Hypervelocity StarsA New Probe for Near-Field Cosmology

Omar Contigiani

Supervisor: Dr. E.M. Rossi

Student Colloquium, 20/06/2017, Leiden

Co-supervisor: Msc. T. Marchetti

Near-Field Cosmology

And why a new probe would useful

Credit: V.Springel, Max-Planck Institut für Astrophysik, Garching bei München // Adam Evans

Cosmic Web

Andromeda

50 Mpc

10 kpc

Near-Field Cosmology - Structure Formation

MILKY WAY

Near-Field Cosmology - Structure FormationDM HALO DENSITY PROFILE

Navarro–Frenk–WhiteOblate/Prolate

MILKY WAY

Near-Field Cosmology - Structure FormationDM HALO DENSITY PROFILE

Navarro–Frenk–White

PREDICTIONS, e.g.

- Self interacting DM ⇒ Inner spherical halo (Peter+ 2013)

- Light MW halo ⇒ No more “missing satellites” (Wang+ 2011)

Oblate/Prolate

MILKY WAY

Near-Field Cosmology - Structure FormationDM HALO DENSITY PROFILE

Navarro–Frenk–White

DYNAMICAL TRACERS, e.g.:

Stellar streamsGlobular clusters

Credit: ESO, F. Ferraro // NASA/JPL-Caltech

Oblate/Prolate

MILKY WAY

Near-Field Cosmology - Measurements To Date

Credit: Wang+ 2015

Near-Field Cosmology - Measurements To Date

Credit: Wang+ 2015

Streams Spherical (Bovy 2016)Halo stars Oblate (Loebman+ 2014) Tracers Problate (Bowden+ 2016)

Oblate/Prolate

Near-Field Cosmology - Measurements To Date

Credit: Wang+ 2015

Streams Spherical (Bovy 2016)Halo stars Oblate (Loebman+ 2014) Tracers Problate (Bowden+ 2016)

Oblate/Prolate

Systematic biases

Thorough statistical analysis required

Hypervelocity Stars

And why they are a hot topic right now

Credit: Brown 2015

- High velocity: v ≫ v

- Orbits crossing Galactic center

NUMBER OF PAPERS vs YEAR

Hypervelocity Stars - Observations To Date[2005]

RADIAL VELOCITY

NUMB

ER

Hypervelocity Stars - Observations To Date[2005] [2014]

RADIAL VELOCITY

NUMB

ER

DISTANCE FROM G.C.RA

DIAL V

ELOCITY

Hypervelocity Stars - Leading mechanism [1988]

Credit: Brown 2015

- Three body interaction binary system and MBH

Hypervelocity Stars - Leading mechanism [1988]

Credit: Brown 2015

- Three body interaction binary system and MBH

- S-star is left behind

Hypervelocity Stars - Leading mechanism [1988]

V ~1000 km/s Credit: Brown 2015

- Three body interaction binary system and MBH

- S-star is left behind

- Hypervelocity star is ejected

Hypervelocity Stars - Promising Past[2005]

Hypervelocity Stars - Promising Past[2005] [2017]

not likely

not likely

not likely

likely

Hypervelocity Stars - Promising Future

Credit: ESA/Gaia/DPAC. A. Moitinho & M. Barros (CENTRA – University of Lisbon)

SDSS

Quantity Quality

109 stars

Spectroscopic subsample w/ full 3D velocity and position

Statistical Inference

Crash Course

ModelData

Constraints on model parameters

Statistical Inference - Unit (Fisher) Information

≥Depends only on how

sensible the model is to a change of parameters

Research Project GoalsStudy the kinematics of HVS to obtain:

Research Project GoalsStudy the kinematics of HVS to obtain:

1) FISHER FORECASTTo assess the potential.

Compute the information and display the contours for DM halo parameters.

rh

Mh

1) FISHER FORECASTTo assess the potential.

Compute the information and display the contours for DM halo parameters.

2) ESTIMATED POPULATIONSHow many HVSs could be there?

Construct mock catalog of the galactic population and infer how many of them will be observed by Gaia.

Research Project GoalsStudy the kinematics of HVS to obtain:

rh

Mh

Research Project GoalsStudy the kinematics of HVS to obtain:

3) LIKELIHOOD PIPELINEDevelop a technique!

Feed the mock catalog into it and obtain realistic constraints.

1) FISHER FORECASTTo assess the potential.

