Galaxy-cluster gravitational lenses can magnify background galaxies by a total factor of up to ~50. Here we report an image of an individual star at redshift z = 1.49 (dubbed MACS J1149 Lensed Star 1) magnified by more than ×2,000. A separate image, detected briefly 0.26″ from Lensed Star 1, is probably a counterimage of the first star demagnified for multiple years by an object of ≳3 solar masses in the cluster. For reasonable assumptions about the lensing system, microlensing fluctuations in the stars’ light curves can yield evidence about the mass function of intracluster stars and compact objects, including binary fractions and specific stellar evolution and supernova models. Dark-matter subhaloes or massive compact objects may help to account for the two images’ long-term brightness ratio.
The pattern of magnification arising from a foreground strong gravitational lens changes with distance (increasing redshift) behind it. At each specific distance behind the lens, the locations that are most highly magnified are connected by a so-called caustic curve. Near the caustic curve in the source plane, magnification changes rapidly. Over a distance of only tens of parsecs close to the MACS J1149 galaxy cluster’s caustic at z = 1.5, for example, magnification falls from a maximum of approximately ×5,000 to only approximately ×50. Since the sizes of even compact galaxies are hundreds of parsecs, their total magnifications cannot exceed approximately ×50.
However, a well-aligned individual star adjacent to the caustic of a galaxy cluster could, in theory, become magnified by a factor of many thousands1. When a galaxy cluster’s caustic curve is mapped from the source plane defined at a specific redshift to the image plane on the sky, it is called the critical curve. Consequently, a highly magnified star should be found close to the foreground galaxy cluster’s critical curve.
A lensed blue supergiant at redshift z = 1.49
In Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) infrared (IR) imaging taken on 29 April 2016 to construct light curves of the multiple images of supernova (SN) Refsdal (refs 2,3,4,5,6,7,8,9,10,11), we detected an unexpected change in flux of an individual point source (dubbed MACS J1149 Lensed Star 1 (LS1)) in the MACS J1149 galaxy-cluster field12. As shown in Fig. 1, the unresolved blue source lies close to the cluster’s critical curve at its host galaxy’s redshift of z = 1.49 (refs 5,6,7,8,9,10,11). Figure 2 shows that, while the location of the critical curve differs by ~0.25″ among lens models, the blue source is no farther than ~0.13″ from the critical curves of all publicly available high-resolution models.
The MACS J1149 galaxy-cluster lens creates two partial merging images of LS1’s host galaxy separated by the cluster’s critical curve, as well as an additional full image. As shown in Supplementary Fig. 1, LS1’s predicted position inside the third, full image is near the tip of a spiral arm. According to our lens model, LS1 is 7.9 ± 0.5 kpc from the nucleus of the host galaxy. The multiply imaged SN Refsdal exploded at a different position in the same galaxy13,14,15,16.
At the peak of the microlensing event in May 2016 (lensing event ‘Lev16A’), LS1 was ~4 times brighter than it appeared in archival HST imaging during 2013–2015. Figure 3 shows that the additional flux we measured at LS1’s position has a spectral energy distribution (SED) statistically consistent with the source’s SED during 2013–2015. As shown in Fig. 3, model spectra of mid-to-late B-type stars at z = 1.49 with photospheric temperatures of 11,000–14,000 K (ref. 17) provide a good match to the SED of LS1 (χ2 = 12.9 for 6 degrees of freedom (ν); ), given that our model does not account for changes in magnification between the epochs when observations in separate filters were obtained. SED fitting finds probability peaks at ~8 Myr and ~35 Myr (see Supplementary Fig. 2) for the age of the arc underlying LS1’s position.
A lensed luminous star provides a perhaps unexpected explanation (and yet the only reasonable one we could find) for the transient’s variable light curve and unchanging SED. Except for finite-source effects, gravitational lensing will magnify a star’s emission at all wavelengths equally. Therefore, as we observe for LS1, the SED of a lensed background star should remain the same, even as it appears brighter or fainter owing to changes in its magnification. By contrast, the SEDs of stellar outbursts and SNe change as they brighten by the factor of ~4 observed in May 2016.
As shown in Fig. 3, LS1’s SED exhibits a strong Balmer break, which indicates that the lensed object has a relatively high surface gravity. Stars, including blue supergiants, exhibit spectra with a strong Balmer break, but stellar outbursts and explosions have low surface gravity and lack a strong Balmer break. The temperature of 11,000–14,000 K inferred from fitting the Balmer break is also substantially larger than that of almost all hydrogen-rich transients during outburst, such as luminous blue variables. While Lyman absorption of a background active galactic nucleus at z ≈ 9 could produce a continuum break at ~9,500 Å, the active galactic nucleus’s flux blueward of the break would be almost entirely absorbed, and additional images would be expected.
Our ray-tracing simulations, which are described in detail in ref. 18, show that the MACS J1149 galaxy cluster’s gravitational potential effectively increases the Einstein radii of individual stars in the intracluster medium (ICM) by a factor of ~100 along the line of sight to LS1. Consequently, even though intracluster stars account for ≲1% of the cluster’s mass along the line of sight to LS1, overlapping caustics arising from intracluster stars should densely cover the source plane of the host galaxy at z = 1.49, as demonstrated by our simulation plotted in Supplementary Fig. 3. By contrast, galactic microlensing magnification can be fully modelled using the caustic of a single star or stellar system.
The ray-tracing simulations show that a star at LS1’s location should experience multiple microlensing events over a period of a decade with typical magnifications of ×103–104. In Fig. 4, we display the 2004–2017 light curve of LS1 constructed from all optical and IR HST observations of the field, and we show ray-tracing simulations that can describe LS1’s light curve.
