The Mismeasure of Mergers: Revised Limits on Self-interacting Dark Matter in Merging Galaxy Clusters

May combine two claims.

The detailed X-ray map of Menanteau et al. (2012) shows a large region of tenuous gas but no identifiable peak.

“The detailed X-ray map of Menanteau et al. (2012) shows a large region of tenuous gas, but no identifiable peak.”

• cites Menanteau et al. (2012) sourceDisputed

  In §2.4 (Chandra X-Ray Observations; page unavailable), the paper identifies a compact peak of X-ray emission and describes it as an X-ray-bright bullet. It also describes a lower-intensity wake, but that does not support the claim that the map has no identifiable peak. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

May combine two claims.

According to Bradač et al. (2008), the galaxy-mass offset for ZwCl 1358 east is -4 +/- 4 (-29 kpc); with the mean Harvey et al. gas mass correction, the final delta_SI is -33 kpc, a substantial change from the H15 value of -151 kpc.

“According to Table 2 of Bradač et al. (2008), the galaxymass offset is -4 4 (-29 kpc).With the mean H15 correction for gas mass, the final value for δ SI is -33 kpc.This is a substantial change from the H15 value of -151 kpc.”

• cites Bradač et al. (2008) sourceDisputed

  Split into 2 atoms — 1 confirmed, 0 partially supported, 1 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Harvey et al. (2015) derived an upper limit on the self-interaction cross section of dark matter of <0.47 cm^2 g^-1 at 95% confidence and <-0.01 cm^2 g^-1 at 68% confidence by averaging DM-galaxy offsets in an ensemble of 30 merging galaxy clusters, using a simple solid-body scattering model.

“In an influential recent paper, Harvey et al. derive an upper limit to the self-interaction cross section of dark matter (DM) ( m DM s <0.47 cm 2 g -1 at 95% confidence) by averaging the DM-galaxy offsets in a sample of merging galaxy clusters.”

• Also stated in: § 1. Introduction · plain

  “Harvey et al. (2015, hereafter H15), who used offsets between galaxies and DM in an ensemble of 30 merging clusters to derive, for a simple solid-body scattering model, an upper limit of m DM s <0.47 cm 2 g -1 at 95% confidence and <-0.01 cm 2 g -1 at 68% confidence.”

• cites Harvey et al. (2015) sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

May combine two claims.

For the Bullet Cluster east, the Harvey et al. position is not credible given the agreement among cited sources, their strong exclusion of the H15 position, and their advantages in data quality.

“Given the agreement among the above-cited sources, their strong exclusion of the H15 position (for example, the H15 position is well outside the 99.7% confidence interval of Clowe et al. 2006), and their advantages in data quality (such as multiple bands for source selection), we argue that the H15 position is not credible.”

• cites Clowe et al. (2006) sourceSupported
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The X-ray morphology of MACS J0417.5-1154 shows a long ridge to the northwest with no peak other than the main peak identified with the southern subcluster.

“the X-ray morphology (Mann & Ebeling 2012) shows a long ridge to the northwest with no peak other than the main peak identified with the southern subcluster.”

• cites Mann & Ebeling 2012 sourcePartly supported

  The Primary candidates section (p. 8) describes MACSJ0417.5-1154 as having a bright, compact X-ray core trailed by diffuse emission toward the second cluster, supporting the broad morphology described. It does not specify a northwest ridge, identify the compact core as the southern subcluster, or explicitly say there is no second X-ray peak. (LLM, conf=0.84)

  Experimental — accuracy not yet measured

May combine two claims.

Jee et al. (2014a) and Clowe et al. (2012) broadly agree on the main A520 peaks labeled 1 and 4, and both maps show extensions toward the H15 peak labeled 5.

“The latter two analyses broadly agree, with clear agreement on the main peaks (labeled 1 and 4 here) and both maps showing extensions toward the H15 peak labeled 5.”

