An Extensive Hubble Space Telescope Study of the Offset and Host Light Distributions of Type I Superluminous Supernovae

We present an extensive Hubble Space Telescope rest-frame UV imaging study of the locations of Type I superluminous supernovae (SLSNe) within their host galaxies. The sample includes 65 SLSNe with detected host galaxies in the redshift range z ≈ 0.05–2. Using precise astrometric matching with SN images, we determine the distributions of the physical and host-normalized offsets relative to the host centers, as well as the fractional flux distribution relative to the underlying UV light distributions. We find that the host-normalized offsets of SLSNe roughly track an exponential disk profile, but exhibit an overabundance of sources with large offsets of 1.5–4 times their hosts' half-light radii. The SLSNe normalized offsets are systematically larger than those of long gamma-ray bursts (LGRBs), and even Type Ib/c and Type II SNe. Furthermore, we find from a Monte Carlo procedure that about 37−8+6% of SLSNe occur in the dimmest regions of their host galaxies, with a median fractional flux value of 0.16, in stark contrast to LGRBs and Type Ib/c and Type II SNe. We do not detect any significant trends in the locations of SLSNe as a function of redshift, or as a function of explosion and magnetar engine parameters inferred from modeling of their optical light curves. The significant difference in SLSN locations compared to LGRBs (and normal core-collapse SNe) suggests that at least some of their progenitors follow a different evolutionary path. We speculate that SLSNe arise from massive runaway stars from disrupted binary systems, with velocities of ∼102 km s−1.

Shortly after their discovery, it became clear that SLSNe are not powered by the radioactive decay of 56 Ni (Arnett 1982) as in Type Ib/c SNe (SNe Ib/c).This is due to the unusually large mass of radioactive nickel required to match the observed luminosity, often exceeding the total ejecta mass, and in conflict with the lack of suppression of their UV emission due to line blanketing from iron-peak elements (e.g., Dessart et al. 2012;Inserra et al. 2013;Nicholl et al. 2013;Liu et al. 2017;Nicholl et al. 2017a,c;Yan et al. 2017a;Gal-Yam 2019).Instead, alternative mechanisms have been proposed as the main power source of SLSNe, including a central engine with a rapidly spinning (∼ few ms) and highly magnetized (∼ 10 14 G) neutron star (magnetar model; Kasen & Bildsten 2010;Woosley 2010;Dessart et al. 2012;Metzger et al. 2015;Nicholl et al. 2017c), or shock interaction with a hydrogen-poor circumstellar medium (CSM model;Chevalier & Irwin 2011;Chatzopoulos et al. 2012).
The magnetar model has been highly successful in accounting for the broad range of peak luminosities and timescales (e.g., Nicholl et al. 2017c;Blanchard et al. 2020;Hsu et al. 2021), for the early UV/optical spectra (e.g., Nicholl et al. 2017b), for the nebular phase spectra (e.g., Nicholl et al. 2016Nicholl et al. , 2019;;Jerkstrand et al. 2017), and for the power law decline rates observed in SN 2015bn and SN 2016inl at ≳ 10 3 days (Nicholl et al. 2018;Blanchard et al. 2021).On the other hand, there are a handful of events supporting CSM interaction as the dominant power source for SLSNe based on the presence of interaction lines (e.g., Yan et al. 2015Yan et al. , 2017b) ) and equally well-explained light curves (e.g., Chatzopoulos et al. 2012;Chen et al. 2022b).However, the spectroscopic properties exhibited by the majority of SLSNe (e.g., Pastorello et al. 2010;Quimby et al. 2011Quimby et al. , 2018;;Inserra et al. 2013;Liu et al. 2017) and limits placed by Xray/radio observations (Margutti et al. 2018;Eftekhari et al. 2021) are hard to reconcile with the CSM model alone.
In addition to the power source of SLSNe, it is critical to explore and constrain possible progenitor systems.The lack of hydrogen spectral features in SLSNe point to a connection with the stripped-envelope massive star progenitors of SNe Ib/c (e.g., Pastorello et al. 2010).However, it has been shown with a uniformly modeled light curve sample that SLSN progenitors are systematically more massive (≈ 3.6 − 40 M ⊙ ; Blanchard et al. 2020) than SNe Ib/c progenitors (≈ 3.7 − 5.4 M ⊙ ; Barbarino et al. 2020).Comparing the SLSN progenitor mass distribution at the time of explosion to stellar evolutionary models suggests that low-metallicity binary systems may be plausible progenitors (e.g., Liu et al. 2015;Moriya et al. 2015;Blanchard et al. 2020;Stevance & Eldridge 2021).
Studies of SLSN host galaxies have also been leveraged to shed light on their progenitors.These studies revealed a preference for low-metallicity dwarf galaxies with higher specific star formations rates (sSFRs) and lower luminosity than CCSNe (e.g., Chen et al. 2013;Lunnan et al. 2013Lunnan et al. , 2014Lunnan et al. , 2015;;Perley et al. 2016;Angus et al. 2016;Schulze et al. 2018).An investigation of the sub-galactic environments of 16 SLSNe using high-resolution HST data suggested that SLSN locations track bright UV regions of their host galaxies (Lunnan et al. 2015;hereafter, L15), consistent with massive progenitors.The relatively small sample size, however, did not allow for a statistically meaningful comparison with other classes of transients such as long gamma-ray bursts (LGRBs) and CCSNe.
With about 150 spectroscopically confirmed SLSNe to date (Gomez et al. 2020;Chen et al. 2022a), it is now possible to significantly expand on the early analysis of SLSN locations (L15).Here, we take advantage of a large set of archival HST SLSN host galaxy restframe UV observations from a wide range of programs, to produce the first large (65 SLSNe) and statistically meaningful sample of SLSN sub-galactic locations.We follow the same methodology that has been employed to explore the progenitors of other populations of transients, including SNe Ia (Wang et al. 2013;Anderson et al. 2015), SNe Ib/c and II (Kelly et al. 2008;Prieto et al. 2008;Svensson et al. 2010;Kelly & Kirshner 2012), LGRBs (Bloom et al. 2002;Fruchter et al. 2006;Svensson et al. 2010;Blanchard et al. 2016;hereafter B16), and short GRBs (Fong & Berger 2013).
The paper is structured as follows.We present the sample, HST imaging, data processing techniques, and astrometric matching to determine the SLSN locations in §2.In §3 we describe our measurement methodology for determining host associations, offsets, and fractional fluxes.In §4 we present the resulting offset and fractional flux distributions and compare these to other transients.In §5 we explore trends and correlations with redshift, as well as with inferred SLSN explosion and magnetar engine properties, and discuss implications for SLSN progenitors.We conclude with a summary of our findings in §6.
Throughout the paper, we assume a flat ΛCDM cosmology with Ω m = 0.310 and H 0 = 67.7 km s −1 Mpc, based on the Planck 2018 results (Planck Collaboration 2018).All observations are reported in AB magnitudes (Oke & Gunn 1983) and corrected for Galactic extinction using Schlafly & Finkbeiner (2011), following the Gordon et al. (2023) extinction law with R V = 3.1.