A separate microlensing event at a different position
A foreground gravitational lens made of smoothly distributed matter should form a pair of images of a static background source at equal angular offsets from the critical curve. However, only a single, persistent point source is apparent near the critical curve in HST imaging taken during 2004–2017. We initially considered the possibility that LS1 happens to be sufficiently close to the galaxy cluster’s caustic that its pair of images have a small angular separation unresolved in HST data. As we continued to monitor the MACS J1149 cluster field, however, we detected an unexpected new source (‘Lev16B’) on 30 October 2016 offset by 0.26″ from LS1. We measure magnitudes of F125W = 25.78 ± 0.12 mag (AB magnitude system) (pivot wavelength λpivot = 1.25 μm) and F160W = 26.16 ± 0.22 mag (λpivot = 1.54 μm) (where F125W and F160W are the bands corresponding to the WFC3 IR filters of the same names). The F125W − F160W colour (which corresponds approximately to rest-frame V−R c ) of the new source is consistent with that of LS1, which has F125W − F160W = −0.11 ± 0.10 mag.
We consider that the new source could either be the counterimage of LS1 or a different lensed star. As can be seen in Fig. 5, the pair of images of LS1’s host galaxy that meet at the critical curve appear flipped relative to each other. These images are said to have opposite parity, a property of lensed images set by the sign of the determinant of the lensing magnification matrix. Assuming they are counterimages, Lev16B and LS1/Lev16A would have negative and positive parity, respectively.
We have found from our ray-tracing simulations that the parity of an image of a lensed background star strongly affects its microlensing variations18. Supplementary Fig. 3 shows that, while an image of a background star on LS1/Lev16A’s side of the critical curve always has magnification of greater than approximately ×300, its counterimage on Lev16B’s side has extensive regions of much lower magnification (approximately ×30) in the source plane. If LS1 fell within such a low-magnification region on Lev16B’s side for much of 2004–2017, that could explain why LS1/Lev16B was not detected except on 30 October 2016, as shown in Supplementary Fig. 4. An object with a mass of ≳3 solar masses (M⊙), such as a stellar binary system, or a neutron star or black hole, can cause an image of a star to have low magnification for sufficiently long periods on Lev16B’s side of the critical curve.
Properties of LS1
If we assume that LS1/Lev16A and Lev16B are counterimages, then our model predicts each has an average magnification of × 600. Different cluster models, however, show a disagreement of a factor of ~2 about the magnification at LS1’s position5,6,7,8,9,10. LS1 had F125W ≈ 28.15 mag in 2004–2008, corresponding to an absolute V band rest-frame magnitude MV of −9.0 ± 0.75 mag for a magnification of approximately ×600 per image.
Post-main-sequence stars in the Small Magellanic Cloud that have U−B and B−V colours (where U, B and V are measured magnitudes for the respective broadband filters) approximately matching those of LS1 (−0.40 and −0.05 mag, respectively) have luminosities reaching MV ≳ −8.8 mag (ref. 19). The two statistically significant peaks in May 2016 could correspond to a projected separation for a binary star system of ~25 au for a transverse velocity of 1,000 km s−1 (see Methods).
If LS1 instead consists of an unresolved pair of counterimages, then the lensed star would need to have an offset of ≲0.06 pc of the caustic curve to be unresolved in HST imaging (see Methods). Its total magnification would be approximately ×10,000, corresponding to a star with MV ≈ −6 mag.
Monte Carlo simulation of stellar population near caustic
We next perform simulations that allow us to estimate the probabilities (1) that LS1/Lev16A and Lev16B are counterimages of each other and (2) of discovering a lensed star in HST galaxy-cluster observations. We use measurements of the arc underlying LS1’s position to estimate the number and luminosities of stars near the galaxy cluster’s caustic. For different potential stellar luminosity functions, we calculate the number of expected bright lensed stars and microlensing events.
The underlying arc extends for ~0.2″ (~340 pc in the source plane) along the galaxy cluster’s critical curve. If LS1/Lev16A and Lev16B are counterimages, then the lensed star is offset from the caustic by 2.2 pc in the source plane according to our lensing model. In our simulation, we populate the source plane region within 0.4″ of the critical curve, or 21.9 pc from the caustic, with stars.
We first need to infer the total luminosity in stars in the 21.9 pc × 340 pc region adjacent to the galaxy cluster’s caustic. Gravitational lensing conserves the surface brightness, and we use the arc’s F125W ≈ 25 mag arcsec−2 surface brightness to compute its absolute rest-frame V surface brightness, which yields an estimate for the luminosity density of 120 L⊙ pc−2, where L⊙ is the solar luminosity.
The next step is to place stars in the 21.9 pc × 340 pc region adjacent to the caustic (within 0.4″ of the critical curve), whose area of 7,100 pc2 should enclose a total luminosity of 8.5 × 105 L⊙. We consider power-law luminosity functions where the number of stars with luminosity between L and L + dL is proportional to L−αdL. For luminosity functions with −1.5 ≤ α ≤ 3, we normalize the luminosity function so that the integrated luminosity is equal to 8.5 × 105 L⊙, and compute the expected number of stars in each 0.1 L⊙ interval. We draw from a Poisson distribution to determine the number of stars in each luminosity bin, and assign each star a random position within 21.9 pc of the caustic.
We next compute the average magnification of each star. For a lens consisting of only smooth matter, the predicted magnification at an offset R in parsecs from the caustic is . Our ray-tracing simulations find that the average magnification deviates from this prediction closer than ~1.3 pc from the caustic curve (0.1″ from the critical curve) due to microlensing. To estimate for stars closer than 0.10″ to the critical curve, we interpolate in the image plane between at the critical curve and at an offset of 0.10″.
Our next step is to estimate the number of bright microlensing peaks (F125W ≤ 26 mag) that we expect to find in existing HST observations of the MACS J1149 galaxy-cluster field. LS1 is expected to have a transverse velocity of order 1,000 km s−1 relative to the cluster lens (see Methods), which corresponds approximately to LS1/Lev16A’s two-week peak duration1. If HST observations taken within 10 days are counted as a single observation, then there were Nobs = 50 observations of the MACS J1149 field in all optical and IR wideband filters to 13 April 2017, and Nobs = 37 observations to 15 April 2016 just before the detection of LS1.
