raphaël peralta réza samadi & eric...

Raphaël PERALTA

Réza Samadi & Eric Michel

Seismic indices give global informations about stars oscillations

Some stars exhibits pulsations from the Main sequence, like the sun, to Red Giant passing through sub-giants. These pulsations are possible because these stars have convective zones on its envelope and in its core to pulsate. Two modes exist : p-mode: Acoustic or pressure (p) modes, driven by internal pressure fluctuations within a star; their dynamics being determined by the local speed of sound. g-mode: Gravity (g) modes, driven by buoyancy.

Stellar Seismic Indices - Peralta, Samadi, Michel 2


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Couin coouin couuuuiin*!!

*Bravo to the organizers of Elbereth!!

Seismic indices give global informations about stars oscillations


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We use spherical harmonics to caracterise the differents oscillations modes :

n, the order (correspond to radial modes) ; l, the degree (non radial modes, means the total number of cutting)

and finaly m, the azimuthal degree (the number of vertical cutting)

Spherical Harmonics

n : radial order

number of radial nodes

l : angular degree

number of surface nodes

m : azimuthal order

number of longitudinal nodes


νmax : Frequency of the maximum height in the power spectrum

νc : Cut-off frequency

ν𝑐

This graph shows the power density spectrum of the sun. Here we have νmax which is the frequency of the maximum height in the power spectrum. here is the cut off frequency which is the frequency above which there is no more total reflection at the star surface. The amplitudes of the solar like oscillations are modulated by an enveloppe that is approximately Gaussian.

And the peak of the enveloppe is at numax, the frequency of maximum power. Near numax, the oscillations have the most power.

ν𝑚𝑎𝑥


Chaplin et al. (2010)

Mean Large separation:

Small separation:

Catala 2009

Δν𝑛,𝑙 = ν𝑛+1,𝑙 − ν𝑛,𝑙

𝑑𝑙,𝑙+2 = ν𝑛,𝑙 − ν𝑛−1,𝑙+2

If we do a zoom of the previous plot, we can see individual modes.

Deltanu, the mean large separation corresponds to the distance between two consecutives order (n) with the same degree l

And d, the small separation that is the difference between two degrees of different order

Deltanu : temps caractéristiques de l'aller retour d'une onde de pression à l'intérieur de l'étoile

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Seismic scaling laws : Relation between global seismic parameters and fundamental stellar parameters

Seismic scaling relations do the link between global seismic parameters (numax, deltanu for example,

Because there are lot of seismic paramters) with fundamental stellar parameters,

such as the Mass, radius, log g etc.

ν𝑚𝑎𝑥, Δν, . . . Mass, Radius, log g, …


Peak frequency (Brown 1991, Kjeldsen & Bedding 1995)

Mean large separation (e.g. Ulrich 1986)

Δν ∝ 2 𝑑𝑟

𝑐𝑠

−1𝑅

0

Δν ∝ ρ 1 2 ∝𝑀

𝑅3

1 2

ν𝑚𝑎𝑥 ∝ ν𝑐 ∝𝑐𝑠2H𝑝

∝𝑔

𝑇𝑒𝑓𝑓∝

𝑀

𝑅2 𝑇𝑒𝑓𝑓

Recent reviews : Belkacem (2012 SF2A, arXiv:1210.3505) Belkacem et al (2013, arXiv:1307.3132)

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In 1991, Brown proposed that the νmax is proportional to νc and to make short, is proportional to the mass M, the radius and the effective temperature Deltanu represents the time that take a pressure wave to do the “aller-retour’ of the star. So, in 1986, Ulrich stressed that Δν is proportional to the square root of the mean density of the star, which is proportional to the Mass and Radius.

As we have seen in the previous slide, we can estimate the Masse and the Radius thanks numax, deltanu and Teff determined by the spectroscopy for example.

νmax, Δ𝜈 + 𝑇𝑒𝑓𝑓 M, R


𝑀

𝑀⊙≃

ν𝑚𝑎𝑥ν𝑚𝑎𝑥,⊙

3Δν

Δν⊙

−4𝑇𝑒𝑓𝑓

𝑇𝑒𝑓𝑓,⊙

3 2

𝑅

𝑅⊙≃

ν𝑚𝑎𝑥ν𝑚𝑎𝑥,⊙

Δν

Δν⊙

−2𝑇𝑒𝑓𝑓

𝑇𝑒𝑓𝑓,⊙

1 2

For stellar community :

16 (Red-Clump stars: post-He flash and core He burning)

Give valuable constraint on stellar evolution: e.g. evidence of mass loss

e.g. Mosser et al. 2012

Asteroseismic quantities and scaling relations can be used by many communities :


seismic R + observed Teff => absolute Luminosity compared to apparent Magnitude => Distance

by galactic community giving masses and radii for a large sample of stars.