HST Data
We compiled an initial sample of 109 Type I SLSNe with HST host galaxy observations from archival and ongoing programs, imaged with either the Advanced Camera for Surveys (ACS) or the Wide Field Camera 3 (WFC3).The names, redshifts, and details of the HST observations are listed in Table 1.The initial sample spans a wide redshift range of z = (0.05 − 1.998), where the HST filters used in the observations predominantly probe a rest-frame wavelength range in the UV of ≈ 2300 − 3300 Å; see Figure 1.This allows us to probe the locations of the SLSNe relative to the underlying star formation activity in their hosts.Note-List of all SLSNe with archival HST host galaxy observations.We also report the telescope/instrument and filter for the events with available SN imaging used for astrometric matching.
We obtained the HST data from the Mikulski Archive for Space Telescopes (MAST 1 ), and retrieved some have either a two-point pattern, a three-point pattern, or multiple visits in the same filter.By combining dithered exposures, we reconstruct a final image for each host galaxy with higher resolution than the original ones sampled by the instrumental pointspread function (PSF).We further apply distortion corrections, which improve the precision of our astrometric alignment.The CTE-corrected images were processed and combined with the AstroDrizzle task as a part of the DrizzlePac software package provided by STScI (Gonzaga et al. 2012).We use final pixfrac=0.8or 0.9 depending on the pixel variation of the output image, and final scale= 0.020 ′′ and 0.025 ′′ per pixel2 for WFC3/UVIS and ACS, respectively.All the HST data used in this paper can be found in MAST: 10.17909/skn3-8756.

SLSN Imaging
Precisely locating each SLSN within its host galaxy requires relative astrometry and hence images of the SLSNe.We use the deepest, highest resolution optical images available.Specifically, we use the PanSTARRS1  (Steele et al. 2004) Data Archive8 .Finally, in some cases, we use our own data from the 1.2-m telescope at Fred L. Whipple Observatory (KeplerCam), the 6.5-m Magellan telescopes (IMACS), and the 6.5-m MMT (Binospec).
Five SLSNe in our sample have multiple HST epochs available, which include detections of the SNe themselves.As previously analyzed in L15, the constant Rest-frame effective wavelengths probed by the HST datat as a function of the SLSN redshifts.Grey points denote the full sample, while red points indicate the final sample used in the analysis (see §2).We note that only 5/65 SLSN hosts in the final sample are not observed in the rest-frame UV.The top and right panels show the projected distributions of redshift and rest-frame wavelength, respectively.
and ≈ 1130 rest-frame days past peak, respectively) to confidently rule out the possibility of residual SN emission in the final epochs.We use the first epoch of HST observations of PS1-11aib, SCP06F6, and SN2016eay as the SN images, performing image subtraction to ensure that host galaxy light does not affect the SN centroid determination.We use PyZOGY9 (Zackay et al. 2016) after aligning the different HST images with our astrometry procedure (see §2.3).
On the other hand, for SN 2015bn and SN 2016inl, all available HST observations contain SN emission, and we therefore disentangle the SN and host galaxy contributions using galfit (Peng et al. 2010).For SN 2015bn, we use the Sérsic profile model from Nicholl et al. (2018) and use the host-subtracted image containing only SN light to calculate the centroid location.In the case of SN 2016inl, we use the model from Blanchard et al. (2021), where the SN and its host galaxy were simultaneously fit with a PSF and a Sérsic profile.Since the galfit models do not include positional uncertainties, we take the centroid locations given by galfit and measure the SN positional uncertainty in the same fashion as the rest of our sample and assume a typical host positional uncertainty of σ host = 0.005 ′′ for smoothly varying galaxies in the sample (e.g., PS1-10bzj and PS1-11ap).We note that for these 2 SLSNe we can measure an offset, but due to the blending of SN and host galaxy light we cannot reliably determine the fractional flux statistic (see §3).
Taking into account the availability of SLSN images (ground-based and HST), the sample size is reduced to 95 SLSNe; we do not find any publicly available SN images for the remaining 14 events; see Table 2.

