A Redshifted Inner Disk Atmosphere and Transient Absorbers in the Ultracompact Neutron Star X-Ray Binary 4U 1916–053

The parameters for the best-fit models to spectra A, B, and Γ are listed in Table 1. For simplicity, we only list the model that best describes each spectrum. In all observations, the bulk of the absorption occurs in zone 1 in the form of a disk atmosphere: a (nearly) static absorber with consistent properties, such as high absorbing columns (N_He ∼ 40 × 10²² cm⁻²) and ionization (log ξ ∼ 4.4), across all observations. Absorption owing to a static disk atmosphere of this kind is not only common but expected among near edge-on ultracompact systems. Of the three spectra, only spectrum A required an additional, blueshifted absorber (zone 2) in order to simultaneously capture both the blue wing in the Fe xxvi line profile and the shift in Si xiv. We discuss this possible wind in Section 3.4.2.

Table 1.  Parameters for Best-fit Absorption Models

Individual Spectra
Spectrum	Model	Parameter	Zone 1	Zone 2	Zone 3	χ2/ν
Spectrum A	3 zone	NHe (1022 cm−2)	${50}_{-10}^{\unicode{x02021}}$	${10}_{-9\unicode{x02021}}^{+40\unicode{x02021}}$	${1.3}_{-1.1}^{+15.0}$	536/488 = 1.10
		log ξ	${4.45}_{-0.05}^{+0.25}$	${4.80}_{-1.6}^{\unicode{x02021}}$	${3.8}_{-1.1}^{1.0\unicode{x02021}}$	⋯
		${v}_{\mathrm{abs}}$ ($\mathrm{km}$ ${{\rm{s}}}^{-1}$)	${230}_{-270}^{+500}$	$-{1700}_{-1300}^{+1700\unicode{x02021}}$	${4200}_{-1600}^{+2900}$	−
		vturb (km s−1)	${270}_{-220\unicode{x02021}}^{+230\unicode{x02021}}$	300†	1000†	⋯
		σemis (km s−1)	${5400}_{-4000}^{+15000}$	⋯	⋯	−
		Lphot (1036 erg s−1)	8.2 ± 2.2	⋯	⋯	⋯
Spectrum B	1 zone	NHe (1022 cm−2)	${33}_{-4}^{+47}$	⋯	⋯	491/493 = 0.996
		log ξ	${4.4}_{-0.1}^{+0.4}$	⋯	⋯	⋯
		vabs (km s−1)	${230}_{-130}^{+140}$	⋯	⋯	⋯
		vturb (km s−1)	${150}_{-50}^{+80}$	⋯	⋯	⋯
		σemis (km s−1)	⋯	⋯	⋯	⋯
		Lphot (1036 erg s−1)	5.2 ± 1.5	⋯	⋯	−
Spectrum Γ	2 zone	NHe (1022 cm−2)	${34}_{-4}^{+25}$	⋯	50†	482/486 = 0.99
		log ξ	${4.25}_{-0.05}^{+0.20}$	⋯	${5.3}_{-0.3}^{+0.7}$	⋯
		vabs (km s−1)	280 ± 160	⋯	${6500}_{-1200}^{+1300}$	⋯
		vturb (km s−1)	${200}_{-70}^{+150}$	⋯	1000†	⋯
		${\sigma }_{\mathrm{emis}}$ (km s−1)	9300 ± 6000	⋯	⋯	⋯
		${L}_{\mathrm{phot}}$ (1036 erg s−1)	10 ± 3	⋯	⋯	−

Note. Best-fit parameter values for the absorption model that best describes each spectrum, as described in the text. The parameters of the absorber include the equivalent helium column (N_He), ionization parameter (ξ), systematic velocity shift of the absorber (v_abs), turbulent velocity of the absorber (v_turb), dynamical broadening of the reemission (σ_emis), and ionizing luminosity (from 13.6 eV to 13.6 keV). Quoted errors are at the 1σ level. The absorption in all spectra is dominated by a disk atmosphere (zone 1), a nearly static absorber that has fairly constant properties (N_He, log ξ, and v_abs) for all observations. Frozen parameters are marked with †. Errors that reach the fitting range for the parameter before the required change in χ² are marked with ‡. For zones 2 and 3, v_turb was kept frozen, as these components are optically thin and not sensitive to line ratios. A large v_turb of 1000 km s⁻¹ was chosen that would approximately capture the width of the highly redshifted features (zone 3) seen in spectra A and Γ. For spectrum Γ, N_He was frozen at 5 × 10²³ cm⁻² (approximately the point at which a helium absorber becomes Compton-thick) as an alternative to the Compton-thin zone 3 scenario in spectrum A.