• cites Jee et al. (2014a) sourcePartly supported

  Section 6, “Detailed Comparison with C12,” says the two A520 mass maps have similar overall large-scale distributions, supporting broad agreement. It describes an extension from P4 toward the paper’s P3′ location in the Clowe map, but does not establish that both maps show extensions toward the H15 peak labeled 5 or specifically identify agreement on peaks labeled 1 and 4 in the citing document. (LLM, conf=0.82)

  Experimental — accuracy not yet measured
• cites Clowe et al. (2012) sourcePartly supported

  Section 3.2 (Mass Reconstruction; page unavailable) identifies peaks 1, 4, and 5 in Clowe et al.’s A520 map, supporting the claim that its map contains those structures. Our copy does not establish that Clowe’s map has an extension toward peak 5 or that it agrees with Jee et al. (2014a) on that feature; the paper’s comparison is with Jee et al. (2012). (LLM, conf=0.84)

  Experimental — accuracy not yet measured

May combine two claims.

The strong-lensing analysis of Zitrin et al. (2013) has critical curves consistent with the mass distribution of Jee et al. (2014b) but not that of H15.

“We find further support for this suggestion in the strong-lensing analysis of Zitrin et al. (2013), whose critical curves are consistent with the mass distribution of Jee et al. (2014b) but not that of H15.”

• cites Zitrin et al. (2013) sourceSupported
• cites Jee et al. (2014b) sourceSupported
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

SIDM simulations show a low-density bridge forming between the two peaks after first pericenter in a bimodal merger, which shifts the centroid but not the peak, which stays with the galaxies.

“In fact, SIDM simulations (Kahlhoefer et al. 2014;Kim et al. 2016;Robertson et al. 2017) show a low-density bridge forming between the two peaks after first pericenter in a bimodal merger.This shifts the centroid but not the peak, which stays with the galaxies.”

• cites Kahlhoefer et al. (2014) sourcePartly supported

  Section 4 (p. 10) reports that differing tails separate the dark-matter and galaxy centroids while their peaks remain coincident; Section 5 (p. 12) reiterates this result. The paper does not describe a low-density bridge between the two cluster peaks, so that specific feature is not supported by this source. (LLM, conf=0.85)

  Experimental — accuracy not yet measured
• cites Kim et al. (2016)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Robertson et al. (2017) sourcePartly supported

  Section 4.3 (p. 15) says that, after core passage, scattered dark-matter particles lag behind their halo and form a wake that can affect measured positions. Section 4.3.1 (p. 16) says stellar and dark-matter peak offsets become very small, but it does not describe a low-density bridge between the two peaks; it also cautions that the diffuse particles could shift a reconstructed dark-matter peak. (LLM, conf=0.84)

  Experimental — accuracy not yet measured

May combine two claims.

Von der Linden et al. (2014) weak-lensing map has rather low resolution but shows the same southeast-northwest axis as the H15 lensing map.

“Their lensing map has rather low resolution and so is not presented here, but it does show the same southeast-northwest axis as the H15 lensing map (Figure 10).”

• cites Von der Linden et al. (2014) sourcePartly supported

  Section 6.1 (p. 17) describes the paper’s weak-lensing maps, and Section 7.1 (p. 19) notes that smoothing limits the precision of reconstructed mass peaks. Section 6.4 (p. 18) describes a southeast–northwest filament with a secondary cluster visible in a lensing map. Our copy does not establish that this is the map meant by the citing sentence or compare it with the H15 map. (LLM, conf=0.79)

  Experimental — accuracy not yet measured
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Dahle et al. (2013) lensing contours agree with H15 in showing each mass concentration slightly to the north and, in the east-west direction, slightly closer to the center of the system compared to the corresponding galaxies.

“The Dahle et al. (2013) lensing contours (in red) agree with H15 in showing each mass concentration slightly to the north and, in the east-west direction, slightly closer to the center of the system compared to the corresponding galaxies.”

• cites Dahle et al. (2013) sourcePartly supported

  Section 4.4 describes two weak-lensing mass peaks close to the corresponding galaxy-light concentrations, and the Figure 7 caption identifies contours for both mass and light. Our copy does not state that each mass peak lies north of its galaxies and closer to the system’s east–west center; Section 6.2 instead describes the mass as centered on the galaxies. It also does not address agreement with H15. (LLM, conf=0.79)

  Experimental — accuracy not yet measured
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

H15 put the mass concentration slightly farther north than Dahle et al. (2013), but this displacement is nearly perpendicular to the merger axis and so has little effect on δ_SI.

