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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.
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