After taking into account stellar microlensing, the fraction of the source plane where the magnification exceeds the total amplification μ is (N. Kaiser et al., manuscript in preparation)
where κ is the surface density of stars making up the intracluster light (ICL) in units of the critical density and is the expected magnification if the cluster consisted entirely of smoothly distributed matter. Equation (1) does not apply at offsets smaller than ~1.3 pc from the cluster’s caustic where the optical depth for microlensing exceeds unity. Our ray-tracing simulations indicate, however, that the formula should provide a reasonable first-order approximation at smaller distances from the caustic when we use our estimate of the average magnification near the critical curve18. The number of expected microlensing events with magnification exceeding μ for each star will be .
The simulations provide support for the hypothesis that Lev16A and Lev16B are counterimages of LS1. Supplementary Fig. 5 shows that, if a star has an average apparent F125W brightness of at least 27.7 mag, similar to LS1, then it will be responsible for ≳99% of F125W ≤ 26 mag events. Likewise, Supplementary Fig. 6 shows that observing a bright lensed star sufficiently close to the caustic that its images are unresolved (≲0.06 pc from the caustic) is a factor of 10 less probable than observing a resolved pair of bright images of a lensed star.
In nearby galaxies, the bright end of the luminosity function has a power-law index of α ≈ 2.5. Young star-forming regions such as 30 Doradus, however, can have shallower functions where α ≈ 2. Supplementary Fig. 6 suggests that the probability of observing a persistent bright lensed star (F125W ≤ 27.7 mag) in the underlying arc may be ~10% in existing HST observations, given a shallow stellar luminosity function where α ≈ 2. For the steeper mean luminosity function (α ≈ 2.5) measured for nearby galaxies20, we find a probability of 0.01–0.1%. The probability of observing at least one bright (F125W ≤ 26 mag) microlensing event is ~3% for α ≈ 2 and ~0.1% for α ≈ 2.5. Supplementary Fig. 7 plots the expected distributions of angular offsets from the critical curve and luminosities of lensed stars. We have repeated our simulation using the distribution of stars in 30 Doradus in the Large Magellanic Cloud, which yields similar probabilities as for the case where α ≈ 2.
To estimate to first order the probability of finding a lensed star in all existing HST galaxy-cluster observations, we make the simplifying assumption that all strong-lensing arcs have properties similar to that underlying LS1. Of the total time used to image cluster fields with the HST, only at most ~10% has been used to observe MACS J1149. Each of several dozen galaxy-cluster fields monitored by the HST contains ~4 giant arcs21. Consequently, to take into account all HST galaxy-cluster observations, we need to multiply our above Monte Carlo probabilities by an approximate factor of 10 × 4 = 40. This suggests that the probability of finding a lensed star may be reasonable, but only if the average stellar luminosity function at high redshift is shallower than α ≈ 2.5.
Note that we detected a new potential source (‘Lev17A’), which has a ~4σ significance in the WFC3 IR imaging acquired on 3 January 2017, although the significance is only ~2.5σ considering all HST imaging and the independent apertures adjacent to the critical curve.
Multiple limits on the physical size of LS1
Each bright microlensing peak must correspond to light from an individual star in the source plane, given the small area of high magnification adjacent to the microcaustics of intracluster stars. Additional considerations provide evidence that the persistent source, LS1, is too compact to be a typical stellar cluster and is instead a single stellar system (for example, an individual star or a binary). If LS1 consists of two unresolved counterimages at the location of the critical curve, then LS1 must be more compact than ~0.06 pc given the upper limit on its angular size (≲0.040″; see Methods).
If Lev16A and Lev16B are instead mutual counterimages, the limit on LS1’s angular size constrains it to have a physical dimension perpendicular to the caustic of ≲1–2 pc, which is significantly smaller than the typical size of a stellar cluster.
The absence of a persistent image at Lev16B’s position places a stronger potential limit on LS1’s size. To explain the lack of a persistent counterimage at Lev16B’s location, all stars in a hypothetical stellar association at LS1’s position would need to fall inside a region of low magnification on the Lev16B side of the critical curve. Ray-tracing simulations indicate that LS1 would need to be smaller than ~0.1 pc. A hypothetical dark-matter (DM) subhalo, however, could also demagnify a counterimage at Lev16B’s position.
Inferences from light curves of LS1/Lev16A and Lev16B
Assuming they are mutual counterimages, we next compare the HST light curves for LS1/Lev16A and Lev16B with simulated light curves created for different intracluster stellar populations and the abundances of 30 M⊙ primordial black holes (PBHs). In our ray-tracing simulations, LS1/Lev16A and Lev16B are counterimages with average magnifications of ×600 from the cluster.
We either (1) assume all ICL stars are single or (2) apply mass-dependent binary fractions and mass ratios22. We use a stellar-mass density of M⊙ kpc−2 for a Chabrier initial mass function (IMF), or higher densities estimated in an improved analysis, of M⊙ kpc−2 and M⊙ kpc−2 for Chabrier and Salpeter IMFs, respectively (see Supplementary Fig. 8). The most massive surviving star found in the ICM at z = 0.54 is assumed to have a mass M of 1.5 M⊙. In Supplementary Figs 9, 10 and 11, we plot the simulated light curves for a lensed star with a radius of 100 solar radii, where we adopt the ‘Woosley02’23, ‘Fryer12’24 or ‘Spera15’25 models of stellar evolution and core-collapse physics.
For steps of 50 km s−1 in the range 100–2,000 km s−1, we stretch the simulated light curves and identify the regions that best match the data. Table 1 lists the average χ2 values for the 150 best matches, . To interpret differences in values, we fit simulated light curves, and compute the difference Δ values between the values of the generative (‘true’) model and of the best-fitting model. For 68% of simulated light curves, Δ ≲ 13, and for 95% of simulated light curves, Δ ≲ 25.