“Although H15 put the mass concentration slightly farther north than do Dahle et al. (2013), this displacement is nearly perpendicular to the merger axis and so has little effect on δ SI .”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Dahle et al. (2013) sourceSupported

May combine two claims.

In general, a strong+weak lensing position potentially disfavors SIDM by missing possible bridge effects, so the paper uses the Bradač et al. (2008) position to build the case that analysis choices favorable to SIDM are not needed.

“In general, strong+weaklensing position potentially disfavors SIDM by missing possible bridge effects, so we use the Bradač et al. (2008) position to build the case that we need not make analysis choices favorable to SIDM to show that the”

• cites Bradač et al. (2008) sourceSupported

May combine two claims.

For MACS J2243 east, there is no convincing concentration of galaxies at the Harvey et al. position in either panel or in Schirmer et al. (2011), and neither von der Linden et al. (2014) nor Schirmer et al. (2011) find a lensing peak there.

“However, there is no convincing concentration of galaxies at this position in either panel of Figure 6, nor in Schirmer et al. (2011).Furthermore, neither von der Linden et al. (2014) nor Schirmer et al. (2011) find a lensing peak here.”

• cites Schirmer et al. (2011) sourceCould not verify

  Section 3.3 describes a galaxy-luminosity map with weak-lensing contours, and Section 3.5 reports a detection of MACS J2243. Neither passage identifies the Harvey et al. position or says whether a galaxy concentration or lensing peak is present there. Searches for an eastern substructure and a peak at that position did not resolve the claim. (LLM, conf=0.69)

  Experimental — accuracy not yet measured
• cites von der Linden et al. (2014) sourceCould not verify

  Section 7.2.1 (p. 21) mentions MACSJ2243.3−0935 as having a bimodal galaxy distribution, but does not locate a lensing peak at the Harvey et al. position or say that one is absent. Section 6.4 (pp. 17–19) discusses lensing peaks generally. Searches for MACSJ2243, its eastern position, and Schirmer et al. (2011) found no passage settling the location-specific claim. (LLM, conf=0.72)

  Experimental — accuracy not yet measured

May combine two claims.

The H15 triangle suggests a southwest-northeast merger axis, but other evidence supports a southeast-northwest merger axis, and there is no evidence in the literature for a southwest-northeast merger axis.

“Furthermore, the H15 triangle suggests a southwest-northeast merger axis, but an overwhelming variety of other evidence (all of the above-cited papers plus the radio relics presented in Lindner et al. 2014) supports a southeastnorthwest merger axis; nowhere in the extensive literature on El Gordo is there any evidence for a southwest-northeast merger axis.”

• cites Lindner et al. 2014 sourceSupported

May combine two claims.

Dahle et al. (2013) do not list a value of δ_SI, but measurements of their map yield ≈10 kpc, close to the H15 value of 28 kpc.

“Dahle et al. (2013) do not list a value of δ SI , but measurements of their map yield ≈10 kpc, close to the H15 value of 28 kpc.”

• cites Dahle et al. (2013) sourcePartly supported

  Section 6.2 describes Figure 7 as showing X-ray, light, and mass contours, and reports that the western X-ray gas is displaced from the dominant galaxy. It does not give a δ_SI value or an approximately 10 kpc separation; that figure-based estimate is the citing authors’ own measurement. Nor does this paper establish the comparison with the H15 value of 28 kpc. (LLM, conf=0.78)

  Experimental — accuracy not yet measured
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim. May combine two claims.

Jee et al. (2014b) found two mass concentrations roughly coincident with the northwest and southeast galaxy concentrations and found no other mass concentrations in the area.

“Jee et al. (2014b) found two mass concentrations roughly coincident with the northwest and southeast galaxy concentrations and found no other mass concentrations in the area.”

• cites Jee et al. (2014b) sourcePartly supported

  Section 4.1 identifies two main mass peaks in the northwest and southeast that closely resemble the galaxy light distribution. But Section 4.3 also describes an extra substructure in the southeast region, so the claim that the authors found no other mass concentration in the area is not supported. Page numbers are unavailable in our copy. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

May combine two claims.

For MACS J2243 west, the Harvey et al. luminosity peak just south of the bright star cannot be due to galaxy luminosity; the most plausible explanation is residual light from the exceptionally bright star.

