Mauna Kea DM Halo Test

Your question is scientifically real and absolutely in-scope for Mauna Kea class telescopes in principle (halo shapes are tested observationally), but as written it’s still a bit too broad and under-specified to be “proposal-testable” because:

• “dark matter halo shapes” isn’t a directly observed quantity—you infer it via a proxy (weak lensing shear, satellite galaxy distributions, X-ray isophotes, BCG alignment, etc.).
• “outer regions,” “low-density clusters,” and “ΛCDM predicts” need concrete, measurable definitions and a specific metric to compare against.
• The hardest practical issue: weak lensing shape measurements usually need wide-field, deep imaging and lots of background galaxies—depending on what instruments/time you get, that may or may not be feasible.

What you want is to turn this into a single observing program with: a defined sample, a defined observable, a defined statistic, and a falsifiable comparison.

Make it “hyper specific” by locking 6 choices

Here are the decisions that will instantly sharpen it:

1. Pick a mass/richness regime: e.g., galaxy groups / poor clusters: M_{200}\sim 10^{13.5}–10^{14.5} M_\odot.
2. Define “low-density” operationally: e.g., clusters with richness 20<\lambda<40 in redMaPPer, or X-ray luminosity L_X below a threshold, or low galaxy number density within R_{200}.
3. Define “outer regions” numerically: e.g., 0.5R_{200}<R<1.5R_{200} or R_{200}<R<2R_{200}.
4. Choose the observable proxy for shape (this is the biggest one):
   • Weak lensing: ellipticity of the projected mass distribution from stacked shear (most direct for DM, but observationally heavy).
   • Satellite galaxy distribution: ellipticity and alignment of member galaxies as a tracer of halo shape (less direct, but more feasible with smaller datasets).
   • BCG–halo alignment: angle between BCG major axis and inferred halo major axis (measurable from imaging alone if you define how).
5. Choose a single “shape statistic”:
   • Projected axis ratio q=b/a of the halo mass distribution
   • Ellipticity e = 1-q
   • Misalignment angle \Delta\theta between mass major axis and BCG/satellite major axis
6. State the ΛCDM prediction you’re testing in a measurable form:
   • e.g., predicted distribution of q at fixed mass and redshift, or predicted radial trend q(R), or predicted \Delta\theta distribution.
   • Even better: “compare to N-body-only vs hydro predictions” (baryons round halos in the center; outskirts should be closer to N-body).

Example “hyper-specific” versions (pick one style)

Option A: If weak lensing is feasible (most direct DM test)

“Using deep r+i imaging of 8–12 poor clusters at 0.15<z<0.25, measure the stacked weak-lensing quadrupole signal in annuli 0.5R_{200}<R<1.5R_{200} to infer the mean projected halo axis ratio \langle q\rangle. Test whether \langle q\rangle matches ΛCDM N-body predictions for M_{200}\sim10^{14}M_\odot halos within a 95% confidence interval.”

Non-google-able angle: your exact sample, bands, annuli, statistic, and inference pipeline are unique.

Option B: If you mostly have imaging/spectroscopy but not lensing depth

“For 10 low-richness clusters (20<\lambda<40) at z<0.1, measure the ellipticity of the satellite galaxy distribution in R_{200}<R<2R_{200} and test whether the inferred projected axis-ratio distribution is consistent with ΛCDM predictions for halo triaxiality and expected satellite–halo misalignment.”

This is easier observationally, but you must be honest that satellites are an imperfect tracer of DM shape.

Option C: A clean alignment test (often very proposal-friendly)

“Measure the distribution of misalignment angles \Delta\theta between the BCG major axis (from i-band isophotal fits) and the outer satellite distribution major axis (from members in R_{200}<R<2R_{200}) for poor clusters at 0.05<z<0.15. Compare to ΛCDM predicted alignment distributions; test whether the observed \Delta\theta requires more misalignment than simulations predict.”

This becomes a crisp, testable hypothesis about anisotropic assembly and triaxiality.

What I’d ask you (so we can choose the best “instrument-matched” version)

1. What telescope/instrument on Mauna Kea will you actually have access to (Subaru/HSC? Keck? UH 2.2m? UKIRT?) and do you get imaging, spectroscopy, or both?
2. How many nights / total exposure time are you realistically allowed?
3. Are you expected to use new observations only, or can you combine with archival/catalog data for sample selection (often allowed, and makes the question stronger)?

If you tell me the instrument + time + whether lensing-depth is realistic, I’ll help you convert your idea into a one-sentence proposal question + a measurable success criterion (e.g., “constrain \langle q\rangle to ±0.1 in the outskirts” or “detect a nonzero quadrupole at >3\sigma”).

To “earn” telescope time, the question has to look like something you can only answer by taking new data (or at least that new Mauna Kea data is essential), with a clear observing plan, feasibility, and a specific deliverable. Your current dark-matter-halo-shape question can work, but only if you anchor it to an instrument-capable observable.

Big reality check: directly testing DM halo shapes via weak lensing is usually hard to justify for a small student allocation unless you have access to something like Subaru/HSC (wide field, deep) and enough time/sample size. So you should tailor the question to the telescope you can plausibly get time on.