For stars with −7.5 > MV > −9.5 mag, a range consistent with the most luminous stars in the Small Magellanic Cloud and Large Magellanic Cloud given the uncertainty in magnification, models constructed using a prescription for the binary fraction22 are favoured over those where all stars are single (see Supplementary Fig. 12). The statistics also favour the Fryer12 stellar model, and a Salpeter IMF over a Chabrier IMF (see Methods). The fitting also provides evidence against models where 1% and 3% of DM consists of 30 M⊙ PBHs26. Within the confidence intervals, the differences remain robust when extending the upper MV limit to −10.5 mag.
Table 1 also shows values if we restrict the absolute magnitude to −7.5 < MV < −8.5 mag (for μ = 600), although such a low luminosity would be difficult to reconcile with LS1’s light curve. The Fryer12 model and a Salpeter IMF are still favoured, but there is no preference for the binary prescription.
Although our confidence intervals assume that our estimates for the stellar-mass density and magnification are correct, it may be reasonable to assume that differences in values will be robust to modest errors in these parameters. Our cluster model also does not include DM subhaloes, which could affect the average fluxes of the images. Although our fits do not favour models where 30 M⊙ PBHs account for 1% or 3% of DM, PBHs consisting of ≳3% of DM could produce a slowly varying average magnification and explain the absence of flux at Lev16B’s position.
The HST observations include those from General Observer programmes (and Principal Investigators (PIs)) 12065 (M. Postman), 13459 (T.T.), 13504 (J. Lotz), 13790 and 14208 (S.R.) and 14041, 14199, 14528, 14872 and 14922 (P.L.K.).
Constructing light curve
All optical and IR HST imaging of the MACS J1149 field with moderate depth has yielded a detection of LS1. For each instrument and wideband filter combination, we constructed a light curve for LS1. We first measured LS1’s flux in a deep template coaddition of Hubble Frontier Fields and early SN Refsdal follow-up imaging. The Hubble Frontier Fields programme27 acquired deep imaging of the MACS J1149 galaxy cluster between November 2013 and May 2015 in the Advanced Camera for Surveys (ACS) WFC F435W (central wavelength λc = 0.43 μm), F606W (λc = 0.59 μm) and F814W (λc = 0.81 μm), and the WFC3 IR F105W (λpivot = 1.05 μm), F125W (λpivot = 1.25 μm), F140W (λpivot = 1.39 μm) and F160W (λpivot = 1.54 μm) wideband filters. The second step was to measure the differences in LS1’s flux between the deep template coadded image and at each imaging epoch. We accomplished this latter step by subtracting the deep template coaddition from coadditions of imaging at each epoch, and measuring the change in LS1’s flux from these resulting difference images.
To measure LS1’s flux in each deep template coaddition, we first fit and then subtracted the ICL surrounding the brightest cluster galaxy. We next measured the flux at LS1’s position inside an aperture radius of r = 0.10″ using the PythonPhot package28. To measure the uncertainty in the background from the underlying arc, we placed a series of four non-overlapping apertures having r = 0.10″ along it. We use the standard deviation of these aperture fluxes as an estimate of the uncertainty in the background. Aperture corrections were calculated from coadditions of the standard stars P330E and G191B2B (ref. 29).
For each HST visit, we created a coadded image of all exposures acquired in each wideband filter. We next subtracted the deep template coaddition from the visit coaddition to create a difference image. Using the PythonPhot package28, we measured the flux inside an r = 0.10″ circular aperture in the difference image. We finally computed the total flux at each epoch by adding the flux measured from the deep template coaddition and that measured from each difference image.
No source is apparent at Lev16B’s position in deep template coadditions. Therefore, we do not add any flux measured from the deep template coaddition to the light curve we construct for Lev16B, which is plotted in Supplementary Fig. 4.
Estimating LS1’s colour
LS1’s brightness changed between the epochs when the deep template imaging was acquired by the Hubble Frontier Fields and SN Refsdal follow-up programmes. However, the MACS J1149 cluster field was monitored using F125W (and F160W) with a cadence of ~2 weeks after the discovery of SN Refsdal in November 20142. We measured LS1’s F125W light curve from these data, and performed a fit to the light curve using a third-order polynomial.
We used the polynomial to estimate LS1’s F125W flux at the average epoch when the deep template imaging in each detector and filter was acquired. The ratio between the F125W flux and that in the other filter (for example, F140W) provides a measurement of LS1’s colour (F140W − F125W, in this example). We restricted the Hubble Frontier Fields imaging to that taken between November 2014 and May 2015, since monitoring of SN Refsdal is available to construct LS1’s IR light curve beginning in November 2014.
Creating a combined light curve
We used our estimates of LS1’s colour to convert the light curves measured in all available optical and IR filters to F125W light curves, and combined them. We also binned all F125W observations to construct the combined light curve plotted in Fig. 4 and used to fit models.
Constraints on the age of stellar population in underlying arc
To compute models using Flexible Stellar Population Synthesis (FSPS)30,31, we adopt a simple stellar population with an instantaneous burst of star formation, and include nebular and continuum emission. We use Python bindings (http://dan.iel.fm/python-fsps/current/) to FSPS to calculate simple stellar populations with a Kroupa IMF32 and a Cardelli extinction law33 with RV = AV/(AB−AV) = 3.1, where AV and AB are extinction by dust in the rest-frame B and V bands, respectively. These models use the Padova isochrones34,35.
A recent analysis finds a solar oxygen (O) abundance of 12 + log(O/H) = 8.69 ± 0.05 units of decimal exponent (dex) and a solar metallicity36Z⊙ of Z = 0.0134, where Z is the fraction of mass that is neither hydrogen nor helium. We therefore calculate models using , which corresponds to Z = 0.006 and is best matched with the FSPS stellar model metallicity parameter zmet = 15.
