The Radial Acceleration The Radial Acceleration Relation of - PowerPoint PPT Presentation

The Radial Acceleration The Radial Acceleration Relation of Galaxies Relation of Galaxies Federico Lelli Federico Lelli ESO Fellow (Garching, Germany) ESO Fellow (Garching, Germany) In collaboration with In collaboration with Stacy McGaugh (Case Western Reserve University) (Case Western Reserve University) Stacy McGaugh James Schombert (University of Oregon) (University of Oregon) James Schombert Marcel Pawlowski (University of California - Irvine) (University of California - Irvine) Marcel Pawlowski

Database for 175 Late-Type Galaxies at z~0 (spirals and dwarf irregulars): astroweb.case.edu/SPARC Lelli, McGaugh, Schombert 2016, AJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

175 HI Rotation Curves from Literature WSRT - 30 years of radio interferometric observations - PhD theses from the University of Groningen Begeman 1987; Broeils 1992; Verheijen 1997; de Blok 1997; Swaters 1999; Noordermeer 2005; Lelli 2013 + other studies Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

175 HI Rotation Curves from Literature WSRT - 30 years of radio interferometric observations - PhD theses from the University of Groningen Begeman 1987; Broeils 1992; Verheijen 1997; de Blok 1997; Swaters 1999; Noordermeer 2005; Lelli 2013 + other studies Homogeneous Photometry at 3.6 μ m Spitzer - Optimal tracer of the stellar mass: M * = ϒ * L - Smaller variations of ϒ * in the NIR than optical Verheijen 2001; Bell & de Jong 2001; Martinsson+2013; Meidt+2014; McGaugh & Schombert 2014; Schombert & McGaugh 2014; Querejeta+2015; R ö ck+2015; Herrmann+2016; Norris+2016. Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Widest possible range of disk properties HSBs Basically any known galaxy type with a rotating HI disk. 4 dex LSBs Dwarf Irrs Spirals 5 dex M gas /M bar Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Example: High-Mass, High-Density Spiral Spitzer 3.6 μ m ∇ 2 Φ bar (R,z) = 4πG ρ bar (R,z) V flat - Vertical Structure: Disks: exp(-z/h z ) with h z ∝h R Bulges: spherical symmetry total disk - Stellar mass-to-light ratio: bulge gas ϒ * = 0.5 M ⊙ /L ⊙ for disks ϒ * = 0.7 M ⊙ /L ⊙ for bulges Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Example: Low-Mass, Low-Density Dwarf Spitzer 3.6 μ m V flat ∇ 2 Φ bar (R,z) = 4πG ρ bar (R,z) - Vertical Structure: Disks: exp(-z/h z ) with h z ∝h R Bulges: spherical symmetry total gas - Stellar mass-to-light ratio: disk ϒ * = 0.5 M ⊙ /L ⊙ for disks ϒ * = 0.7 M ⊙ /L ⊙ for bulges Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

1. Basic Data & Structural Relations: Lelli+2016a, AJ 2. Baryonic TF Relation: Lelli+2016b, ApJL 3. Central Density Relation: Lelli+2016c, ApJL 4. Radial Acceleration Relation (I): McGaugh+2016, PRL 5. Radial Acceleration Relation (II): Lelli+2017a, ApJ 6. Testing DM Halo Profiles: Katz+2017, MNRAS 7. Testing Emergent Gravity: Lelli+2017b, MNRAS Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