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Strikingly, the disk atmospheres in all three spectra show a consistent and unambiguous redshift of ∼250 km s⁻¹ that is evident and statistically significant (see Section 3.2) in both the Fe xxvi and Si xiv lines (the two most prominent lines) and in agreement with other absorption features. The redshift is not a product of fitting a skewed line with a red wing in what otherwise would be a static absorber. As can be seen in Figure 2, the line centers of both Fe and Si lines are redshifted to the best-fit value, and the bulk of their equivalent widths are below their rest energies (vertical dashed lines). This redshift is also present regardless of whether one or two absorbers are used to model each spectrum. We discuss the origin of the redshift in Section 3.2.

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The detection of ionized absorption lines at or near their rest energies in near edge-on sources is clear evidence of a static atmosphere above the disk surface, as these are nearly ubiquitous at high inclinations and absent at moderate-to-low-inclination sources. As noted in Section 3.1, the atmospheric absorption found in all Chandra/HETG spectra of 4U 1916–053 (which encompasses the majority of the absorption) has a consistent redshift ranging from 230 to 290 km s⁻¹. The presence of this shift is notable, as it is unusually high compared to the expected relative radial velocity (and dispersion) in the galaxy and could be evidence of a kick. If the radial velocity of a system is small, however, the shift could instead originate in an inflow or a gravitationally redshifted atmosphere. In this section, we analyze each of these possibilities.

First, we established the significance of the redshift by performing a simultaneous fit of the three spectra. We performed three variations of the same test, where we tracked the increase in χ² between the best-fit redshifted atmosphere model and the best-fit atmosphere model with velocities fixed at zero. In the first test, the absorber used to fit the three spectra shared the same column, ionization, and velocity. In the second test, only the velocity was linked between the three spectra, while all parameters were fit independently in the third test. We obtained Δχ² values of 36, 37, and 38 for three, seven, and nine free parameters, respectively. This corresponds to a significance above 5σ for the first test and above 4σ for the second and third tests. The significance of the redshift is high despite using only one absorption zone with no reemission to model all three spectra. Finally, we added the three spectra into a single combined A + B + Γ spectrum and fit the time-averaged absorption. We obtained an average redshift of ${260}_{+80}^{-80}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ with lower limits of 150 (2σ), 120 (3σ), 90 (4σ), and 50 (5σ) km s⁻¹. These results are summarized in Table 2.

Table 2.  Velocity Shift Comparisons

Disk Atmosphere Redshift			Relative Radial Velocity
Combined A + B + Γ Spectrum					Expected Galactic Motion	Dip Absorption	Posterior Probability
		(km s−1)			(km s−1)	(km s−1)	(km s−1)
Best-fit value		${260}_{-80}^{+80}$	Best-fit or mean value		40 ± 50	−80 ± 110	5 ± 42
Lower limits	2σ	>150	Upper limits	2σ	<140	<90	85
	3σ	>120		3σ	190	170	<130
	4σ	>90		4σ	⋯	⋯	⋯
	5σ	>60		5σ

Note. Comparison between the redshift measured in the disk atmosphere (left) and the radial velocity of the system (right). Best-fit or mean expected values are quoted with their 1σ confidence regions. Lower limits to the redshift in the disk atmosphere and upper limits to the systematic radial velocity of the system are quoted based on their 2σ, 3σ, 4σ, and 5σ errors. Values in bold correspond to the closest integer significance at which the redshift in the disk atmosphere does not match the radial velocity. The posterior probability resulting from the thick-disk kinematics and the measured excess absorption in the outer disk yields a near 3σ difference from the shift in the disk atmosphere.

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An overview of the Chandra X-Ray Observatory's performance (Marshall et al. 2004) reports average systematic errors on the absolute wavelength calibration for both the MEG and HEG of less than 100 km s⁻¹. Systematic errors in the absolute wavelength calibration of the HETG arise from reconstructing the wavelength grid relative to the location zeroth order of the spectrum. This absolute wavelength calibration error, however, corresponds to the error in individual lines in individual spectra, as opposed to the exercise of determining the shift of an absorber by fitting multiple lines. The aforementioned study demonstrates how the average error in the shift of the emitter is considerably lower once multiple lines are considered. Given that our three spectra were produced by combining 11 total observations, each with their own independent spectral extraction (and therefore independent wavelength error), yet still produce a consistent redshift suggests that systematic errors in the energy grid of the HETG are not significant. Much smaller uncertainties on velocities, such as an analysis of Capella that achieved errors at the 90% level of ∼30 km s⁻¹ (Ishibashi et al. 2006), are commonly accepted.