Astrometry
We perform relative astrometry when possible, and absolute astrometry otherwise, on the 95 HST images with available SN images, to align and precisely locate each SLSN relative to its host galaxy.
We identify common point-like sources between the SN and HST images with photutils (Bradley et al. 2022) and measure the position of each source.We then match the sources using the function wcs.fit wcs from points in astropy to fit a Simple Imaging Polynomial of degree 1 − 3 (depending on the number of common sources) to align the SN images to the world coordinate system of the HST images.We measure the root-mean-square (rms) of the positional residuals for the common sources as the 1σ astrometric tie uncertainty, σ tie .We require a minimum of 4 common sources for a reliable fit, which is satisfied for 66 of the 95 SLSNe.For the remaining 29 events we instead use absolute astrometry by matching both the SN and the HST images to the Gaia DR3 catalog (Gaia Collaboration et al. 2016Collaboration et al. , 2023)).The rms positional residuals from each fit are then combined in quadrature to determine σ tie .
For the sources aligned with relative astrometry, we find a median value of σ tie ≈ 33 mas.For sources aligned with absolute astrometry, the combined tie uncertainty is somewhat higher, with a median value of σ tie ≈ 87 mas.The number of common sources used in the astrometric matching, and the resulting values of σ tie are listed in Table 3.We note that for 11 sources, there are a lack of point-like sources in the HST images, rendering astrometric match impossible.The sample size after astrometric alignment is reduced to 84 SLSNe; see Table 2.

Host Galaxy Assignment
Before offsets and fractional flux values can be determined, we need to associate a host galaxy to each SLSN.We assign the most probable host galaxy for each SLSN by calculating the probability of chance coinci-dence (P cc ) for galaxies in the vicinity of the SN location, specifically focusing on a region of 30 × 30 kpc.For context, the largest projected physical offsets measured in L15 was 4.3 kpc, and the offsets measured in this work are well-contained within this field of view.
Following the methodology of Bloom et al. (2002) (as also used by Berger 2010, Fong &Berger 2013, andB16), we calculate P cc for each galaxy using: where σ(≤ m) is the observed surface density of galaxies brighter than magnitude m and R e is the effective radius, defined as R e = max(3 σ 2 tie + σ 2 SN , R 2 + 4R 2 50 ) (Bloom et al. 2002), where R is the projected offset and R 50 is the half-light radius (see §3.2).For about 2/3 of our sample, the localizations are sufficiently precise such that the second term dominates.
For each HST image, we use photutils to detect extended sources that are potential host candidates.To avoid spurious associations with noise fluctuations, we consider sources with a minimum of 10 connected pixels detected at ≥ 2.5σ above the background level.If the object with the lowest P cc exceeds a threshold value of 0.1, we consider the actual host galaxy to be undetected at the limit of our images, and exclude the source from subsequent analysis; this is the case for 19 sources of the 84 sources with successful astrometric matching.
In addition to calculating P cc , we also compare our most probable host galaxy assignment with previous studies that have identified SLSN hosts (L15; Angus et al. 2016Angus et al. , 2019;;Perley et al. 2016;Cikota et al. 2017;Schulze et al. 2018;Taggart & Perley 2021).We find that our assignments are in excellent agreement with previous studies, including those with the most complex morphology (e.g., PTF12dam, PTF12hni).In 7 cases10 , we find multiple objects in the vicinity of the SLSN position, which we consider to be disjointed components of the same host galaxy (due to patchy nature of UV emission).In these instances, we combine the components to calculate all relevant host properties.For the remainder of the sample, the most probably host galaxy is either coincident with the SLSN position or the most proximal extended source.
Our final sample of detected host galaxies contains 65 events (Table 2), which is nearly four times larger than the sample analyzed in Lunnan et al. (2015).The assigned host galaxies have P cc ≈ 1.8 × 10 −4 − 7.5 × 10 −2 ; see Table 3.In Figure 2 we show the drizzled HST images, along with the location and uncertainty  region of each SLSN (the quadrature sum of σ tie and the SN centroid uncertainty, σ SN ; §3.2), as well as the centroid and the half-light radius of each host galaxy (see §3.2).The drizzled HST images for SLSNe without an identified host are shown in Figure 12.