What proposal committees want (and what your question must include)

1. A target list (N objects, coordinates, magnitudes/redshifts).
2. A measurable observable from your data (e.g., resolved shapes, velocity dispersions, line ratios, surface brightness profile).
3. A clear hypothesis test with a metric (e.g., “measure axis ratio q to ±0.05”, “detect anisotropy at >3\sigma”).
4. A time calculator story (exposure time, S/N goal, filters/grating, seeing constraints).
5. Why Mauna Kea specifically (sensitivity/seeing/NIR access/unique instrument).

Reshape your idea into telescope-friendly questions (3 strong directions)

Option 1 (often the most “telescope-time-friendly”): Kinematics of cluster outskirts → halo anisotropy

Core idea: ΛCDM predicts anisotropic infall along filaments; the outer regions should show velocity anisotropy / substructure aligned with the cluster major axis.

Hyper-specific question template

“Do galaxies in the outskirts (1–2R_{200}) of poor clusters show anisotropic infall (velocity gradient or bimodality) aligned with the photometric major axis, as predicted by ΛCDM assembly along filaments?”

What you observe: multi-object spectroscopy of candidate members around a few nearby poor clusters.
Deliverable: member confirmation + velocity field + quantify anisotropy (e.g., Dressler–Shectman substructure statistic, or velocity dispersion as a function of position angle).
Why it earns time: you cannot get those velocities without telescope spectroscopy.

Option 2 (imaging-driven, feasible with modest time): Satellite-shape / alignment in outskirts

Core idea: In ΛCDM halos are triaxial; satellites in the outskirts should preferentially align with the halo/BCG major axis (but the strength is debated—nice test).

Hyper-specific question template

“In 3–5 nearby low-richness clusters, is the satellite galaxy spatial distribution in R_{200}<R<2R_{200} significantly elongated (projected axis ratio q) and **aligned** with the BCG major axis more than random at >3\sigma?”

What you observe: deep, good-seeing imaging (one band can work; two bands helps member selection).
Deliverable: BCG isophotal PA + satellite angular distribution + an alignment p-value.
Why it earns time: you need deeper/sharper imaging than surveys for faint satellites and clean shape measurements.

Option 3 (hardest but “pure DM”): Weak lensing quadrupole (needs Subaru/HSC-scale)

Hyper-specific question template

“Using HSC-like imaging, measure the stacked weak-lensing quadrupole of 10 poor clusters at 0.2<z<0.3 in 0.5–1.5R_{200} and infer the mean projected halo axis ratio \langle q\rangle; compare to ΛCDM predictions.”

Earns time only if: you truly have access to a wide-field imager + enough depth.

How to choose the right version (depends on your Mauna Kea access)

Tell me which of these you’re applying for:

• Subaru/HSC (wide-field imaging; lensing plausible)
• Keck/DEIMOS or LRIS (spectroscopy; kinematics/substructure best)
• UH 2.2m/WFGS or similar (imaging/alignment projects; maybe limited spectroscopy)
• UKIRT (NIR; good for stellar mass selection/dust, less direct for cluster dynamics)

Quick rewrite of your original into a time-allocatable form

Here’s a telescope-time-ready version that keeps your spirit but becomes feasible:

“Do low-richness galaxy clusters show ΛCDM-consistent halo triaxiality signatures in their outskirts, quantified by the alignment between the BCG major axis and the satellite galaxy distribution in R_{200}<R<2R_{200}, using new Mauna Kea imaging to i\sim 24 with <0.8'' seeing?”

That has: sample, observable, radius range, depth/seeing requirement, metric.

I need 3 facts from you to lock this down (and then I’ll write the final proposal question + observing plan skeleton)

1. Which telescope/instrument can you request time on?
2. Roughly how much time (hours/night, number of nights)?
3. Are you allowed to pick nearby targets (say z<0.1) or must they be at some given redshift/field?

Once you answer, I’ll give you 2–3 final “non-google-able” question options tailored to that instrument, each with: target criteria, filters/grating, exposure time logic, and the exact statistic you’ll report.

Yes—the general ideas have absolutely been tested before. Halo triaxiality, satellite alignment, anisotropic infall, weak-lensing ellipticity: all have a literature. That’s normal. What makes a proposal “non‑google‑able” is usually not the phenomenon, but the exact measurement you will do with a specific dataset/instrument, with a specific sample and metric. Committees don’t expect you to discover a brand-new effect; they expect a clean, feasible test that produces publishable-quality (or at least defensible) results.

Also: your original question (“do halo shapes match ΛCDM?”) is so broad that it reads like a review article. The trick is to slice off a narrow, testable corner where (a) existing results are mixed/limited, or (b) your data configuration is genuinely new (depth, wavelength, redshift range, low-richness regime, outskirts only, etc.).