In Galactic coordinates, 4U 1916–053 is located −85 away from the Galactic plane. With distance estimates ranging from 7 to 11 kpc (Smale et al. 1988; Yoshida et al. 1995), it lies ∼1.5 kpc above the disk of the Milky Way, most likely making it a member of the thick disk of the Milky Way. Figure 3 shows the expected systematic velocity of the source for a range of distances, where we adopted a thick-disk rotational lag (relative to the thin disk, ∼220 km s⁻¹) of ∼50 km s⁻¹ and a thick-disk velocity dispersion of ∼50 km s⁻¹ (Pasetto et al. 2012). The mean relative velocity is plotted in blue, and the shaded regions represent 1× and 2× the local velocity dispersion. Based on the recent distance estimate of 9.0 ± 1.3 kpc (Galloway et al. 2008), the expected velocity of the system is 37 ± 54 km s⁻¹ with a 2σ upper limit of 142 km s⁻¹, below the 2σ lower limit on the redshift in the disk atmosphere of 150 km s⁻¹. Even without constraints on the distance, there is little to no overlap between the 2σ regions in Figure 3.

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Although the predicted Galactic motions are small, a natal kick may produce a radial velocity corresponding to the observed redshift. Indeed, pulsar kicks have been observed in the 100–1000 km s⁻¹ range (see Atri et al. 2019), making it difficult to rule out radial motion. If the redshift is indeed the result of the radial velocity of the system, however, then all absorption features otherwise expected to be at rest velocities should display the same redshift. In 4U 1916–053 and other dippers, particularly strong absorption lines are detected during dipping events and typically associated with the outermost edge of the accretion disk (Díaz Trigo et al. 2006). Based on the orbital phase and kinematics of dipping events, the velocity shift of these excess absorption lines from the outer disk should be dominated by the systematic velocity of the source. All dips were initially filtered out from the spectra analyzed in this work. However, the 250 ks of new Chandra exposures makes it possible to extract sensitive spectra from the numerous dip events in spectrum B.

If the inner disk atmosphere is truly static, and if the dips truly originate in the outermost disk, then dip spectra should contain absorption lines from the inner disk atmosphere and the outermost disk. We therefore modeled the dip spectrum using the same best-fit model for spectrum B listed in Table 1, plus an additional absorber. Due to the modest S/N in the Fe K region of the dip spectrum, we focused only on the MEG spectrum between 1.5 and 2.5 keV. Our resulting fits suggested a relatively low ionization of log ξ ∼ 2.2, a helium column of N_He ∼ 10²² cm⁻², and a small turbulent velocity of v_turb ∼ 50 km s⁻¹.

Figure 4 shows the Si xiv line for both dip (black) and nondip (red) spectra with their corresponding best-fit models. The rest energy of the Si xiv line is plotted as the vertical dashed line, and the contribution of the redshifted atmosphere is plotted in red for both spectra. It is clear that there is significant absorption in the dip spectrum that is not being captured by the absorber used to model the atmosphere in the nondip spectrum. Visually, the excess absorption does not share the same velocity shift as the line originating in the atmosphere (red), with most of the excess dip absorption contributing at slightly higher energies, consistent with no velocity shift. The combined line profile itself is not quite centered at the rest energy of Si xiv. This is confirmed by spectral fitting, where the excess (plotted in blue) is best fit with a slightly blueshifted ionized absorber, v_dip = −80 ± 110 km s⁻¹ (with a 2σ upper limit of 90 km s⁻¹). Despite the lower S/N of the dip spectrum, we can rule out the possibility of both the atmosphere and dip absorption sharing the same redshift at a modest confidence level of 2.5σ by fitting the strongest lines in the 1.5–2.5 keV range. Indeed, the posterior probability resulting from combining the thick-disk kinematics (the prior) with this outer disk shift suggests a near-zero velocity shift and a 3σ upper limit of ∼130 km s⁻¹.

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The lack of a positive velocity shift in the outer disk suggests that the systematic velocity of 4U 1916–053 (its projected kick velocity, if any) is significantly lower than the ∼260 km s⁻¹ redshift observed in the atmosphere and formally consistent with zero. This analysis strongly suggests that the persistent redshift seen in all spectra is associated with an inner disk atmosphere.