To estimate the age and dust extinction of the adjacent stellar population along the arc, we use ‘emcee’37, which is an implementation of a Markov Chain Monte Carlo ensemble sampler. We adopt a uniform prior on the stellar population age from 0 to 3 Gyr, and a uniform prior on the extinction AV from 0 to 2 mag.
Ability to detect pair of images of a star adjacent to cluster’s caustic
A possibility is that we do not observe a pair of images of LS1 because it is very close to the cluster’s caustic and the available HST imaging is not able to resolve its two images. Here, we calculate how close the star must be to the caustic. If LS1 lay very close to the critical curve, then Lev16B would correspond to the microlensing event of a different star, at an offset of 0.26″ from the cluster’s critical curve.
For a star sufficiently close to the caustic, the pair of images will not be resolved with the HST. Our simulations suggest that demagnifying one of the two images will be unlikely when the star is close to the cluster’s caustic, although they do not include expected DM subhaloes. The angular resolution of the HST is greatest in the F606W band (λc = 0.59 μm) and almost as sharp in the F814W band (λc = 0.81 μm), and observations in these wideband filters provide the best opportunity to test whether LS1 consists of two adjacent images. We use coadditions of imaging taken by the Hubble Frontier Fields programme. To determine the limit that we can place on the separation of two possible images, we inject pairs of point sources having the same combined magnitude as the images made using the ACS WFC F606W and ACS WFC F814W exposures at each epoch.
The full-width at half-maximum (FWHM) intensity of our ACS point spread function (PSF) models constructed from observations of the standard stars P330E and G191B2B agrees only within 10% with the measured FWHM of the stars in our coadded images. Consequently, the measured FWHM of the injected pairs of PSFs should not correspond directly to what we would measure in the ACS data. Therefore, we compute the fractional increase in the measured FWHM with the increasing separation between the pair of injected PSFs. Next, we multiply the FWHM estimated from the stars in each image by this factor to compute limits from the ACS imaging.
We inject 100 fake stars with the same magnitude using models of the ACS WFC F606W and F814W PSF. After injecting the point sources in a grid, we use the IRAF (image reduction and analysis facility) task ‘imexam’ to estimate the Gaussian FWHM using the ‘comma’ command from the simulated data. The imexam model we use has a Gaussian profile, and we specify three radius adjustments while the fit is optimized. Pixels are fit within 3 pixels (0.03″ per pixel) of the centre, and we use a background buffer of 5 pixels.
These simulations show that any separation between the two images greater than 0.035–0.040″ can be detected >95% of the time. The upper limit implies that the star would have to be closer than 0.06 pc to the cluster’s caustic. As we show in Supplementary Fig. 6, the relative probability of a persistently bright (F125W < 27.7 mag) star being located within 0.06 pc is ≲10%.
DOLPHOT (ref. 38) fit parameters for the images of LS1, Lev16B and Lev17A fall inside the range expected for point sources in the DOLPHOT reference manual http://americano.dolphinsim.com/dolphot/dolphot.pdf, although these criteria are not highly sensitive to a pair of images.
Transverse velocity of star
We use the following expression (equation (12) of ref. 1) for the apparent transverse velocity of a lensed source:
where Dl and Ds are the angular-diameter distances of the lens and source, respectively, vo, vl and vs are, respectively, the transverse velocities of the observer, the lens and the source with respect to the caustic, and zs is the redshift of the source. The expression applies only for a universe without spatial curvature.
Cosmological simulations have found that merging galaxy-cluster haloes and subhaloes have pairwise velocities of ~500–1,500 km s−1 with tails to lower and higher velocity39. Given the expected velocity of the lens, the peculiar velocity of Earth (~400 km s−1) and that of the host galaxy relative to the Hubble flow, and the motion of the star (<200–300 km s−1) relative to its host galaxy, a typical transverse velocity should be 1,000 km s−1. In our light-curve fitting analysis, we consider transverse velocities of 100–2,000 km s−1.
Intrinsic luminosity of lensed star
While extremely luminous stars are rare in the nearby Universe, they require smaller magnification and can be at a greater distance from the caustic. For a lens with a smooth distribution of matter, the magnification μ falls within the distance d from the caustic as . Therefore, the area A in the source plane in which the magnification is greater than μ scales as . The observed flux F of a lensed object is F ∝ Lμ, where the object’s luminosity is L. Therefore, a star with luminosity L has an apparent flux brighter than a given flux f inside an area A(>f; L) ∝ L2.
Galaxy-cluster lens model
Before the identification of LS1 in late April 2016, the cluster potential had been modelled using the codes Light Traces Mass (refs 40,41), WSLAP+ (ref. 7), GLAFIC (refs 5,10,42), LENSTOOL (refs 6,8,43) and GLEE (refs 9,44,45). These used several different sets of multiply imaged galaxies11, which included new data from the Grism Lens-Amplified Survey from Space (GLASS; PI: T.T.)46,47, the Multi-Unit Spectroscopic Explorer (MUSE; PI: C.G.)9 and grism follow-up observations of SN Refsdal (PI: P.L.K.)48.
In Fig. 1, we plot as an example the position of the critical curve from the CATS (Clusters as Telescopes) model8 created using LENSTOOL (ref. 43), showing that it passes close to the position of LS1. The critical curves of all of these models, however, pass within similarly small offsets from LS1’s coordinates.
For the simulation of the light curves of a star passing close to the cluster’s caustic, we use the WSLAP+ model of the cluster mass distribution7 and draw stars randomly from a Chabrier IMF49 until the stellar-mass density is equal to our estimated values of M⊙ kpc−2 for a Chabrier IMF and M⊙ kpc−2 for a Salpeter IMF.
