X-Ray, Optical, and Near-infrared Monitoring of the New X-Ray Transient MAXI J1820+070 in the Low/Hard State

2.1.1. MAXI Data

We reduced the MAXI/GSC event data with the processed version 1.3.6.6, through the MAXI analysis tools implemented in "MAXI/GSC on-demand web interface"¹⁸ (Nakahira et al. 2013). The source events were extracted from a circular region with a radius of 20, centered at the target position. Background events were collected from the source-free region within 30 of the source position, determined by excluding the source region and 20 from nearby bright sources.

Figure 1 shows the MAXI/GSC light curves of MAXI J1820+070 at 2–6 keV and 6–20 keV and their hardness ratios (HRs), together with the Swift/BAT light curve at 15–50 keV, downloaded from the "BAT Transient Monitor" website (Krimm et al. 2013),¹⁹ with a time bin the length of their orbital periods (∼92 minutes; black points in Figure 1). The soft and hard X-ray fluxes rapidly increased in the initial phase of the outburst, and around March 20, they reached their peak level of ∼5 photons s⁻¹ cm⁻² at 2–20 keV, corresponding to ∼2 crab. The source started dimming in early April, then from the middle of June it increased its flux again. The HR was almost constant before the re-brightening. To reduce the statistical errors, we binned 1–40 adjacent data points that have similar flux levels, as shown in red in Figure 1, and created time-averaged GSC spectra in these individual bins.

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We also investigated whether or not the source was detected with MAXI/GSC before the 2018 outburst. We created light curves with bins of 72 days at 3–4 keV, 4–10 keV, and 10–20 keV, applying the image fitting technique to the GSC data from 2009 September to 2016 July, in the same manner as those adopted in the MAXI Galactic and extragalactic X-ray source catalogs (Hori et al. 2018; Kawamuro et al. 2018). We found, however, that the source was not detected significantly at any period, and estimated 3σ upper limits of the seven-year averaged fluxes as ∼0.2 mcrab at 4–10 keV, ∼0.1 mcrab at 3–4 keV, and ∼1.0 mcrab at 10–20 keV.

2.1.2. Swift Data

2.2.1. Long-term Evolution Studied with MAXI/GSC and Swift/BAT-survey Data

We first analyzed the MAXI/GSC and Swift/BAT-survey spectra to study the long-term spectral evolution, before the re-brightening in June. Figure 2 displays two typical spectra at low and high luminosities, obtained on 2018 March 14 UT 9:42–17:44 and March 25 UT 03:45–19:51, respectively. Both of them have a power-law-like profile, as is usually seen in the low/hard state of BHBs. A significant spectral turnover can be seen in the March 25 spectrum at 50–100 keV, which is not very clear in the March 14 spectrum.

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We applied the Comptonization model nthcomp to the individual GSC+BAT-survey spectra, assuming that the seed photons originate in the emission from the standard accretion disk. The nthcomp model calculates a Comptonized spectrum from a photon index, an electron temperature, and a characteristic temperature of the seed photons (which is the inner disk temperature T_in in the case of the disk blackbody radiation). We fixed T_in at 0.1 keV, because it cannot be constrained in the GSC+BAT spectra, covering energies only above 3 keV. We have confirmed that the results remained unchanged within the 90% error ranges when T_in = 0.5 keV and 0.05 keV were adopted. To account for the interstellar absorption, we combined the TBabs model (Wilms et al. 2000) with a hydrogen column density of 1.5 × 10²¹ cm⁻², which was determined from the spectrum of the Neutron Star Interior Composition Explorer (NICER) on March 12–14 (Uttley et al. 2018). We varied the cross-normalization factor of the BAT data with respect to the GSC data. We obtained ∼1.0 with a 90% confidence range of ±∼20% as its typical value.

