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Discovering Undercooked Galaxies using Satellite Galaxy Counts

Yi-Lun Hsu (NTHU)

Supervisor: Prof. Andrew Cooper (NTHU)

2026 TARA Summer Student Program - Final Presentation

2026.08.31 @ NTHU

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Introduction

What is an ”Undercooked" Galaxy?

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Stellar Mass–Halo Mass Relation

Stellar Mass–Halo Mass Relation (SMHM) average is well-known.
Galaxy formation mechanism

Small DM halo: supernovae
Big DM halo: SMBH

The scatter in undercooked region?

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Universal Baryon

Fraction ~ 17.1%

This figure illustrates the Galaxy-Halo Connection, which is the most fundamental concept in galaxy evolution

and serves as the primary motivation for our research.

As we can see, star formation efficiency is not a constant; rather, it is highly dependent on the dark matter halo mass:

First, around 1012M⊙(ten to the twelfth): Where the Milky Way is located, star formation reaches its peak efficiency.
At the low-mass: The curve drops steeply. The cold gas of these small galaxies can be easily blown out by supernova feedback.
Conversely, at the high-mass end: The curve flattens out because AGN feedback from the central SMBH prevents gas from cooling.

Because of these drastic variations, understanding the scatter—especially in the undercooked region—is crucial for testing our cosmological models.

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Galaxies here are closest to the 100% theoretical limit line, successfully converting about 17% of their available gas into stars.

Gray line: conversion of 100%t of available baryons to stars

The average relationship between stellar mass and halo mass is well understood, but the scatter of galaxies around the average is still constrained by observations.

How much spread is there in the stellar masses of galaxies at a fixed halo mass, and what is the physical reason for that spread?

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Stellar Mass–Halo Mass Relation

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Simulations of the accreted stellar haloes of low-mass field galaxies (Cooper et al., 2025)

This is a recent simulation work.

We see the standard relation as the purple median band.

And look below, you will notice a significant downward scatter, highlighted in red.

These points reveal a fascinating theoretical prediction: there exists a population of 'undercooked' or 'failed' Milky Ways.

Therefore, our research targets host galaxies that are fainter than the Milky Way in this region.

However, confirming the true halo mass of such faint galaxies observationally has always been a challenge, because the DM is invisible.

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左圖 (Left Panel) ——「標準規律」：

中央主星系的恆星質量與暗物質暈質量關係。With abundance matching.

紫色的帶狀區是標準模型（Behroozi+ 2019）。在（銀河系質量，橘色星星）附近，星系造星效率最高。太大或太小，造星效率都會因為黑洞反饋（AGN）或超新星反饋（SN）而降低。這是一切比較的基準。

中圖 (Central Panel) ——「衛星星系」：

黑點變得極度發散，且完全掉到紫色標準帶的左下方。衛星星系掉入主星系後，暗物質暈被「潮汐剝離（Tidal Stripping）」扯碎（往左移），氣體被吹走導致「淬滅（Quenching）」，恆星無法增加。這證明了環境會嚴重破壞星系-暗物質暈的連結。

右圖 (Right Panel) ——「異常者（我們的目標）」：

在「銀河系質量區間」的局部放大圖。

把目光聚焦在紫色標準帶「下方」的極端異常區

淺藍色方形 (Cyan points, Zaritsky & Behroozi 2023)

測光學（Photometry）與星系尺寸，套用經驗公式「間接推測」它們擁有巨大的暗物質暈。

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Approach

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Aquarius Project (Springel et al. 2008)

Halo Occupation Distribution (Guo et al. 2016)

So, how do we weigh the dark matter halo?

The solution is: Counting Satellite Galaxies

In the CDM (Cold Dark Matter) paradigm, the abundance and kinematics of satellite galaxies are strictly governed by the host's halo mass.

�Based on this rule, we established our core approach:

We use the number of satellites to estimate the Dark Matter Halo Mass,

and use the host galaxy's magnitude to estimate its Stellar Mass.

By cross-comparing these two, we can find our targets: the visually faint central galaxies that are surrounded by an abnormally rich satellite populations.

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On the left, the Aquarius dark matter simulation proves that sub halo count is proportional to host halo mass.