The WSLAP+ cluster lens model, which includes only smoothly distributed matter and cluster galaxies, yields several important relations describing the magnification near the critical curve, and the relationship between the lensed θ and unlensed β angular offsets from the critical curve in arcseconds. The magnification for a smooth cluster model (for example, equation (35) of ref. 50) can be described as , where relates the unlensed angular position β and . The angles β and θ follow the relation β = θ2/66.5, and both β and θ are in units of arcseconds.
We simulate the light curves of caustic-crossing events using a resolution of 1 μas per pixel over an area of ~83 pc × 6.5 pc in the lens plane. This area is aligned in the direction where a background source moving toward the cluster’s caustic would appear to be moving. If the background star is moving with an apparent velocity of 1,000 km s−1 in the source plane, its associated counterimage would take ~400 yr to cross the 83 pc of the simulated region, which corresponds to 1.2 × 10−7 arcsec yr−1. The lensed star is given a transverse velocity of 1,000 km s−1 in the source plane; the resulting light curve can be stretched to simulate different transverse velocities. Owing to the high magnification, the counterimages’ apparent motion in the image plane is large.
N-body simulations show that clusters of galaxies contain (and are surrounded by) a large number of subhaloes. Smaller subhaloes near the cluster centre may not survive the tidal forces of the cluster and are easily disrupted. The larger surviving haloes and smaller subhaloes along the line of sight can produce small distortions in the deflection field that could in principle distort the critical curve (and caustic). Lens models of MACS J1149 do predict such distortions around the member galaxies. However, since the typical scales of the distortion in the deflection field are proportional to the square root of the mass of the lens, the distortions from the surviving haloes are orders of magnitude larger than the scale of the distortion associated with the microlenses (from the ICL). Consequently, on the scales relevant for this work (~0.2″), the combined deflection field of the cluster plus the DM substructure can still be considered as a smooth distribution, and the critical curve could still be well approximated by a straight line.
For a cluster model populated with stars in the ICM, Supplementary Fig. 13 shows the ‘trains’ or multiple counterimages of a single background star near the cluster’s caustic. Replacing the cluster’s smoothly varying matter distribution with an increasing fraction of ~30 M⊙ PBHs yields an increasingly long train, although its expected extent (~3 mas) when PBHs account for 10% of DM would be smaller than would be possible to detect in the HST imaging.
IMF for stellar and substellar objects
Strong-lensing and kinematic51,52,53,54 as well as spectroscopic55,56 analyses of early-type galaxies have found evidence that the IMF of stars in early-type galaxies may be ‘bottom heavy’—a larger fraction of stars have subsolar masses than is observed in the Milky Way. Spectroscopic evidence for a Salpeter-like bottom-heavy IMF in the inner regions of early-type galaxies comes from the strength of spectral features sensitive to the surface gravity of stars with M ≲ 0.3 M⊙ (refs 55,56). However, these two sets of diagnostics do not always show agreement in the same galaxies, and the discrepancy is not yet understood57. In Supplementary Fig. 9, we show that a Salpeter IMF yields a substantially higher frequency of microlensing peaks than a Chabrier IMF.
In stellar kinematics and strong lensing, the DM is assumed to follow a simple parametric (for example, power-law) function near the galaxy centre, while stellar matter is assumed to trace the optical emission. The total matter profile inferred from observations is decomposed into stellar and DM components, and the M★/L ratio of the stellar component, where M★ is the stellar mass, is used to place constraints on the IMF.
Substellar objects having masses below the H-burning limit (M ≈ 0.08 M⊙) are not generally included as a component of the stellar mass in kinematic and lensing analyses. Substellar masses, however, should also trace the stellar-mass distribution. The inferred M★/L ratios near the centres of elliptical galaxies are approximately twice as large as those expected for Milky-Way-like Chabrier IMFs, for example, refs 51,52,53. If the stellar IMF in early-type galaxies has a Salpeter slope, the ratio of ~2 would imply that a Salpeter IMF cannot extend to object masses significantly smaller than the H-burning limit58.
Indeed, the integral of the Salpeter IMF from zero mass through the H-burning limit diverges, so the IMF of substellar objects must be less steep than Salpeter below the 0.08 M⊙. The integral of a Chabrier IMF in the range 0 < M < 0.10 M⊙ is ≲10% of the integral in 0.10 < M < 100 M⊙. High signal-to-noise-ratio spectra of NGC 1407 are best fit by a super-Salpeter IMF (Γ = 1.7, where dN/d log m ∝ m−Γ) to the H-burning limit59.
In the Milky Way, surveys of substellar objects find that their mass function is probably flat or declining with decreasing mass. IR imaging of the young Milky Way cluster IC 348 yields a population of brown-dwarf stars consistent with log-normal mass distribution60. Γ = 0.0 and Γ = −0.3 provide a reasonable fit to the populations of objects with masses smaller than 0.1 M⊙ in IC 348 and Rho Ophiuchi, respectively. Analysis of the Pleiades open clusters to 0.03 M⊙ found a population consistent with a log-normal distribution with mean mc = 0.25 M⊙ and σlog m = 0.52 (ref. 61).
For this analysis, we include objects only with initial masses greater than 0.01 M⊙. For the light curves generated with a Chabrier IMF, we assume that the IMF continues to this lower-mass cutoff. For the Salpeter light curves, the Salpeter form truncates at 0.05 M⊙; for lower initial masses, we assume that the number density of objects is constant in logarithmic intervals.
Mass function of surviving stars and compact remnants in the ICM
For a given a star-formation history, GALAXEV (http://www.bruzual.org/) computes the mass in surviving stars and in remnants using the ‘Renzini93’ prescription for the mapping between zero-age main-sequence masses and remnant masses (the initial–final mass function)62. Dead stars with initial masses Mi < 8.5 M⊙ become white dwarfs with mass 0.077 M⊙ + 0.48 Mi, those with 8.5 M⊙ ≤ Mi < 40 M⊙ become 1.4 M⊙ neutron stars, and those with Mi ≥ 40 M⊙ become black holes with 0.5 Mi.
