra of several cataclysmic variables show weak or absent 12CO absorption
(Harrison et al. 2000, 2004). In the dwarf nova U Gem, the NIR CO absorption lines are sig-
nificantly weaker than in the M3V standard star spectrum that provides a good match to the
atomic lines. Model fits to the FUV spectrum of the metal-enriched white dwarf in U Gem
show that the C abundance on the WD surface is [C/H] = -1.0, while the N abundance
is highly super-solar, [N/H] = 0.7 (Sion et al. 1998; Long & Gilliland 1999; Froning et al.
2001). Similarly, in the UV spectrum of the BH XRB XTE J1118+480 in outburst, typically
strong emission lines of C IV and O V are undetectable, while the N V λ1240 Å appears
enhanced (Haswell et al. 2002). The UV line ratios are inconsistent with photoionization
models, leading Haswell et al. to conclude that the emission spectrum is indicative of the
accretion of C-depleted material from the donor star. As a result, A0620-00 can be added
– 15 –
to the ever-increasing list of cataclysmic variables and XRBs that show depleted C (and, in
some cases, enhanced N), pointing to a common history of nuclear processing of C to N in
compact binary systems.
4.2. The Mass of the Black Hole in A0620–00
Based on previous work, the mass of the BH in A0620-00 is known to the value of
one unknown, the binary inclination: M1 = (3.09± 0.09) sin
−3 i (Marsh, Robinson & Wood
1994). The orbital inclination can be obtained by modeling the light curve of the donor star.
The donor star fills its Roche lobe and is distorted in shape, which leads to a double-humped
ellipsoidal variation in the light curve, the amplitude of which is dependent on inclination. If
a source besides the donor star contributes to the light curve, the amplitude of the ellipsoidal
variation will be diluted, leading to an underestimate of the inclination and a corresponding
overestimate of the BH mass if the contaminating source is not taken into account.
The most precise inclination results to date were reported by Gelino et al. (2001), who
modeled JHK light curves of A0620-00. Based on good agreement between the target SED
and that of a dereddened K4 star, they concluded that the donor star is the only NIR
continuum source in A0620-00. Using this assumption, they modeled the ellipsoidal light
curve and found i = 40.◦75± 3◦ and M1 = 11.0± 1.9 M⊙. As discussed above, however, the
NIR SED alone is insufficient to resolve the degeneracy between donor star temperature and
veiling by another flux source in the system. Our results indicate that the donor star cannot
be the only NIR flux source in A0620-00 and that consequently, the Gelino et al. results
overestimate the BH mass in A0620-00.
We previously modeled the H-band light curve in A0620-00 with a donor star plus accre-
tion disk model and determined 38◦ ≤ i ≤ 75◦, or 3.3 ≤ M1 ≤ 13.6M⊙ (Froning & Robinson
2001). The broad range of values was caused by a degeneracy between the inclination
and the fractional contribution of the accretion disk to the H-band light. Table 5 of
Froning & Robinson (2001) gives the inclination in A0620-00 as a function of the fractional
contribution of diluting sources in the H-band. In § 3.2 of this paper, we determined that
the donor star contributes 82±2% of the H-band flux in A0620-00. This result, a diluting
fraction of 18±2%, combined with Table 5 in Froning & Robinson (2001) gives a binary
inclination for A0620-00 of i = 43± 1◦.
Based on this inclination, we obtain the mass of the BH accretor in A0620-00: M1 =
9.7±0.6M⊙. This result is comparable to previous estimates of the BH mass in the literature.
Shahbaz, Naylor & Charles (1994) found a BH mass of 10 M⊙, while Gelino et al. (2001)
– 16 –
found M1 = 11.0±1.9 M⊙. The inclination we derive is within the error interval of Gelino
et al. The difference in BH masses between the two results comes from the slightly higher
inclination we adopt as a result of our determination that the donor star cannot be the sole
NIR emission source.