The model reproduced the spectra well. In Figure 2, we show the best-fit models and the data versus model ratios of the March 14 and 25 data. Figure 3 presents the overall trend in the fit parameters and the reduced chi-squared values. During the rise of the outburst, the electron temperature and the photon index showed a slight decrease and increase, respectively. After the flux peak, the electron temperature increased slightly, whereas the photon index was nearly unchanged within the error range, during the gradual decay of the unabsorbed 1–100 keV flux by a factor of ∼2.

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2.2.2. Short-term Variation Studied with Swift/XRT and BAT-event Data

We next analyzed the simultaneous Swift/XRT and BAT-event data occasionally acquired in the outburst. Figure 4 presents the XRT light curves with 1 s bins of MAXI J1820+070 on March 14 and 25, obtained from Data-1 and Data-2, respectively. The flux varied by a factor of ∼2–5 on timescales of a few to ∼100 s in both epochs. To investigate the energy dependence of the rapid flux variation, we sorted the time bins in these light curves in terms of their count rates. In each observation, we defined the upper and lower 30% time bins among all the data points as the high- and low-flux phases, respectively, and produced time-averaged spectra in these two phases (see Figure 4 for thresholds of the count rates for these phases).

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In Figure 5, we plotted the time-averaged spectra in the low- and high-intensity phases, and the ratio of the former to the latter, produced from the individual data sets. Both spectra in Data-1 can be approximated by a single power law, and the spectral ratio increases with energy, indicating that the photon index in the low-intensity phase is slightly lower than that in the high-intensity phase. For Data-2, both spectra show a clear spectral cutoff at around 30–50 keV. Remarkably, the spectrum in the low-intensity phase displays a hump at ∼1 keV, and the spectral ratio below ∼2 keV decreases with increasing energy, suggesting that a less variable component than the main cutoff power-law component is present in the soft X-ray band.

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We applied a Comptonization model to these intensity-sorted spectra and investigated which physical parameter(s) made the spectral differences. Here we adopted a sophisticated Comptonization model, compps (Poutanen & Svensson 1996), instead of nthcomp. This model calculates a Comptonized spectrum produced in a hot electron cloud, based on exact numerical solutions of the radiative transfer equation, for a given electron temperature kT_e, Compton y-parameter, geometry of the cloud, and energy distribution of the seed photons. We assumed spherical geometry (geom = 4 in the XSPEC terminology) of the Comptonization component, and a multicolor disk blackbody as the seed spectrum. We ignored the reflection component, whose strength was not constrained, likely due to the uncertainties in the cross-normalization between the XRT and BAT-event spectra.

For Data-2, we combined the diskbb model (Mitsuda et al. 1984) with compps, as a direct disk blackbody component, to model the hump seen in the soft X-ray band. The inner disk temperature of diskbb, kT_in, was linked to the seed temperature kT_bb of the compps model. We also employed the TBabs model for interstellar absorption, leaving N_H as a free parameter. In this analysis, we varied the cross-normalization factor of the BAT with respect to the XRT, which was found to be consistent with 1.0, with a 90% error of ±0.1–0.2, in both Data-1 and Data-2.

These models, TBabs*(compps) and TBabs*(diskbb+compps), successfully reproduced the Data-1 and Data-2 spectra, respectively. Figure 6 shows the folded spectra with their best-fit models, and the ratio of data to model. Table 1 lists the best-fit parameters of each phase. In both data sets, the Compton y-parameters in the low-intensity phases were larger than those in the high-intensity phases.

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Table 1.  Best-fit TBabs*compps and TBabs*(diskbb+compps) Parameters for Data-1 and Data-2, Respectively, in the High- and Low-intensity Phases

