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Lecture 12
AST4320 - Cosmology and extragalactic astronomy
Structure of Dark Matter Halos & The Missing Satellites Problem.
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AST4320 - Cosmology and extragalactic astronomy
Lecture 12 Outline
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Comparison of simulated dark matter halos and observations part II (in part I we discussed the `cusp-core’ problem).
Today: `Missing satellite problem’ and `Too Big Too Fail Problem’
Does the standard `cold’ dark matter paradigm face a crisis?
Simulated Dark Matter Profiles
1. Notice the details in structure. Lots of `substructure’, which reflects hierarchical build-up of structure.
2. Spherically averaged density profile follows `Navarro-Frenk-White’ (NFW profile)
line
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`NFW’-Profile
normalization, relates to density of Universe at time of collapse
`characteristic’ radius, or ‘concentration’ of the halo.
NFW profile has a few key properties:
1. Cusp
NFW profiles are cuspy.
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Observational Constraints on Dark Matter Halo Profiles (see review by W. De Blok, arXiv:0910.3538)
Observational constraints obtained from `rotation’ curves.
`rotational’ velocity. Assumes circular orbits. Rotation curves are also referred to as `circular velocity curves.
Note: assumption of circular orbits likely correct for gas. Non-circular orbits of gas likely suppressed by gas pressure.
Mass enclosed within sphere of radius r
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Observational Constraints on Dark Matter Halo Profiles (see review by W. De Blok, arXiv:0910.3538)
(Oh et al. 2011; THINGS* survey. Colored points are the dwarfs.)
Observed profiles are `cored’.
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Simulated Dark Matter Profiles
1. Notice the details in structure. Lots of `substructure’, which reflects hierarchical build-up of structure.
line
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Missing Satellite Problem (MSP)(see review by Weinberg et al. 2013, arXiv:1306.0913)
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Left: simulated dark matter distribution in dark matter halo with M=1012 Msun. Circles denote 9 most massive substructures or `satellites’.Right: Spatial distribution of observed Milky Way `satellites’.
Missing Satellite Problem (MSP)(see review by Weinberg et al. 2013, arXiv:1306.0913)
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Just a visual comparison suggests that the simulated and observed satellite distributions are inconsistent, in the sense that simulations predict many more satellites. This discrepancy is known as the `missing satellite problem’.
Missing Satellite Problem (MSP)
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Klypin et al. 1999
A quantitative comparison of # satellites at r < 400 kpc.
Increasing Mass
Number
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Klypin et al. 1999
Observed
simulated
Missing Satellite Problem (MSP)A quantitative comparison of # satellites at r < 400 kpc.
Number
`MW’108 109 1010 1011
1012
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Klypin et al. 1999
Observed
simulated
Missing Satellite Problem (MSP)A quantitative comparison of # satellites at r < 400 kpc.
Number
Discrepancy apparent at vcirc < 40 km/s.
At vcirc<40 km/s (or M < 1010 Msun)feedback mechanisms become efficient.
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Feedback.
Feedback plays a key role in galaxy formation.
It refers to the `collection of complex processes through which star formation and accretion onto black holes deposit energy and momentum back into their surroundings’.
Examples of feedback include:
1. Radiative feedback; e.g. photoionization feedback, radiation pressure
2. Mechanical feedback: e.g. supernova explosions, pressure exerted by cosmic rays
Radiation that provides feedback can be emitted by stars, or originate from accretion disk surrounding a (supermassive) black hole. We often explicitly differentiate between these two sources and divide feedback into:
1. Stellar feedback2. AGN feedback (thought to operate in more massive galaxies, more later!)
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Feedback Mechanism I: Radiative Feedback by Ionizing Photons (Photoionization Feedback).
Ionizing photons: photons with E>13.6 eV can ionize atomic hydrogen from its groundstate*.
p+ p+
e-
e-1. 2.
E =13.6+x eV
Ee= x eV
* Most of the hydrogen is in its ground state at densities commonly encountered in interstellar medium (and lower).
Photoionization: converts excess energy of photons into thermal energy of electrons. Coulomb interaction distribute this energy over many electrons + protons.
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Feedback Mechanism I: Radiative Feedback by Ionizing Photons (Photoionization Feedback).
Ionizing photons: photons with E>13.6 eV can ionize atomic hydrogen from its groundstate*.
p+ p+
e-
e-1. 2.
E =13.6+x eV
Ee= x eV
Photoionization: converts excess energy of photons into thermal energy of electrons. Coulomb interaction distribute this energy over many electrons + protons.
1. Photoionization heats the gas (heating rate does not depend on intensity of ionization radiation field!).
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Feedback Mechanism I: Radiative Feedback by Ionizing Photons (Photoionization Feedback).