Offset Measurements
Following the astrometric matching and host galaxy assignment, we determine the angular offset of each SLSN from the UV light centroid of its host galaxy.We determine the location of each SLSN by fitting the SN image with a 2D Gaussian and calculate the image centroid and its associated uncertainty, σ SN , which is determined as θ FWHM /2(S/N), where θ FWHM is the full-width at half maximum of the 2D Gaussian, and S/N is the signal-to-noise ratio of the SN detection; see Table 3.
Next, we define the host galaxy flux-weighted centroid, as determined by photutils for pixels designated as part of each host galaxy.Here, the statistical uncertainty on the host centroid from photutils potentially underestimates the systematic uncertainties due to the irregular morphology of some hosts.To address this, we estimate the positional uncertainty (σ host ) by varying the detection threshold from 2.5σ to the highest threshold at which the host is still detected with a step size of 0.005σ, and then taking the standard deviation of the resulting host centroid values.The resulting values of σ host are listed in Table 3.
For each SLSN we measure the projected physical offset, R phys , using the SN redshift, and assign an associated total uncertainty of σ R phys = σ 2 tie + σ 2 SN + σ 2 host .In addition to the projected physical offset, we also normalize the offset of each SLSN by the size of its host galaxy, R norm , allowing us to explore both the population itself and to compare it to other transients that may arise in galaxies with different sizes.We use photutils to measure the half-light radius, R 50 , defined as the effective circular radius that encloses 50% of the total flux within the galaxy Kron aperture.Using R 50 , the hostnormalized offsets is simply given by R norm = R phys /R 50 (Table 3).* Corrected for Galactic extinction.† Aligned with absolute astrometry using Gaia DR3 catalog.In these cases we report the number of common sources between the Gaia DR3 catalog and the SN and HST images, respectively, in the second column.‡ The HST images for these sources contain residual SN emission, allowing for direct astrometry without a tie to another image, but preventing a determination of fractional flux.

Fractional Flux Measurements
As in previous studies of the locations of transients in their host galaxies (Fruchter et al. 2006;Kelly et al. 2008;Prieto et al. 2008;Kelly & Kirshner 2012; L15; B16), we measure the fractional flux statistic for each SLSN following the methodology of Fruchter et al. (2006), with a refined procedure to assess uncertainties.The fractional flux quantifies the fraction of total flux from the host galaxy that is contained in pixels fainter than the flux value at the SLSN location, thereby providing a statistic that measures the brightness of the SLSN location compared to the entire galaxy.The resulting fractional flux value lies between zero and one, where a value of one indicates the SLSN occurred in the brightest region of its host galaxy.
In previous studies, the fractional flux was measured using an area-averaged flux value centered at the transient position, with an error circle radius given by the quadrature sum of σ tie and σ trans .Here, we refine this procedure using a Monte Carlo approach as follows.First, we use photutils to extract host galaxy pixels, using a minimum of 10 connected pixels and a threshold of 1σ above the sky background.Second, exploiting the quasi-Gaussian nature of σ tie and σ SN , we construct a 2D Gaussian probability distribution function centered at the pixel (x SN , y SN ) corresponding to the SLSN cen- troid, with a standard deviation of σ = σ 2 tie + σ 2 SN .Third, we randomly sample a pixel based on the 2D Gaussian probability distribution associated with this pixel, and use the flux value at the chosen pixel to calculate the fractional flux by dividing the sum of flux values in pixels dimmer than the chosen pixel by the total flux of the host.To properly determine the uncertainty on the fractional flux, we repeat this procedure 10,000 times.The resulting median values, as well as the 1σ ranges (corresponding to 16th and 84th percentiles), are reported in Table 3.

RESULTS
Our final sample of 65 SLSNe with offset and fractional flux measurements is four times larger than in the previous study of L15.In this section we describe the results from this large population, and quantitatively compare these with the distributions for other transients with massive star progenitors (LGRBs, Type Ib/c SNe, Type II SNe) using the Kolmogorov-Smirnov (KS) (Smirnov 1948) and Anderson-Darling (AD) (Anderson & Darling 1952) tests.Both tests are designed to determine whether two distributions arise from the same underlying population, with the AD test being a modified version of the KS test that is more sensitive to the tails of a distribution (whereas the KS test gives more weight to the region around the median of a distribution).While the KS test is more widely used in previous works, we regard the AD test to be a more robust statistical measure, especially in the context of the fractional flux distribution where tail contributions are more prominent.We provide comparisons of the distributions of physical and host-normalized offsets, galaxy sizes, and fractional flux values, and summarize the KS and AD test p-values in Table 4.We stress that these statistical comparisons were severely limited by the small sample size in the previous study (L15).