A failed wind or inflow could, in principle, be responsible for the observed redshift. The most direct evidence of such a flow would be the presence of inverse P Cygni profiles. These are missing from our data, yet ruling out an inflow in this fashion likely requires much higher quality spectra. Still, an inflow of this sort seems unlikely. First, an inflow would require some mechanism that removes enough angular momentum from the atmosphere in a much lower density environment compared to those found in the disk. This mechanism would have to produce an inflow with a very low covering factor, as we do not observe ionized absorption lines, much less redshifted lines, in sources viewed at lower inclinations. This means that the inflow, which must originate at relatively large radii, would have a small vertical extent. The presence of X-ray bursts suggests that the magnetic field of the neutron star is likely not strong enough to induce a collimated inflow.

The specific properties of the absorber also render an inflow unlikely. In the almost 300 ks of new and archival Chandra/HETG exposures of 4U 1916–053, the source displays a range of spectral states over a period of ∼14 yr. Despite the large temporal separation, the observed redshift appears to be constant for all observations even as the source undergoes noticeable changes in accretion state. This would suggest that whatever physical mechanism was responsible for removing the angular momentum from the atmosphere would necessarily produce the same redshift despite different physical conditions within the disk.

We find that the most likely explanation for this redshift is that of a static atmosphere, located close enough to the compact object to be subject to an ∼260 km s⁻¹ gravitational redshift. Unlike a putative inflow, a gravitationally redshifted disk atmosphere (GRDA) would be more consistent with the static atmospheres we expect to see in these sources and the behavior of the absorption in this source in particular. This explanation only invokes general relativity in the weak limit, requiring the absorber to be located at around ∼1200 GM/c², or $\sim 1800\left(\tfrac{{M}_{\mathrm{NS}}}{{M}_{\odot }}\right)$ km.

Table 3 lists the properties of the disk atmosphere found in our spectra using three different methods for measuring the radius from the compact object to the absorber. The first is the upper limit on the photoionization radius, R < R_upper ≡ L/N_Heξ, where $R=f\cdot {R}_{\mathrm{upper}}$ and f is the filling factor. We assumed a filling factor of unity for simplicity. The second is the radius given by the dynamical broadening of the reemission from the gas, $R={GM}/{\sigma }_{\mathrm{emis}}^{2}$, assuming the velocity broadening (${\sigma }_{\mathrm{emis}}^{2}$) probes the local Keplerian velocity. In the case of a GRDA, the measured redshift can be used in order to directly measure this radius in units of GM/c², assuming the redshift is entirely due to gravity. The radius, R = R_z, is also included in Table 3.

Table 3.  Disk Atmosphere Geometry and Physical Properties

Spectrum		Radius		${n}_{{He}}$	f	${z}_{{Grav}.}$	${v}_{{corr}.}$	${v}_{{corr},2{M}_{\odot }}$
		(${10}^{8}$ cm)	(${GM}/{c}^{2}$)	(${10}^{14}$ ${{\rm{cm}}}^{-3}$)		(${\rm{km}}$ ${{\rm{s}}}^{-1}$)	(${\rm{km}}$ ${{\rm{s}}}^{-1}$)	(${\rm{km}}$ ${{\rm{s}}}^{-1}$)
Spectrum A	${R}_{{Upper}}$	${5.4}_{\unicode{x02021}}^{+2.0}$	${3600}_{\unicode{x02021}}^{+1300}$	${9.3}_{-4.5}^{\unicode{x02021}}$	${1.0}^{\dagger }$	${70}_{-30}^{\unicode{x02021}}$	${160}_{-220}^{+230}$	$90\pm 230$
	${R}_{{Orbital}}$	${4.65}_{-4.1}^{+4.7}$	${3100}_{-2800}^{+3200}$	${13}_{-10}^{+13}$	${0.9}_{-0.8}^{\unicode{x02021}}$	${100}_{-100}^{+90}$	${120}_{-240}^{+500}$	−
	${R}_{z}$	$2.0\pm 1.7$	$1300\pm 1200$	${70}_{-50}^{+130}$	${0.4}_{-0.4}^{\unicode{x02021}}$	${260}^{\dagger }$	${0}^{\dagger }$	−
Spectrum B	${R}_{{Upper}}$	${5.4}_{-4.4}^{+1.8}$	${3700}_{-3000}^{+1200}$	${6.0}_{-4.9}^{+5.2}$	${1.0}^{\dagger }$	${80}_{-30}^{+70}$	${150}_{-140}^{+160}$	${60}_{-140}^{+200}$
	${R}_{{Orbital}}$	−	−	−	−	−	−	−
	${R}_{z}$	${2.0}_{-1.2}^{+1.1}$	$1300\pm 800$	${50}_{-40}^{+30}$	${0.36}_{-0.25}^{+0.36}$	${228}^{\dagger }$	${0}^{\dagger }$	−
Spectrum Γ	${R}_{{Upper}}$	${17}_{-11}^{+3}$	${11000}_{-7000}^{+2000}$	${4.0}_{-1.9}^{+2.6}$	${1.0}^{\dagger }$	${26}_{-5}^{+16}$	${260}_{-160}^{+170}$	${230}_{-160}^{+170}$
	${R}_{{Orbital}}$	${1.5}_{-1.0}^{+0.9}$	$1000\pm 600$	${480}_{-360}^{+300}$	${0.09}_{-0.06}^{+0.08}$	${290}_{-170}^{+180}$	${0}_{-230}^{+240}$	−
	${R}_{z}$	$1.6\pm 0.9$	$1100\pm 600$	$500\pm 300$	${0.09}_{-0.06}^{+0.08}$	${285}^{\dagger }$	${0}^{\dagger }$	−

