Searching for Highly Magnified Stars at Cosmological Distances: Discovery of a Redshift 0.94 Blue Supergiant in Archival Images of the Galaxy Cluster MACS J0416.1-2403

We aligned all imaging with TweakReg, and then resampled images to a scale of 003 pixel⁻¹ using AstroDrizzle (Fruchter et al. 2010).

We use PythonPhot²⁰ (Jones et al. 2015) to measure the light curves from difference imaging. The PythonPhot package includes an implementation of point-spread function (PSF) fitting photometry based on the DAOPHOT algorithm (Stetson 1987).

For each HST visit, we created a difference image by subtracting a deep template image from a coaddition of exposures acquired during the visit. We next identified all peaks having >2σ significance, where σ corresponds to the standard deviation of the background in the difference image. Then we measured the angular size of each of the candidate transients, and we selected objects with an extent consistent with the size of the PSF.

We retained only the peaks that we detected with >2σ significance in multiple HST visits at the same location within a 10-day interval, a characteristic timescale for microlensing peaks of magnified stars. Our objective was to identify transients that might have been missed by searches that only scanned images acquired during individual epochs.

The transient's J2000 coordinates are α = 4^h16^m087084, δ = −24°04'02945 in the World Coordinate System of the official HFF coadded images. A spectrum of the underlying arc acquired by the CLASH-Very Large Telescope survey yielded z = 0.93910 (Balestra et al. 2016; Caminha et al. 2017), which is a smaller redshift than those of Icarus (Kelly et al. 2018) and the Spocks (Rodney et al. 2018). Patrício et al. (2018) measure an oxygen abundance of 12 + log(O/H) = 8.72 ± 0.6 dex and a low extinction of A_V = 0.15 ± 0.20 from nebular emission lines for the lensed system from Multi Unit Spectroscopic Explorer integral-field unit spectroscopy.

The optical and near-infrared light curve plotted in Figure 3 shows that the microlensing event faded over a period of at least two weeks. The event was at least ∼1.5 times brighter (total flux) in the infrared (IR) band than its underlying arc in archival HST imaging during the HFF project, as the true peak of this microlensing event may have occurred during gaps of HST visits, as shown in Figure 3. Photometry is measured using a 02 aperture (detailed values are listed in Table 1). The light curve may also exhibit slow changes over a period of years, as shown in the bottom panel of Figure 3, consistent with the level of microlensing expected from stars responsible for the intracluster light of the cluster.

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A microlensing peak should have a duration roughly R/v, where R is the size of the lensed source and v is the transverse velocity of the lensing system. Given the ∼1000 km s⁻¹ expected relative transverse velocity between the galaxy cluster and background source (Watson et al. 2013), the several-week timescale of the microlensing peaks implies that the lensed sources can only extend for at most several tens of astronomical units. Consequently, the lensed systems must be stellar systems (e.g., single star or binary system) instead of a star cluster.

A magnified source close to a fold caustic of a foreground galaxy-cluster lens should appear as a pair of images on opposite sides of the critical curve. In the absence of microlensing, which can alter the total magnification of each image, the counterimages should have equal brightness. Warhol's location, marked by the green circle labeled "A" in Figure 4, corresponds to a peak along the underlying arc in coadditions of HFF F606W and F814W imaging acquired before the microlensing event. To examine whether a counterimage of the underlying source may exist along the arc, we measured the flux inside of a 005 diameter aperture as we moved it along the arc. Figure 5 shows a second peak labeled "B" (much fainter than the peak A) along the underlying arc.

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To assess the statistical significance of image B, we fit simultaneously the F606W and F814W coadded images of the arc in a 12 × 06 region using the GALFIT package (Peng et al. 2002). Although GALFIT was written for analysis of galaxy surface-brightness distributions, it has a flexible set of profiles that includes the King (1962), Sérsic (1963), and Moffat (1969) functions. We assume that the underlying arc consists of an unresolved stellar population and therefore can be modeled by a smoothly varying function. Furthermore, the arc's surface-brightness distribution should be symmetric on opposite sides of the critical curve. Consequently, the center of the component corresponding to the unresolved arc is set fixed to the location between images A and B.

We next fit a series of models to the arc. The first set of models consists of a component corresponding to the smoothly varying arc and a point source at the position of image A. Functions used for the smoothly varying arc include King, Sérsic, and Moffat profiles. In the next step, we modify these models by adding a second point source, at the location of the putative image B, and fit this model that includes image B to the same data.