		Data-1		Data-2
Parameters		High	Low	High	Low
TBabs	NH (1022 cm−2)	${0.10}_{-0.04}^{+0.05}$	<0.1	0.12 ± 0.10	${0.15}_{-0.07}^{+0.09}$
comppsa	kTe (keV)	>240	>48	${27}_{-2}^{+3}$	${35}_{-5}^{+8}$
	y-parameter	1.1 ± 0.2	${1.6}_{-0.2}^{+0.1}$	$0.77\,\pm \,0.02$	${0.87}_{-0.02}^{+0.03}$
	kTbb (keV)	0.22 ± 0.02	${0.2}_{-0.1}^{+0.2}$	${0.18}_{-0.04}^{+0.12}$	${0.21}_{-0.04}^{+0.05}$
	norm (104)	${8}_{-3}^{+4}$	${1.3}_{-1.0}^{+6.8}$	${53}_{-27}^{+90}$	${17}_{-10}^{+22}$
diskbb	norm (105)	⋯	⋯	${5.3}_{-5.1}^{+41.0}$	${4}_{-3}^{+14}$
	rin (km)b	⋯	⋯	${372}_{-198}^{+168}$	${240}_{-48}^{+192}$
χ2/d.o.f.		356/328	168/144	200/190	108/107
Fluxc (10−8 erg s−1 cm−2)		4.1	2.1	18	10

Notes.

^aThe seed spectrum was assumed to be a disk blackbody, and the inner disk temperature of compps (kT_bb) was linked to that of diskbb (kT_in) in Data-2. The reflection component was ignored. ^bInner radius estimated from the total photons of the disk blackbody emission, including the Comptonized photons in a spherical corona (see Section 2.2.2). A distance of 3 kpc and an inclination angle of 30^◦ are assumed. The color-temperature correction and the correction of the inner boundary condition are not considered. ^cUnabsorbed 0.01–100 keV flux.

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We estimated the inner disk radius for Data-2, from the photon fluxes of the direct disk component and the Comptonized component, via the equation given in Kubota & Makishima (2004):

$$\begin{eqnarray*}&&\begin{array}{c}\begin{array}{c}\begin{array}{r}\begin{array}{c}{P}_{{\rm{d}}}+{P}_{c}\times 2\cos i=0.0165\left[\displaystyle \frac{{r}_{{\rm{in}}}^{2}\cos i}{{(D/10{\rm{kpc}})}^{2}}\right]{\left(\displaystyle \frac{{{kT}}_{{\rm{in}}}}{1{\rm{keV}}}\right)}^{3}\\ {\rm{photons}}\,{{\rm{s}}}^{-1}\,{{\rm{cm}}}^{-2}\end{array}\end{array}\end{array}\end{array}\end{eqnarray*}$$

(where P_c and P_d are photon fluxes of the Comptonized component and the direct disk component, respectively), by assuming a spherical geometry of the Comptonization component and the conservation of the number of disk photons after Comptonization.

Optical and near-IR observations in the g', R_c, I_c, r, i, z, J, H, and K_s bands were carried out with ground-based telescopes through the target-of-opportunity program in the Optical and Infrared Synergetic Telescopes for Education and Research (OISTER). The g'-, R_c-, and I_c-band data were taken with the three-color imaging system developed for the MITSuME project (Kotani et al. 2005; Yatsu et al. 2007; Shimokawabe et al. 2008; Yanagisawa et al. 2010) on the MITSuME 50 cm telescope in Akeno, the 50 cm telescope at the Okayama Astrophysical Observatory (OAO), and the MURIKABUSHI 105 cm telescope at the Ishigakijima Astronomical Observatory. The r-, i-, and z-band data were taken with the Multi-wavelength Simultaneous High Throughput Imager and Polarimeter (MuSaSHI), installed on the 55 cm SaCRA telescope at Saitama University. The J-, H-, and K_s-band data were taken with the Nishiharima Infrared Camera (NIC; Ishiguro et al. 2011; Takahashi et al. 2013) on the 2.0 m Nayuta telescope at the Nishi-Harima Astronomical Observatory. The data were reduced on IRAF by following standard procedures including bias and dark subtraction, flat-fielding, and bad pixel masking. Photometry was performed with IRAF. The magnitudes of MAXI J1820+070 were calibrated with nearby reference stars. The magnitudes of the reference stars were taken from the UCAC4 catalog (Zacharias et al. 2013) for the g'-, R_c-, and I_c-band data, from Pan-STARRS1 Surveys (Chambers et al. 2016) for the r-, i-, and z-band data, and from the Two Micron All Sky Survey Point Source Catalog (Cutri et al. 2003) for the J-, H-, and K_s-band data. The statistical photometric errors of MAXI J1820+070 and the systematic errors of the reference star magnitudes were taken into account in assessing the observational errors.