We assume that the most massive surviving star found in the ICM at z = 0.54 has a mass of 1.5 M⊙, approximately the expected value for a ~4.5 Gyr stellar population. For stars with masses ≳1.5 M⊙, we use three separate theoretical initial–final mass functions to compute the distribution of remnant masses.
The evolution of massive stars and the mass of their remnants is expected to depend on the stars’ mass-loss rate, which is thought to vary significantly with their metallicity. Integral field-unit spectroscopy of low-redshift galaxy clusters has been able to place approximate constraints on the metallicity and age of the stars found in the ICM. Integral field-unit spectroscopy within ~75 kpc of the brightest cluster galaxies of the nearby Abell 85, Abell 2457 and II Zw 108 galaxy clusters found that the ICL light can be best fit by a combination of substantial contributions from an old population (~13 Gyr) with high metallicity (Z ≈ 2.0 Z⊙) and from a younger population (~5 Gyr) with low metallicity (Z ≈ 0.5 Z⊙) (ref. 63).
To fit the LS1/Lev16A and Lev16B light curves, we identify the peaks in the simulated light curves that are 2σ above each light curve’s mean magnification. We next stretch the model light curves in time for transverse velocities in the range 100–2,000 km s−1 in steps of 50 km s−1. For each light curve and velocity, we find a best-fitting solution for a series of intervals in absolute magnitudes between MV = −7 mag and MV = −10.5 mag in increments of 0.5 mag. For each interval and peak, we find the best-fitting value of MV within the upper and lower bounds in luminosity.
For the set of fits at each transverse velocity and each MV interval, we rank all peaks according to the χ2 values separately for LS1/Lev16A and Lev16B. We then pair these ranked lists of best-fitting peaks (for example, the best-fitting peak for LS1/Lev16A is matched with that for Lev16B), and add the χ2 values for each pair together. Next, we identify the best χ2 values for all values of transverse velocity and ranges in absolute luminosity, and assemble a list of these best χ2 values. Our goodness-of-fit statistic is the average of the 150 best χ2 values.
Interpreting the χ 2 statistic using simulated light curves
To interpret the values, we generate fake light curves for each of the models listed in Table 1. The simulation for each model yields a magnification over a 406 yr period for a transverse velocity of 1,000 km s−1. For lensed stars with absolute magnitudes MV of −8 mag, −9 mag and −10 mag, we create simulated apparent light curves, and we append the light curve after reversing the temporal axis to create effectively an 812 yr light curve.
For each simulated light curve, we identify all peaks where the apparent F125W AB magnitude is brighter than 26.5 mag. For each peak, we randomly select a transverse velocity drawn from a uniform distribution in the interval 100–2,000 km s−1. We use the cadence and flux uncertainties of the measured light curve of LS1 to generate a fake light curve. We next shift the peak of the measured light curve of LS1/Lev16A (or Lev16B) to match the peak of the simulated model light curve. We then create a fake observation by sampling the simulated light curve at the same epochs as the actual measurements, and adding Gaussian noise matching the measurement uncertainties.
For each such simulated light curve, we compute the statistic using the full set of models. The region of the simulated light curve used to create the fake data set is excluded from fitting. As shown in Supplementary Fig. 14, the combined statistic we measure for LS1/Lev16A and Lev16B falls inside the expected range of values. We note that a significant fraction of simulated light curves have average values of > 1,000, implying that they are not well fit by other regions of the simulated light curves.
For all simulated light curves where the average value is within 100 of the value we measure for LS1/Lev16A and Lev16B, we calculate the difference Δ values between the values of the generative (‘true’) model and of the best-fitting model. For 68% of simulated light curves, Δ ≲ 13, and for 95% of simulated light curves, Δ ≲ 25.
Massive stellar evolution models
The fates of massive stars remain poorly understood owing to the complexity of massive stellar evolution and the physics of SN explosions. Indirect evidence suggests that a fraction of massive stars may collapse directly to a black hole instead of exploding successfully64,65, due to (for example) failure of the neutrino mechanism66. We compute light curves and magnification maps using three sets of predictions for the initial–final mass function23,24,25. As a first model, we adopt the initial–final mass function predicted by the solar-metallicity single stellar evolution models23 (Woosley02) (fig. 9 of ref. 24). In the Woosley02 models, the prescription for driven mass-loss rate at solar metallicity causes stars with initial masses ≳33 M⊙ to end their lives with significantly reduced helium core masses, leading such stars to become black-hole remnants with masses no larger than 5–10 M⊙. The Woosley02 mass-loss prescription uses theoretical models of radiation-driven winds for OB-type stars with temperature T > 15,000 K, and empirical estimates for Wolf–Rayet stars67 that have been adjusted downward by a factor of 3 to account for the effects of clumping in the stellar wind68. The mass-loss rate for single O-type stars during their main-sequence evolution may have been overestimated by a factor of 2–3, owing to unmodelled clumping in their winds69.
A second (Fryer12) initial–final mass function was computed for single stars at subsolar metallicity (Z = 0.3 Z⊙; Z = 0.006) ([the ‘DELAYED’ curve in fig. 11 of ref. 24). These predictions use the StarTrack population synthesis code70,71. According to this model, black holes with masses up to 30 M⊙ form from the collapse of massive stars.
Finally, we use a third initial–final mass function (Spera15) (fig. 6 of ref. 25) to calculate the masses of remnants for the stellar population making up the ICM. The Spera15 relation we adopt was computed using the PARSEC (Padova and Trieste Stellar Evolution Code) evolution tracks for stars with metallicity Z = 0.006, and explosion models where the SN is ‘delayed’, occurring ≳0.5 s after the initial bounce. According to the Spera15 initial–final mass relation we adopt, stars having initial masses ≳33 M⊙ become black holes with masses within the range 20–50 M⊙. Approximately 70% of massive stars exchange mass with a companion, while ~1/3 of stars will merge72. It is also possible that the success of explosions is not related in a simple way to the stars’ initial mass or density structure, given the potentially complex dependence of the critical neutrino luminosity for a successful explosion on these progenitor properties66.