Physical Offsets
In Figure 2 we show the cumulative distribution of projected physical offsets (R phys ).The distribution spans ≈ 0.07 − 6.7 kpc, with a median of ⟨R phys ⟩ ≈ 0.73 kpc.The distribution is overall smooth across the full range of offsets, with no notable gaps.The KS and AD tests comparing our distribution with the smaller sample of 16 SLSNe from L15 yield p-values of 0.71 and 0.81, respectively.This is not surprising given that the sources in the L15 sample are also included in our larger data set.
We also compare the projected physical offsets to the distributions for LGRBs from B16, as well as Type Ib/c SNe and Type II SNe from Kelly & Kirshner (2012); see Figure 2. All three populations have systematically larger offsets than SLSNe, LGRBs by a factor 1.4, SNe Ib/c by a factor of 4.4, and SNe II by a factor of 5.5.The KS and AD tests relative to the LGRBs sample yield pvalues of 0.12 and 0.20, respectively, suggesting that the physical offset distributions for SLSNe and LGRBs are consistent with being drawn from the same underlying distribution.For the SNe Ib/c sample, the KS and AD tests yield p-values of 2.8×10 −11 and 2.4×10 −10 , respectively, while for the SNe II the p-valuess are 1.3 × 10 −11 and 3.6×10 −17 , respectively, thus indicating clearly that the SLSN physical offsets are vastly different from those of SNe Ib/c and II.
The offsets have associated uncertainties, σ R phys and σ Rnorm , that are dependent on σ tie , σ SN , and σ host .Since the offset is a positive-definite quantity, we cannot assume a Gaussian distribution for its uncertainty.Instead, we use the Rice distribution to represent the probability distribution function (Bloom et al. 2002): where R and σ R are the offset quantity (physical or normalized) and its uncertainty, and I 0 is the zeroth order modified Bessel function of the first kind.Here we employ a Monte Carlo approach with 10,000 iterations to assess the uncertainties on the measured offset distributions.
Accounting for the uncertainties in the physical offsets, we show in Figure 2 the results of the Monte Carlo simulation by plotting a 2D histogram of the density of points from the cumulative distributions generated at each of the 10,000 iterations.Dark regions indicate a higher density of points, or, in other words, more synthetic distributions from the simulation pass through that region.The median of the distribution of medians from the Monte Carlo simulation is 0.81 kpc with a 90% confidence interval of 0.71 − 0.97 kpc.The overall apparent shift in the Monte Carlo distribution to higher offsets compared to the median distribution is due to the fact that the offset is a positive-definite quantity.Re-calculating the KS and AD tests for each iteration in comparison to LGRBs, SNe Ib/c and SNe II, we confirm the same result as above.
Due to the positive-definite nature of the offsets, offsets with large uncertainties are more likely to be skewed toward higher values.In Appendix B we explore this issue and undertake a simple procedure to correct for this potential bias.In Figure 2 we show the "corrected" distribution, but find that it overall closely matches the directly observed one.Since the correction is small, and since it was not applied for other transients to which we compare our SLSN sample, we do not use it in our analysis to prevent introducing additional bias in comparison to previous works.

Galaxy Sizes
To compare the projected offsets, both for the SLSN sample itself and in comparison to other transients, in a more meaningful way, we need to normalize each offset by the size of the host galaxy, i.e., R norm .We use R 50 , the circular radius containing half of the galaxy light, to normalize the offsets.We show the distribution of R 50 for SLSNe in Figure 3.We find a median value of 0.76 kpc, and an overall range of ≈ 0.1 − 8.6 kpc.We also show the R 50 distribution for LGRBs (B16), which has a median of 1.8 kpc and a range of 0.4 − 5.9 kpc.Thus, SLSN hosts are on average about a factor of 2.4 times smaller than even the overall compact host galaxies of LGRBs.
The KS and AD tests between the SLSN and LGRB R 50 distributions yield p-values of 4.1 × 10 −9 and 3.2 × 10 −11 , clearly indicating that the two distributions are not drawn from the same underlying population.We only compare the R 50 distribution to LGRBs, as the   In Figure 4 we plot the cumulative distribution of host-normalized offsets (R norm ).The distribution has a median value of ≈ 1.06, and spans a range of ≈ 0.09 − 5.28 (with about 3/4 of the SLSNe having R norm ≲ 2).The shaded region in Figure 4 shows the results of our Monte Carlo simulation taking into account the uncertainties on the individual measurements, as described in §4.1.The median of the distribution of medians is 1.17 with a 90% confidence interval of 1.01 − 1.35.
Overall, the distribution is reminiscent of an exponential disk profile, the expected surface brightness profile of star-forming disk galaxies, although the SLSN distribution is broader, especially at large offsets.The KS and AD tests comparing the SLSN and exponential disk distributions yield p-values of 0.34 and 0.17, respectively, indicating that the observed SLSN distribution is consistent with a smooth exponential disk distribution.Using the Monte Carlo range of cumulative distributions, we find that about 54% and 14% yield KS and AD p-values of ≳ 0.05, respectively.
To help visualize the comparison between SLSNe and other transients, and each with the exponential disk, in Figure 5 we plot the difference between each cumulative distribution and the exponential disk distribution.The results illustrate that none of these transient populations strictly follow an exponential disk profile, but that SLSNe differ significantly in the way they deviate from the exponential disk distribution.Specifically, we find that the main deviation for SLSNe is an overabundance of large normalized offsets, R norm ≈ 1.5 − 4, while for LGRBs there is an overabundance of small offsets,

Hsu et al.
R norm ≈ 0.2 − 1; for SNe Ib/c and II there is an overabundance at R norm ≈ 1.

Fractional Flux Distribution
In Figure 6 we show the cumulative distribution of fractional flux for 63 SLSN host galaxies11 .Also shown is a diagonal 1:1 line which marks the expectation of a population of sources that linearly tracks the underlying light distribution of their host galaxies.Remarkably, the SLSN sample exhibits a high fraction of events, ≈ 0.4, with fractional flux value of 0, and has a low median value of ≈ 0.16.Thus, the locations of SLSNe appear to be significantly skewed to dimmer than average UV regions of their host galaxies.We also show the resulting 2D probability density using the Monte Carlo procedure described in §3.3; we still find that all 10,000 draws have a substantial fraction of 0.3−0.45 of the population with fractional flux values of 0. We note that our distribution is in tension with the smaller sample in L15, with KS and AD test p-values of 1.3 × 10 −2 and 3.8 × 10 −4 , respectively.