For each model, we fit jointly the F606W and F814W imaging acquired before 2014 September, using all possible profile functions provided by GALFIT. Figure 6 shows Warhol's F606W and F814W deep HFF images, models, and residuals from the best-fitting model. To be able to perform model comparison, we evaluate the Akaike information criterion (AIC; Akaike 1974) from the best-fit results provided by the two models, as listed in Table 2. The result gives AIC_{single−peak} − AIC_two−peak > 20, indicating that the single-peak model has relatively "no empirical support" (Burnham et al. 2011) compared to the two-peak model. The best-fit result given by the two-peak model indicates that the AB magnitudes of source A and source B are 28.7 ± 0.1 and 29.4 ± 0.2 (respectively) in the ACS-WFC F606W band, and 28.53 ± 0.06 and 29.9 ± 0.3 in the ACS-WFC F814W band.

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Table 2.  Comparison between GALFIT Models Including Underlying Arc and One or Two Stellar Images Fit Simultaneously to F606W and F814W Coadded Images

Two-peak Model			Single-peak Model
Profile	ΔAICa	χ2ν	Profile	ΔAIC	${\chi }_{\nu }^{2}$
Moffat	0	1.073	King	20.78	1.087
King	2.77	1.075	Moffat	23.91	1.089
Sérsic	4.82	1.076	Sérsic	28.48	1.092

Note. Models in the left column include point source at positions A and B, and those in the right column include only a source at position A. The differences between the Akaike information criterion (AIC) imply that the single-image models have "no empirical support" (Burnham et al. 2011) compared to those that include a pair of images.

^aΔAIC = AIC − AIC_min.

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Sources near a cluster fold caustic (with no microlenses) should appear as a pair of images with equal magnification. Therefore, if the new transient were a stellar outburst, we would expect to see a pair of transients with a relative time delay of less than a day. The outbursts of luminous stars persist for longer than a single day, and, as shown in Figure 3, Warhol had a duration of least two weeks. By contrast, a microlensing event should only appear as a single transient, as a star or remnant in the cluster becomes temporarily aligned with one of the magnified images of the background star. Our GALFIT analysis finds that image B is, on average, ∼1 mag fainter than image A, a difference that can be attributed to microlensing. Consequently, if the peak observed at image A's location were a stellar outburst, it would have also appeared at image B's position with a flux that was ∼1 mag fainter. Given the peak fluxes of image A, the peak at image B's position would have had F814W ≈ 27.3 mag, F125W ≈ 27.3 mag, and F160W ≈ 27.1 mag, and these would have been detected with ∼2.1σ, ∼3.4σ, and ∼3.2σ significance. However, no evidence for a peak at image B's position is apparent in difference images, as shown in Figure 4.

We calculate magnification maps at z = 0.94 using 10 independent Frontier Fields Lens Models (Lotz et al. 2017) for the MACS0416 galaxy cluster, as shown in Figure 2. The predicted magnification μ due to the galaxy-cluster lens at Warhol's position is listed in Table 3. In general, the locations of galaxy-cluster critical curves are constrained by current models to within a tenth of an arcsecond in the best cases. Given Warhol's proximity to the critical curve, the uncertainty in the critical curve's location results in a large magnification uncertainty at its position.

We compute the offsets between models' predictions for the location of the critical curve and the midpoint of the line between counterimages A and B (θ_c), as listed in Table 3. The offsets show that a majority of published lensing models place the critical curve within 03 of the midpoint. The Bradač (v3) and CATS (v4) models locate the critical curve at the greatest offset (>05) from the midpoint. The Zitrin-nfw (v3) model's predicted critical curve yields the smallest offset (002).

After correcting for extinction expected for the Galactic foreground (A_V = 0.112 mag; Schlafly & Finkbeiner 2011), we fit the SED of the microlensing peak. ACS-WFC F606W and F814W, as well as WFC-IR F125W and F160W, imaging was acquired during a first epoch on 2014 September 15–16; the optical and IR integrations were interspersed with each other in time. As shown in Figure 3, the transient was still detected during a second imaging epoch on 2014 September 22.