Figure 7 shows the g'-, R_c-, and I_c-band light curves of MAXI J1820+070, together with the MAXI/GSC light curve at 2–20 keV. The optical fluxes were found to gradually increase as the X-ray flux became higher, and they show a significant variation on each night by 0.5–1 mag (by a factor of 1.6–2.5 in the flux units). As described in the following section, we studied the averaged properties of the multi-wavelength spectral energy distribution (SED) around the flux peak, by combining the one-night averaged optical and near-IR data, and the quasi-simultaneous X-ray data obtained with MAXI/GSC and Swift/BAT. Investigation of the short-term variations of the optical fluxes and their correlation to those in X-rays is left for future work.

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We also searched the archival optical and IR data²¹ for possible activity of MAXI J1820+070 before the 2018 outburst. The source was detected multiple times by Palomar Transient Factory (PTF) in 2013 May with R-band magnitudes of 18.3–18.7 mag and typical errors of ∼0.06 mag. It was also detected in the mid-IR band with Wide-field Infrared Survey Explorer (WISE)/Near-Earth Object WISE (NEOWISE) in 2010 September/2014–2017 March and September. The WISE/NEOWISE apparent magnitudes were 15.3–16.3/13.7–14.8 mag with typical errors of ∼0.3/0.08 mag in the W1 band (3.4 μm), and 14.7–15.4/13.4–14.6 mag with typical errors of ∼0.3/0.2 in the W2 band (4.6 μm). The fluxes in both the W1 and W2 bands showed significant variations by 0.5–1 mag (a factor of ∼2 in the flux units) within a few to several days.

Figure 8(a) shows the multi-wavelength SED on 2018 March 24, when the data in the g', r, i, z, J, H, and K_s bands, together with the X-ray data from MAXI/GSC and Swift/BAT, were available. The X-ray data were corrected for interstellar absorption using the TBabs model with ${N}_{{\rm{H}}}=1.5\times {10}^{21}$ cm⁻² (Uttley et al. 2018), and optical/IR data for interstellar extinction using the redden model in XSPEC with the extinction E(B − V) = 0.26, which was converted from the N_H value through the relation in Bohlin et al. (1978). As is noticed from the figure, the SED in the IR to optical band is not smoothly connected to the X-ray spectrum. For comparison, we also plotted, in Figure 8(b), an SED obtained from the archival optical/IR data before the 2018 outburst, and the upper limits of the X-ray fluxes estimated with the MAXI/GSC.

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The optical and IR photons of BHBs can originate in the accretion disk, jet, or companion star. In the case of the disk emission, the optical and IR bands correspond to the radiation from the outer disk region, which is often irradiated by the X-rays from the inner disk region. To obtain the upper limit of the contribution of the disk emission to the optical/IR fluxes, we applied the irradiated disk model diskir (Gierliński et al. 2008, 2009) to the multi-wavelength SED on 2018 March 24 (see Section 4.3 for discussion of the contributions of the other emission components).

The diskir model computes the spectrum of the disk emission and its Comptonization, considering the irradiation of the disk. The model has nine input parameters: the inner disk temperature kT_in, the photon index Γ and electron temperature kT_e of the Comptonized component, the luminosity ratio L_c/L_d of the Comptonized component to the disk component, the fraction f_in of the luminosity of the Comptonized component that is thermalized in the inner disk, the fraction f_out of the bolometric flux illuminating the outer disk, the radius r_irr of the inner disk irradiated by the Comptonized component with respect to the inner disk radius, the outer disk radius R_out, and the normalization, determined by the inner disk radius R_in in the same manner as diskbb.