Observations of similar cluster fields with the HST
Massive galaxy clusters have been the target of extensive HST imaging and grism-spectroscopy campaigns in the last several years, and these need to be taken into account when considering the probability of finding a highly magnified star microlensed by stars making up the ICL. Detecting transients requires at least two separate observing epochs, which is possible only for programmes designed with more than a single visit, or when archival imaging is available. In addition to smaller search efforts73, large programmes have been the Cluster Lensing and Supernova survey with Hubble (CLASH)74, the GLASS46,47, the Hubble Frontier Fields27 and the Reionization Lensing Cluster Survey. Transients in Hubble Frontier Fields and GLASS imaging have been subsequently observed by the FrontierSN programme.
With a total of 524 orbits, CLASH acquired imaging of 25 galaxy-cluster fields. A search for transients in the CLASH imaging made use of template archival imaging when available. The survey acquired imaging over a period of three months of each cluster field with repeated visits in each filter. Each epoch had an integration time of 1,000–1,500 s. The systematic search for transients in CLASH imaging had near-infrared (NIR) limiting AB magnitudes at each epoch of F125W ≈ 26.6 mag and F160W ≈ 26.7 mag (see table 1 of ref. 75).
The Hubble Frontier Fields programme used 140 orbits to observe each of six galaxy-cluster fields (total of 840 orbits). For each cluster, ACS optical and WFC3 IR imaging split into two campaigns, each of which lasted for approximately a month. These were separated from each other by a period of around six months to allow the telescope roll angles to differ by ~180°, to image a parallel field adjacent to the cluster with the same instruments. Each of 6 to 12 epochs in each WFC3 IR wideband filter for each cluster field had an integration time of ~5,500 s. The systematic search for transients in NIR Hubble Frontier Fields imaging by the FrontierSN team (PI: S.R.) had NIR limiting AB magnitudes at each epoch of F125W ≈ 27.5 mag and F160W ≈ 27.2 mag.
The probability of observing a luminous star adjacent to a caustic will depend on the number of lensed galaxies that overlap a galaxy cluster’s caustic. For massive clusters, caustic curves coincide with the ICL, so magnified stars should exhibit microlensing fluctuations. Earlier work has estimated that a 105 L⊙ star (MV ≈ −7.5 mag) in a giant arc (with z = 0.7) and crossing the caustic of cluster Abell 370 (z = 0.375), a Hubble Frontier Fields target, would remain brighter than V = 28 mag for 700 yr, given a V-band limiting magnitude of 28 mag and a 300 km s−1 transverse velocity1.
A study of HST imaging of CLASH galaxy-cluster fields21 has found that each cluster field contains 4 ± 1 giant arcs with length ≥6″ and length-to-width ratio ≥7. Given that the host galaxy of LS1 would not be classified as a giant arc according to these criteria, it is likely that additional galaxies in each field may lie on the cluster’s caustic.
An approximate census finds that ≲10% of HST galaxy-cluster observing time has been used to image MACS J1149. Considering the full set of HST cluster observations, and the results of our Monte Carlo simulations for the single arc underlying LS1 (1–3% for a shallow α ≈ 2 luminosity function; 0.01–0.1% for α ≈ 2.5), the probability of observing at least one bright magnified star adjacent to a critical curve should be appreciable, in particular if the average luminosity function is more shallow at high redshifts than in the nearby Universe.
Data used for this publication may be retrieved from the NASA Mikulski Archive for Space Telescopes (http://archive.stsci.edu).
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We thank the directors of the Space Telescope Science Institute, the Gemini Observatory, the GTC and the European Southern Observatory for granting us discretionary time. We thank B. Katz, D. Kushnir, B. Periello, I. Momcheva, T. Royale, L. Strolger, D. Coe, J. Lotz, M. L. Graham, R. Humphreys, R. Kurucz, A. Dolphin, M. Kriek, S. Rajendran, T. Davis, I. Hubeny, C. Leitherer, F. Nieva, D. Kasen, J. Mauerhan, D. Kelson, J. M. Silverman, A. Oscoz Abaz and Z. Levay for help with the observations and other assistance. The Keck Observatory was made possible with the support of the W. M. Keck Foundation. NASA/STScI grants 14041, 14199, 14208, 14528, 14872 and 14922 provided financial support. P.L.K., A.V.F. and W.Z. are grateful for assistance from the Christopher R. Redlich Fund, the TABASGO Foundation and the Miller Institute for Basic Research in Science (U. C. Berkeley). The work of A.V.F. was completed in part at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. J.M.D. acknowledges support of projects AYA2015-64508-P (MINECO/FEDER, UE) and AYA2012-39475-C02-01 and the consolider project CSD2010-00064 funded by the Ministerio de Economia y Competitividad. P.G.P.-G. acknowledges support from Spanish government MINECO grants AYA2015-70815-ERC and AYA2015-63650-P. M.O. is supported by JSPS KAKENHI grants 26800093 and 15H05892. M.J. acknowledges support by the Science and Technology Facilities Council (grant ST/L00075X/1). R.J.F. is supported by NSF grant AST-1518052 and Sloan and Packard Foundation fellowships. M.N. acknowledges support from PRIN-INAF-2014 1.05.01.94.02. O.G. was supported by NSF Fellowship under award AST-1602595. J.H. acknowledges support from a VILLUM FONDEN Investigator Grant (16599). HST imaging was obtained at https://archive.stsci.edu.
Supplementary Figures 1–14, Supplementary Tables 1–4, Supplementary References 1–35 and Supplementary Text.