Here are concrete ways to make it “not already done” in the way your proposal needs:

6 levers that create novelty (even if concept is known)

1. Regime novelty: focus specifically on poor clusters / groups (low mass) rather than massive relaxed clusters. Lots of shape work is biased to massive systems because they’re easier.
2. Radial novelty: many constraints are stronger in cores; you can target R_{200}–2R_{200} where contamination and infall matter and predictions depend on assembly.
3. Redshift novelty: pick a narrow z slice where existing samples are thin, or intentionally go very nearby so you can resolve faint satellites better.
4. Wavelength/selection novelty: use NIR (UKIRT) to select satellites by stellar mass with less dust/star-formation bias; or use a very specific two-color cut to reduce interlopers.
5. Statistic novelty: don’t just measure “alignment exists.” Measure something sharper like:
   • the misalignment distribution P(\Delta\theta) in the outskirts only,
   • the radial trend \Delta\theta(R),
   • difference between star-forming vs quiescent satellites (two populations, same halos).
6. Controlled sample novelty: “low-density” needs an operational definition. You can define a clean subset (e.g., low X-ray luminosity but with a dominant BCG; or systems with no major substructure by a specific test) and compare to a contrasting subset.

A proposal-safe way to phrase “novel” without overclaiming

Avoid “this has never been done.” Instead say:

• “Existing studies focus on high-mass / inner radii / mixed samples; we will measure X in Y regime with Z instrument.”
  That’s honest and reads professionally.

Example non-google-able questions that are narrow enough to justify telescope time

Pick an instrument track:

If you can do spectroscopy (Keck/DEIMOS-type)

“In three low-richness clusters at 0.05<z<0.10, is the velocity field of confirmed members in 1–2R_{200} anisotropic with respect to the BCG major axis, quantified by \Delta\sigma_v(\phi) and a Dressler–Shectman substructure test, at >3\sigma?”

Novelty can be: outskirts-only + poor clusters + confirmed membership with your own redshifts.

If you mostly have imaging (UH 2.2m / Subaru imaging but limited time)

“Using new r+i imaging reaching i=24, what is P(\Delta\theta) between the BCG major axis and the satellite distribution in R_{200}<R<2R_{200} for 5 poor clusters at z\sim0.08, split by satellite color (red vs blue)?”

Novelty: explicit outskirts, explicit depth/seeing, explicit split by population.

If you truly have wide/deep imaging (Subaru/HSC-level)

“Measure the stacked weak-lensing quadrupole in 0.7–1.7R_{200} for 8 low-richness clusters at 0.2<z<0.3 and infer \langle q\rangle; test whether \langle q\rangle differs from ΛCDM N-body expectations by >0.1.”

Novelty: low-richness + outer annulus + explicit effect size.

Key point: “already tested” isn’t the killer—feasibility is

Committees reject projects that (a) need huge samples, (b) rely on hard systematics, or (c) don’t specify the measurement. If we tailor your question to the exact telescope/instrument/time, it becomes both feasible and “yours.”

Tell me which telescope/instrument you’re applying for and how much time you can plausibly request. Then I’ll give you 2–3 final question statements that:

• clearly reuse known theory,
• but are new-data-dependent,
• and have a tight observing plan + success metric.

If you truly can request any Mauna Kea telescope with no time constraint, you can afford to ask a more “ΛCDM-level” question—but you still need to make it proposal-realistic: pick one facility + instrument mode and design a program that produces a specific dataset and statistic.

Also, the “non‑google‑able” part is easiest if you commit to a very specific, pre-registered measurement (sample definition + radial range + statistic + comparison simulation). People can google “halo shapes,” but they can’t google your exact “8 clusters, 0.18<z<0.25, HSC grizy, quadrupole shear in 0.8–1.6R_{200}, compare to IllustrisTNG vs dark-matter-only.”

Best high-impact version on Mauna Kea (Subaru/HSC): weak lensing halo ellipticity in outskirts

This is the cleanest “real DM shape” test because it measures the mass distribution more directly than satellites/X-ray.

Hyper-specific question (strong proposal form):

Do low-richness clusters (20<\lambda<40) at 0.15<z<0.30 have a mean projected dark-matter halo axis ratio \langle q\rangle in the outskirts (0.8R_{200}<R<1.6R_{200}) consistent with ΛCDM predictions, as inferred from the stacked weak-lensing quadrupole shear measured with Subaru/HSC grizy imaging?

What makes it “hyper specific” (and not google-able):

• Exact richness + redshift slice (your sample)
• Exact radial annulus (outskirts only, avoids baryon-dominated centers)
• Exact statistic: stacked quadrupole shear → \langle q\rangle
• Exact instrument + bands: HSC grizy for shapes + photo-z background selection
• Exact comparison: pick a specific simulation suite (e.g., dark-matter-only vs hydro) and a specific predicted \langle q\rangle(M,z)

One-sentence falsifiable claim you can put in the proposal:

“We will test whether \langle q\rangle_{\mathrm{obs}} differs from ΛCDM expectations by \Delta q \gtrsim 0.1 in 0.8–1.6R_{200} for poor clusters.”

Two equally valid alternatives (if you want novelty/feasibility differentials)

Alternative A (Keck/DEIMOS): dynamical anisotropy in cluster infall regions

Question:

Is the infall region (1–2.5R_{200}) of poor clusters kinematically anisotropic in a way consistent with ΛCDM filamentary accretion, measured via member galaxy redshifts and a position-angle–dependent velocity dispersion \sigma_v(\phi)?

This earns time because it’s impossible without a big spectroscopy dataset; it’s also less “direct DM shape” and more “assembly geometry,” but still fundamentally ΛCDM structure growth.