“West: the color image from von der Linden et al. (2014) demonstrates that the H15 luminosity peak just south of the bright star cannot be due to galaxy luminosity.Although H15 implemented an algorithm for removing stars before smoothing the visible-light distribution, the most plausible explanation for this H15 luminosity peak is residual light from the exceptionally bright star.”

• cites von der Linden et al. (2014) sourceSupported
• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

All the cited lensing analyses of the Bullet Cluster are in good agreement, and none show a displacement between mass and galaxy light in either substructure.

“We stress that regardless of the specific reconstruction technique, all the above-cited analyses are in good agreement, and none show a displacement between mass and galaxy light in either substructure.”

• cites Clowe et al. (2004) sourcePartly supported

  The Summary reports that the main cluster’s lensing mass peak coincides with its galaxies and that the subclump’s mass peak is consistent with its optical component. It also reports an observed subclump mass–galaxy offset at 70% confidence, so ‘none show a displacement’ needs a statistical-significance qualifier. This paper does not establish that all the other cited analyses agree. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites Clowe et al. (2006) sourcePartly supported

  The Analysis section reports that both lensing-mass peaks lie within 1σ of their respective galaxy-light centroids, supporting the absence of a significant mass–galaxy-light displacement in either component. It also reports offsets of about 2σ from the brightest cluster galaxies. The paper does not establish that all the other cited lensing analyses agree across reconstruction techniques. (LLM, conf=0.85)

  Experimental — accuracy not yet measured
• cites Bradač et al. (2009) sourceCould not verify

  Section 4 describes this paper’s Bullet Cluster mass reconstruction and its use of earlier lensing data, but does not compare all the cited analyses or assess whether mass is displaced from galaxy light in either substructure. Searches for mass–galaxy-light offsets and agreement among reconstructions found no passage addressing those claims; page numbers are unavailable in our copy. (LLM, conf=0.72)

  Experimental — accuracy not yet measured

May combine two claims.

Infrequent interactions with large momentum transfer (as in hard scattering) can eject particles from the cluster and are potentially observable as a decrease in the mass-to-light ratio; Randall et al. (2008) used the Bullet Cluster to constrain these models with an upper limit of m_DM_s < 0.7 cm2/g (68% confidence).

“Infrequent interactions with large momentum transfer (as in hard scattering), in contrast, can eject particles from the cluster and are potentially observable as a decrease in the massto-light ratio; Randall et al. (2008) used the Bullet Cluster to constrain these models with an upper limit of m DM s <0.7 cm 2 g -1 (68% confidence).”

• cites Randall et al. (2008) sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

May combine two claims.

The equation used by H15 to relate β to m_DM_s was developed assuming only small (≤30 kpc) displacements between DM, galaxies, and gas; Harvey et al. (2014) show how the analogy between galaxy and gas restoring forces (and hence the inferred drag force) breaks down quickly beyond 30 kpc displacements.

“The equation used by H15 to relate β to m DM s was developed assuming only small (30 kpc) displacements between DM, galaxies, and gas; Harvey et al. (2014) clearly show how the analogy between galaxy and gas restoring forces (and hence the inferred drag force) breaks down quickly beyond 30 kpc displacements.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Harvey et al. (2014) sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

May combine two claims.

Cluster mergers can also be used to test SIDM effects that cannot be modeled with a drag force; as noted by Kahlhoefer et al. (2014), the drag-force model maps well to frequent interactions with low momentum transfer, as in a long-range force.

“Cluster mergers can also be used to test SIDM effects that cannot be modeled with a drag force; as noted by Kahlhoefer et al. (2014), the drag-force model maps well to frequent interactions with low momentum transfer, as in a long-range force.”

• cites Kahlhoefer et al. (2014) sourceSupported

May combine two claims.

The Harvey et al. mass position for DLSCL J0916 south is outside the Dawson (2013) 2-sigma confidence ellipse, although the H15 uncertainties are large enough to encompass the Dawson value.

“While the H15 uncertainties are large enough to encompass the Dawson (2013) value, the H15 mass position is outside the Dawson (2013) 2σ confidence ellipse (the larger dashed ellipse).”

• cites Dawson (2013)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The 1.6 kpc uncertainty in the mean of 72 substructures suggests a sample standard deviation of 13.6 kpc.