The error bar on our derived BH mass represents the propagated statistical errors in
the result. A potential source of systematic uncertainty is our assumption that the atomic
absorption spectrum of A0620-00 can be modeled by template spectra with solar abundances.
The fact that the C abundance in A0620-00 has to be decreased significantly to match the
CO lines suggests the need for caution in this regard. However, the relative line ratios of
the atomic transitions largely agree with each other in the derived fractional donor star
contributions. These lines are also strong transitions that lie on the flat portion of the curve
of growth and will not be sensitive to small abundance variations. Finally, we note that while
González Hernández et al. (2004) derived slightly super-solar abundances for the metal lines
in A0620-00, they used a stellar temperature that is too hot to be consistent with the NIR
SED. The adoption of a cooler temperature for the donor star will cause the metal line
abundances required to fit the optical spectrum to decrease.
Another potential source of systematic error is the large time interval (8 years) between
acquisition of the NIR light curve and the spectra. Our analysis assumed that the donor star
diluting fraction found by analyzing the spectra applies equally well to the light curve data.
This assumption is valid, we believe, because while A0620-00 is variable, its NIR colors typi-
cally don’t vary by more than 0.2 mag, and six observations of the H-band light curve spaced
over days to years had mean colors that agreed to within 0.04 mag (Froning & Robinson 2001;
Gelino et al. 2001). Our rough estimate of the absolute calibration of our time-averaged
spectrum was also consistent with the previous measurements. We can estimate the uncer-
tainty in the non-donor star contribution by assuming that it could vary by ±4%, consistent
with the previous measurements. This would cause the donor star fraction to range from
79 ≤ f ≤ 86, which results in i = 43± 1◦, consistent with our statistical uncertainties.
We thank Nathaniel Cunningham for assistance in observing A0620-00, and the staff at
the IRTF for their support. We also thank Chris Sneden and Niall Gaffney for their help in
calculating the LinBrod donor star spectra and for useful discussions.
Facilities: IRTF(SpeX)
– 17 –
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This preprint was prepared with the AAS LATEX macros v5.2.
– 20 –
– 21 –
Table 1. SpeX Observations
Object Date (UT) Instrument Texp (min) Φ
A0620-00 2004 Jan 8 SpeX 290 0.59 – 1.47
A0620-00 2004 Jan 9 SpeX 280 0.69 – 1.49
A0620-00 2004 Jan 10 SpeX 250 0.92 – 1.61
HD42606 (K2.5 III) 2004 Jan 18 SpeX 1.2 · · ·
HD 3765 (K2 V) 2004 Jan 18 SpeX 2 · · ·
HD16160 (K3 V) 2004 Jan 19 SpeX 1.8 · · ·
61 Cyg A (K5 V) 2000 Sept 15 SpeX 0.5 · · ·
61 Cyg B (K7 V) 2000 Sept 15 SpeX 0.5 · · ·
aOrbital phase coverage of A0620–00 for each night’s observations, based
on the ephemeris of McClintock & Remillard (1986).
– 22 –
Table 2. Equivalent Widths of Selected Absorption Lines
Feature EWa (Å) EWb (Å)
Si I 1.5892 1.52±0.04 · · ·
12CO (6,3) 1.6187 0.86±0.07 · · ·
Na I 2.2076 0.94±0.06 2.18±0.04
Fe I 2.2263 0.36±0.05 · · ·
Fe I 2.2387 0.40± · · ·
Ca I 2.2636 1.06±0.06 3.21±0.03
Mg I 2.2814 0.43±0.04 0.68±0.06
12CO (2,0) 2.2935 0.38±0.06 2.26±0.08
12CO (3,1) 2.3227 0.22±0.02 · · ·
13CO (2,0) 2.3448 0.64±0.04 · · ·
aEWs calculated using the integration lim-
its of Förster Schreiber 2000.
bEWs calculated using the integration lim-
its of Ali et al. (1995).
