AST4320 - Cosmology and extragalactic astronomy Lecture ......The Cusp-Core Problem LSBs + gas rich dwarf galaxies suggest density in the center evolves as ~r0, density proﬁle in

Lecture 11

AST4320 - Cosmology and extragalactic astronomy

Structure of Dark Matter Halos & The Cusp/Core Problem.

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


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

J. Navarro C. Frenk S. White

`NFW’-Profile

normalization, relates to density of Universe at time of collapse

`characteristic’ radius, or ‘concentration’ of the halo.

NFW profile provides a remarkable universal fitting formula for the simulated structure of dark matter halos, irrespective of their mass and formation redshift.

The mass and formation time/redshift is encoded in two parameters.

`NFW’-Profile



NFW profile has a few key properties:

1.Differs from isothermal solution we derived before for which

2. NFW density diverges at r approaches zero.

`NFW’-Profile



NFW profile has a few key properties:

1. Cusp

NFW profiles are cuspy.

Observational Constraints on Dark Matter Halo Profiles

Simulated dark matter halos contain lots of `substructure’ - which reflects hierarchical build-up of structure. Comparison of this predicted substructure to observations will be done later.

First focus on the predicted dark matter halo profile.

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


Observational constraints obtained from `rotation’ curves.

Rotation curves provide a direct measure of density distribution.

Measuring Rotation Curves in Galaxies

Traditionally, rotation curves have been derived from observations of the 21-cm (hyperfine transition) of atomic HI gas inside galaxies.

Advantage 1.: HI observed out to much larger distance than stars. Probes M out to larger r

Advantage 2.: 21-cm is a line of atomic H. Can use line to directly probe gas kinematics.


Example of 2D velocity field of a galaxy M33 inferred from 21-cm observations.

Bright = high HI column densityVelocity field. Red/blue is receding faster/slower


Infer rotation velocity vROT(r) from 2D velocity field using `tilted-ring model’.

Each ring `j’ has its own radius Rj, velocity vj, two angles (inclination i and position angle PA) describing the orientation of the (normal to the) ring relative to the observer.


Infer rotation velocity vROT(r) from 2D velocity field using `tilted-ring model’.

Each ring `j’ has its own radius Rj, velocity vj, two angles (inclination i and position angle PA) describing the orientation of the (normal to the) ring relative to the observer.

Obtain best fit for all these parameters by matching to the observed 2D velocity field.

Measuring Rotation Curves in GalaxiesExamples of tilted ring models (from Battaglia et al. 2006).

Radius (kpc)

ìnclination’

`position angle’vsys

vrot

Tilted ring models can reveal `warping’ of the disk.

Measuring Rotation Curves in GalaxiesExamples of tilted ring models for M33(from Corbelli et al. this month!).

`position angle’

ìnclination’

vrot

Radius (kpc)


Examples of tilted ring models: observation (left) vs model (right).

This shows velocity as a function of distance from center of galaxy, along major axis.

Measuring Rotation Curves in GalaxiesSample of rotation curves1: a nice image.

Measuring Rotation Curves in GalaxiesSample of rotation curves II: a practical image showing how precise rotation curves have been measured from HI observations.

Measuring Rotation Curves in GalaxiesSample of rotation curves III: showing diversity of galaxy rotation curves.

Measuring Rotation Curves in GalaxiesSample of rotation curves IV: dwarf galaxies rotation curve rises slower.

(from Verheijen 1997)

Inferring Dark Matter Contribution & Distribution

Having determined vrot(r), it becomes possible to constrain M(<r) and therefore the density.

Some useful relations to keep in mind:



Some useful relations to keep in mind:

Cusp

isothermal

`keplerian’



It is possible to decompose M(<r) into several components: • Atomic hydrogen gas itself, MHI(<r).• Stars, M*(<r).• Dark matter, MDM(<r)




Can get this from 21-cm observations directly.

Can infer this from light distribution in galaxies.

Whatever is left, must be the dark matter......




Can get this from 21-cm observations directly.

Can infer this from light distribution in galaxies.

M*(<r) can be derived from by assuming mass-to-light ratio M/L of stars.Two comments on this:• there exists some degeneracies between MDM(<r) and M/L• independent constraints on M/L can be obtained from SED modeling or measurements of velocity dispersion in disk.

Inferring Dark Matter Contribution & DistributionExample of a rotation curve decomposition.

Keplerian fall-off vrot ~ r-1/2

Observations of rotation curve + rotation curve decomposition have consistently demonstrated that there is more mass and at larger distance than can be accounted for observationally (or that gravity needs to modified)

Results are especially interesting in gas rich dwarf galaxies and low surface brightness galaxies.


Gas rich dwarf galaxies because• dynamics dominated by dark matter (contain few stars + HI mass well known)

Notice how in dwarfs vrot risesrelatively slowly in inner regions.


vROT

Radius (kpc)

Dashed lines are denoted `Hernquist’ & represent Hernquist-profile. These profiles have the same central cusp, i.edensity ~ r-1 in inner region.

(from Moore 1994)Rotation curves of gas rich dwarf galaxies.


(Oh et al. 2011; THINGS* survey. Colored points are the dwarfs.)