Following previous works (e.g., Shidatsu et al. 2017), we fixed r_irr and f_in, which were unconstrained with our data, at default values, 1.1 and 0.1, respectively, which are appropriate for spectra of the low/hard state (Poutanen et al. 1997). The other parameters were left as free parameters. We multiplied TBabs with N_H fixed at 1.5 × 10²¹ cm⁻² and redden with E(B − V) at 0.26 to the diskir model, as X-ray interstellar absorption and optical/IR extinction, respectively. We have confirmed, however, that the conclusions below do not change if we increase or decrease N_H by a factor of 2, and change E(B − V) accordingly.

As shown in Figure 8(a), the model was able to reproduce the SED on March 24, giving a χ²/d.o.f. value of 106/122. In this best-fit model, the reprocessed emission from the outer disk dominates the flux in the IR bands, where a profile flatter than the optical SED is seen. The parameter values were constrained to be ${{kT}}_{\mathrm{in}}={0.23}_{-0.13}^{+0.03}$ keV, ${\rm{\Gamma }}={1.67}_{-0.03}^{+0.01}$, ${{kT}}_{{\rm{e}}}={29}_{-3}^{+2}$ keV, L_c/L_d = 0.24 ± 0.06, ${f}_{\mathrm{out}}={6.4}_{-2}^{+4}\times {10}^{-5}$, and ${R}_{\mathrm{out}}\gt 3\times {10}^{4}{R}_{\mathrm{in}}\,=2\times {10}^{7}$(D/3 kpc)($\cos i/\cos 30^\circ$)^−1/2 km. The Γ and kT_e values were consistent with those obtained in the analysis of the X-ray spectra alone, and the kT_in value was the same as that determined from the Swift/XRT and BAT-event data on March 25, within the 90% error ranges.

Like other X-ray novae, the new X-ray source MAXI J1820+070 displayed a rapid rise in flux, up to as high as ∼2 crab at 2–20 keV, and then a slower decay for ∼3 months. Using MAXI/GSC data, we found that the source increased its X-ray flux by ≳4 orders of magnitude from the quiescent level, to ∼2 crab in the 2–20 keV band, at the peak at the end of 2018 March. Before the re-brightening in the middle of June, the source did not show any drastic spectral softening, and kept presenting a hard spectrum roughly characterized by an exponentially cutoff power-law model with a photon index of ∼1.5 and a cutoff energy of ∼50 keV, which is consistent with those of black hole X-ray binaries in the low/hard state.

The observed peak flux of MAXI J1820+070 was quite high, compared with typical flux levels at which many known BHBs in the central regions of the Galaxy show the transition to the high/soft state (∼0.1 crab; e.g., Yu et al. 2007; Zhou et al. 2013). This can be explained if MAXI J1820+070 is located closer to us than they are. Indeed, D ≈ 3 kpc has recently been obtained from the astrometry with Gaia data (Gandhi et al. 2018b). Using the unabsorbed 1–100 keV flux, obtained with the best-fit nthcomp model of the simultaneous MAXI/GSC and Swift/BAT spectrum on 2018 March 25, the peak luminosity at the end of March is calculated to be ∼2 × 10³⁸(D/3 kpc)² erg s⁻¹, which is converted to an Eddington ratio of L_X/L_Edd ∼ 0.1(D/3 kpc)²(M_BH/10 M_☉)⁻¹.

After the period of ∼3 months in the low/hard state, the source caused re-brightening and entered into the state transition, at a luminosity similar to the first peak in March. Such a long period before the state transition is unusual in transient BHBs, although similar behavior was observed in the 2009 outburst of XTE J1752−223 (Nakahira et al. 2010), where the source stayed in the low/hard state for three months before the transition, with two plateau phases in its X-ray light curve. In that case, the complex evolution was explained by a gradual increase in the mass accretion rate for some unknown reasons.