“The 1.6 kpc uncertainty in the mean of 72 substructures suggests a sample standard deviation of 13.6 kpc.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The prior becomes more important when interpreting the H15 pdf, because most of its area is at negative cross section.

“The prior becomes more important when interpreting the H15 pdf, because most of its area is at negative cross section.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

Classified as probably not a substantial claim. May combine two claims.

The H15 galaxy position does not look like a galaxy overdensity in color images, and the H15 figure panel lacks green contours at this location.

“The H15 galaxy position does not look like a galaxy overdensity in color images, and even the H15 figure panel lacks green contours at this location (the middle vertex of the triangle).”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

These limits are substantially higher than found by H15 and increase further by about 0.5 cm2/g if one uses only the reviewed subsample of highly weighted subclusters.

“These limits are substantially higher than found by H15 and increase further by about 0.5 cm 2 g -1 if one uses only the reviewed subsample of highly weighted subclusters.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The two results differ only slightly, with peak locations shifted by ≈0.25 cm2/g, or ≈0.6 times the uncertainty given by H15.

“The two results differ only slightly, with peak locations shifted by ≈0.25 cm 2 g -1 , or ≈0.6 times the uncertainty given by H15.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The red solid and dashed curves in Figure 13 are nearly identical; the constraint using the H15 offsets and uncertainties is nearly unaffected by the prior.

“In contrast, the red solid and dashed curves in Figure 13 are nearly identical; this means that the constraint using the H15 offsets and uncertainties is nearly unaffected by the prior, as predicted in the previous paragraph.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

May combine two claims.

Regardless of the prior, using the best available information about each cluster gives m_DM_s < 1.71 cm2/g at 95% confidence for the full sample, or 2.27 cm2/g for the reviewed subsample.

“Regardless of the prior, Figure 13 reveals a dramatic relaxation of upper limits when using the best available information about each cluster: m DM s <1.71cm 2 g -1 at 95% confidence for the full sample, or 2.27 cm 2 g -1 for the reviewed subsample.”

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

May combine two claims.

The corresponding upper limit (at 95% confidence) is 1.71 cm2/g if one adopts a physical prior, or 1.57 cm2/g if one does not.

“The corresponding upper limit (at 95% confidence) is 1.71 cm 2 g -1 if one adopts a physical prior (as we recommend), or 1.57 cm 2 g -1 if one does not.”

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

Probably not a substantial claim: may not pass S3 (load-bearing).

The physical prior will have little effect when using the red likelihood because this likelihood already nearly vanishes for m_DM_s < 0.

“Note that this will have little effect when using, say, the red likelihood in Figure 12, because this likelihood already nearly vanishes for m DM s <0.”

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

May combine two claims.

Both Bullet Cluster substructures are highly weighted in the Harvey et al. analysis: the eastern main subcluster ranks fourth with 6.1% of the total weight, and the western bullet subcluster ranks ninth with 3.8%.

“Both substructures in this system are highly weighted in the H15 analysis: the eastern (main) subcluster ranks fourth with 6.1% of the total weight, and the western (bullet) subcluster ranks ninth with 3.8% of the total weight.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The black peak is shifted from the gray by about twice the uncertainty given by H15, still not highly significant.

“The black peak is shifted from the gray by about twice the uncertainty given by H15, still not highly significant.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Applying the mean Harvey et al. gas mass correction leads to final Bullet Cluster offsets of delta_SI = -4.3 kpc in the east and 21 kpc in the west.

“This correction leads to a final offset of δ SI =-4.3kpc in the east and 21 kpc in the west.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Omission of A2744 west lowered the most likely value of m_DM_s by 0.19 cm2/g, and the update to DLSCL J0916 south raised it by 0.24 cm2/g; other individual updates had at most half this effect.

“The omission of A2744 west lowered the most likely value of m DM s by 0.19 cm 2 g -1 , and the update to DLSCL J0916 south raised it by 0.24 cm 2 g -1 ; other individual updates had at most half this effect.”

May combine two claims.

In four cases the literature is consistent with the offset measured by H15; in five cases there is compelling evidence that the offset differs from that of H15; and in seven cases the H15 substructure either does not exist or does not support a clear association between a gas peak, a mass peak, and a galaxy peak.