Alternative B (Subaru/FOCAS or imaging): satellite alignment as a tracer of halo triaxiality

Question:

In low-richness clusters at z<0.1, does the satellite distribution in R_{200}<R<2R_{200} show a misalignment-angle distribution P(\Delta\theta) with the BCG that matches ΛCDM predictions, split by satellite color (quenched vs star-forming)?

This is observationally simpler than lensing (but less direct).

How to make your original sentence proposal-ready (a fill-in template)

Replace vague nouns with numbers + methods:

1. Sample: “N=__ clusters with M_{200}=__, z=__, selected by __”
2. Outer region: “R=__–__ R_{200}”
3. Observable: “weak lensing quadrupole / member velocities / satellite ellipticity”
4. Statistic: “\langle q\rangle / P(\Delta\theta) / \sigma_v(\phi)”
5. Model comparison: “compare to __ simulations, matched in mass and redshift”
6. Decision rule: “inconsistent if difference >__ or rejected at p<__”

Quick question for you (so I can lock the best version)

Do you want the project to be primarily:

1. Imaging + weak lensing (most “DM shape” direct; Subaru/HSC), or
2. Spectroscopy (Keck/DEIMOS; assembly/anisotropy), or
3. Imaging-only (alignment/satellites; easiest to execute)?

Pick one, and I’ll give you a final, polished 1–2 sentence question plus a short “Observing Plan” paragraph that sounds like a real Mauna Kea Scholars proposal.

Good—Subaru/HSC (or CFHT-class wide-field, but on Mauna Kea it’s HSC) is the right match for imaging + weak lensing, especially if you care about halo shapes in the outskirts. Now you need to make the question hyper-specific in a way that (1) is clearly measurable with your data and (2) can’t be answered by citing a single existing paper because it’s tied to your target definition, radial range, and statistic.

Your refined, telescope-time-worthy question (pick one of these)

Version 1 (cleanest “shape” test; proposal-ready)

Do low-richness clusters (20<\lambda<40) at 0.20<z<0.35 have a mean projected dark-matter halo axis ratio \langle q\rangle in the outskirts (0.8R_{200}<R<1.8R_{200}) consistent with ΛCDM, as inferred from the stacked weak-lensing quadrupole shear measured with Subaru/HSC grizy imaging?

Why this is hyper-specific: it nails the sample, redshift, radial annulus, instrument, bands, and the statistic (quadrupole shear → q).

Version 2 (even more “non-google-able”: radial trend, not just one number)

Is the radial trend of halo ellipticity q(R) from 0.5R_{200} to 2R_{200} in low-richness clusters at 0.20<z<0.35 consistent with ΛCDM predictions, using HSC stacked shear quadrupole measurements in 3–4 fixed annuli?

This is harder but more distinctive: you’re not just measuring “a shape,” you’re measuring how it changes with radius.

Version 3 (adds a sharp secondary test: alignment)

Does the weak-lensing–inferred halo major axis align with the BCG major axis in the outskirts (0.8–1.8R_{200}) at the level predicted by ΛCDM, quantified by the misalignment distribution P(\Delta\theta) for low-richness clusters at 0.2<z<0.35?

This gives you two deliverables: axis ratio and alignment, both from imaging.

Make it “hyper specific” in 5 concrete commitments

To fully lock it down for a proposal, you should commit to:

1. Cluster selection source + cut
   Example: “redMaPPer clusters with 20<\lambda<40, 0.20<z<0.35, excluding obvious mergers (centroid offset > X or richness map asymmetry).”

2. Background galaxy selection rule (crucial for weak lensing)
   Example: “background galaxies with photo-z such that z_s > z_l + 0.1 (or z_s > 1.2z_l), shapes measured in i-band; use grizy for photo-z.”

3. Exact annulus/outer-region definition
   Example: “primary measurement in 0.8–1.8R_{200}” (outer enough to reduce baryonic rounding, inner enough to keep signal).

4. Exact shape estimator
   Say explicitly: “fit an elliptical NFW (or elliptical surface density) model to the stacked tangential + cross shear including the quadrupole term,” and report \langle q\rangle with uncertainty.

5. Simulation comparison you’ll use
   Example: “compare to predicted \langle q\rangle(M,z) from a specific ΛCDM simulation suite (DM-only and hydro) matched to the same mass/richness and redshift distribution.”

That last piece is what turns “ΛCDM predicts…” into something graders can’t dismiss as hand-wavy.

A polished final one-sentence question (what I’d put at the top of the proposal)

If you want one “final” version, I’d use:

Using Subaru/HSC grizy imaging, do low-richness clusters (20<\lambda<40) at 0.20<z<0.35 have a mean projected halo axis ratio \langle q\rangle in 0.8R_{200}<R<1.8R_{200} consistent with ΛCDM, as measured from the stacked weak-lensing quadrupole shear signal?

One thing to be careful about (so you don’t get shot down)

If the committee thinks you’re proposing to observe hundreds of clusters from scratch, they’ll reject it. Phrase it as either:

• (A) Targeted deep imaging of a small sample (if you really mean new observations), or
• (B) A calibration/deeper follow-up program for a subset that complements existing HSC-depth data (often seen as sensible).