1. Photoionization heats the gas.
2. Photoionization ionizes HI in the gas (duh..). Ionization of hydrogen strongly affect ability of gas to cool.
Recall that collisional excitation of transitions within atomic hydrogen providesan important channel to `drain’ gas from its thermal energy.
Recall: Gas Cooling Curve
remove density dependence
Cooling rapidly becomes efficient just above T=1e4 K because of collisional excitation of HI (atomic hydrogen). Photoionization removes these atoms!
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Feedback Mechanism I: Radiative Feedback by Ionizing Photons (Photoionization Feedback).
1. Photoionization heats the gas.
2. Photoionization ionizes HI in the gas (duh..). Ionization of hydrogen strongly affect ability of gas to cool.
Recall that collisional excitation of transitions within atomic hydrogen providesan important channel to `drain’ gas from its thermal energy.
Photoionization therefore both heats + reduces efficiency with which gas can cool!
There is a 3rd effect:
3. In hot gas (T > 2e4 K) collisions can reduce HI fraction further. Heating by photoionization will be less efficient at T > 2e4 K (as there is no HI no photoionize).
Photoionized gas is typically T=1-2e4 K
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Feedback Mechanism I: Radiative Feedback by Ionizing Photons (Photoionization Feedback).
Photoionized gas is typically T=1-2e4 K
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
In presence of ionizing radiation. Cooling + heating rate depend on density.
`old’calculation
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Cooling in presence ionizing radiation
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
at low T enhanced cooling due to free electrons in gas (?).
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
reduced cooling due to reduced HI content (as discussed before).
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Cooling via collisional excitation of singly ionized He (HeII) starts.
Importance of HeII cooling depends on how many HeII ionizing photons (E> 54.4 eV) exist. Depends on `hardness’ of spectrum.
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Heating rate of the gas: heating efficiency reduces as T increases due to reduced fraction of neutral H in gas.
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
abs(cooling rate-heating rate)
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Efficient heating
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Efficient heating
Efficient cooling
Photoionized gas is typically T=1-2e4 K
Gas Cooling/Heating Curve in Presence Ionizing Radiation.
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Thoul & Weinberg. 1995
Efficient heating
Efficient cooling
Photoionized gas is typically T=1-2e4 K
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Observations indicate that gas in most of the volume outside of galaxies is photoionized.
Shown here: simulated large-scale distribution of matter in the Universe.
Most galaxies reside in overdense regions (filaments, walls, nodes).
Galaxies provide incomplete (or not-representative, or `biased’) sampling of matter distribution. So how do we obtain less biased tracers of the matter?
Feedback Mechanism I: Photoionization Feedback.
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Observations indicate that gas in most of the volume outside of galaxies is photoionized.
Galaxies provide incomplete (or not-representative, or `biased’) sampling of matter distribution. So how do we obtain less biased tracers of the matter?
Answer: via the so-called Lyman alpha forest (wait for Lecture 14, or 15)
Feedback Mechanism I: Photoionization Feedback.
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Observations indicate that gas in most of the volume outside of galaxies is photoionized.
The Lyman alpha forest (wait for Lecture 14, or 15)
Lyman alpha forest consists of collection of Lyman alpha absorption lines by atomic HIas seen in spectra of (luminous) background objects (red dots). The blue lines represent sightlines to these objects. Each sightline passes through overdense filaments and underdense `voids’
Feedback Mechanism I: Photoionization Feedback.
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Observations indicate that gas in most of the volume outside of galaxies is photoionized.
The Lyman alpha forest (wait for Lecture 14, or 15)
Lyman alpha forest observations indicate that gas outside of galaxies in the intergalactic medium is:
•highly ionized (only 1 atom in 1e4-1e6 is neutral. Number depends on redshift).• temperature is about 1-2e4 K, as expected from photoionization.
The Jeans mass inside the photoionized `intergalactic medium’ is
Pressure prevents baryons (ordinary matter) from collapsing into dark matter halos with M < MJ.
Feedback Mechanism I: Photoionization Feedback.
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Observations indicate that gas in most of the volume outside of galaxies is photoionized.
More appropriate would be the `filter mass’ (takes into account time evolution of T and density during collapse of a cloud).
Gnedin 2000
Jeans Mass
Filter Mass
Not possible (or more difficult) for baryons to collapse into Dark matter halos with M < 109 Msun.
This corresponds to
Feedback Mechanism I: Photoionization Feedback.
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Photoionized gas is typically T=1-2e4 K.
Feedback Mechanism I: Photoionization Feedback.
Pressure of this gas prevents efficient gas collapse in DM halos with vcirc < 30 km/s.
Missing Satellite Problem exists at vcirc < 40 km/s.
Photoionization feedback provides natural explanation for Missing Satellite Problem.