On the right, the Halo Occupation Distribution model confirms this for luminous satellites.

我們如何測量看不見的暗物質暈質量？這兩張經典圖表給了我們解答。

在 CDM 理論中，衛星星系的豐度（Abundance）與動力學，是檢驗暗物質暈質量最嚴格、最直接的標準。

「左圖是 Aquarius 純暗物質模擬的理論預測，證明了『暗物質次暈』的數量與主暈質量呈現嚴格的正比關係。」

「右圖則是結合觀測數據的 HOD 模型，同樣證實了當暗物質暈夠大時，『發光衛星星系』的數量也會隨暗物質質量提升。」

「基於這項鐵律，我們確立了本研究的核心手段：『數衛星星系的數量，就等於在秤暗物質暈的真實重量！』」

「接著，我們將這個推導出的『暗物質體重』，與主星系自身的『發光亮度（代表恆星質量）』進行強烈對比。」

「如果我們發現一個主星系極度黯淡，周圍卻環繞著驚人數量的衛星星系，這就代表我們找到了目標。」

「這將從觀測上完美證實，它是一個潛伏在巨大暗物質暈中的『半熟星系（Undercooked MW）』，研究理論預測的極端散佈」

在純理論的電腦模擬環境下，比較「寄宿在較大暗暈內的子暗暈（紅點）」與「獨立存在於宇宙中的場暗暈（黑點空心圓）」

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Method

Data Sets

Host: Siena Galaxy Atlas (SGA 2020)
Satellite: DESI DR1 Spectroscopic Catalog

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Target Selection – Hosts

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Target Selection – Satellites

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Target Selection – Satellites

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When searching for satellites around a host galaxy.

First, the satellites must be fainter than -19 to ensure it is a true satellite and not a major merger pair.�

Spatially, we search within a projected radius of 300 kiloparsecs.

Kinematically, we require their line-of-sight velocity difference to be within 500 kilometers per second from the host.

This velocity depth acts as a proxy for the virial velocity, ensuring the satellites are gravitationally bound to the host.

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接著是衛星星系的篩選。為了避免選到雙星系（Major pairs），我們規定衛星星系的亮度不能超過 -19 等。

我們也實際測試過相對星等差（ΔM）與絕對星等上限這兩種方法，最終選擇了乾淨的 -19 等作為絕對門檻。

在尋找衛星星系時，我們在主星系周圍畫出一個 3D 的搜尋錐體：

平面投影半徑設定在 300 kpc 以內，

並利用視向速度差正負 500 km/s 作為深度的邊界條件，這剛好能涵蓋預期的維里速度（Virial velocity）範圍。

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Results – Satellite Count Distribution

Processed 17,801 SGA hosts.
4,362 (24.5%) hosts with ≥1 satellite.

However, the real number could be lower…

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Results – LOS Velocity Offset

Clear physical association confirmed by velocity peaks.

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Results – Satellite Count vs. Hosts Redshift

Observational volume limit at higher z.

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Challenges

Environmental Confusion

Cannot assign satellites to a specific host within galaxy groups or clusters.

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Challenges

Photometric Shredding

Source detection software can split single extended objects into multiple false targets during catalog generation.
High rate of false positives near the host galaxy's center.
Solution: Implement a 10 kpc exclusion zone around the core. (Also can miss some.)

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Conclusions & Future Works

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Reference

Geha, M., et al. (2017). ApJ, 847, 4. (SAGA I)
Mao, Y.-Y., et al. (2021). ApJ, 907, 85. (SAGA II)
Mao, Y.-Y., et al. (2024). ApJ, 976, 117. (SAGA III)
Licquia, T. C., & Newman, J. A. (2015). ApJ, 809, 96.
Zaritsky, D., & Behroozi, P. (2023). MNRAS, 519, 871.
Guo, H., et al. (2016). MNRAS, 459, 3040.
Guo, Q., et al. (2011). MNRAS, 417, 370.
Cooper, A. P., et al. (2025). MNRAS, 540, 2049.
Liao, L.-W., & Cooper, A. P. (2023). MNRAS, 518, 3999.

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Acknowledgements: Prof. Andrew Cooper, TARA, NTHU CICA Cluster

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