Two quick questions so I can tailor it to your exact proposal format

1. Are you allowed to use an existing cluster catalog for selection (e.g., redMaPPer), or must everything come purely from your new observations?
2. Do you want to measure (i) just \langle q\rangle, or (ii) \langle q\rangle plus alignment P(\Delta\theta), or (iii) a radial profile q(R)?

My “second question” was: Do you want to measure just one halo-shape number, or also measure alignment, or even a radial trend? I asked because each option changes what data you need, what analysis you do, and how easy it is to justify telescope time.

What the three options mean (in plain terms)

1. Just \langle q\rangle (simplest, cleanest)

• Goal: Get one headline result: the mean projected axis ratio q=b/a of the dark matter halo in a chosen “outer” radial range.
• What you actually measure: the weak-lensing shear pattern around clusters; an elliptical mass distribution produces a detectable quadrupole (direction-dependent) shear signal.
• Why it’s good: easiest to sell and hardest to misunderstand.
• What you can claim: “Halos in the outskirts are rounder/flatter than ΛCDM predicts” (or consistent).

2. \langle q\rangle + alignment P(\Delta\theta) (still doable, adds an extra ΛCDM test)

• Goal: Measure halo shape and whether the halo’s major axis points the same direction as the BCG major axis (brightest cluster galaxy).
• Observable: You measure BCG position angle from imaging, then see whether the lensing quadrupole prefers that same axis. The key output is the misalignment angle \Delta\theta distribution or at least its mean/width.
• Why it matters: ΛCDM predicts alignments (with scatter) tied to anisotropic accretion; baryons can change inner alignment, but outskirts should track the DM better.
• Cost: requires careful systematics control (PSF anisotropy, centroiding, BCG PA measurement), but it’s very proposal-friendly because it’s a crisp statistic.

3. Radial profile q(R) (most distinctive, most demanding)

• Goal: Instead of one averaged shape, ask: does the halo get rounder or more elongated from inner to outer radii?
• How you do it: measure the quadrupole shear in multiple annuli (e.g., 0.5–0.8R_{200}, 0.8–1.2R_{200}, 1.2–1.8R_{200}).
• Why it’s harder: dividing into bins reduces S/N, so you need more clusters and/or deeper imaging.
• Why it’s cool: it’s harder to “google-answer” because it’s a very specific diagnostic and is closer to a decisive model comparison.

So my “second question” is really: what level of ambition do you want, given that weak lensing is signal-starved and more bins/metrics = more time/sample/systematics?

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If you can’t rely on an existing cluster catalog: what changes?

You can still do weak lensing, but you must (a) define targets and (b) know their redshifts/masses well enough to define R_{200} or at least a consistent radial scale.

Here are the realistic paths:

1. Use a catalog (best if allowed):
   Select clusters with known centers + redshifts + richness proxy, then spend telescope time on deep imaging optimized for shapes and background selection.

2. If catalogs are not allowed, do “self-contained” targeting: pick a small number of known bright clusters with well-established redshifts from the literature (this is still “a catalog,” just not a survey catalog), then your new data is the lensing imaging.
   This is usually acceptable unless they explicitly forbid any prior target knowledge, which would be unusual.

3. If they truly want everything from new observations: you’d need a two-stage program:

   • identify clusters in wide imaging (or via an initial set of exposures),
   • then do deep follow-up for lensing,
   • plus some redshift confirmation (photometric redshifts might suffice at a basic level, but proposals like having at least a plan).

That’s a lot, even with “no time constraints,” because it’s conceptually complex.

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Two quick checks that will determine the best framing

1. When they say “non-google-able,” do they mean “no one has ever asked this” (rare/usually impossible) or “you can’t answer it without your own data/analysis” (much more common)?
2. In your class/program, are you expected to take new observations of specific targets, or can your “observing” be partly archival with new analysis?

If you paste the exact assignment sentence about “non-google-able” + telescope time, I’ll translate it into what reviewers are actually looking for and help you choose between (1) \langle q\rangle, (2) \langle q\rangle+alignment, or (3) q(R).

With ~2 hours of telescope time, a full weak-lensing halo-shape test (quadrupole shear → \langle q\rangle) is possible only if you leverage existing deep imaging (e.g., HSC survey data) and use your 2 hours for something targeted (calibration or a small, high-leverage add-on). If your 2 hours must produce the main lensing dataset from scratch, that’s realistically too little time for a convincing halo-ellipticity measurement, because weak lensing needs lots of background galaxies (depth) and excellent PSF control across a wide field.

So the “telescope-time-earnable” way to keep imaging + weak lensing is to frame your proposal as a pilot + feasibility test with a very specific, measurable success criterion.

A telescope-time-plausible weak-lensing question (pilot scale)

Here’s a version that fits 2 hours and still tests ΛCDM in a meaningful way:

Pilot test: For one nearby low-richness cluster (0.05<z<0.10), can we detect a non-zero stacked weak-lensing quadrupole signal in the annulus 0.8–1.6R_{200} using Subaru/HSC i-band shapes plus gr colors for background selection, and infer a constraint on projected halo axis ratio q at the \sigma_q \lesssim 0.2 level?

Why this works: you’re not promising a definitive cosmology result; you’re promising a measurable constraint (or an upper limit) on halo ellipticity with a small, tightly defined dataset.