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Feedback Mechanism II: Stellar Feedback.Photoionization feedback provides natural explanation for Missing Satellite Problem,but... though plausible, no direct evidence exists for photoionization feedback in action
in contrast, there exists ample evidence for so-called `stellar’ feedback, e.g.
M82, nearby dwarf galaxy with a recent star burst. Red indicates H-alpha emission from outflowing gas. Outflow driven by supernova explosions, and/or radiation pressure.
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Feedback Mechanism II: Stellar Feedback.There exists ample evidence for so-called `stellar’ feedback. Outflowing gas is omni-present in star forming galaxies. Some process is driving it out.
Outflowing gas that is detected in absorption in spectrum of galaxy is blueshifted.
velocity off-set-500 km/s 0 500 km/s
blue red
1
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Feedback Mechanism II: Stellar Feedback.There exists ample evidence for so-called `stellar’ feedback. Outflowing gas is omni-present in star forming galaxies. Some process is driving it out.
Outflowing gas that is detected in absorption in spectrum of galaxy is blueshifted.
blue red
Steidel et al. 2010
Steidel et al. 2010 obtained sample of 92 star forming galaxies. Detection transitions of e.g. CII, SII (produced in stars), almost all outflowing.
Feedback Mechanism II: Stellar Feedback.
Stellar feedback is increasingly efficient in removing gas from galaxies towards lower mass dark matter halos (derive on board).
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Assume that we convert some fraction f* of baryonic matter into stars. The higher f*, the more stars explode as supernovae.
If supernovae drive out gas from galaxies, then this limits how much gas is available to star formation. In other words, supernova-feedback can put a limit on how large f* can be.
We derive (on the board + lecture notes 12) that this maximum f* scales with Vcirc as
In other words, supernova feedback suppresses star formation preferentially in low mass halos.
Feedback Mechanism II: Stellar Feedback.
Stellar feedback is increasingly efficient in removing gas from galaxies towards lower mass dark matter halos (derive on board).
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From Lecture 10(credit S. White)
log M
log M*Supernova feedback cannot fully explain this steep slope.
This observation likely suggests that there is more than just SN feedback (perhaps photoionization)
Feedback.There is no shortage of feedback models to explain reduced star formation efficiency inside low-mass dark matter halos. It is therefore possible to explain missing satellite problem with baryonic physics.
This baryonic physics lies at the core of understanding galaxy formation, and is (not surprisingly) not well understood.
The next slide: an example of a model that invokes various feedback processes to explain distribution of satellites around Milky Way.
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Missing Satellite Problem in Models that Include Feedback
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Predicted number of satellites with no feedback
Predicted number of satellites with feedback*
* Note: feedback tuned to reproduce observations.
Munoz et al. 2009
Missing Satellite Problem: Observational Advancements
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2005: Discovery of new Milky Way companion Willman 1 (dwarf galaxy).
Missing Satellite Problem: Observational Advancements
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Difficult to find these structures. Circles highlight an overdensity of faint, blue stars.
2005: Discovery of new Milky Way companion Willman 1. This object is classified as an `ultra-faint dwarf’ galaxy (MV=-3.0; 400.000 times fainter than faintest, most distant galaxies we talked about earlier!)
Missing Satellite Problem: Observational Advancements
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Difficult to find these structures. Circles highlight an overdensity of faint, blue stars.
To date, another 15 ultra-faint dwarfs have been found!
2005: Discovery of new Milky Way companion Willman 1. This object is classified as an `ultra-faint dwarf’ galaxy (MV=-3.0; 400.000 times fainter than faintest, most distant galaxies we talked about earlier!)
Missing Satellite Problem in Summary
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There is no shortage of baryonic processes which suppress the efficiency at which stars can form in low mass satellites of Milky Way.
Reasonable to (for now) regard the relation between low mass dark matter halos & `ultra-faint dwarfs’ as puzzle of galaxy formation physics (feedback) instead of a contradiction of the standard cold-dark matter paradigm.
New ultra-faint dwarf galaxies have only recently been discovered. Stellar kinematics suggests that there exists a large spread in relation between luminosity + dark matter halo mass.
A bigger - more pressing - problem is related to the most luminous satellites.
The Missing Satellite Problem refers to the apparent discrepancy between the predicted number of dark matter satellites and observed number of dwarf galaxies around the Milky Way
`Too Big To Fail’ Problem.
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Boylan-Kolchin et al. 2011/2012
Boylan-Kolchin took 6 hydrodynamical simulations designed to simulate`Milky-Way dark matter halos’ with a variety of mass & force resolution.
Compared the properties of the most massive simulated satellites with the most luminous satellites.
`Too Big To Fail’ Problem.