What caused the two-step rise of MAXI J1820+070 is still unclear, but possibly the first rise was caused by an enhancement in the mass transfer from the companion star, and the second rise by a rapid increase in the mass accretion rate caused by the disk instability that was triggered somewhere in the outer disk during the first rise and propagated inward. The viscous timescale of the disk is expressed as ${t}_{{\rm{v}}}{(R)\sim {\alpha }^{-1}{{\rm{\Omega }}}_{{\rm{K}}}^{-1}(H/R)}^{-2}$, where α, H, and Ω_K are the viscosity parameter, the disk scale height, and the Keplerian angular velocity at the radius R, respectively. The timescale t_v ∼ 90 days corresponds to R ∼ 2 × 10¹⁰ cm for H/R ∼ 0.01 and ∼4 × 10¹¹ cm for H/R ∼ 0.1, when a black hole mass of 10 M_☉ and α = 0.1 are assumed.

An alternative interpretation for the two-step flux increase may be provided in terms of the irradiation of the companion star, as invoked by Nakahira et al. (2014) to explain the re-flare observed in the outburst of Swift J1910.2−0546 (or MAXI J1910−057). The first rise in flux could be produced by the enhancement of the mass accretion rate through the inner disk due to the disk instability, and the fact that the strong X-rays irradiated and inflated the companion star, causing an increase in the gas supply to the accretion disk. The second flux enhancement could then be produced by triggering the disk instability again.

Looking at the MAXI/GSC and Swift/BAT spectra during the low/hard state in more detail, we found that the spectrum became slightly softer and bent at lower energies and higher luminosities. According to the best-fit nthcomp models for the individual spectra (Section 2.2.1), the photon index increased from 1.4 to 1.7 and the electron temperature decreased from 50 to 30 keV, during the rise phase of the outburst. This long-term spectral evolution would be explained by the change in the mass accretion rate; the standard disk is developed inwards as the mass accretion rate increases, and the soft X-rays from the standard disk cool the hot inner flow and/or corona around the standard disk, providing a softer Comptonized spectrum with a lower electron temperature.

We also detected spectral variation on much shorter timescales, a few to ∼100 s, using the Swift/XRT and BAT-event data taken on March 14 and 25, corresponding to the beginning and the peak of the outburst. In both periods, the spectrum of MAXI J1820+070 was softer/harder in the high-/low-intensity phases of the short-term variation. Applying the compps model, a smaller y-parameter (and a lower electron temperature on March 25) were obtained during phases of higher flux. Similar trends were obtained in the shot analysis of Cyg X-1 (Negoro et al. 1994, 2001; Yamada et al. 2013b), and the density fluctuation in the radiation-inefficient accretion flow was suggested as one possibility to drive the variation, on the basis of the evolution of the spectrum and X-ray time lags during the shots. Further studies of timing properties of MAXI J1820+070 would be required to understand the actual cause of its short-term variation.

Thanks to the good statistics of the Swift/XRT data, we detected, in the March 25 spectrum, a structure below ∼2 keV that cannot be reproduced by the TBabs*nthcomp model and is less variable than the main Comptonization component. Assuming it to be the component due to direct disk emission, we obtained the inner disk temperature as ∼0.2 keV and the inner disk radius as ∼180–540(D/3 kpc)${(\cos i/\cos 30^\circ )}^{-1/2}$ km, which was estimated from the photon flux of the component due to total intrinsic disk emission, including both the direct and Comptonized emission. This radius can be converted to ∼12–36 R_g(M_BH/10 M_☉)⁻¹(D/3 kpc)${(\cos i/\cos 30^\circ )}^{-1/2}$, where R_g = GM_☉/c², and this means that the standard disk is truncated, around the flux peak at the end of March.

We cannot rule out the possibility, however, that the soft component seen on March 25 was not the direct standard disk emission but a Comptonized emission produced around the inner edge of the standard disk, as discussed (Chang et al. 2010; Yamada et al. 2013a; Shidatsu et al. 2014). If this is the case, the direct disk component was below the energy range of the XRT, and the standard disk was further truncated, with a lower inner disk temperature than what we estimated above. The mass accretion rate at the flux peak can then be close to the Eddington rate, considering the radiation efficiency of the standard disk, ∼0.1 R_ISCO/R_in (where R_in and R_ISCO the radii of the inner edge of the standard disk and the innermost stable circular orbit, respectively), and the peak luminosity estimated in Section 4.1.