“In four cases the literature is consistent with the offset (δ SI ) measured by H15; in five cases there is compelling evidence that the offset differs from that of H15; and in seven cases the H15 substructure either does not exist or does not support a clear association between a gas peak, a mass peak, and a galaxy peak.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Both MACS J2243 subclusters have substantial weight in the Harvey et al. analysis: 4.9% for the east and 3.4% for the west.

“Both subclusters in this system have substantial weight (4.9% for the east and 3.4% for the west), so we treat them together.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The relaxation of upper limits is driven by the data, not the prior: the upper limits change by 0.15 cm2/g or less when dropping the prior for these data.

“This is driven by the data, not the prior: the upper limits change by 0.15 cm 2 g -1 or less when dropping the prior for these data.”

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

May combine two claims.

The dashed gray (H15) curve in Figure 13 indicates 70% confidence that m_DM_s < 0 and 95% confidence that m_DM_s < 0.5 cm2/g with no prior, but the solid curve indicates substantially less confidence in those limits after applying the prior.

“the dashed gray (H15) curve in Figure 13 indicates 70% confidence that m DM s <0 and 95% confidence that m DM s <0.5 cm 2 g -1 with no prior, but the solid curve indicates substantially less confidence in those limits after applying the prior.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionThe authors state this as an assumption: Models with m_DM_s < 0 are not physical.

May combine two claims.

When using the H15 offsets, we find a most likely value of m_DM_s that is slightly higher than, but consistent with, the H15 value.

“when using the H15 offsets we find a most likely value of m DM s that is slightly higher than, but consistent with, the H15 value.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Our updates have modestly reduced the spread of δ_SI values, but many violations of the small-displacement approximation remain.

“Our updates have modestly reduced the spread of δ SI values, but many violations of this approximation remain.”

May combine two claims.

Of the seven H15 substructures we omitted, five had positive offsets in H15, and only two had negative offsets.

“we note that of the seven H15 substructures we omitted, five had positive offsets in H15, and only two had negative offsets.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Some substructures have much more weight than others in the ensemble, and single-band imaging enables errors on individual substructures to be quite large, up to hundreds of kiloparsecs.

“We showed, however, that some substructures have much more weight than others in the ensemble and that single-band imaging enables errors on individual substructures to be quite large, up to hundreds of kiloparsecs.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Harvey et al. analyzed 72 substructures in 30 systems.

“H15 analyzed 72 substructures in 30 systems.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Harvey et al. averaged over 72 substructures and found beta = 0.04 +/- 0.07; negative values are unphysical but indicate that the data are in tension with momentum transfer between DM halos.

“H15 averaged over 72 substructures and found 0.04 0.07; b á ñ = - negative values are unphysical but indicate that the data are in tension with the idea of momentum transfer between the DM halos.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Dawson (2013) found the DLSCL J0916 south offset to be +129 kpc based on the lensing peak alone and +80 kpc after modeling out the gas mass to yield the DM mass alone.

“Dawson (2013) found the offset to be +129 kpc based on the lensing peak alone and +80 kpc after modeling out the gas mass to yield the DM mass alone.”

• cites Dawson (2013)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Although Harvey et al. multiplied Gaussian probability density functions rather than computing a single inverse-variance weighted mean, the effect is the same: substructures with large delta_SG predominantly determine the result.

“Although H15 multiply Gaussian probability density functions (pdf's) rather than compute a single inverse-variance weighted mean, the effect is the same: substructures with large i SG, d predominantly determine the result.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

With the gas-galaxy-DM association itself in question for A2744 northwest, the offsets are not meaningful and the substructure should be omitted from the ensemble.

“With the gas-galaxy-DM association itself in question, the offsets are not meaningful and the substructure should be omitted from the ensemble.”

May combine two claims.

Omitting the A2744 northwest substructure does nothing to loosen the constraints on the self-interaction cross section; the final conclusion that the ensemble constraints are loose owes nothing to this omission.

“For A2744, we reiterate that omitting this substructure does nothing to loosen the constraints on m DM s , quite the opposite in fact.Our final conclusion that the ensemble constraints are quite loose will owe nothing to the omission of this particular substructure.”

May combine two claims.