– 23 –
Table 3. Wavelength Ranges for Spectral Fits
Waveband λ Range (mum) Description
J 1.10 – 1.26 Long J
1.175 – 1.215 Blend incl. Mg I, Fe I, Si I
H 1.4 – 1.8 Full H band
1.48 – 1.52 Mg1 lines.
1.56 – 1.61 Blend incl. Mg I, Si I
1.70 – 1.72 Mg1
K 1.90 – 2.02 Several Ca I lines.
2.07 – 2.15 Short K incl. Mg I, Si I, Al I.
2.18 – 2.42 Long K incl. CO bandhead.
2.18 – 2.28 No CO, lines incl. Na I, Fe I, Ca I, Mg I.
– 24 –
Table 4. Template Star Fits to A0620–00 Spectrum
Template Wavelength Range Template Fraction rms
Spectral Type (µm) (f)
K3V 1.10–1.26 0.78 0.012
1.175 – 1.215 0.82 0.010
1.4–1.8 0.76 0.016
1.48 – 1.52 0.71 0.011
1.56 – 1.61 0.81 0.011
1.70 – 1.72 0.91 0.009
K5V 1.10 – 1.26 0.90 0.013
1.175 – 1.215 1.0 0.010
1.4 – 1.8 0.78 0.016
1.48 – 1.52 0.82 0.010
1.56 – 1.61 0.88 0.015
1.70 – 1.72 0.78 0.010
1.90 – 2.02 0.37 0.02
2.07 – 2.15 0.52 0.01
2.18 – 2.42 0.45 0.012
2.18 – 2.28 0.81 0.009
K7V 1.10 – 1.26 0.87 0.013
1.175 – 1.215 0.99 0.011
1.4 – 1.8 0.76 0.017
1.48 – 1.52 0.82 0.010
1.56 – 1.61 0.85 0.015
1.70 – 1.72 0.77 0.009
1.90 – 2.02 0.39a 0.021
2.07 – 2.15 · · · b · · ·
2.18 – 2.42 0.37 0.014
2.18 – 2.28 0.76 0.009
– 25 –
aFits too diluted due to noise in spectra.
bFits compromised by spurious feature in template.
– 26 –
Table 5. LinBrod Fits to A0620–00 Spectrum
Model Temperature Model C Abundance Wavelength Range Template Fraction rms
(K) (log[C/H]/[C/H]⊙) (µm) (f)
4000 0.0 2.18 – 2.28 0.72 0.011
4250 0.0 2.18 – 2.28 0.76 0.011
4500 0.0 2.18 – 2.28 0.99 0.011
Full Long K Region Including CO Lines
4000 0.0 2.18 – 2.38 0.14 0.015
4000 -0.5 2.18 – 2.38 0.28 0.014
4000 -1.0 2.18 – 2.38 0.54 0.012
4000 -1.5 2.18 – 2.38 0.78 0.011
4000 -2.0 2.18 – 2.38 0.74 0.012
4250 0.0 2.18 – 2.38 0.14 0.015
4250 -0.5 2.18 – 2.38 0.28 0.014
4250 -1.0 2.18 – 2.38 0.56 0.013
4250 -1.5 2.18 – 2.38 0.82 0.012
4250 -2.0 2.18 – 2.38 0.81 0.012
4500 0.0 2.18 – 2.38 0.17 0.015
4500 -0.5 2.18 – 2.38 0.35 0.014
4500 -1.0 2.18 – 2.38 0.71 0.013
4500 -1.5 2.18 – 2.38 0.96 0.012
4500 -2.0 2.18 – 2.38 0.93 0.013
Longward of the 2.29 µm Bandhead Onlya
4000 -0.5 2.28 – 2.38 0.77 0.025
4000 -1.0 2.28 – 2.38 0.77 0.014
4000 -1.5 2.28 – 2.38 0.77 0.012
4000 -2.0 2.28 – 2.38 0.77 0.013
4250 -0.5 2.28 – 2.38 0.77 0.024
– 27 –
Table 5—Continued
Model Temperature Model C Abundance Wavelength Range Template Fraction rms
(K) (log[C/H]/[C/H]⊙) (µm) (f)
4250 -1.0 2.28 – 2.38 0.77 0.014
4250 -1.5 2.28 – 2.38 0.77 0.012
4250 -2.0 2.28 – 2.38 0.77 0.013
4500 -0.5 2.28 – 2.38 0.77 0.020
4500 -1.0 2.28 – 2.38 0.77 0.014
4500 -1.5 2.28 – 2.38 0.77 0.013
4500 -2.0 2.28 – 2.38 0.77 0.014
aDonor star fraction fixed in these models to the best-fit value to the nearby atomic lines
from the template star fits.