The optical and near-IR flux of BHBs is considered to originate in the blackbody emission from the companion star, jet emission, and/or the emission from the outer region of the accretion disk, which is often enhanced by the irradiation of X-rays from the inner disk region. In the case of MAXI J1820+070 during the outburst, the contribution of the companion star is negligible, because the previous PTF data suggest that the optical flux in the quiescent phase was at least ∼3 orders of magnitude smaller than at the peak of the outburst (see Section 3.2). The multi-wavelength SED around the X-ray flux peak could technically be fit with an irradiated disk model. However, the resultant value of f_out, the strength of the reprocessed component, was unusually small compared with those of typical BHBs in the low/hard state (>10⁻³; e.g., Gierliński et al. 2009).

Considering the above results, we suggest that the optical and near-IR emission of MAXI J1820+070 in the outburst was not entirely produced by the disk emission, but substantially contributed by the jet emission, particularly in the near-IR band. A similar conclusion was also obtained from optical polarimetry (Veledina et al. 2018). Indeed, as shown in Figure 9, the SED can be fairly well reproduced, for example, by adding a power-law component (as the optically thin synchrotron emission from jet) with a photon index of 1.7 and a normalization adjusted to the K_S-band flux, and setting f_out, kT_in, L_c/L_d, and R_out of diskir to be 5 × 10⁻³, 0.35 keV, 70, and 10⁵R_in, respectively. In this model, the inner disk region is efficiently irradiated by the Comptonization component dominating the X-ray luminosity, and the heated disk produces a weak hump seen around ∼5 keV. We note that the parameters related to the irradiation of the outer disk are not significantly changed by the irradiation efficiency of the inner disk alone, because they are determined by the bolometric flux. Remarkably, the stronger contribution of the jet component at longer wavelengths, indicated by this model, is consistent with the observed sub-second optical variations (Gandhi et al. 2018a) likely originating in the jet activity, which was found to be stronger in redder bands.

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Indeed, previous studies of BHBs suggest that steady compact jets are present during the low/hard state, and that their emission dominates the radio to IR or optical fluxes (see Fender 2010; Gallo 2010; Markoff 2010, and references therein). The SEDs of BHBs in the low/hard state exhibit a flat, power-law profile at the radio frequencies (e.g., Corbel et al. 2000; Fender 2001), with a spectral index of β ∼ 0 (where the flux density F_ν ∝ ν^β), and have a break in the submillimeter to IR band, above which a smaller β is obtained (Corbel & Fender 2002; Migliari et al. 2010; Gandhi et al. 2011; Shidatsu et al. 2011; Russell et al. 2013, 2014). As discussed also for jets in active galactic nuclei (Blandford & Königl 1979), this SED profile can be described with the synchrotron radiation from conical jets, where optically thick and thin synchrotron components are observed below and above the break, respectively.

Such an SED with the shape of a broken power law, extending from the radio to the near-IR band, was actually obtained in MAXI J1820+070 (Russell et al. 2018) around the X-ray flux peak at the end of March, with spectral indices of β ∼ 0.3 and β ∼ −0.7, below and above the break frequency ν_b of ∼3 × 10¹³ Hz. Following Shidatsu et al. (2011), we attempt here to estimate the physical parameters of the jet base, from ν_b and the flux density at ν_b of ${F}_{{\nu }_{{\rm{b}}}}\sim 400$ mJy. For simplicity, we assume a single-zone jet base and ignore the effects of relativistic beaming by the bulk motion of the jet. If the electron number density at the Lorentz factor γ is proportional to γ^p, the synchrotron luminosity in an optically thin part, νL_ν, depends on ν, p, the magnetic field strength B and the volume V of the emission region (where V = 4πR³/3 in the case of a spherical region), and the pitch angle θ of the jet, while the synchrotron self-absorption coefficient α_ν is expressed as a function of ν, p, B, and θ (see Shidatsu et al. 2011 for complete expressions). The former parameter, νL_ν, is proportional to ${\nu }^{(3-p)/2}$, and thus we obtain p = 2.4 for MAXI J1820+070, from the observed spectral index, β ∼ −0.7.

