Davi C. Rodrigues

Department of Physics, Federal University of Espírito Santo (UFES),

Vitória, ES - Brazil

In collaboration with: Valerio Marra (UFES, Brazil) Antonino Del Popolo (U. di Catania, Italy) Zahra Davari (Bu Ali Sina U., Iran) Nature Astronomy (2018)

Campos do JordãoXXXIX ENFPC

Absence of a fundamental acceleration scale in galaxies

September 26, 2018

www.cosmo-ufes.org

Vitória

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration in galaxies

One galaxy different bands

�2

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration in galaxies

Galaxy rotation curves: a draft

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ity [k

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0 10 20 30 40

0

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150Observed

Gas + starsStars

Gas

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

✴ There is a sharp relation between the observed acceleration and the acceleration inferred from baryonic matter alone. [McGaugh, Lelli, Schombert, PRL 2016].

✴ No assumptions on dark matter.

✴ Derived from 153 of the 175 SPARC galaxies [Lelli, McGaugh, Schombert, Astron.J. 2016].

✴ Why there is an acceleration-scale dependent dynamics?

�4

The Radial Acceleration Relation

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

✴ A simple function describes very well this correlation

✴ is a constant (the acceleration scale). The residuals have a scatter of 0.11 dex.

✴ It is found that the average expected errors (on rotation velocity, mass-to-light ratios,

distance and inclination) lead to an average uncertainty of 0.12 dex, hence are similar to the scatter found in the data.

�5

The correlation and the scatter

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a0 = 1.20 × 10−13 km/s2

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

✴ Although not obvious a priori, some resultsusing hydrodynamical simulations showthat LCDM may satisfy the RAR [Keller, Wadsley ApJ 2017; Ludlow et al PRL 2017; Navarro et al MNRAS 2017] with only a mild dependence on feedback.

✴ The RAR may be a complex result from LCDM, but the existence of such correlation is a straightforward prediction from MOND.

✴ Two interpretations for the RAR:

1. The acceleration scale a0 is an emergent phenomena. Possibility a product of complex baryonic and dark matter interactions; the scale would be an outcome of galaxy evolution.

2. The acceleration is fundamental (at least at the galaxy level). It could be the outcome of a modified theory of gravity theory that introduces a fundamental acceleration scale.

�6

Interpretations…

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

✴ This is the main question addressed our paper [DCR, Marra, Del Popolo, Davari, Nat. Astron. 2018].

✴ To address this issue, it is not sufficient to have a correlation with "small" scatter.

✴ The credible intervals of the acceleration scale need to be evaluated.

✴ Similar to what is commonly done in cosmology: different measurements of the same quantity (say, ) should be compatible.

✴ Nonetheless, galaxies are subjected to less controlled systematics than cosmology; hence some additional care is necessary.

�7

Is galaxy data compatible with a fundamental ?a0

Ωm

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

✴ We reduce the dependence of our results on possible uncontrolled systematics by:

✴ Using nuisance parameters with flat priors;

✴ Considering different sets of quality cuts;

✴ Considering two different samples of data from different groups;

✴ Looking for results with high statistical significance.

�8

General considerations

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�9

The parameters and the priors

Due to the systematical uncertainties on , flat priors with constraints are natural and were used in a number of papers within Bayesian statistics [Hees et al, MNRAS 2015; Katz et al MNRAS 2017; Allaert et al A&A 2017; de Almeida et al arXiv [astro-ph.GA]

2018…].

Flat prior for the distance with a 20% tolerance.

Flat prior for a0.

Parameter Prior

Stellar disc mass-to-light ratio Factor 2 on the RAR central value: 0.25-1.0

Stellar bulge mass-to-light ratio Factor 2 on the RAR central value: 0.35-1.4

Distance variation 20% variation from the central value.

acceleration scale

Υ⋆D

Υ⋆B

δa0 a0 > 0

Υ⋆

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

Quality cuts are important in our analysis and were not used as extensively as we did.

We find the a0 posteriors of all the 175 SPARC and 18 THINGS galaxies, but only some of the galaxies passed to the final analysis.

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The quality cuts

Quality cut Description

“RAR” It removes some SPARC galaxies not considered robust enough, as used in the original paper on the RAR. (175 -> 153)

Closed 5 σ posteriors

Removes the galaxies that are compatible with a0 = 0 at 5σ level. It is a requirement for finding well defined 5 σ contours.

5 σ Removes galaxies with too high &2 : those that are already individually rejected at 5σ. (Eliminates 41 galaxies from SPARC).

Other quality cuts beyond the main analysis

3σ quality cut (62 galaxies eliminated), surface brightness quality cuts and luminosity quality cuts.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

MAGMATable Generate a table with the selected data computed from the exported results of MAGMAFits and mBayes. Prepare variables for correlation analysis.

MAGMAPlots Generate plots for all the fitted galaxies from the exported results of MAGMAFits.

MAGMAFits Finds the best fit for a given model. Performs fits for a complete sample with one line command. Automatically does many minimizations per galaxy with different numerical assumptions. Uses parallel processing on two stages. The second stage refines the first results. Minimizations based on Differential Evolution. Export the results to be used by other functions. Export the chi2 function and the best fit to mBayes.

�11

Codes to automatically analyse hundreds of galaxiesMAGMA

Mathematica Automatized Galaxy Mass Analysis

Can be found at Github: https://github.com/davi-rodrigues/MAGMA

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

MAGMATable Generate a table with the selected data computed from the exported results of MAGMAFits and mBayes. Prepare variables for correlation analysis.

MAGMAPlots Generate plots for all the fitted galaxies from the exported results of MAGMAFits.