– 28 –
Fig. 1.— The NIR spectrum of A0620–00, obtained in 2004 January. The solid line shows
the time-averaged spectrum of A0620. Individual exposures were shifted to remove the
orbital motion of the donor star before averaging. The dotted line shows the spectrum after
dereddening, assuming E(B–V) = 0.39 (Wu et al. 1976).
Fig. 2.— The spectrum of A0620-00 in J. Prominent spectral features are labeled. An error
bar representative of the statistical uncertainty per resolution element is plotted on the far
right of the plot. Also shown at the bottom of the figure is the spectrum of HD45137, the
A0V star used for telluric correction of the A0620–00 spectra. The spectrum retains the
throughput profile of each spectral order but is not shown with absolute flux calibration.
The H I lines intrinsic to the A0V spectrum have been fitted and removed using the xtellcor
program developed by the IRTF.
Fig. 3.— The spectrum of A0620-00 in H. Prominent spectral features are labeled. A
representative error bar for a resolution element is plotted on the far right. The telluric
spectrum is also shown at the bottom of the figure.
Fig. 4.— The spectrum of A0620-00 in K. Prominent spectral features are labeled. A
representative error bar for a resolution element is plotted on the far right. The telluric
spectrum is also shown.
Fig. 5.— Shown in black is the dereddened spectrum of A0620-00. Shown in gray is the
spectrum of 61 Cyg A, a K5V spectral type star. The spectrum of 61 Cyg A has been
normalized to the flux of A0620 just blueward of the 12CO 2.29 µm bandhead.
Fig. 6.— The normalized H-band spectrum of A0620–00 with a scaled spectral type standard
star fit. The standard star, shown in red, is 61 Cyg A, a K5V star. It has been scaled by
f = 0.76.
Fig. 7.— The normalized K-band spectrum of A0620–00 with a scaled spectral type standard
star fit. The template star is 61 Cyg A, a K5V star. The solid red spectrum shows the
template scaled by f = 0.45, the best fit over the full 2.18 – 2.42 µm range. The dashed red
spectrum shows the template scaled by f = 0.81, the best fit to the 2.18 – 2.28 µm region.
Fig. 8.— The normalized K-band spectrum of A0620–00 with scaled LinBrod T = 4000 K
model spectra fits. The solid red line shows the LinBrod model with [C/H] = -1.5, while the
dashed red line shows the solar abundance model. To avoid confusion, the latter is shown
only for λ > 2.288 µm. The models are scaled by f = 0.77.
Fig. 9.— The top panel shows the dereddened spectrum of A0620-00 in black and the
spectrum of 61 Cyg A, a K5V star, in gray. The spectrum of the K5V template has been
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scaled to 82% of the A0620-00 flux at the center of the H band, 1.6 µm. The lower panel shows
the NIR spectrum of the accretion disk in A0620-00, created by subtracting the template
spectrum from that of A0620-00.
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	Introduction
	Observations and Data Reduction
	Analysis
	Classification Based on Spectral Indices
	Fitting Spectral Type Standard Stars to the Spectrum of A0620-00
	Fitting Model Spectra to the Spectrum of A0620-00
	Discussion and Conclusions
	The Donor Star in A0620–00
	The Donor Star Spectral Type and Fractional Contribution to the NIR Spectrum
	Weak CO Features in the Donor Star Spectrum
	The Mass of the Black Hole in A0620–00