Assuming the equipartition of the magnetic field energy and the kinetic energy of electrons in the jet, and considering the condition of the optical depth and the luminosity at ν_b as $\sim {\alpha }_{{\nu }_{{\rm{b}}}}R\sim 1$ and ${\nu }_{{\rm{b}}}{L}_{{\nu }_{{\rm{b}}}}$ ∼ 1 × 10³⁵(D/3 kpc)² erg s⁻¹, respectively, we obtain B = 1 × 10⁴(D/3 kpc)^−0.22($\sin \theta /\sin 30^\circ$)^0.55 G and R = 2 × 10⁹(D/3 kpc)^0.94($\sin \theta /\sin 30^\circ$)^0.11 cm for the jet base of MAXI J1820+070. These values are comparable to those estimated in GX 339−4 (Shidatsu et al. 2011), XTE J1550−564 (Chaty et al. 2011), and MAXI J1836−194 (Russell et al. 2014) during the low/hard state.

The magnetic energy density is derived from the above B value as u_B = B²/8π ∼ 8 × 10⁶ erg cm⁻³. The Lorentz factor of electrons emitting ν_b = 3 × 10¹³ Hz photons is ∼10. Following Chaty et al. (2011), we can calculate the timescales of adiabatic cooling and radiative cooling at the jet base as ≳B/c ∼ 70 ms and $\propto {u}_{B}^{-1}{\gamma }^{-1}\sim 400$ ms, respectively. This indicates that the former is the dominant cooling process.

The total synchrotron luminosity L_sync is roughly estimated as ∼10³⁶ erg s⁻¹, from the SED profile obtained in Russell et al. (2018), and the energy density of the synchrotron radiation, ${u}_{\mathrm{sync}}\sim {L}_{\mathrm{sync}}/(4\pi {R}^{2}c)$, is calculated to be 3 × 10⁵ erg cm⁻³. The luminosity of the synchrotron self-Compton radiation, L_SSC, is thus estimated as L_syncu_sync/u_B ∼ 0.05L_sync. This suggests that the synchrotron self-Comptonization emission is negligible, contributing only ∼0.05% to the X-ray flux. The energy density of external photons from the accretion disk is roughly estimated as 9 × 10⁷ erg cm⁻³, from the 1–100 keV X-ray luminosity, ∼1 × 10³⁸ erg s⁻¹. The contribution of the external Comptonization emission is thus ∼1 × 10³⁷ erg s⁻¹, which is still only ∼10% of the total X-ray luminosity. As noticed in Figure 8(a), the observed near-IR fluxes are somewhat lower than what is expected from the simple extrapolation of the power-law component seen in the X-ray band, suggesting that the jet synchrotron emission itself is also unlikely to be a main contributor to the X-ray flux. These results would justify the assumption in our X-ray spectral modeling that the X-ray photons were predominantly produced by Comptonization of the disk emission.

We found weak optical and IR emission of MAXI J1820+070 before the start of the 2018 outburst, using the archival PTF, WISE, and NEOWISE data. The source exhibited R-band flux variation by 0.4 mag (by 0.4 in the flux units) on a timescale of ∼1 day, and mid-IR variations by ∼1 mag (by 2.5) on a timescale of ≲several days and a few years. Assuming a distance of 3 kpc, the averaged PTF apparent magnitude in the R band, ∼18.5 mag, is converted to an absolute magnitude of ∼6 mag. This magnitude corresponds to a K-type companion star if it is a main-sequence star and dominated by the optical flux in the PTF observations. Because of the significant variations, however, we suggest that a large fraction of the optical and IR fluxes did not originate in the blackbody emission from the companion star, but perhaps in the outer disk and/or jet emission.