We simultaneously fit a Castelli & Kurucz (2004) stellar atmosphere model and a host-galaxy extinction curve to the measured SED of the Warhol microlensing event. We assume that the source did not vary significantly while the optical and IR images were acquired during the first epoch. We include as a fit parameter the change in the magnification (relative normalization of the SED) between the first and second epochs. Given the Patrício et al. (2018) measured abundance of 12 + log(O/H) = 8.72 ± 0.6 dex, we use stellar models that have a solar abundance.

Figure 7 shows the best fits to the measured photometry when we allow the temperature of the stellar photosphere to vary as a free parameter. For a Milky Way (R(V) = 3.1; Cardelli et al. 1989) extinction law, we find a best-fitting temperature of 22,500 K, consistent with an early B-type star. Instead, adopting the extinction law for the Small Magellanic Cloud (SMC; R(V) = 2.73; Gordon et al. 2003) yields 23,700 K. We expect that microlensing may only potentially be chromatic when a microcaustic is close to the limb of the star, but this should occur over a very short timescale, smaller than the ∼2 days during which observations near peak were acquired. While the surface gravity of early-type blue supergiants has values of $\mathrm{log}g\approx 2$–2.8 (e.g., Urbaneja et al. 2005; Przybilla et al. 2010), the Castelli & Kurucz (2004) models have $\mathrm{log}g\geqslant 3$ for photospheric temperatures exceeding 20,000 K, and this limitation may have some effect on the value of the inferred photospheric temperature.

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The low to moderate best-fitting host-galaxy dust extinction is consistent with the A_V = 0.15 ± 0.20 mag extinction inferred by Patrício et al. (2018) from an analysis of nebular emission lines from the lensed galaxy.

We next estimate approximately the star's luminosity from the apparent magnitude of image A during HFF observations prior to the 2014 September microlensing event. To determine the star's magnification, we first compute a K-correction K_xy as

$$\begin{eqnarray}&&{m}_{y}={M}_{x}+{dm}+{K}_{{xy}},\end{eqnarray} \tag{ 1 }$$

where m_y is the observer-frame apparent magnitude in the y band, M_x is the rest-frame absolute magnitude in the x band, and dm is the distance modulus. To calculate a K-correction, we use Equation (2) of Kim et al. (1996),

$$\begin{eqnarray}&&K=2.5\,{\mathrm{log}}_{10}(1+z)+{m}_{{\rm{y}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{V,\mathrm{syn}}^{\mathrm{Vega}},\end{eqnarray} \tag{ 2 }$$

where z = 0.94, ${m}_{{\rm{y}},\mathrm{syn}}^{\mathrm{AB}}$ is the synthetic magnitude of a redshifted model spectrum in an observer-frame y band (e.g., ACS-WFC F814W), and ${m}_{V,\mathrm{syn}}^{\mathrm{Vega}}$ is the synthetic Johnson V-band magnitude of the rest-frame model spectrum. Using the best-fitting spectral models, we calculate K_V,F814W ≈ −1.2 and K_V,F125W ≈ −0.4, and adopt dm = 43.96 mag at z = 0.94 (with no correction for magnification).

We have found that, during HFF observations before the microlensing peak, image A had an average ACS-WFC F814W magnitude of ∼28.5. For an early B-type supergiant star with photospheric temperature of 22,400 K (B1V) from the Pickles (1998) library and M_V = −8.3 mag and without dust extinction, a magnification of ∼266 would be implied. Such a magnification at images A's and B's separation from the critical curve is consistent with those expected from the existing lens models of the cluster listed in Table 3. The luminosities of blue supergiant stars in the SMC reach M_V ≳ −8.8 mag (Dachs 1970).

There are examples of extremely luminous, main-sequence O-type stars such as Melnick 34 in the 30 Doradus complex in the Large Magellanic Cloud (LMC) with an absolute magnitude of M_V = −7.9 mag (Doran et al. 2013). However, such very luminous O-type stars or Wolf–Rayet stars showing H in their spectra (WNH; Smith & Conti 2008) are extremely rare in comparison to cooler B-type supergiants at lower bolometric luminosity but similar M_V.

For example, Figure 3 of Fitzpatrick & Garmany (1990) presents a Hertzsprung–Russell diagram of the luminous stellar population of the LMC. After removing the bolometric corrections listed in Tables 1 and 2 of Fitzpatrick & Garmany (1990; see also Figure 6 of Flower 1996), we find that there are ∼25 B-type supergiants (10,000 ≲ T ≲ 30,000 K) but no O-type stars (≳30,000 K) having M_V ≲ −8 mag in the LMC. The comparatively small abundance of WNH stars arises from their initial masses (very approximately 100 M_⊙ versus 10–20 M_⊙), but also the significantly longer lifetimes at the lower masses. Among binary stars, blue supergiants can also be blue stragglers from mass gainers and mergers.