Because the Dawson (2013) value is supported by multiband selection of lensing sources and member galaxies and by extensive spectroscopy, the paper adopts delta_SI = 80 kpc for DLSCL J0916 south.

“Because the Dawson (2013) value is supported by multiband selection of lensing sources and member galaxies, backed up by extensive spectroscopy, we adopt δ SI =80 kpc.”

• cites Dawson (2013)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Multiband imaging and spectra are necessary to support a strong-lensing analysis, which can locate mass much more precisely than a weak-lensing analysis.

“Multiband imaging and spectra are also necessary to support a strong-lensing analysis, which can locate the mass much more precisely than a weak-lensing analysis.”

May combine two claims.

Discarding the A2744 northwest substructure should strengthen the Harvey et al. case against SIDM, because it is a very highly weighted substructure that, contrary to the H15 ensemble overall, has a DM offset in the direction predicted by SIDM.

“Discarding this substructure should strengthen the H15 case against SIDM, because this is a very highly weighted substructure that-contrary to the H15 ensemble overall-does have a DM offset in the direction predicted by SIDM.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

For most substructures the nominal uncertainty in each offset is 60 kpc, so the uncertainty in the gas mass correction is highly subdominant and is neglected unless otherwise specified.

“For most substructures the nominal uncertainty in each offset is 60 kpc, so the uncertainty in the gas mass correction is highly subdominant and will be neglected unless otherwise specified.”

May combine two claims.

Lensing is sensitive to all forms of mass, not just DM, so the lensing position must be corrected for the gas mass contribution to obtain a position for the DM alone.

“Third, lensing is sensitive to all forms of mass, not just DM, so the lensing position must be corrected for the gas mass contribution to obtain a position for the DM alone.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Multiband data allow better selection of lensing sources and better exclusion of foreground galaxies when mapping the light distribution.

“Multiband data allow for better selection of lensing sources and better exclusion of foreground galaxies when mapping the light distribution.”

May combine two claims.

Many clusters in the Harvey et al. sample violate the assumptions behind the prescription relating offsets to cross sections, so even the revised upper limit should be used with caution.

“Furthermore, many clusters in the sample violate the assumptions behind this prescription, so even this revised upper limit should be used with caution.”

Classified as probably not a substantial claim. May combine two claims.

A520 substructure 2 has no gas peak, which prevents defining any gas-star-DM geometry, so it should be omitted from the catalog.

“However, there is no gas peak in the area.The absence of a gas peak prevents us from defining any gas-star-DM geometry.We therefore recommend omitting this putative substructure from the catalog.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Although the agreement is not perfect, this level of variation is to be expected in independent analyses.

“Although the agreement is not perfect, this level of variation is to be expected in independent analyses.”

Classified as probably not a substantial claim.

H15 found a mass concentration not at the northwest galaxy location, but about 700 kpc away.

“H15 differ starkly in finding a mass concentration not at the northwest galaxy location, but ∼700 kpc away.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

This suggests that our scheme for estimating the weight of each subcluster in the ensemble analysis is effective and that the most important subclusters have indeed been reviewed.

“This suggests that our scheme for estimating the weight of each subcluster in the ensemble analysis is effective and that the most important subclusters have indeed been reviewed.”

Classified as probably not a substantial claim. May combine two claims.

With more smoothing of the light, the luminosity location would be intermediate and the implication for SIDM would be intermediate.

“Or, with more smoothing of the light, the luminosity location would be intermediate and the implication for SIDM would be intermediate.”

May combine two claims.

For MACS J2243 west, the green contours east of the bright star represent a more valid galaxy luminosity position, yielding delta_SI approximately 0 because the galaxy-lensing offset is perpendicular to the galaxy-gas offset.

“The green contours to the east of the bright star in the H15 panel represent a more valid galaxy luminosity position.This yields δ SI ≈0 because the galaxy-lensing offset is perpendicular to the galaxy-gas offset.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Automatically matching the nearest peak may introduce a bias: if the brighter luminosity peak had been adopted, this substructure would have different implications for SIDM, with δ_SI ≈ 50 kpc over a longer (~200 kpc) galaxy-gas baseline providing a great deal of weight.

“Automatically matching the nearest peak may introduce a bias: if the brighter luminosity peak had been adopted, this substructure would have different implications for SIDM, with δ SI ≈50 kpc over a longer (∼200 kpc) galaxy-gas baseline providing a great deal of weight.”

