The Donor of the Black Hole X-Ray Binary MAXI J1820+070

MAXI J1820+070 is relatively nearby, with a distance of D ≈ 2.96 ± 0.33 kpc measured based on a radio parallax (Atri et al. 2020). This agrees well with the current Gaia EDR3 parallax measurement of $D={2.81}_{-0.39}^{+0.70}$ kpc (Bailer-Jones et al. 2021). Then, Wood et al. (2021) determined D ≤ 3.11 ±0.06 kpc based on the proper motion of two moving transient ejecta (Mirabel & Rodríguez 1994) during the hard-to-soft state transition, assuming the approaching and receding ejecta were identical. The upper limit of 3.17 kpc corresponds, however, to the minima of both angular velocities and to the bulk Lorentz factor of Γ → ∞. The Lorentz factors of the transient ejecta measured in X-ray binaries are generally low, at most a few (Miller-Jones et al. 2006). In the present case, D = 3 and 3.1 kpc correspond to rather large Γ ≥ 3.4 and 5.1, respectively. Therefore, the measurement by Wood et al. (2021) appears to imply D ≲ 3 kpc for realistic ejecta Lorentz factors.

The binary orbital period is P = 0.68549 ± 0.00001 days (Torres et al. 2019), and the inclination of the binary is constrained at 3σ to i ≈ 662–808 (Torres et al. 2020). While the latter is consistent with the inclination of the jet, i_j ≈ 64 ± 5° (Atri et al. 2020; Wood et al. 2021), the jet and binary axes have been estimated to be strongly misaligned (Poutanen et al. 2022), in which case the jet inclination cannot be used to constrain the system masses.

Torres et al. (2020) established the rotational line broadening of the companion of ${v}_{\mathrm{rot}}\sin i=84\pm 5$ km s⁻¹, which, in combination with the radial velocity semiamplitude (K₂ = 417.7 ± 3.9 km s⁻¹), yields (assuming corotation and Roche-lobe filling) the mass ratio of q = M₂/M₁ ≈ 0.072 ± 0.012, where M₁ and M₂ are the masses of the BH and its companion star. These uncertainties are 1σ. Torres et al. (2020), following Marsh et al. (1994), obtained 2σ limits of 5.73 < M₁/M_☉ < 8.34 and 0.28 < M₂/M_☉ < 0.77 by combining the 1σ uncertainties in the measured orbital parameters with the extreme limits for the range of allowed inclinations. On the other hand, here we have performed Monte Carlo simulations assuming Gaussian distributions of ${v}_{\mathrm{rot}}\sin i$ and K₂ (which give q via Equation (4) of Ziółkowski & Zdziarski 2017), P, and a flat distribution of $\cos i$ within the range given above. This gives us probabilistic estimates of M₁ and M₂ and the donor radius, R₂ $[=P({v}_{\mathrm{rot}}\sin i)/(2\pi \sin i)$]. The results are shown in Figure 1, and they imply ${M}_{2}={0.49}_{-0.10}^{+0.10}\,{M}_{\odot }$, ${R}_{2}={1.19}_{-0.08}^{+0.08}\,{R}_{\odot }$, and ${M}_{1}={6.75}_{-0.46}^{+0.64}{M}_{\odot }$, where we give the median and the 68% confidence ranges. Because the radii of main-sequence stars can be roughly approximated by ${R}_{\mathrm{MS}}/{R}_{\odot }\approx {(M/{M}_{\odot })}^{0.9}$, the above range of the donor radius implies that the donor is a moderately evolved star (a subgiant).

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The donor average spectrum from observations by the Gran Telescopio Canarias (GTC) during the quiescence after the outburst was found to approximately match those of the K3–5 V main-sequence templates (Torres et al. 2020). The effective temperatures of those stars are given by Pecaut & Mamajek (2013) to be 4840–4450 K. We have, however, reanalyzed that spectrum and found a strict limit of T > 4200 K based on the lack of molecular bands (TiO and CN) expected at T ≤ 4200 K. This limit approximately corresponds to a K6 stellar type, and we use it in our analyses below.