We have found that a B-type star with A_V ≈ 0.5 mag provides the best fit to the SED of the microlensing event with the Castelli & Kurucz (2004) library. Our estimate of the star's absolute magnitude from the HFF imaging implies that it is highly luminous at rest-frame optical wavelengths, and indicates that it is a blue supergiant, given the comparatively small numbers of O-type stars with M_V ≲ −8 mag. For reference, we list in Table 4 the magnifications that would be required for both main-sequence and post-main-sequence stars of different spectroscopic types to yield the peak observed magnitude of F125W ≈ 26.25 during the 2014 September microlensing event.

Blue supergiant stars would require magnifications that are factors of ten to hundreds smaller than typical main-sequence stars. For fold caustics, assuming the lens has a smooth mass distribution, the magnification μ decreases with the distance d in the source plane from the caustic as μ ∝ d^−1/2. Hence, the source-plane area A within which the magnification exceeds μ scales as A(>μ) ∝ μ⁻², which implies that the magnifications needed for typical main-sequence will be much less common. Indeed, the presence of stars responsible for the intracluster light along the line of sight precludes almost all main-sequence stars, because stellar microlenses cause magnification exceeding 20,000 to become extremely unlikely (Diego 2019).

We next show that stellar microlensing can be expected at Warhol's offset from the critical curve, and that the timescale of the 2014 September microlensing event indicates that the lensed source corresponds to an individual star or stellar system. The separation between A and its possible counterimage B is ∼012. Near the critical curve, the GLAFIC galaxy-cluster mass model yields the following magnification for each of the images, in the case of a smooth model (i.e., with no microlensing):

$$\begin{eqnarray}&&{\mu }_{\mathrm{each}}\approx (11^{\prime\prime} )/{\theta }_{h},\end{eqnarray} \tag{ 3 }$$

where θ_h is the angular distance from the critical curve. At an offset of θ_h ≈ 006 from the galaxy-cluster critical curve, μ_each ≈ 180 (μ_t ≈ 120, μ_r ≈ 1.5), which may be a plausible location for caustic crossing given the saturation argument presented by Diego et al. (2018).

We also compute the source crossing time as

$$\begin{eqnarray}&&{t}_{\mathrm{src}}\approx 0.031\displaystyle \frac{{R}_{\mathrm{source}}/{R}_{\odot }}{v/(500\,\mathrm{km}\,{{\rm{s}}}^{-1})}\,\mathrm{days},\end{eqnarray} \tag{ 4 }$$

where v is a transverse velocity of the cluster and R_source is a radius of a background star that is magnified. From the light curve, we have t_src < 10 days (see Figure 2 of Miralda-Escude 1991 to see how t_src relates to the expected timescale of the light curve's evolution), which yields a limit of R_source < 320 R_⊙. Assuming μ_t = 120 and μ_r = 1.5, the maximum magnification estimated using Equation (48) of Oguri et al. (2018) is

$$\begin{eqnarray}&&{\mu }_{\max }\approx (4.5\times {10}^{4}){\left({M}_{\mathrm{lens}}/{M}_{\odot }\right)}^{1/4}{\left({R}_{\mathrm{source}}/{R}_{\odot }\right)}^{-1/2}.\end{eqnarray} \tag{ 5 }$$

For M_lens = 0.3M_⊙ (typical mass of a star responsible for the intracluster light of the cluster), we have μ_max ≈ 33,000 for R_source = 1 R_⊙, μ_max ≈ 10,000 for R_source = 10 R_⊙, and μ_max ≈ 3300 for R_source = 100 R_⊙, where a larger M_lens yields a greater maximum magnification. The comparison with Table 4 suggests that normal main-sequence stars are unlikely to be observed as microlensing events, and we need to consider either blue supergiants or extremely luminous O-type stars to explain the Warhol event.

As shown in Figure 5, the sources A and B appear to be unresolved in HFF F606W and F814W imaging acquired before the microlensing event. An approximate estimate, assuming a transversal magnification of ∼100, indicates that the coincident source at positions A and B detected in HFF imaging occurred must be ∼3 pc at most, so it must be a single star, stellar system, or a compact stellar cluster.