Note. Physical properties of the disk atmosphere of spectra A, B, and Γ as a function of the upper limit of the photoionization radius (${R}_{\mathrm{Upper}}=f\cdot L/{N}_{\mathrm{He}}\xi$), the radius given by the dynamical broadening of the reemission (R_Orbital), and the radius given by the observed redshift (R_z). A neutron star mass of 1 M_⊙ was assumed to calculate some values. When using R_Upper, only z_Grav and v_corr. depend on mass. Values for v_corr. assuming 2 M_⊙ are listed in the last column. A filling factor of unity is assumed using R_Upper. In the case of both R_Orbital and R_z, only the density (n_He) and filling factor (f) depend on mass. For a 2 M_⊙ neutron star, the density decreases by a factor of 4, and the filling factor increases by a factor of 2.

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For simplicity, the gravitational redshift (z_Grav) and resulting corrected velocity (v_corr) values at R = R_Upper listed in Table 3 were calculated assuming a neutron star mass of 1 M_⊙ (values for v_corr for 2 M_⊙ were also included). Being an upper limit on the distance of the absorber from the central engine, R_Upper places a lower limit on z_Grav that only increases with neutron star mass. In the case of spectra A and B, R_Upper suggests that the disk atmosphere must be gravitationally redshifted by at least ∼70 km s⁻¹, which increases to ∼150 km s⁻¹ for a mass of 2 M_⊙. In the case of spectrum Γ, this lower limit is significantly smaller. Uncertainties on the distance and spectral energy distribution (SED) shape make R_Upper an imperfect upper limit. It is notable that the radius given by the broadening of the reemission, R = R_Orbital, is consistent with the radii determined by associating the redshift with a gravitational shift. However, this velocity broadening value is poorly constrained and assumes a semiarbitrary choice of emission covering factor; therefore, we advise caution when interpreting this result. Ultimately, the picture of a static, photoionized disk atmosphere deep in the gravitational potential is self-consistent. See Table 3 for all of the relevant measurements and velocities corrected to the assumed rest frame of the absorption.

If the observed redshift is entirely gravitational, it is possible to constrain other aspects of the disk atmosphere by insisting on the radii being equal. For instance, the filling factors, f, for spectra A and B range from ∼0.3 to ∼0.8 for neutron star masses of 1 and 2 M_⊙, respectively. This suggests a low degree of clumping within the atmosphere; in this respect, the atmosphere may differ substantially from winds that are observed downstream in this and other sources. At 1 M_⊙, the atmosphere in spectrum Γ would be significantly more clumpy by comparison, although this low filling factor of f ∼ 0.1 is far from unphysical. It is also possible to derive gas densities in the atmosphere; these are in the range 15 < log n_He < 16.7. This range of gas densities is comparable to those inferred in studies of disk winds in accreting black holes (e.g., Miller et al. 2016; Trueba et al. 2019). At the higher end, these values are comparable with densities expected within the disk (15 < log n_e < 19; see García et al. 2016). Finally, we note that when the radial location of the absorber is known, the local Keplerian velocity is defined; then, if the turbulent broadening can be measured via fits to multiple lines, the measured width of the time-averaged absorption lines gives the size of the central engine. Using these data, a value of $R\simeq {60}_{-30}^{+20}$ GM/c² results. However, it is likely more appropriate to treat this as an upper limit. This technique is the subject of a forthcoming paper (N. T. Trueba et al. 2020, in preparation).