(* The HI Nearby Galaxy Survey)



Low Surface Brightness Galaxies (LSBs) because• small stellar content• no central bulges (i.e. no high central baryonic densities)• reside in relatively low density environment (mergers* unlikely to disturb galaxies)• low surface brightness but integrated luminosities are 2-4 magnitudes brighter than dwarfs.



Low Surface Brightness Galaxies (LSBs) because• small stellar content• no central bulges (i.e. no high central baryonic densities)• reside in relatively low density environment (mergers* unlikely to disturb galaxies)• low surface brightness but integrated luminosities are 2-4 magnitudes brighter than dwarfs.

* Simulations indicate that merging cuspy halos create a new cuspy halo, and that only merger of two `cored’ halos give a new cored halo -> shifts problem to early Universe?



Low Surface Brightness Galaxies (LSBs) because• small stellar content• no central bulges (i.e. no high central baryonic densities)• reside in relatively low density environment (mergers unlikely to disturb galaxies)• low surface brightness but integrated luminosities are 2-4 magnitudes brighter than dwarfs.

Well suited to study central distribution of dark matter.

Inferring Dark Matter Contribution & Distribution(De Blok 2004; Filled circles are the LSBs)

Inferring Dark Matter Contribution & Distribution(De Blok 2004; Filled circles are the LSBs)

LSBs + gas rich dwarf galaxies suggest density in the center evolves as ~r0, density profile in the core in flat.

Observations show evidence for so-called `cored’ density profiles.

Discrepancy between observed `cores’ and simulated `cusps’ is known as the cusp-core problem.

The Cusp-Core Problem

LSBs + gas rich dwarf galaxies suggest density in the center evolves as ~r0, density profile in the core in flat.

Observations show evidence for so-called `cored’ density profiles.

Discrepancy between observed `cores’ and simulated `cusps’ is known as the cusp-core problem.

Even though LSBs + dwarfs represent a subset of all galaxies, it was thought that the dark matter density was most èasily’ inferred in this subset, which suggests the problem is serious.

There exist a number of explanations for the cusp-core problem:

1. NFW profile follows from simulations with cold dark matter (massive dark matter particles). Alternative warm dark matter models (Mdm~1-4 keV) have been proposed*. Likely cannot produce cores at which they appear to exist.

2. Modification of gravity (see yesterday’s cosmology seminar by D. Rodrigues).

3. NFW profile obtained from dark matter only simulations. Baryonic physics can affect the predicted dark matter profiles, even in dwarfs + LSBs.

Possible Resolutions to the Cusp-Core Problem

* e.g. Sterile neutrino constitute a Fermi-Dirac fluid. There is an upper limit to how many fermions can fit into a volume. This limit should create cores.

Some recent simulations indicate that the gravitational impact of baryonic physics is much bigger than previous expectations:

New Developments on the Theory Side

From Pontzen & Governato, 2014




(THINGs survey)

`When less than 106.5 Msun of gas has turned into stars there is insufficient energy to flatten the cusp.’




(THINGs survey)

Òbservations of systems with stellar masses less than 1e6 Msun would be highly valuable’

There are cases in which a cusp is favored by the data.

New Developments on the Observational Side

Adams et al. 2011

Commissioning of massive integral field spectrographs enables to measure kinematics of hydrogen gas via H-alpha (Balmer-alpha n=3 -> n=2)



Adams et al. 2011: comparison of observed 2D velocity field + best-fit tilted ring model.



H-alpha[OII]

Adams et al. 2011: inferred rotation curves for H-alpha and [OII] emission line, which traces same gas (note solid line shows rotation curve inferred from stellar dynamics).



H-alpha[OII]

Adams et al. 2011: inferred rotation curves for H-alpha and [OII] emission line, which traces same gas (note solid line shows rotation curve inferred from stellar dynamics).

Adams et al. 2011: The combined fit suggests a DM cusp (α = 0.90 ± 0.15 at 1σ) and excludes a DM core at 2σ significance.

Conclusions

1. Simulations indicate the spherically averaged density inside dark matter halos is given by NFW profile.

2. The NFW profile diverges as r-1 as r goes to zero. NFW profiles have cusps.

3. Observations galaxies where dark matter is expected to dominate gravitational potential indicate that HI gas kinematics prefers density profiles that are practically constant at small radii. These profiles are `cored’ profiles

4. This apparent discrepancy between simulated and observationally inferred density profile is called the cusp-core problem.

Conclusions

5. Several solutions have been proposed for the cusp-core problem (incl. modying gravity, warm dark matter).

6. Some recent simulations that include baryonic physics suggest that the impact of baryons on the dark matter may be stronger than previously anticipated. Predicts that cusps should be observed in galaxies with M*<1e6 Msun.

7. IFU observations of one galaxy suggest that a cusp is preferred over a cored profile. These observations will be more common in the future.

OutlookWe have not discussed the substructure seen in the simulations at all.

Comparison of this substructure to observations also leads to interesting (possibly related) problems.

Documents

AST4320 - Cosmology and extragalactic astronomy Lecture ......The Cusp-Core Problem LSBs + gas rich dwarf galaxies suggest density in the center evolves as ~r0, density proﬁle in