May combine two claims.

The galaxy distribution and X-ray morphology follow the same axis, so there is no reason to doubt the H15 lensing map for MACS J0417.5-1154.

“The galaxy distribution and X-ray morphology follow the same axis, so there is no reason to doubt the H15 lensing map.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

For A520 substructure 3, the literature confirms neither the gas, nor the galaxy luminosity, nor the lensing mass peak, so it is removed from the ensemble analysis.

“In summary, the literature confirms neither the gas, nor the galaxy luminosity, nor the lensing mass peak for this substructure, so we remove it from the ensemble analysis.”

Probably not a substantial claim: may not pass S2 (checkable).

Although few of the H15 offsets are retained, this set of changes is the minimum necessary to bring the H15 offset catalog in line with the literature.

“Although few of the H15 offsets are retained, this set of changes is the minimum necessary to bring the H15 offset catalog in line with the literature.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Even a peak-agnostic algorithm such as a centroid would have a very large associated uncertainty for this substructure, implying that it would have little influence on the ensemble.

“In this situation, even a peak-agnostic algorithm such as a centroid would have a very large associated uncertainty, implying that this substructure would have little influence on the ensemble.”

Classified as probably not a substantial claim.

For A520 substructure 5, lacking a clear association of gas, galaxy, and DM peaks, the paper recommends removing it from the ensemble analysis.

“Lacking a clear association of gas, galaxy, and DM peaks, we recommend removing this putative substructure from the ensemble analysis.”

May combine two claims.

Without a clear X-ray peak along this ridge, there is great uncertainty in the galaxy-gas vector and therefore in the weight this substructure should receive, as well as in the projection of the DM-galaxy vector onto the galaxy-gas vector.

“Without a clear X-ray peak along this ridge, there is great uncertainty in the galaxy-gas vector and therefore in the weight this substructure should receive, as well as in the projection of the DM-galaxy vector onto the galaxy-gas vector.”

Classified as probably not a substantial claim. May combine two claims.

The H15 catalog was produced in a mostly uniform way and uses only ACS data for photometry and lensing, but our corrections are based on a variety of data and analyses from the literature.

“the H15 catalog was produced in a mostly uniform way and uses only ACS data for photometry and lensing, but our corrections are based on a variety of data and analyses from the literature.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The ratio of displacements β cannot remain constant over time, and could even change sign at times.

“Thus, the ratio of displacements β cannot remain constant over time, and could even change sign at times.”

Classified as probably not a substantial claim. May combine two claims.

Of the changes to δ_SI that we recommend, the majority go in the direction of lifting m_DM_s from its H15 value, but the literature on these systems is so compelling that it speaks for itself.

“Of the changes to δ SI that we recommend, the majority do go in the direction of lifting m DM s from its H15 value, but the literature on these systems is so compelling that it speaks for itself.”

• cites H15Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable).

If DM does interact with itself, comparing the two types of cluster constraints could point the way to a particle model of the interactions.

“if DM does interact with itself, comparing the two types of cluster constraints could point the way to a particle model of the interactions.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The analogy between gas and self-interacting DM can break if the gas is completely stripped at pericenter crossing.

“The analogy between gas and self-interacting DM can break in other ways as well, for example, if the gas is completely stripped at pericenter crossing.”

May combine two claims.

Because the maximum galaxy-DM displacement is smaller than the maximum gas-DM displacement, the two components cannot fall through the DM on the same timescale.

“Because the maximum galaxy-DM displacement is smaller than the maximum gas-DM displacement, the two components cannot fall through the DM on the same timescale.”

Classified as probably not a substantial claim.

We have attempted to minimize bias concern by systematically examining the highest-weight substructures rather than the most negative or most suspect offsets.

“We have attempted to minimize this concern by systematically examining the highest-weight substructures rather than the most negative or most suspect offsets.”

May combine two claims.

The ensemble result is driven by substructures that violate the small-displacement approximation, because the weight of each substructure is approximately proportional to δ_SG^2.

“In fact, the ensemble result is driven by substructures that violate the approximation, because the weight of each substructure is approximately proportional to SG 2 d (Equation ( 3)).”