A disk atmosphere located at ∼1200 GM/c² would likely require magnetic pressure support in order to produce the columns we observe along our line of sight, as any plausible gas temperatures produce far less thermal energy than required. Numerical models of MRI disks (the magnetorotational instability; see Balbus & Hawley 1991) suggest that magnetic pressure support can not only dominate the upper layers of the disk but also result in a more extended vertical structure (Blaes et al. 2006), much like the absorbing atmosphere along our line of sight. As an order-of-magnitude comparison, we estimated the local magnetic field ($B\sim \sqrt{8\pi P}$) required to maintain hydrostatic equilibrium via ${dP}/{dz}\simeq \sin \,\theta \cdot {GM}\rho /{r}^{2}$, where sin θ ≃ r/z and dP/dz ∼ P/z, and therefore $P\,\simeq {GM}\rho /r\cdot {z}^{2}/{r}^{2}$. Using the largest densities in Table 3 and a large z/r of 0.3, we get a local magnetic field of ∼2 × 10⁵ G, which is still below the upper limit on the magnetic field given by Shakura & Sunyaev (1973) of ∼5 × 10⁵ G (their Equation (2.19)).

A large number of neutron star X-ray binaries are currently known, so it is unlikely that a GRDA would be unique to 4U 1916–053. However, no redshifts like those now discovered in 4U 1916–053 have been reported in the literature. In longer-period systems with larger disks, a longer path length through the extended disk atmosphere may simply wash out the signature of the inner disk atmosphere. Particularly among ultracompact and short-period dipping/eclipsing X-ray bursters, however, wherein the magnetic field of the neutron star is weak and the accretion disk is small, we should find evidence of redshifted atmospheres. We examined the available Chandra/HETG archival data for sources that fit these criteria. The same data reduction procedure as in Section 2 was followed.

Of the few sources in our sample, we found very similar redshifts of ∼300 km s⁻¹ in the spectra of both XTE J1710–281 and AX J1745.6–2901. As per the absorption seen in 4U 1916–053, it is the bulk of the line absorption that is redshifted, with multiple lines displaying the same redshift. In the only HETG spectrum of AX J1745.6–2901, the redshift is present in both He- and H-like iron absorption lines at a significance of ∼2.5σ. Unfortunately, the neutral interstellar column is too high to confirm this redshift via Si xiv. This is not the case for the brighter of the two archival spectra of XTE J1710–281, which instead showed multiple strong redshifted absorption lines between 1.0 and 2.6 keV, as well as Fe K. The ∼320 km s⁻¹ redshift is unmistakable and significant at well over 5σ (N. T. Trueba et al. 2020, in preparation).

The Chandra observation of AX J1745.6–2901 was conducted as part of a campaign involving both XMM-Newton and NuSTAR (see Ponti et al. 2018). To date, a spectral analysis of this spectrum has not been published, and no redshift has been reported. This is likely due to the relatively low S/N of the spectrum. More surprising is the case of XTE J1710–281, where the highly significant redshift has also not been reported. It is possible that carefully screening against dips and bursts and our use of the relatively new "optimal" binning algorithm has enabled us to extract more information from new and archival data.

We note that possible redshifts were also found in the spectra of other sources (e.g., EXO 0748–676), but these were either low-S/N spectra or displayed complex absorption with multiple velocities. The remaining spectra contained either no absorption lines or, in the case of sources with longer orbital periods, lines at rest velocities. Based on the Galactic coordinates of both XTE J1710–281 (356.3571 +06.9220, likely in the thick disk) and AX J1745.6–2901 (359.92030 −00.04204), a natal kick would likely be required in order to attribute the observed redshifts entirely to the relative radial velocities of either of these systems. Ultimately, robust radial velocity measurements are required in order to confirm the origin of these redshifts. However, these results are promising in that they are consistent with a physical connection between the processes that give rise to disk atmospheres with redshifted lines, be it gravitational redshift from an inner disk atmosphere or some persistent, semispherical inflow.

In the previous section, we mentioned evidence of transient absorption features in our spectra aside from the primary absorber, which we attribute to a redshifted inner disk atmosphere. The first is evidence of absorption between 6.8 and 6.9 keV in both spectrum A and spectrum Γ, which we attribute to a much more highly redshifted disk atmosphere. The second is evidence of a disk wind in spectrum A, which appears as a blue wing in the Fe xxvi absorption line at ∼6.97 keV (as well as perhaps some complexity in the Si xiv line near ∼2 keV). In this section, we will discuss alternative interpretations and fits to the data, their significance, and some physical implications of these results.

3.4.1. The Transient Redshift

3.4.2. Evidence of a Disk Wind

Previous studies of the best Chandra/HETG low-mass X-ray binary (LMXB) wind spectra have been able to model and identify multiple velocity components of the absorbing wind complex. In cases such as 4U 1630–472 (Miller et al. 2015; Trueba et al. 2019) and GRS 1915+105 (Miller et al. 2016), although the individual velocity components are all blended to produce multiple skewed line profiles, the resulting line spectrum displays different velocity shifts for lines corresponding the different ionization and column densities of the separate absorbers. In these cases, models with multiple absorbers are required to describe the data.