We have compiled available ultraviolet to mid-infrared measurements of the binary during its quiescence from literature and public databases. These are listed in Tables 1 to 3, which also provide references to the photometric databases that were explored. In order to constrain the spectral distribution of the donor star, the collected fluxes need to be corrected for interstellar extinction. The total reddening through the Galaxy in the direction of the source has been estimated by Schlafly & Finkbeiner (2011) to be E(B – V) = 0.197 and E(B – V) = 0.23 by Schlegel et al. (1998). Because the source is located ≈ 0.5 kpc above the Galactic disk (see Section 2.3), the extinction toward it is likely to equal the total one in the direction of the target. We can also use the relationship between the extinction in the V band (A_V ) and the H column density (N_H) estimated from fitting X-ray data (Güver & Özel 2009), N_H = (2.21 ± 0.09) × 10²¹ A_V cm⁻². Here, A_V is given by A_V = 3.1E(B − V). The values of N_H obtained from fitting XMM-Newton (Kajava et al. 2019), NICER (Bharali et al. 2019), and the X-Ray Telescope (Burrows et al. 2000) on board Neil Gehrels Swift (Wang et al. 2021) data for MAXI J1820+070 are ${1.4}_{-0.3}^{+0.3}\times {10}^{21}$, ${1.6}_{-0.2}^{+0.3}\times {10}^{21}$, and ${1.73}_{-0.07}^{+0.10}\times {10}^{21}$ cm⁻², respectively. These values correspond (including the uncertainty of the conversion) to the range of E(B – V) ≈ 0.20–0.26. To calculate the extinction at other wavelengths, A_λ , we used A_V and the fitting formulae of Cardelli et al. (1989). Then, the observed magnitudes, m_λ , can be transformed into the observed, F_{ν, obs}, and unabsorbed, F_ν , fluxes, as

$$\begin{eqnarray}&&{F}_{\nu ,\mathrm{obs}}={F}_{0}{10}^{-{m}_{\lambda }/2.5},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{F}_{\nu }={F}_{\nu ,\mathrm{obs}}{10}^{{A}_{\lambda }/2.5},\end{eqnarray} \tag{ 2 }$$

where F₀ is the flux corresponding to a zero magnitude.

Table 1. The Minimum Observed Fluxes for MAXI J1820+070

Source	Band	〈λ〉 (μ m)	Fν, obs (μJy)	〈Fν,obs〉 (μ Jy)	${10}^{{A}_{\lambda }/2.5}$	Dates
PS1	y	0.963	265 ± 10	290 ± 3	1.33	2011-9-11, 2012-3-30
PS1	z	0.868	238 ± 1	256 ± 1	1.40	2013-4-24
PS1	i	0.755	141 ± 6	220 ± 1	1.55	2013-5-31
PS1	r	0.622	89.8 ± 4.5	197 ± 1	1.77	2013-5-31, 2013-6-19
PS1	g	0.487	54.9 ± 3.9	117 ± 1	2.15	2012-6-11, 2013-6-10
ZTF	r	0.622	139 ± 5		1.77	2021-2-09
ZTF	g	0.487	60.4 ± 4.1		2.15	2020-10-13

Notes. Here and in Tables 2 and 3, F_ν,obs is the observed flux and the intrinsic one is ${F}_{\nu ,\mathrm{obs}}{10}^{{A}_{\lambda }/2.5}$ for E(B – V) = 0.23 (1 Jy ≡ 10⁻²³ erg cm⁻² s⁻¹ Hz⁻¹). For PS1, the values of F_{ν, obs} are the averages from pairs of observations separated by ≲0.5 hr with the individual fluxes differing by <25%; the uncertainties are the errors of those averages. The average fluxes from the PS1 stacked images, 〈F_ν,obs〉, are given for comparison. For ZTF, the flux uncertainties correspond to the original magnitude uncertainties.