Compute the information and display the contours for DM halo parameters.

2) ESTIMATED POPULATIONSHow many HVSs could be there?

Construct mock catalog of the galactic population and infer how many of them will be observed by Gaia.

rh

Mh

FormalismStarting from the physics

Treat HVS as a

statistical ensemble defined in the configuration space

Phase-space coordinate

Stellar mass

Number density in configuration space

Phase-space distribution - Assumptions 1) Steady stateTime-independent potential

Time-independent ejection rate

Phase-space distribution - Assumptions 1) Steady state

2) SourceHow many HVSs are ejected per unit mass, volume, velocity?

Usually done with Monte Carlo simulations.

In our case, analytic function (Rossi+ 2014) which fits MC.

(init

ial)

Phase-space distribution - Assumptions 1) Steady state

2) SourceAnalytic function which fits MC.

3) SinkWhen to HVS “disappear”?

Phase-space distribution - Assumptions 1) Steady state

2) SourceAnalytic function which fits MC.

3) SinkWhen to HVS “disappear”?

Uniformly distributed between [0, 1]

Phase-space distribution - Solving continuity equation

SOURCE

SINK

Phase-space distribution - Solving continuity equation

Unfortunately, it requires the numerical integration of the trajectory

Analytic formula, that can be computed for any assumed

&

Dying rateEjection rate

Fisher ForecastEstimates based on Unit

Information - assuming a 1D toy model of the galaxy

Credit: Selletin+ 2014

ASSUMPTIONS:

- 1D toy model

- 5 M☉

HVSs

Fisher Forecast - Contours

Fisher Forecast - Contours

BAD NEWS:

Large relative errors.

BAD NEWS:

Large relative errors.

GOOD NEWS:

Strong degeneracy, worth investigating.

Fisher Forecast - Contours

Mock catalogsSimulation of the HVS Galactic

and Gaia populations

Previous Results

Predicted ejection rate theory (Yu+Tremaine 2013) & observations (Kollmeier+ 2010)

Predicted pop. of 2.5-4 M☉

within 100 kpcObservations (Brown 2015)

Mock catalogs- Ingredients 1) Ejection Rate &

Flight time distributionPreviously modelled

Mock catalogs- Ingredients 1) Ejection Rate &

Flight time distributionPreviously modelled

2) Galactic Model

Kenyon+ 2008 (Potential) Bovy+ 2015a ( 3D Dustmap)

Halo + Bulge (spherical) Disc (axisymmetric )

Green+ 15, Marshall+ 06, Drimmel+ 03

Mock catalogs- Ingredients 1) Ejection Rate &

Flight time distributionPreviously modelled

2) Galactic Model

Kenyon+ 2008 (Potential) Bovy+ 2015a (Dustmap)

3) Gaia Selection FunctionGRVS < 16

pyGaia (A. Brown) to reconstruct Errorbars on proper motions / parallax / radial velocity

Mock catalogs- HVS Galactic population60% unbound

Total Galactic population

Mock catalogs- HVS Galactic population10% unbound

Gaia 3d velocities and positions

Mock catalogs- HVS Galactic populationGaia 3d velocities and positions (high velocity)

~200 stars

Full likelihoodFinally!

“Observed” data from mock catalogs

Formalism can predict different PDF for different parameters

Mh, rh, c/a

Full Likelihood

Full Likelihood

GOOD NEWS

1) No bias

2)

Full Likelihood

MIXED NEWS

Effective constraint:

GOOD NEWS

1) No bias

2)

Summary

1) FISHER FORECASTTo assess the potential.

2) ESTIMATED POPULATIONSHow many HVSs are expected.

3) LIKELIHOOD PIPELINEDevelop a technique!

1) BARYONIC POTENTIALCan HVSs constrain the disk/bulge?

2) CHECK CONTAMINATIONWeighted likelihood?

3) BREAK DEGENERACYMore contours!

Scientific Outlook

FORMALISM

Mock catalogs- HVSs Galactic population vs Gaia

Fisher Forecast - P-S distribution

ASSUMPTIONS:

- 2D toy model

- 5 M☉

HVSs

Fisher Forecast - P-S distribution

Statistical Inference - Likelihood

Likelihood Principle:

All knowledge about the real parameters is in the likelihood.

Parametric PDF

Likelihood

Maximum Likelihood Estimation:

The point of maximum of thelikelihood is a good estimator of

the real parameters.