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Boylan-Kolchin et al. 2011/2012
Satellite Luminosity function
observed
simulated
Models that best reproduce observed satellite luminosity function - and hence best `solves’ the missing satellite problems, predicts that all satellites have significantly larger rotational velocities!
`Too Big To Fail’ Problem.
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Boylan-Kolchin et al. 2011/2012
Satellite Luminosity function
observed
simulated
Because rotational velocity provides a measure of enclosed mass, predicted satellites are too massive (`too big’).
`Too Big To Fail’ Problem.
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Boylan-Kolchin et al. 2011/2012
Because rotational velocity provides a measure of enclosed mass, predicted satellites are too massive (`too big’).
If the most luminous observed satellites around the Milky Way indeed reside in dark matter halos with vcirc < 25 km/s, then why do all 10 (!) more massive dark halos not have observed low-luminosity counter parts?
Why is star formation(relatively) efficient SF in vcirc < 25 km/s, but much less so in the more massive objects (which presumably are more `immune’ to feedback effects, i.e. `too big to fail’).
`One possible explanation is that the matter concentration is less concentrated than what current dissipationless simulations predict’ (see next slides.)
From previous lecture: Observational Constraints on Dark Matter Halo Profiles
vROT
Radius (kpc)
I showed this to illustrate the `cusp-core’ problem.
Simulated profiles have cusps (density ~ r-1), while observed rotation curvesfavor `cored’ profiles (density is constant).
(from Moore 1994)
`Rotation curves’ of gas rich dwarf galaxies.
From previous lecture: Observational Constraints on Dark Matter Halo Profiles
vROT
Radius (kpc)
(from Moore 1994)`Rotation curves’ of gas rich dwarf galaxies.
Cusp-core problem: simulated density profiles 1. are steeper. 2. have higher central densities3. steeper rotation curves.
Appears related to the discrepancy in predicted and observed circular velocities?
At fixed r, can get significant differences!
`Too Big To Fail’ Problem.
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Boylan-Kolchin et al. 2011/2012
Models that best reproduce observed satellite luminosity function - and hence best `solves’ the missing satellite problems, predicts that all satellites have significantly larger rotational velocities (i.e. are more massive, or more centrally concentrated).
There is a possible connection with the cusp-core problem, which also states that simulated dark matter profiles have higher central densities than what has been inferred from gas (and stellar) kinematics in dark-matter dominated galaxies (dwarf galaxies, and low-surface brightness galaxies)
The Small-Scales Crisis in Cold Dark Matter Cosmologies
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Summary (Incl. Lecture 11.)
When comparing the structure of dark matter halos as obtained from cosmological simulations to structure inferred from gas & stellar kinematics, some problems surfaced:
Problem 1 ‘cusp-core problem’: Simulated density profiles are `cuspy’, inferred profiles are `cored’.
Some proposed solutions:1. Cuspy profiles originally predicted in dark-matter only simulations. Baryonic physics can transform cusps into cores (e.g. via supernova feedback, but this requires a minimum stellar content).2. Modify dark matter properties (next lecture).3. Modify gravity.
The Small-Scales Crisis in Cold Dark Matter Cosmologies
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Summary (Incl. Lecture 11.)
When comparing the structure of dark matter halos as obtained from cosmological simulations to structure inferred from gas & stellar kinematics, some problems surfaced:
Problem 2 ‘missing satellite problem’: The simulated and observed satellite distributions around the Milky Way are inconsistent, in the sense that simulations predict many more satellites.
Solution:1. Feedback. Can bring down the predicted number to the observed number - which has increased in recent years (about 15 ultra-faint dwarfs have been discovered in the past 10 years)
Caveat:This problem has `transformed’ into the `too big to fail’ problem (discussed next).We are not missing satellites, rather simulations predict them to be too massive.
The Small-Scales Crisis in Cold Dark Matter Cosmologies
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Summary (Incl. Lecture 11.)
When comparing the structure of dark matter halos as obtained from cosmological simulations to structure inferred from gas & stellar kinematics, some problems surfaced:
Problem 2 (absorbed `missing satellite problem’) ‘too-big-to-fail-problem’: Predicted masses of Milky Way satellites are significantly higher than observationally inferred values.
Solution:The problem appears connected to the cusp-core problems. So solutions range from baryonic physics, to modifying dark matter or gravity.
Interestingly:The `severity’ of the problem depends on mass of Milky-Way halo, which is still somewhat uncertain (see video).
Plan for Next 2 Lectures
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In this & previous lectures, we discussed structure of `dark matter halos’.
In the next lectures, we discuss.
Lecture 13: `Cold’ Dark Matter: what, why, and how much do we know?Lecture 14: How galaxies get their gas: gas in the intergalactic medium, and gas assembly in dark matter halos.
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