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We first consider spectral data from Pan-STARSS1 ⁴ Data Release 2 (PS1 DR2), which give measurements in the y, z, i, r, and g bands for years prior to the outburst. We have searched for the overall minimum fluxes in each photometric band using the psfFlux and psfFluxErr values in the Detection Table provided in PS1 DR2. Those fluxes were obtained using an automated pipeline; thus, single detections at the faint end may not be real but arise from a systematic noise (Chambers et al. 2016) and be indistinguishable from real detections. In order to avoid them, we have applied a stringent selection criterion. Namely, we used only double detections from subsequent exposures separated by ≲0.5 hr and with the fluxes differing by <25%. The results are given in Table 1 and plotted in red in Figure 2 after correcting for the extinction assuming E(B – V) = 0.23. For comparison, Table 1 also gives the average fluxes from the DR2 stacked images, which are significantly higher than the minimum fluxes in the i, r, and g bands.

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Next, we have obtained the r and g light curves observed by the Zwicky Transient Facility ⁵ (ZTF; Bellm et al. 2019), covering the discovery outburst and subsequent decay up to 2021 August. They are shown in Figure 3. We see that several mini outbursts or reflares occurred after the end of the main outburst event, with the last major reflare in 2020 April. For comparison, we also show the hard X-ray light curve ⁶ from the Burst Alert Facility (Barthelmy et al. 2005; BAT) on board Neil Gehrels Swift. We see that the optical reflares have been accompanied by X-ray activity. From the ZTF light curves, we have obtained the weakest fluxes measured in each filter, which are given in Table 1 and are plotted in blue symbols in Figure 2.

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Then, we compiled some other available optical and infrared measurements of MAXI J1820+070 during quiescence. We list them in Table 2 and plot them in Figure 2 with black error bars. Table 2 also gives the values of F₀. Most of the fluxes are higher than the minima from PS1. In particular, we analyzed the observations made during the states near quiescence in the r band (of the SDSS photometric system) reported in Torres et al. (2019, 2020). After calibrating the photometry of MAXI J1820+070 against the PSF mean magnitude of a nonvariable star in the field, the range of those magnitudes is $r^{\prime} \approx 17.87\pm 0.02$–17.35 ± 0.02, and its midpoint is $r^{\prime} \approx 17.6$. Finally, we plot the average optical and UV fluxes obtained by Poutanen et al. (2022); see Table 3. The arrows in Figure 3 indicate the middle times of the observations of Torres et al. (2019, 2020) and Poutanen et al. (2022).

Table 2. Selected Infrared and Optical Observations of MAXI J1820+070 in Quiescent States

Source	Band	〈λ〉 (μm)	F0 (Jy)	mλ	Fν,obs (μJy)	${10}^{{A}_{\lambda }/2.5}$	Date	Reference
WISE	W2	4.6	3631	17.95 ± 0.06	${239}_{-13}^{+14}$	1.02	2010-1-14–2010-7-17	Cutri et al. (2021)
WISE	W1	3.35	3631	17.59 ± 0.04	${334}_{-11}^{+12}$	1.04	2010-1-14–2010-7-17	Cutri et al. (2021)
2MASS	K	2.22	655	15.12 ± 0.12	${588}_{-61}^{+69}$	1.08	1999-7-23	Cutri et al. (2003)
2MASS	H	1.60	1150	15.44 ± 0.10	${764}_{-69}^{+75}$	1.13	1999-7-23	Cutri et al. (2003)
2MASS	J	1.26	1580	15.87 ± 0.07	${711}_{-42}^{+45}$	1.20	1999-7-23	Cutri et al. (2003)
GSC2.3.2	I	0.812	2681	17.24 ± 0.43	${341}_{-111}^{+166}$	1.46	1989–2000	Lasker et al. (2008)
USNO-B1.0	R	0.658	3247	16.76 ± 0.30	${642}_{-155}^{+204}$	1.71	1949–1965	Monet et al. (2003)
GSC2.3.2	R	0.658	3247	18.05 ± 0.42	${196}_{-63}^{+69}$	1.71	1987–1999	Lasker et al. (2008)
GTC	$r^{\prime}$	0.623	3631	17.61 ± 0.25	${328}_{-67}^{+75}$	1.77	2019-6-8–2019-8-7	Torres et al. (2019, 2020)
USNO-B1.0	B	0.442	4067	17.94 ± 0.30	${271}_{-65}^{+86}$	2.37	1949–1965	Monet et al. (2003)
GSC2.3.2	B	0.442	4067	18.87 ± 0.41	${115}_{-36}^{+53}$	2.37	1987–2000	Lasker et al. (2008)

Notes. See Straižys (1992) for the values of F₀. The magnitude for GTC gives the midpoint of the observed range, and the uncertainty gives that range.