MAGMAFits Finds the best fit for a given model. Performs fits for a complete sample with one line command. Automatically does many minimizations per galaxy with different numerical assumptions. Uses parallel processing on two stages. The second stage refines the first results. Minimizations based on Differential Evolution. Export the results to be used by other functions. Export the chi2 function and the best fit to mBayes.

�11

Codes to automatically analyse hundreds of galaxiesMAGMA

Mathematica Automatized Galaxy Mass Analysis

Can be found at Github: https://github.com/davi-rodrigues/MAGMA

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies

MAGMATable Generate a table with the selected data computed from the exported results of MAGMAFits and mBayes. Prepare variables for correlation analysis.

MAGMAPlots Generate plots for all the fitted galaxies from the exported results of MAGMAFits.

MAGMAFits Finds the best fit for a given model. Performs fits for a complete sample with one line command. Automatically does many minimizations per galaxy with different numerical assumptions. Uses parallel processing on two stages. The second stage refines the first results. Minimizations based on Differential Evolution. Export the results to be used by other functions. Export the chi2 function and the best fit to mBayes.

�11

Codes to automatically analyse hundreds of galaxiesMAGMA

Mathematica Automatized Galaxy Mass Analysis

Can be found at Github: https://github.com/davi-rodrigues/MAGMA

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Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�12

mBayes Bayesian inference with Mathematica https://github.com/valerio-marra/mBayes

Codes to automatically analyse hundreds of galaxies

MAGMA

χ2 functions& Best-fits (to optimize the Bayesian analysis)

Credible intervals on a0

Data analysis

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�13

Is there a common acceleration scale? - Main analysis

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Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�14

Is there a common acceleration scale? - Main analysis

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To sintetize this result into a single number, we use:

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�15

Is there a common acceleration scale? - THINGS

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For the THINGS galaxies, the situation is qualitatively similar.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�16

Is there a common acceleration scale? - Correlations?

We considered possible systematical effects that depend on luminosity or surface brightness.

But there is no significant correlation with a0.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�17

Is there a common acceleration scale?

Our answer is no.

Rotation curve of galaxies yield acceleration scales not compatible among themselves.

The acceleration scale that appears in the RAR is of emergent nature.

Consequences?

The most obvious consequence is for MOND and some other related approaches.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�18

What is MOND?

✴ MOND stands for Modified Newtonian Dynamics [Milgrom ApJ 1983; Famaey,

McGaugh Living Rev. Res. 2012]. Removes Dark Matter in favour of a fundamental acceleration.

✴ Some newer approaches towards MOND have been put forward [e.g., Milgrom PRD 2015], but the existence of a0, and that it is found from galaxies are central assumptions.

✴ From MOND, the RAR is a clear consequence.

Interpolating function

Fundamental acceleration scale

Observed acceleration

Newtonian accelerationµ

✓a

a0

◆a = aN

µ(x) =

(x, if x ⌧ 1

1, if x � 1.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�19

What is interesting about MOND?

✴ I would stress the following features, but see [Famaey, McGaugh Living Rev. Rel. 2012]:

- Tully-Fisher relation residues.

- Extension of the Tully-Fisher relation: the Baryonic TFR.

- Prediction of some general properties of LSB galaxies.

- Just a single universal fitted parameter theory with “satisfactory" rotation curve fits without dark matter.

- It is compatible with the stellar mass-to-light ratios currently considered viable.

- The existence of the RAR (or MDAR) is an immediate outcome.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�20

What if another interpolating function is used?

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Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�21

MOND and the Milky Way: a comment

✴ In [Iocco, Pato, Bertone PRD 2015], several possible baryonic models for the Milky Way are considered, but MOND could only provide a reasonable fit to the Milky Way if one uses an a0 value that is incompatible with the standard value by more than 5σ.

✴ The result above is very interesting, however, it is dependent on the interpolating function.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�21

MOND and the Milky Way: a comment

✴ In [Iocco, Pato, Bertone PRD 2015], several possible baryonic models for the Milky Way are considered, but MOND could only provide a reasonable fit to the Milky Way if one uses an a0 value that is incompatible with the standard value by more than 5σ.

✴ The result above is very interesting, however, it is dependent on the interpolating function.

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�22

Criticism✴ From groups that work on MOND, we received different criticisms based

on best fit analysis.

✴ This is not a robust approach to criticise our results, since we do not test best fits: we test the compatibility of the credible intervals.

✴ One cannot prove that a constantis fundamental, one can only show that a set of tests iscompatible with its interpretationas fundamental.

✴ In particular, it was stated that our SPARC results would be in contradiction to[Li et al, Astron.Astrophys. (2018)].

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�23

Our reply

-1.0 -0.5 0.0 0.5 1.00.0

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R18 priorsR18 priors with variable iAs above, but with fixed a0L18 priors

b.

We reproduced and extended the analysis of [Li et al, Astron.Astrophys. (2018)] (to appear in Nat.Astron. communications).

That approach is only qualitative and has arbitrariness on the definition of (left plot). Nonetheless, it actually favours our priors (right plot).χ2

ν

Davi C. Rodrigues | UFESAbsence of a fundamental acceleration scale in galaxies�24

Conclusions

✴ The RAR [McGaugh, Lelli, Schombert, PRL 2016] is an updated and sharper version of MDAR [Sanders, Astron. Astrophys. Rev. 1990; McGaugh ApJ 2004].

✴ The RAR is a non-trivial relation that boosted the interest on MOND.

✴ Ironically, we used the RAR to show that its acceleration scale is not fundamental, and hence that MOND itself cannot be a gravitational theory at the scale of galaxies.

✴ Is this the end of MOND? We believe so, when seen as a gravity theory; but phenomenologically it will continue to live as a useful relation.