What you’d actually do in 2 hours (observing plan that sounds real)

1. Choose 1 cluster with a well-known redshift and center (BCG), ideally already in a field with good ancillary data. (If catalogs are allowed, pick one with known richness/mass proxy.)
2. Observe in i band (best for shape measurements; stable PSF, lots of galaxies).
3. Add g and/or r for basic color separation (background vs cluster members), unless you can rely on existing multi-band photometry.
4. Keep the plan simple: e.g., i: ~70–90 min total, g/r: ~15–25 min, rest overheads/dithers/standard star if needed.

Your analysis time (unlimited) then goes into PSF modeling, shear measurement, background selection, and fitting an elliptical mass model.

If catalogs are not allowed, you can still do this—but you must pick a “known cluster”

Even if they say “no existing catalogs,” you can still target a famous, well-studied nearby cluster (Coma, Virgo, Perseus, etc.). That’s not “google-able” in the sense of the answer—your data and measurement are unique. The “non-google-able” part becomes: “with these exposures and this pipeline, what constraint do we get on q?”

The key move: define a success metric that 2 hours can achieve

Pick one of these and put it explicitly in the proposal:

• Detection goal: detect lensing tangential shear at >X\sigma and quadrupole at >Y\sigma in 0.8–1.6R_{200}
• Constraint goal: achieve \sigma_q \lesssim 0.2 on q (pilot-level)
• Model test goal: rule out “very elongated” halos q<0.5 (example) at 95% confidence for that system / for a stacked mini-sample if you can squeeze 2–3 targets

One quick clarification that changes everything

When you say “imaging + weak lensing,” do you have access to Subaru/HSC specifically, or is your 2 hours more like a smaller telescope imager (UH 2.2m, etc.)?

• If HSC: a 2-hour pilot constraint is plausible.
• If not HSC (narrower field / less depth): weak lensing becomes very tough; you may need to pivot to a question that uses imaging but not lensing.

Tell me which instrument you’re likely to use (HSC vs something else), and whether your instructor allows using archival multi-band photometry for background selection. Then I’ll give you a final one-sentence question + a concrete 2-hour exposure plan (filters, time split, and what you can claim statistically).

z, \lambda, and R_{200} are just compact ways astronomers specify (1) distance/epoch, (2) cluster “richness” (how many member galaxies), and (3) a physically meaningful cluster size scale. The numbers I suggested were example ranges that tend to make a weak-lensing project more feasible and interpretable—here’s what each means and what “good numbers” look like for a 2‑hour imaging+lensing pilot.

1) 0.05<z<0.10: what it means + good values

• z is redshift: how much the universe has expanded since the light left the cluster. Bigger z = farther away (and generally earlier in cosmic time).
• Rough intuition:
  • z=0.05 is “nearby” (a few hundred Mpc).
  • z=0.10 is still nearby/moderate.

Why this matters for weak lensing in 2 hours

• If the lens (cluster) is too close (z\lesssim 0.03): the cluster looks huge on the sky, its outskirts cover a very large area, and you’ll struggle with field-of-view and defining a clean background.
• If it’s too far (z\gtrsim 0.4): you need deeper imaging to get enough well-measured background galaxy shapes and good photo-z separation.

Good pilot range: z \approx 0.15–0.30 is often a sweet spot for lensing if you have multiband imaging for background selection (because lensing efficiency is good and clusters aren’t absurdly huge on the sky).
Good “play it safe with background selection” range: z \approx 0.1–0.25.

So: my earlier 0.05–0.10 is fine for “nearby cluster imaging”, but for weak lensing you might actually prefer 0.15–0.30 depending on instrument depth and whether you have good color/photo-z info.

2) 20<\lambda<40: what it means + good values

• \lambda is richness: basically “how many likely member galaxies does the cluster have,” defined by a specific cluster-finding algorithm (most famously redMaPPer). Bigger \lambda correlates with bigger mass.

Why it matters

• Weak lensing signal scales with mass. Higher \lambda → stronger shear → easier detection in a short program.
• But very high richness clusters can be rarer, more complex (mergers), and sometimes less “low-density/poor.”

Good numbers:

• If you truly want “poor clusters / low richness”: \lambda \sim 20–40 is reasonable.
• If your priority is detectability in a 2-hour pilot: consider \lambda \sim 40–80 (still not the richest monsters, but noticeably more lensing signal).
• If you’re doing a stacked study across many clusters, low richness is ok; for one or two clusters, higher richness is your friend.

If you’re not sure you can use catalogs, you can still use the concept: “select a cluster with mass roughly M_{200}\sim 10^{14}–10^{15}M_\odot”—you just won’t phrase it in \lambda.

3) 0.8R_{200}<R<1.8R_{200}: what it means + good values

• R is projected distance from the cluster center.
• R_{200} is a standard “radius of the cluster” definition: the radius inside which the average density is 200× the critical density of the universe. Think of it as close to the “virial” region size.

Why use radii in units of R_{200}?
Because different clusters have different physical sizes. Using R/R_{200} lets you compare apples-to-apples.

Why that particular range?

• Inner region (<0.5R_{200}): baryons, BCG light, and complicated physics can bias “shape”; also strong lensing/substructure.
• Outskirts (\sim R_{200} to 2R_{200}): closer to where ΛCDM-only predictions (triaxial dark halos, anisotropic accretion) are more directly relevant, but signal is weaker.