The same analysis can be applied to 4U 1916–053, where, instead of a wind complex, the presence of both a static atmosphere and a weakly absorbing wind may require the use of multiple absorbers. Of the three spectra, compelling evidence for a disk wind can only be found in spectrum A. Although the shape of the Fe xxvi line in spectrum B is similar to that in spectrum A, a two-component model resulted in no significant improvement to the fit because of the lower S/N of the spectrum, as well as the asymmetry in the line being less pronounced.

The three-component model of spectrum A (including a wind; see Table 1) yields a χ²/dof = 536/488 = 1.10, a modest but nontrivial improvement of Δχ² = 23 over the best-fit single-component model (χ²/dof = 559/495 = 1.14). An F-test quantifies this as a 3σ improvement over the one-component model. Visually, the one-component model is unable to capture the shifts and depths of both the Si xiv and Fe xxvi simultaneously. Since the redshift of the single-absorber model is lower than that in the atmosphere-plus-wind model, the resulting fit underestimates the red portion of Si xiv and greatly overestimates the absorption in the red portion of Fe xxvi. In our fitting experiments, we found that adding dynamically broadened reemission from the same absorbing gas could help achieve better fits to both the Si and Fe lines. Although this is true even in the single-component model, adding broad emission lines to the wind or the highly redshifted component (zone 3) only makes these features more pronounced. Adding reemission, therefore, did not improve the fit of the single-component model. Individually, the addition of either a wind absorber (zone 2) or the highly redshifted absorber (zone 3) resulted in only marginal improvements to the model. Instead, the model requires reemission and two additional absorbers in order to adequately describe the data. However, the errors reported in Table 1 indicate that most parameters for this absorber are poorly constrained. In particular, the negative 1σ error on the absorbing column (${N}_{\mathrm{He}}={10}_{-9}^{40}\times {10}^{22}\,{\mathrm{cm}}^{-2}$) approaches unity with the best-fit value and would suggest that the wind is only significant to 1σ. This is in part driven by the complexity of the model that requires a larger change in χ². Given the tension between the significance suggested by the F-test and the error in N_He, we advise caution when interpreting this result.

The large uncertainty in the outflow velocity of the absorber, however, is due to a local χ² minimum in a different region of parameter space. The best-fit model reported in Table 1 fits the bulk of the absorption lines with the absorber corresponding the redshifted disk atmosphere, and the blueshifted absorber fits the blue wing of the Fe xxvi line only (see Figure 5). As can be seen in the middle panels of Figure 2, however, the Si xiv line profile also demonstrates some evidence of complexity in the form of a blue wing. We performed an alternative fit to spectrum A in order to capture the blue wings of both the Fe xxvi and Si xiv line profiles, which we report in Table 4. Although the parameters are quite different, statistically, the fits are nearly identical. Strikingly, this new fit suggests that the redshift in the atmosphere is much stronger (∼600 km s⁻¹), while the blueshift in the "wind" component is much lower (∼–200 km s⁻¹) and essentially consistent with zero. A plausible interpretation is that, in this spectrum, we are probing different regions of the disk atmosphere, where the inner atmosphere is noticeably redshifted while the outer regions are only slightly redshifted. It is important to note that the redshift of the atmosphere given by the former model is consistent with the fits of spectrum B, spectrum Γ, and the combined A + B + Γ spectrum, while the alternative model gives a much larger redshift (∼600 km s⁻¹) and less self-consistency.

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Table 4.  Alternative Fit to Spectrum A

Parameter	Zone 1	Zone 2	Zone 3
NHe (${10}^{22}\,{\mathrm{cm}}^{-2}$)	${45}_{-20}^{+5\unicode{x02021}}$	${20}_{-18}^{+30\unicode{x02021}}$	${1.3}_{-1.1}^{+15.0}$
log ξ	${4.5}_{-0.1}^{+0.3\unicode{x02021}}$	${4.4}_{-0.5}^{+0.4\unicode{x02021}}$	${3.7}_{-0.9}^{1.0}$
${v}_{\mathrm{abs}}$ ($\mathrm{km}$ ${{\rm{s}}}^{-1}$)	${580}_{-550}^{+740}$	$-{220}_{-1800\unicode{x02021}}^{+220\unicode{x02021}}$	${4200}_{-2600}^{+2800}$
${v}_{\mathrm{turb}}$ ($\mathrm{km}$ ${{\rm{s}}}^{-1}$)	${70}_{-20\unicode{x02021}}^{+430\unicode{x02021}}$	${300}^{\dagger }$	${1000}^{\dagger }$
${\sigma }_{\mathrm{emis}}$ ($\mathrm{km}$ ${{\rm{s}}}^{-1}$)	${8000}_{-7000\unicode{x02021}}^{+12000\unicode{x02021}}$	⋯	⋯
${\chi }^{2}/\nu$			533/488 = 1.09

Note. Parameter values for the alternative fit to spectrum A. Unlike the fit listed in Table 1, zone 2 captures the blue wing in both the Fe xxvi and Si xiv lines. The fact that the data can be described by this alternative fit drives much of the degeneracy when fitting this spectrum.