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Table 3. The Average UV–Optical Spectrum of MAXI J1820+070 Observed on 2020-7-20–23

ν [1014 Hz]	16.0 ± 2.7	13.5 ± 1.5	11.7 ± 1.6	8.76 ± 0.99	6.82 ± 0.34	5.51 ± 0.33	4.87 ± 0.45	4.01 ± 0.32	3.36 ± 0.14
Fν,obs [μ Jy]	9.99 ± 1.17	14.0 ± 2.0	31.2 ± 3.3	59.5 ± 5.9	87.9 ± 11.3	148 ± 4	238 ± 15	303 ± 6	415 ± 10
${10}^{{A}_{\lambda }/2.5}$	5.39	7.65	4.28	2.92	2.27	1.84	1.62	1.34	1.12

Notes. The measurements from 16.0 to 8.76 × 10¹⁴ Hz are from the Neil Gehrels Swift Ultraviolet/Optical Telescope and those from 6.82 to 3.36 × 10¹⁴ Hz are from the Liverpool Telescope, La Palma (Poutanen et al. 2022). The first row gives the middle frequencies and the band half-widths.

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The PS1 DR2 minimum fluxes shown in Figure 2 constrain the stellar contribution, which we approximate as a blackbody, ${F}_{\nu }^{* }=\pi {B}_{\nu }{(T)({R}_{2}/D)}^{2}$, where B_ν (T) is the blackbody intensity and T is the effective temperature. The most restrictive measurement is that in the i band, for which we take its upper limit (Table 1) and assume E(B – V) = 0.23. We have found that the blackbody relationship for this monochromatic flux can be locally approximated as a power law of $T\propto {(D/{R}_{2})}^{0.45}$. The constraint, together with the temperature limit from our analysis of the average spectrum of Torres et al. (2019, 2020), can be written as

$$\begin{eqnarray}&&\displaystyle \frac{D/2.95\,\mathrm{kpc}}{{R}_{2}/1.11{R}_{\odot }}\gtrsim A{\left(\displaystyle \frac{T}{4200\,{\rm{K}}}\right)}^{2.22},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&T\gt 4200\,{\rm{K}},\end{eqnarray} \tag{ 4 }$$

where Equation (3) is scaled to the lower limit on the stellar radius; see Section 2.1. Here the constant A accounts for the accretion disk being expected to be present at some level during the entire quiescence (see, e.g., the models of Dubus et al. 2001), in which case A > 1. On the other hand, the flux measurements may be affected by ellipsoidal variability, whose full amplitude we estimate to be <0.2 mag, i.e., less than ±10% with respect to the average flux. This estimate is based on the ellipsoidal variability of the BH LMXB A0620–00, which has the mass ratio q = 0.067 ± 0.01 (Marsh et al. 1994) and 665 < i < 735 (Haswell et al. 1993), consistent, within the uncertainties, with those of MAXI J1820+070. The full amplitude of the ellipsoidal variability of A0620–00 was measured by Marsh et al. (1994) as 0.13 mag. They also performed detailed simulations of this effect for a range of inclinations, and their Table 4 gives the theoretical range of 0.15–0.18 mag at i = 70°. Given the relative weakness of this effect, we ignore it. We also set A = 1. The fiducial distance of 3 kpc and the minimum R₂ correspond to T ≤ 4230 K. We plot a blackbody spectrum at T = 4230 K in the solid black curve in Figure 2. This spectrum gives a ≈26% contribution (at E(B – V) = 0.23) to the average flux in the r band of Torres et al. (2019, 2020). This is moderately higher than the stellar contribution of 16%–21% estimated by them.

