Mirror images of lensed star clusters with mismatched spectral energy distributions: A possible signature of top-heavy stellar initial mass functions and extreme stars in high-redshift star clusters

TL;DR

The paper demonstrates that microlensing by intracluster stars can create observable mismatches in the SEDs of mirror-image macroimages of strongly lensed star clusters, especially for young ($\lesssim 5$ Myr) clusters with $M_\mathrm{tot} \lesssim 10^5\,M_\odot$. By modeling star-by-star magnifications near caustics and combining standard and extreme IMFs (including Pop III top-heavy cases), the authors show that SED differences are enhanced when the long-wavelength light is dominated by a few very massive stars. JWST/NIRCam color diagnostics (e.g., $F115W-F444W$) can reveal these effects for clusters in specific mass-age windows, offering a potential probe of very massive stars and early-Universe stellar populations. The study also discusses caveats from nebular emission, dust, binarity, microlensing density, redshift effects, IMF sampling, and dark-matter microlenses, which inform the practicality and interpretation of such detections.

Abstract

Strongly lensed star clusters have recently been detected up to redshift $z\approx 10$ in galaxy cluster fields using the James Webb Space Telescope (JWST). When pairs of mirror images of such star clusters appear across the lensing critical curve, it is usually assumed that both images will display identical spectral energy distributions (SEDs). However, this assumption may be invalidated in the presence of gravitational microlensing from stars or other compact objects in the lens, since microlensing will affect the SED contribution from bright stars within the star cluster independently in the two mirror images. Here, we explore under what circumstances mismatched mirror-image SEDs are likely to be observable, and argue that SED differences detectable in JWST observations of lensing-cluster fields will be limited to star clusters of mass $< 10^5\ M_\odot$ and ages $\lesssim 5$ Myr. The probability of severely mismatched mirror-image SEDs increases if the stellar initial mass function is very top-heavy and extends to stellar masses $\gg 100\ M_\odot$, as has been suggested to be the case for Population III stars. The prevalence of lensed star clusters with highly discrepant mirror-image SEDs could therefore serve as a probe of very massive stars and extreme stellar populations in the early Universe.

Figures (9)

• Figure 1: Schematic illustration of the mechanism by which mirror images of star cluster may develop mismatched SEDs. Left: A star cluster featuring a small number of red, evolved stars (here just one; red circle) and a larger number of blue stars (for illustrative purposes just three; blue circles) is located close to the macrolensing caustic in the source plane. Right: In the image plane, the light from the blue and red stars blends into two unresolved star cluster macroimages (green circles) located symmetrically on either side of the critical curve (a third image is also formed directly on the critical curve, but is highly demagnified and not shown). In the case of macrolensing only, the two star cluster images contain the highly stretched images of each star, appearing as mirror-flipped versions of each other. Microlensing by stars or other compact objects (black circles) located in the galaxy cluster that acts as the macrolens distort the magnification of individual stars within the two star cluster images. Due to the separation of the star cluster macroimages in the image plane (typically $\approx 0.1$--1 arcsec), different compact objects microlens the two sets of stellar images independently, which can alter the balance of red to blue light between the two unresolved star cluster images.
• Figure 2: Macro- and microlensing of stars within a $10^5\ M_\odot$ star cluster at a distance of 10 pc from the macrolensing caustic. a) Projected spatial distribution of the $\geq 10\ M_\odot$ stars (blue dots) with respect to the caustic (dashed black line). b) Magnification distribution for stars within a single macroimage of the star cluster, when placed at $z=6$, under the assumption of $\Sigma_\star=10\ M_\odot$ pc$^{-2}$ in microlenses in the $z_\mathrm{l}=0.5$ lens plane: positive-parity image (blue line), negative-parity image (red line), macrolensing only (black line, same for positive/negative parity). Stars to the left of the caustic in panel do not produce counterimages and are not included here. Due to gravitational microlensing, both the positive- and negative parity distributions are wider than the distribution due to macrolensing only. Compared to the positive-parity distribution, the negative-parity probabiliity distribution exhibits a prominent tail to very low magnifications, but also a subtle boost of the probabilities for very high magnifications.
• Figure 3: The photometric evolution in JWST/NIRCam bands of the star light from a young, unlensed $10^5\ M_\odot$, $Z=0.002$ single-age star cluster at $z=6$, under the assumption of a fully-sampled Kroupa01 IMF from 0.1--120 $M_\odot$: a) Brightness evolution in filters F115W, F200W and F444W as a function of age; b) JWST/NIRcam SEDs at ages 1, 3, 10 and 20 Myr. The contribution from evolved, red stars is seen as an upturn in the SEDs for wavelengths above 2 $\mu$m at ages 3 Myr and above.
• Figure 4: Discrepant SEDs of star cluster mirror images at $z=6$, formed by $Z=0.002$ star clusters at 10 pc from the macrocaustic and affected by $\Sigma_\star=10\ M_\odot$ pc$^{-2}$ microlensing. a) Examples of JWST/NIRCam SEDs of positive (blue line) and negative-parity (red line) mirror images of a $3\times 10^4\ M_\odot$ star cluster at ages 3 and 20 Myr. The black line shows the corresponding SEDs predicted by macrolensing alone (the same for both mirror images). b) Variation in $m_{115}-m_{444}$ colour between positive- and negative-parity images ($\Delta(m_{115}-m_{444})=(m_{115}-m_{444})^{+} - (m_{115}-m_{444})^{-}$), as a function of the F200W apparent magnitude of the positive-parity image ($m_{200}^{+}$), for star clusters with total masses $1\times 10^4$ (red circles), $3\times 10^4$ (orange circles), $1\times 10^5\ M_\odot$ (green circles) at ages 3 and 20 Myr. Every differently cloud of points correspond to 100 Monte Carlo realizations. The colour differences between the mirror images are seen to be larger at 3 Myr than at 20 Myr (please note the different y-axis limits in panel b). At fixed age, the colour differences between the mirror images is also seen to become larger for lower-mass star clusters, while at the same time occurring at fainter overall SED magnitudes (F200W$^{+}$).
• Figure 5: Median absolute colour difference between the F115W and F444W filters for mirror images of young $Z=0.002$, $z=6$ star clusters affected by microlensing with $\Sigma_\star=10\ M_\odot$ pc$^{-2}$, as a function of the median apparent F200W flux of the positive-parity star cluster image. Models for star clusters of mass $1\times 10^4\ M_\odot$ (red circles), $3\times 10^4\ M_\odot$ (orange squares) and $1\times 10^5\ M_\odot$ (green triangles) are shown at ages 3, 5, 10 and 20 Myr (from right to left). The dashed line indicates the part of the diagram where we consider that colour differences may be detectable in JWST observations of cluster-lens fields (see main text for details). For star clusters in the mass range $1\times 10^4$--$3\times 10^4\ M_\odot$, the median colour difference is in the observable range for ages $\approx 3$--5 Myr.