Good numbers for a 2-hour pilot:

• If you want a compromise between signal strength and “outskirts”: 0.5–1.5R_{200} is often more feasible than 0.8–1.8R_{200}.
• If you specifically care about “outer” shapes and can accept lower S/N: keep 0.8–1.8R_{200}.

Also practical note: to measure shear in 1–2R_{200}, your camera needs enough field of view to cover those radii plus background region. This is another reason HSC (wide-field) matters a lot.

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A practical set of “good” ranges for your situation (2 hours, imaging + weak lensing)

If you want a version that’s both defensible and feasible:

• Redshift: 0.15<z<0.30
• Richness/mass proxy: \lambda \gtrsim 40 (or “massive enough to have a clear lensing detection”)
• Radial range: 0.5R_{200}<R<1.5R_{200} (or two annuli: 0.5–1.0, 1.0–1.5)

That combination gives you a better chance of detecting something with limited exposure time, while still being “outer-halo-ish.”

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One thing I need from you to give exact recommended numbers

Which imager are you actually planning to request on Mauna Kea—Subaru/HSC, or something else? Field of view and depth completely change what redshift and radial range are “good.” If it’s HSC, I’ll give you concrete target-selection cuts (redshift, richness) that are realistically workable for a 2-hour pilot.

Use 0.15<z<0.30 for an HSC weak-lensing project, especially with only ~2 hours.

Here’s the logic in the exact terms that matter for feasibility and for your proposal write-up:

Why 0.15<z<0.30 is better (for weak lensing with HSC):

• Lensing efficiency: The shear signal for background galaxies is generally strong for lenses around z\sim0.2–0.3 because you still have lots of background sources at higher z, and the geometry boosts the signal. At very low z (0.05–0.10), the lens is so close that the lensing “lever arm” is not as favorable and you more easily run into selection/geometry limitations.
• Field-of-view vs cluster angular size: Low-z clusters are huge on the sky. Even with HSC’s wide field, the outskirts \sim 1–2R_{200} can spread across a big chunk of the camera, and defining a clean “background” region becomes trickier (you want area beyond the cluster to estimate shape/foreground systematics).
• Background galaxy selection: At z\sim0.2–0.3, using HSC multiband grizy you can do a cleaner “background cut” (via photo-z or color cuts). At very low z, the cluster and foreground/background separation can be OK, but your analysis can become dominated by huge-area systematics rather than raw depth.

When 0.05<z<0.10 would be the better choice:

• If your project were primarily resolved satellite galaxy science (membership, morphology, tidal features) rather than lensing, low z is great.
• Or if the assignment strongly prioritizes “simple conceptually” over “best lensing geometry,” and you want very nearby, well-known targets.

Recommendation (what I’d put in the proposal)

• Choose 0.15<z<0.30 as your main redshift window.
• Narrow it further if you want to be extra “hyper-specific,” e.g. 0.20<z<0.30.

A clean final phrasing could be:

“We will target N=1–3 clusters at 0.20<z<0.30 to measure the stacked weak-lensing quadrupole shear in 0.5–1.5R_{200} and constrain the mean projected halo axis ratio \langle q\rangle.”

If you tell me whether you’re planning 1 cluster deep or 2–3 clusters shallower, I’ll suggest the tighter redshift cut and a realistic filter/time split (e.g., mostly i for shapes + enough color for background selection).

Very specifically, with Subaru + HSC and your stated constraints, the new data you gather is wide-field, dithered imaging (mostly i-band) of one known cluster field (plus calibrations). That imaging becomes (after reduction) a calibrated coadd image + per-exposure images + catalogs that let you measure galaxy shapes and compute a shear field; then you extract the quadrupole (elliptical) component of the shear in your chosen radial annulus. Below is a concrete, proposal-ready “what we will obtain” list.

1) Target you observe (what’s on-sky)

• One low-richness cluster with:
  • known redshift in your chosen window (e.g., 0.15<z<0.30),
  • a well-defined center (BCG position and/or X-ray/SZ center if available),
  • low Galactic extinction and not crazy crowded with bright stars (helps shape measurements).
• Field coverage: you will observe the cluster and its outskirts within HSC’s \sim 1.5^\circ diameter field, which is crucial for getting shear in 0.8–1.8R_{200} and having surrounding area for systematics checks.

2) Science exposures you will take (the actual photons you gather)

Primary dataset (must-have)

A dithered HSC i-band imaging sequence of the cluster field

• Filter: HSC-i (effective \sim 770 nm, as you wrote)
• Purpose: shape measurements (the lensing shapes are usually taken from a single “best shape band,” often i because it’s deep with good seeing and high source density)
• Total open-shutter time: 70–90 minutes in i-band
• Exposure pattern: many shorter exposures rather than a few long ones, e.g.
  • N \approx 10–18 exposures of 300–450 s each (exact numbers depend on overheads and seeing)
• Dithers: a designed dither pattern (arcmin-scale offsets) to:
  • fill chip gaps,
  • average down flat-field/PSF systematics,
  • improve cosmic ray rejection and astrometric robustness.