Fractional Flux-Offset Relationship
In Figure 7  determined by integrating the exponential disk profile at each normalized offset value.We calculate the Spearman's rank correlation coefficients (ρ; Spearman 1904) to quantify the strength of correlation between fractional flux and normalized offset, as well as its associated 1σ bound uncertainty using the method described in Curran (2014).We find a clear negative correlation between fractional flux and normalized offsets for SLSNe, with ρ ≈ −0.77, such that sources with smaller offsets have high fractional flux values.We find similar negative correlations for the other populations (ρ ≈ −0.75 for LGRBs, ρ ≈ −0.70 for Type Ib/c SNe, and ρ ≈ −0.76 for Type II SNe).Thus, all populations follow a similar trend, which overlaps well with the exponential disk profile.This trend is not surprising given that the central regions of galaxies are brighter.
However, what does stand out in the SLSN population compared to the other transients (and to an exponential disk) is the unusually large fraction of sources with fractional flux values of 0 and normalized offsets of ≳ 1.These can clearly be seen along the bottom of Figure 7.To further illustrate this point, in Figure 8 we plot the cumulative fractional flux distributions for SLSNe and the other transients, separated into sub-populations with R norm ≤ 1 and R norm > 1.We find that SLSNe with R norm ≤ 1 overall follow the 1:1 line expected for  Cumulative Distribution . Same as Figure 6, but with the distributions separated into sources with Rnorm < 1 (solid) and Rnorm ≥ 1 (dashed).
The SLSN population exhibits the lowest fractional flux values in both subsets of the population, but sources with Rnorm < 1 roughly track the underlying UV light.
sources the linearly track the UV light distribution of their hosts.However, even within this sub-population the SLSNe are somewhat more skewed to lower fractional values compared to LGRBs and SNe Ib/c and II.On the other hand, of the SLSNe with R norm > 1 about 2/3 have fractional flux values of 0, while in the other populations the fraction of such events is ≲ 0.15.

DISCUSSION
The distributions of offsets, fractional fluxes, and host galaxy sizes presented in §4 provide the most indepth analysis of the locations and local environments of SLSNe to date.In this section we explore whether the locations of SLSNe and their host sizes exhibit trends with redshift, as well as any correlations with the inferred properties of their magnetar engines as determined from modeling of the optical light curves.We further explore implications of our results for SLSN progenitors.The Spearman's correlation coefficients are summarized in Table 5.

Trends with Redshift
In Figure 9  In each panel we also list the Spearman rank correlation coefficient.We find no clear correlations, with the most significant correlation being the one between half-light radius and redshift (ρ ≈ 0.49).
as functions of SLSN redshift.No obvious correlation is seen between offset and redshift, with ρ = 0.28 +0.12 −0.12 and ρ = −0.02+0.13  −0.12 for the physical and host-normalized offsets, respectively.Similarly, no obvious trend is seen between fractional flux and redshift, with ρ = 0.13 +0.13  −0.14 .However, we find that nearly all SLSNe with low fractional flux values of ≲ 0.2 are preferentially located at low redshifts, z ≲ 0.5.Finally, we do find a mild correlation between host galaxy half-light radii and redshift, with ρ = 0.49 +0.09 −0.10 , predominantly due to the prevalence of compact hosts with R 50 ≲ 0.25 kpc at z ≲ 0.25.
To further discern parameter trends with redshift, in Figure 10 we present cumulative histograms split into two redshift bins at z = 0.35 (leading to an essentially equal number of 37 and 38 SLSNe per bin).We find no clear difference in the cumulative distributions of phys-ical offsets (KS and AD test p-values of 0.34 and 0.18) and host-normalized offsets (KS and AD test p-values of 0.53 and 0.79).We do find lower fractional flux values at z ≤ 0.35 (due to the prevalence of sources with fractional flux values of 0 at lower redshifts as noted above); however, the KS and AD test yield p-values of 0.27 and 0.12, respectively, indicating no clear statistical difference.Finally, the only distribution that does exhibit a statistically significant trend is the half-light radius, with KS and AD test p-values of 1.4 × 10 −3 and 3.5 × 10 −4 , respectively, indicating that lower redshift SLSN hosts are systematically more compact than at higher redshifts.

Trends with Magnetar Engine Parameters
The optical light curves of SLSNe have been successfully modeled with a magnetar spin-down model (Kasen and observed total radiated energy (E rad ).In Figure 11 we plot the distributions of these 7 SLSN parameters as a function of physical and normalized offsets, fractional flux, and half-light radius.Visual inspection does not reveal any significant correlation between any pair of parameters.The strongest correlation quantified by Spearman's rank correlation coefficient is between halflight radius and kinetic energy, with a median ρ ≈ 0.31.Thus, we find no evidence of correlation between SLSN locations and their magnetar engine or explosion properties.