Table 4. The Results of the Evolutionary Calculations for the Donor

Model	$\tfrac{{M}_{2}}{{M}_{\odot }}$	$\tfrac{{R}_{2}}{{R}_{\odot }}$	$\tfrac{{L}_{2}}{{L}_{\odot }}$	T (K)	$\tfrac{{M}_{{\rm{c}}}}{{M}_{\odot }}$	$-{\dot{M}}_{\mathrm{2,10}}$
A	0.3	1.012	0.278	4169	0.070	0.43
A2	0.3	1.012	0.219	3924	0.290	0.155
B05	0.4	1.114	0.452	4492	0.050	1.0
B	0.4	1.114	0.347	4200	0.065	0.68
B2	0.4	1.114	0.273	3948	0.084	0.27
C05	0.5	1.200	0.587	4621	0.042	1.3
C	0.5	1.200	0.437	4289	0.060	0.91
D	0.6	1.275	0.560	4430	0.051	1.1
D2	0.6	1.275	0.414	4102	0.130	0.49
E	0.7	1.343	0.749	4643	0.034	1.25
F	0.8	1.404	1.019	4903	0.003	1.55

Notes. M_c is the mass of the He core and $-{\dot{M}}_{\mathrm{2,10}}$ is the stellar mass-loss rate in units of 10⁻¹⁰ M_☉ yr⁻¹. The BH mass of M₁ = 7M_☉ was assumed. The models denoted by a single letter have solar metallicity Z = 0.014, while models A2, B2, and D2 have Z = 0.028, and B05 and C05 have Z = 0.007. Model B is at the minimum temperature allowed by the GTC spectrum and corresponds to D ≳ 2.9 pc. Model B05 has the temperature approximately best fitting the spectrum but it requires D ≳ 3.4 kpc. Model C has an intermediate temperature and D ≳ 3.3 kpc. These models are marked in Figure 4.

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Equations (3)–(4) for R₂ ≳ 1.11R_☉ imply D ≳ 2.95 kpc, in agreement with all the constraints on D listed in Section 2.1. On the other hand, these equations do not constrain D from above. We take here D ≲ 3.5 kpc from the Gaia parallax as a tentative conservative upper limit. While the limit of Wood et al. (2021) is stringent at face value, it relies on the two ejecta being exactly symmetric, which may not be the case, and 3.5 kpc is within the 2σ uncertainty of the radio parallax; see Section 2.1. We plot the resulting joint constraints on D and R₂ in Figure 4. At D = 3.5 kpc and R₂ = 1.11R_☉, we have the maximum T ≈ 4540 K, corresponding to a K5 stellar type. This satisfies the original constraint of Torres et al. (2020). We note that the above constraints favor low donor radii if D ≲ 3 kpc. At D ≤ 3 kpc and T = 4200 K, R₂ ≤ 1.13R_☉. Note that the above constraints can still be relaxed if there is some systematic error on the minimum PS1 fluxes, present in spite of our strict selection procedure.

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MAXI J1820+070 appears to be a relatively old system and thus may have come from an environment with a subsolar metallicity. Its position on the Cartesian coordinates (X, Y, Z) centered on the Sun and the velocities calculated from the coordinated proper motion, pm R.A. = −3.093 ± 0.091 mas yr⁻¹ and pm decl. = −6.283 ± 0.094 mas yr⁻¹ (Gaia EDR3; Gaia Collaboration et al. 2021), the systemic velocity of γ = −22 km s⁻¹ (Torres et al. 2019), and the adopted distance of D = 3 kpc, are

$$\begin{eqnarray}\begin{array}{rcl}X & = & 2393\,\mathrm{pc},Y=1730\,\mathrm{pc},Z=529\,\mathrm{pc},\\ U & = & 40.85\,\mathrm{km}\,{{\rm{s}}}^{-1},V=-93.40\,\mathrm{km}\,{{\rm{s}}}^{-1},W=-4.19\,\mathrm{km}\,{{\rm{s}}}^{-1},\end{array}\end{eqnarray} \tag{ 5 }$$