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The possible presence of a disk wind in ultracompact X-ray binaries (UCXBs) such as 4U 1916–053 can provide key insights about the physical mechanisms that drive disk winds in accreting black holes and neutron stars in general. Magnetic winds in LMXBs are of particular interest, as they provide observational evidence of different magnetic processes mediating mass and angular momentum transfer within the disk. Furthermore, evidence of self-similar winds driven via MHD pressure, possibly as a result of the magnetorotational instability, has been uncovered in GRO J1655–40 (Fukumura et al. 2017) and 4U 1630–472 (Trueba et al. 2019) through their density and velocity structure.

Determining whether a wind is driven via magnetic processes has primarily relied on ruling out alternative driving mechanisms via estimates of their launching radii. Although radiation pressure driving (via line driving) can be ruled out given the high degree of ionization within the gas, thermally driven winds could still arise via Compton heating of the disk surface by energetic photons from the central engine. In principle, this can only occur at radii larger the Compton radius (R_C), where the temperature of the disk surface allows a sizable portion of the gas to exceed the local escape velocity (Begelman et al. 1983), although this limit may extend down to 0.1R_C (Woods et al. 1996). In sources such as GRS 1915+105 (Miller et al. 2015, 2016), GRO J1655–40 (Miller et al. 2006, 2008, 2015; Kallman et al. 2009; Neilsen & Homan 2012), and (among others) 4U 1630–472 (Miller et al. 2015; Trueba et al. 2019), wind launching radii derived by modeling the photoionized wind absorption (and, in some cases, wind reemission) have been well below R_C, suggesting magnetic driving. In the helium-rich disk of 4U 1916–053, ${R}_{C}=2\times {10}^{10}\times ({M}_{\mathrm{BH}}/{M}_{\odot })/{T}_{C8}$ cm, where the mean molecular weight of fully ionized helium gas (μ_He ∼ 1.3) makes this limit larger (∼2×) compared to solar abundances.

There are, however, uncertainties that can significantly limit our ability to measure wind launching radii. In most cases, the lack of an independently measured gas density means that we can only place an upper limit on the radius given by the photoionization parameter, ξ = L/nr². This is worsened by our imperfect understanding of the luminosity and shape of the ionizing continuum, as well as poorly constrained distances to these sources. In the case of 4U 1916–053 and UCXBs in general, the outermost radius of their small disks (truncated by the orbit of the companion) is itself a useful upper limit on the launching radius of a possible disk wind. Given the orbital period of the X-ray dips and range of possible neutron star masses, we can obtain estimates of this outermost radius through basic Keplerian mechanics, which we can then compare to the Compton radius. Unlike the photoionization radius, this upper limit is model-independent and does not depend on the distance, luminosity, or SED shape.

Figure 6 shows a contour plot of the ratio of the outermost disk radius over R_C as a function of neutron star mass and spectrum temperature. The outermost radius is given by ${R}_{\mathrm{outer}}\sim {R}_{\mathrm{donor}}\times 0.5/{(1+q)}^{1/3}$ (Paczyński 1967), ${R}_{\mathrm{outer}}\,\sim {R}_{\mathrm{donor}}\times 0.6/(1+q)$, where R_donor is the orbital radius of the donor star and q is the binary mass ratio (we assume q ≪ 1 in order to establish an upper limit). Our understanding of the broadband continuum is poor within the narrow Chandra energy range, making it difficult to constrain the temperatures of the disk (at low energies) and neutron star and which of these determines the Compton temperature. Instead of assuming a single temperature, we chose to plot this ratio for a range of possible temperatures. Our results suggest that the outermost radius of the disk is smaller than the Compton radius, with the largest ratio indicating a disk smaller than ∼0.2R_C. Although 0.1R_C is the commonly used analytical lower limit for thermal driving, only winds launched from the outermost edge of the disk from the low-mass neutron stars and the highest Compton temperatures seem compatible with thermal driving. The strict upper limit set by the size of the accretion disk suggests that the possible disk wind found in spectrum A of 4U 1916–053 would likely be magnetic.

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