Progenitor Implications
Our key finding is that SLSNe are on average located further away from their galactic centers than LGRBs and CCSNe, and unlike LGRBs and CCSNe, a substantial fraction of ≈ 40% are not correlated with the underlying UV emission of their hosts.The difference relative to LGRBs is particularly intriguing given that both populations represent a rare mode of massive star death (≲ 1% of the overall CCSN rate), and both are thought to be powered by central engines that require The magnetar model parameters are from a uniform study using MOSFiT (Gomez et al. 2022).We do not find any significant correlation between the SLSN parameters and the SLSNe environments.rapid rotation (black holes in LGRBs, and magnetars in SLSNe).Our results, however, indicate that they arise from massive stars that reside in different environments.Since a strong correlation with bright UV regions, as is the case for LGRBs, can be interpreted as evidence for a particularly young and massive progenitor population (e.g., Fruchter et al. 2006;Kelly et al. 2008;Anderson et al. 2012), the results for SLSNe may be evidence for less massive and somewhat older progenitors.However, this appears to be in conflict with the inferred pre-explosion mass distribution of SLSNe, which points to systematically more massive progenitors compared to SNe Ib/c (and the small number of LGRBs with inferred progenitor masses; Blanchard et al. 2020).Similarly, van den Heuvel & Portegies Zwart (2013) proposed a dynamical formation model in young dense star clusters for SLSNe and LGRBs, in which SLSNe are the product of multiple runaway collisions, but our results cast doubt on such a common formation path.
A possible explanation for the substantial fraction of SLSNe occurring outside of UV-bright regions is that their progenitors arise in disrupted binary systems, thereby gaining a velocity kick.As shown in Figures 5,  7, and 8 the dominant contribution to events at low fractional flux is from SLSNe at offsets of R norm ∼ 1 − 4, or equivalently R phys ∼ 0.75 − 3 kpc.Traveling such distances in the progenitor lifetime span of ∼ 10 Myr requires velocities of ≳ 10 2 km s −1 .Such high velocities may not be unexpected in models of runaway mas-sive stars from disrupted binary systems, especially for a rare population in predominantly low-metallicity dwarf galaxies (e.g., Eldridge et al. 2011).
The SLSN results are also reminiscent of the isolated locations of luminous blue variables (LBVs) in the Milky Way and Magellanic Clouds (Smith & Tombleson 2015), explained as possible evidence for LBV formation as mass gainers in binary systems, which are subsequently disrupted.Such a scenario would explain both the large fraction of SLSNe outside of UV-bright regions, and the higher masses of their progenitors at the time of explosion compared to SNe Ib/c.Of course, stars exploding in the LBV phase, with an intact massive hydrogen envelope, cannot be the direct progenitors of SLSNe, but an analogous process involving disruption of a binary system after the progenitor's hydrogen envelope was stripped may be relevant.
Regardless of the exact formation pathway of SLSN progenitors, the offset and fractional flux distributions indicate that factors other than just progenitor mass and metallicity have a significant impact on the formation of SLSNe.However, the details of this pathway do not seem to influence the eventual SN explosion itself, as we do not find any obvious correlation between the SLSN locations and their explosion properties.This suggests that the explosion properties are mainly governed by the state of the progenitor pre-explosion (e.g., mass, angular momentum).We have carried out the most comprehensive study of the locations of SLSNe within their host galaxies to date using archival HST data for 65 SLSNe.We determine both the offset and fractional flux distributions for the sample, and compare these to other transients with massive star progenitors (LGRBs and CCSNe).Our key findings are as follows:

CONCLUSIONS
1. SLSN host galaxies are more compact than the host galaxies of LGRBs (median of 0. 7.There is no significant correlation between the locations of SLSNe and their explosion and magnetar engine parameters.
8. The substantial difference in SLSN and LGRB locations indicates that while both are rare classes of CCSNe most likely powered by central engines, their progenitors follow different formation pathways.
9. The large fraction of SLSNe outside of UV-bright regions may point to progenitors formed as runaway stars from disrupted binary systems with kick velocities of ∼ 10 2 km s −1 .
With the upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time, we expect a substantial increase in the SLSN discovery rate, extending to higher redshifts than at the present (e.g., Villar et al. 2018).Studies of this larger SLSN population with HST and JWST will be critical for exploring redshift trends, and perhaps subtle correlation between SLSN environments and their explosion properties that cannot be discerned in the current sample.an STScI Postdoctoral Fellowship.
This research is based in part on observations made with the NASA/ESA Hubble Space Telescope obtained from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.These observations are associated with programs GO-9500, GO-12529, GO-12786, GO-13022, GO-13025, GO-13326, GO-13858, GO-14743, GO-15140, GO-15162, GO-15303, GO-15496, GO-16239, GO-16657, and GO-17181.
The Pan-STARRS1 Surveys have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under Grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE).
This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National This paper includes data gathered with the 6.5-m Magellan Telescopes located at Las Campanas Observatory, Chile.Observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution.This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia),processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

Figure 2 .
Figure2.HST images of the 65 SLSN host galaxies with available SN imaging and successful astrometric alignment (HST images of non-detected hosts are shown in Figure12).The images are centered on the centroid of each host galaxy (purple crosses) and aligned with North up and East to the left.The dashed purple circles marks R50 (half-light radius).Solid circles mark the location of the SLSNe, with a radius corresponding to the 1σ uncertainty.Red and blue circles indicate positions determined using relative or absolute astrometry, respectively.The images have been smoothed with a 3 pixel Gaussian filter.In the case of SN 2015bn and SN 2016inl, the images also contain light from the SLSNe.

Figure 2 .
Figure 2. Cumulative distribution of projected physical offsets for 65 SLSNe from this work (red).Also shown are the distributions for LGRBs (blue; B16), SNe Ib/c (cyan) and II (green) from Prieto et al. (2008).The red shaded region shows the results of our Monte Carlo simulation using the associated uncertainties as a 2D histogram.Arrows at the bottom denote the medians of each distribution.The dashed red line includes a correction factor to account for the positive-definite nature of offsets (see Appendix B for details).