where U, V, W are velocities along the same axes, with X, U positive toward the Galactic center, Y, V positive in the direction of the Sun motion around the Galaxy, and Z, W positive out of the plane of the Galaxy. MAXI J1820+070 is thus located in the thick Galactic disk as indicated by its distance from the Galactic plane, Z = 529 kpc, and a high peculiar velocity, V_pec = 94 km s⁻¹, moving almost parallel to the Galactic plane. The Galactic U, V, W velocities also locate it among the extended thick-disk population objects in the Toomre diagram (e.g., Figure 1 in Feltzing et al. 2003). The Galactocentric distance of MAXI J1820+070 is 5.9 kpc, which locates it in the inner Galactic disk, where the average value of the metallicity is 〈[Fe/H]〉 = −0.55 ± 0.17 (e.g., Bensby et al. 2011). The subsolar metallicity of the donor is further supported by relatively strong Ca I and Ti I absorption lines compared to Fe I lines in the spectrum presented in Figure 3 of Torres et al. (2019), similar to other thick-disk objects (e.g., Feltzing et al. 2003).

We also note that high peculiar velocities of BH LMXBs are often attributed to a BH natal kick velocity; see, e.g., Atri et al. (2019). That study included MAXI J1820+070 and three other systems with no known (at that time) systemic velocities and accurate distances, using instead a hypothetical kick velocity distribution modeled by Monte Carlo simulations. Based on them, they tentatively preferred the natal kick origin of the peculiar velocity in MAXI J1820+070. Still, they also note that most LMXBs are relatively old systems, and thus may have come from low-metallicity environments like globular clusters.

On the other hand, metallicities higher than solar were found in a number of donor stars in LMXBs (see the review in Casares et al. 2017). Still, this does not appear to be universal. One example is the binary V934 Her/4U 1700+24 consisting of a red giant accreting on a neutron star. Detailed photospheric abundance analysis for this system resulted in a slightly subsolar metallicity, [Fe/H] ≈ −0.5 and [α/Fe] = +0.27 (where α represents the average of the Mg, Si, and Ca elements), and an [α/Fe] versus [Fe/H] relation close to the mean one without any notable peculiarity to this object (Hinkle et al. 2019). Similar α-element and Fe abundances were found in many symbiotic giants with white dwarf companions (Gałan et al. 2016, 2017).

The bolometric flux of the source varied within only a factor of 2–3 during most of the 2018 discovery outburst, i.e., ≈200 days; see, e.g., Shidatsu et al. (2019); Fabian et al. (2020), namely within ≈(0.5–1.5) × 10⁻⁷ erg cm⁻² s⁻¹. In order to estimate the total fluence of that outburst, we adopt the flux of 1.0 × 10⁻⁷ erg cm⁻² s⁻¹ during 200 days. Assuming D = 3 kpc and the accretion efficiency of = 0.1, we obtain the accreted mass of M_accr ≈ 2 × 10²⁵ g. However, given the uncertainties on the fluence, distance, and accretion efficiency, the uncertainty of this mass is probably of a factor of 2.

After the 2018 discovery outburst, two historical outbursts in 1898 and 1934 were discovered by examining publicly available photographic plates (Kojiguchi et al. 2019). Based on these data, the typical interval between outbursts of this source was estimated by those authors to be 40 yr. This implies that the outburst within 1970–1980 was missed by observers of the period. However, intervals between outbursts of BH LMXBs are often unequal, and it is also possible that there was no outburst since 1934, giving the interval from the previous outburst of 84 yr. If we assume that the mass accreted onto the BH in 2018 equals that transferred from the donor during the interval since the previous outburst (the theoretical assumption of which is clearly uncertain), the average mass-transfer rate is $-{\dot{M}}_{2}\approx 1.2\times {10}^{-10}{M}_{\odot }$ yr⁻¹, with an uncertainty we estimate to be of a factor of 2. Alternatively, the estimate of $-{\dot{M}}_{2}$ would increase to ≈2.6 × 10⁻¹⁰ M_☉ yr⁻¹ if the actual interval between outbursts was 40 yr.