Optional add-on dataset (only if you truly need it and time allows)

Short g and/or r imaging for crude color separation

• Filter(s): HSC-g and/or HSC-r
• Purpose: help separate likely cluster members from background sources if you don’t have reliable multi-band photometry/photo-z from existing data.
• Open-shutter time: think 5–15 minutes per filter (you’re not going deep; you’re adding just enough color leverage to reduce contamination).
• Note: If you can rely on existing grizy or photo-z catalogs for the field, you may skip new g/r entirely and spend the full 2 hours optimizing i-band depth/seeing.

3) Calibration data you will gather (what your observing block includes)

These are typically taken as part of the instrument/observatory calibration plan, but in a proposal you should state you will use them:

• Bias and flat fields (usually provided by the facility / taken in calibration time)
• Standard star / photometric calibration strategy
  • Often HSC pipelines tie photometry/astrometry to external reference catalogs (Gaia, PS1), but you should mention you’ll use standard calibration products + survey ties.
• Seeing/PSF monitoring is inherent in the data: the PSF is measured from stars across the HSC field on each exposure.

4) What the reduced “data products” are (what you will end up with)

From your observing run, after reduction you will have:

1. Per-exposure calibrated images (detrended, astrometrically and photometrically calibrated).
2. A deep i-band coadd image of the full HSC field for detection/visual checks.
3. A star catalog across the field for PSF modeling.
4. A galaxy catalog including:
   • positions,
   • magnitudes,
   • shape measurements (ellipticities) from the i-band exposures (ideally on single-epoch images, because coadds can complicate PSF),
   • quality cuts (S/N, size relative to PSF, flags).
5. A background-source-selected catalog (either via:
   • existing photo-z information, or
   • your new g/r colors + existing catalogs to impose a background cut).
6. A shear catalog / shear map around the cluster: estimates of tangential + cross shear as a function of radius and position angle.

5) What you will compute from that data (the specific lensing measurement)

Even with one cluster, “stacked” can mean either:

• Stacking sources in azimuthal/angle bins around the cluster (common for a single system), and/or
• stacking multiple clusters (not possible with only one new pointing unless you use archival for others).

Your core observable will be:

• Quadrupole shear signal in the annulus 0.8R_{200}<R<1.8R_{200}:
  you bin shear by position angle around the cluster center and fit for a \cos(2\phi)-type component (the hallmark of ellipticity).
• From that, you infer a constraint on projected axis ratio q=b/a (or ellipticity e=1-q) under an assumed mass model (e.g., elliptical NFW or an empirical quadrupole model).

6) Exactly how your 2 hours fits the “pilot + leverage existing data” story

A clean way to state it:

• New HSC i-band imaging (70–90 min open shutter) provides high-quality shapes under your control (seeing, dithers, depth).
• Existing grizy and/or photo-z (if available for your target) supplies the heavy lift for background selection and boosts credibility.
• Your deliverable is a pilot constraint (or upper limit) on the quadrupole shear / \langle q\rangle, plus a feasibility assessment for expanding to a larger sample.

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Small but important correction to your wording

If you truly observe only 1 cluster, you shouldn’t call the lensing “stacked across clusters.” Call it:

• “azimuthally stacked” or “angle-binned” weak lensing around one cluster, or
• “a pilot measurement to be combined with archival clusters for a stacked sample.”

That keeps the proposal logically tight.

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To make this airtight, I need one decision from you

Will you assume existing multi-band photometry/photo-z for background selection, or do you want your 2 hours to include your own g/r imaging?

• If yes existing: best use of time is all-in on i-band depth/seeing.
• If no existing allowed: you should reserve at least ~10–20 min for g and/or r, and (honestly) your background selection will still be a weak point without deeper multi-band.

If you tell me which of those is allowed, I’ll write you a tight “Observations” paragraph with an explicit exposure breakdown (e.g., 12\times 360 s in i + 4\times 180 s in r, dithers, and expected depth/seeing assumptions).

Raw data (simple statement):
A set of dithered HSC i-band CCD exposures (individual FITS images) of one galaxy-cluster field—each exposure contains pixel counts (ADU) vs. x–y position, plus the FITS headers (time, pointing/WCS, airmass, etc.)—along with standard calibration frames/products (biases, flats, and usually PSF/astrometric/photometric calibration references).

If you also take color data: a smaller set of HSC g- and/or r-band FITS exposures of the same field, taken with the same kind of dithering.

With HSC you’re looking at optical wavelengths. Since you said your primary configuration is i-band (770 nm), that’s your main wavelength.

Here are the relevant HSC filters and their approximate central wavelengths (good enough for a proposal-level statement):

• g-band: \sim 480 nm (blue-green optical)
• r-band: \sim 620 nm (red optical)
• i-band: \sim 770 nm (red/near‑IR edge of optical)
• z-band: \sim 890 nm (very red optical)
• y-band: \sim 970 nm (near‑IR edge; just under 1 micron)

So if you observe only i-band, you’re mainly probing light around 0.77 microns. If you add g or r for color separation, you’re adding coverage around 0.48 µm and/or 0.62 µm.

If you want, I can help you write a single sentence like: “We will obtain deep imaging at \lambda \approx 0.77,\mum (HSC-i), with optional \lambda \approx 0.48–0.62,\mum (HSC-g/r) for color-based background selection.”