1. Basic Data & Structural Relations: Lelli+2016a, AJ 2. Baryonic TF Relation: Lelli+2016b, ApJL 3. Central Density Relation: Lelli+2016c, ApJL 4. Radial Acceleration Relation (I): McGaugh+2016, PRL 5. Radial Acceleration Relation (II): Lelli+2017a, ApJ 6. Testing DM Halo Profiles: Katz+2017, MNRAS 7. Testing Emergent Gravity: Lelli+2017b, MNRAS Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Radial Acceleration Relation ~2700 independent points at difgerent R For all galaxies: ϒ disk = 0.5 M ⊙ /L ⊙ ϒ bulge = 0.7 M ⊙ /L ⊙ McGaugh+2016, PRL Lelli+2017, ApJ Baryonic Force: V 2 bar /R= -∇Φ bar Total Acceleration: V 2 obs /R = -∇Φ tot ∇ 2 Φ bar = 4πG ρ bar Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Radial Acceleration Relation g obs = g b ar For all galaxies: ϒ disk = 0.5 M ⊙ /L ⊙ ϒ bulge = 0.7 M ⊙ /L ⊙ g obs = √ g b ar g 0 g bar g obs = McGaugh+2016, PRL − √ g bar / g 0 1 − e Lelli+2017, ApJ Baryonic Force: V 2 bar /R= -∇Φ bar Total Acceleration: V 2 obs /R = -∇Φ tot ∇ 2 Φ bar = 4πG ρ bar Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Very different galaxies but ONE relation V 2 bar /R= -∇Φ bar V 2 obs /R = -∇Φ tot ∇ 2 Φ bar = 4πG ρ bar Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Building up the Radial Acceleration Relation Large Diversity in Rotation Curves Regularity in Acceleration Plane Lelli et al. (2017), ApJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Is There Any Intrinsic Scatter? Uncertainties drive scatter! err (g bar ) → ϒ * , 3D geometry err(g obs ) → Dist, Inc, V rot σ obs 2 = σ err 2 + σ int 2 σ obs → measured rms σ err → error propagation σ int → consistent with zero! McGaugh+2016, PRL; Lelli+2017, ApJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

We can infer the DM profile from the baryons! g DM = g tot − g bar = F ( g bar ) From the observations: 2 M DM ( R )= R For a spherical DM halo: G F ( g bar ) g bar M DM ( R )= R 2 For our fiducial fitting F: exp ( √ g bar / g 0 )− 1 G Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

We can infer the DM profile from the baryons! g DM = g tot − g bar = F ( g bar ) From the observations: 2 M DM ( R )= R For a spherical DM halo: G F ( g bar ) g bar M DM ( R )= R 2 For our fiducial fitting F: exp ( √ g bar / g 0 )− 1 G Purely Empirical Relations (accuracy ~30%). Only inputs are M/L and Poisson’s equation. Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Open Issues for ΛCDM models: 1. Why is the RAR scatter so small? Is this consistent with stochastic hierarchical merging? Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Open Issues for ΛCDM models: 1. Why is the RAR scatter so small? Is this consistent with stochastic hierarchical merging? 2. Why is the RAR outer slope ~0.5? g obs =√(g 0 g bar ) → V flat = M bar / (g 0 G) → Observed BTFR. 4 Whatever sets the RAR should also set the BTFR. Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Open Issues for ΛCDM models: 1. Why is the RAR scatter so small? Is this consistent with stochastic hierarchical merging? 2. Why is the RAR outer slope ~0.5? g obs =√(g 0 g bar ) → V flat = M bar / (g 0 G) → Observed BTFR. 4 Whatever sets the RAR should also set the BTFR. 3. Why an acceleration scale? What sets its value? Different roles of g 0 : baryon-to-DM transition (RAR) & global baryon-to-DM content (BTFR)! Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Conclusions: - There is a local coupling between baryons and DM in galaxies over ~5 dex in M bar . - There is an acceleration scale ~10 -10 m s -2 . Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Questions? Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Radial Acceleration Relation for ETGs X-rays ETGs: g obs from hot gas haloes in hydrostatic equilibrium (Humprey+2006,2009,2012) Rotating ETGs: g obs from stellar kinematics + Jeans Axisymmetric Models (Atlas 3D - Cappellari+2010) Dwarf Spheroidals: g obs from stellar kinematics + Jeans Spherical Models (many many references...) Lelli+2017a, ApJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

MCMC Fits to Individual Galaxies Extremely tight relation! σ obs = 0.054 dex (~10%) err(V rot ) ~ 10% Pengfei Li et al. (submitted) Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

A “ Natural ” outcome of galaxy formation? AM-based Models: Di Cintio & Lelli 2016 Desmond 2017 Navarro+2017 Numerical Sims: Keller & Wadsley 2016 Ludlow+2017 Tenneti+2017 Basic Results: 3.5 σ discrepancy! 1) Similar relation but shape is model-dep. 2) Scatter is too large: σ obs 2 = σ int 2 +σ err 2 Desmond 2017, MNRAS Can’t forget errors! Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Residuals vs Local Galaxy Properties Lelli+2017, ApJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Residuals vs Global Galaxy Properties Lelli+2017, ApJ Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies

Alternative versions of the RAR Federico Lelli (ESO Fellow) The Radial Acceleration Relation of Galaxies