Figure 4 .
Figure 4. Cumulative distribution of host-normalized offsets for 65 SLSNe from this work (red).Also shown are distributions for LGRBs (blue; B16), SNe Ib/c (cyan) and II (green) SNe fromKelly & Kirshner (2012).We also plot the distribution expected for an exponential disk profile (purple).The red shaded region shows the results of our Monte Carlo simulation using the associated uncertainties as a 2D histogram.Arrows at the bottom denote the medians of each distribution.The dashed red line includes a correction factor to account for the positive-definite nature of offsets (see Appendix B for details).

Figure 5 .Figure 6 .
Figure5.The differences between the cumulative host-normalized offset distributions of our SLSN sample (red), LGRBs (blue), SNe Ib/c (cyan), and SNe II (green) SNe and the cumulative distribution for an exponential disk profile.We find an overabundance of SLSNe at Rnorm ≳ 1.5, compared to an overabundance of LGRBs at Rnorm ≈ 0.2 − 1, and SNe Ib/c and II overabundance at Rnorm ≈ 1.values were not reported for SNe Ib/c and SNe II inKelly & Kirshner (2012).

Figure 7 .
Figure7.Scatter plots of fractional flux versus hostnormalized offsets for SLSNe (red), LGRBs (blue), Type Ib/c SNe (cyan), Type II SNe (green), and predicted relationship for a transient population that follows the exponential disk model exactly (purple).To avoid clutter, we omit showing the associated uncertainties on fractional flux and hostnormalized offsets.We find a strong correlation between fractional flux and host-normalized offset for SLSNe, with a median ρ ≈ −0.77 and low uncertainties.

Figure 9 .
Figure 9. Physical offsets, host-normalized offsets, fractional flux values, and host half-light radii plotted as a function of redshift.In each panel we also list the Spearman rank correlation coefficient.We find no clear correlations, with the most significant correlation being the one between half-light radius and redshift (ρ ≈ 0.49).

Figure 11 .
Figure11.Magnetar model parameters (P , B, Mej, vej, and E kin ), as well as observed peak luminosity (L peak ) and observed total radiated energy (E rad ), as a function of physical and host-normalized offsets, fractional flux values, and host half-light radii.The magnetar model parameters are from a uniform study using MOSFiT(Gomez et al. 2022).We do not find any significant correlation between the SLSN parameters and the SLSNe environments.
Figure 11.(continued) Aeronautics and Space Administration and operated by the California Institute of Technology.This research uses services or data provided by the Astro Data Lab at NSF's NOIRLab.NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation.This project used public archival data from the Dark Energy Survey (DES) as distributed by the Astro Data Archive at NSF's NOIRLab.Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute for Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Enérgeticas, 22 Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l'Espai (IEEC/CSIC), the Institut de Física d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the NSF's NOIRLab, the University of Nottingham, the Ohio State University, the OzDES Membership Consortium, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University.The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council.Based in part on observations obtained at the international Gemini Observatory, a program of NSF's NOIR-Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

Figure 12 .
Figure 12.HST drizzled images of 19 SLSNe with available SN imaging and successful astrometric alignment, but no detected host.The images are centered on the centroid location of the SLSNe and aligned with North up and East to the left.Solid circles indicating the location of the SLSNe, with a radius corresponding to 1σ uncertainty.Red and blue circles indicate positions determined using relative or absolute astrometry, respectively.

Figure 13 .
Figure 13.Left: Physical offset uncertainty (σR phys ) versus physical offset (R phys ).Right: Host-normalized offset uncertainty (σR norm ) versus host-normalized offset (Rnorm).The dashed line in each panel indicates the 1:1 line where the offset is equal to its uncertainty.The dearth of sources with small offsets and large uncertainties (the upper left quadrant of each panel) is due to the positive-definite nature of the offset quantity.

Figure 14 .
Figure 14.Left: 2D probability density plot showing the host-normalized offsets for a population drawn from an exponential disk profile with randomly assigned uncertainties.The blue line marks the peak value as a function of σR norm .Plotted in red are the "corrected" Rnorm values for SLSNe.Middle: 2D probability density plot showing the host-normalized offsets after sampling with the Rice distribution.The blue line marks the peak value as a function of σR norm ; the distribution is clearly skewed to larger values of Rnorm at larger σR norm .Plotted in red are the measured values for SLSNe.Right: The mean correction factor as a function of σR norm is calculated as the ratio of the peaks (blue lines) between the two populations.

Table 1 .
Prelimary Sample of SLSNe with Available HST Host Galaxy Images

Table 2 .
SLSN Sample with HST Data

Table 3 .
Astrometric Results and Key Measurements The SLSN host galaxies have a median size of ⟨R50⟩ ≈ 0.76 kpc, about a factor of 2.4 times smaller than the LGBR host galaxies.We note that the R50 distributions for SNe Ib/c and SNe II were not reported in previous studies.

Table 4 .
Summary of KS and AD Test p-values

Table 5 .
Summary of Spearman Rank Correlation Coefficients The host-normalized offsets of SLSNe strongly correlate with their fractional fluxes, in a similar man-ner to those of LGRBs and CCSNe; the main distinction is the overabundance of SLSNe with fractional flux values of 0 and normalized offsets of R norm ≳ 1.We find that SLSNe with R norm ≤ 1 have a fractional flux distribution that linearly tracks the underlying UV light of their hosts, but about 60% of those with R norm > 1 have fractional flux values of 0 in clear distinction from LGRBs and CCSNe with R norm > 1.