For galactic community :

e.g. masses and radii for a large sample of stars

(e.g. Chaplin et al 2011, Miglio et al. 2009)


For exoplanets community :

e.g. provide better estimates of radii and Masses (e.g. Borucki et al. 2011)

Kepler 22b

Tirée de White et al. ApJ 743:161

2011:

Accurate and precise radii of the

detected planets depend on knowing

the radius of the host star accurately,

which is difficult unless the

temperature and luminosity of the

star are known precisely.

Asteroseismology program that will

provide seismic variables that can

characterize stellar radii easily,

accurately, and extremely precisely.

and finally by exoplanets community providing better estimates of radii and masses

Project title: Exploitation of Space Data for Innovative Helio- and Asteroseismology

Starting on January 1, 2013

Funded for four years by the European Union under FP7

WP3 – Data Handling and Archiving (Eric Michel)

A Stellar Seismic Indices (SSI) data base providing seismic indices (νmax, Δν ,…) for scientific community within and beyond stellar physic community

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SPACEINN is a projet that started the first January and is founded for four years.

It's aim is the Exploitation of Space Data (CoRoT, Kepler) for innovative Helio- and Asteroseismology.

I belong to the part which have to create a data base which will provide seimic parameters

like numax, deltanu, deltapi, for a wild (répandu) scientific community.

Here the website.

20 Stellar Seismic Indices - Peralta, Samadi, Michel

Many methods exist to extract seismic parameters. So, to do this seismic data base we had to compare them among the most relevant methods. Then, we chose one standard method for each seismic parameter. Of course these selected methods have to be robust and efficient, that mean that we can apply these method for as many stars as possible. And they have to be accurate and precise.

Many methods exist to extract seismic parameters from light curves of stars

Define one standard method for each type of seismic parameter

This « standard » method must be :

Robust and efficient

Accurate

Precise


I'm presenting the algorithm chosen to extract seimics indices from light curves :

On the left side, a light curve from a star observed by the satellite CoRot.

The first step is to compute the PDS (Power Density Spectrum) by the way of the Fast Lomb-Scargle periodogram using

Non-equispaced Fast Fourier Transform (NFFT).

Here We've done a zoom of the PDS where there is the oscillation-bump carateritic of p-mode

PDS : Fast Lomb-Scargle periodogram using Non-equispaced Fast Fourier Transform (NFFT) by B. Leroy (2012, A&A).


I'm presenting the algorithm chosen to extract seimics indices from light curves :

On the left side, a light curve from a star observed by the satellite CoRot.

The first step is to compute the PDS (Power Density Spectrum) by the way of the Fast Lomb-Scargle periodogram using

Non-equispaced Fast Fourier Transform (NFFT).

Here We've done a zoom of the PDS where there is the oscillation-bump carateritic of p-mode

CoRoT ID: 10163604

NFFT

Δν : autocorrelation method (Roxburgh & Vorontsov 2006 : Mosser & Appourchaux 2009) → ACF method


ACF

The second step consists to cut (or subdivide) the PDS in several tranches (parts) thanks a cosine filter centered at different frequencies. By this way, We select only certain parts of the spectrum. For all these parts, we compute the Fourier spectrum. Thereby, we get the autocorrelation of the time series. Indeed, the Fourier spectrum of the Fourier spectrum is equivalent to the autocorrelation of the light curve. In the second figure, I plotted the result of the autocorrelation for all filters. And there is one peak which comes out(emerges) most. This peak corresponds to the filters centered at the frequency around 34µHz, which corresponds to the filter where there is the numax bump

Δν : autocorrelation method (Roxburgh & Vorontsov 2006 : Mosser & Appourchaux 2009) → ACF method

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Δν

ACF

We redo the same thing around the frequency where we get the best autocorrelation peak Finally, we determine a first approximation of deltanu thank to the position of the highest peak. And the position of the filter which corresponds to this highest peak give an estimation of numax

Smoothed PDS

Raw PDS

Fit

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● νmax guess: from ACF method ●Envelop modelling: fit a Gaussian envelop to the smoothed PDS (eg. Huber et al 2009, Mosser & Mathur et al 2010, Hekker et al 2010 …) ●Background: granulation component + white noise component (+ activity component)

νmax guess: from ACF method

Background + Envelope fit (eg. Huber et al 2009, Mosser & Mathur et al 2010, Hekker et al 2010 …)

Guess profile

The third step is to estimate numax (the maximum height in the power spectrum). This plot shows the Power Density Spectrum in loglog. The red curve is the raw PDS, the green one is the smoothed PDS. The dot blue curve corresponds to the background guess determined using the numax found during the previous step. And the dashed blue curve is the background and envelope fit

(Activity component ?)

Granulation component

Noise level

Smoothed PDS

Raw PDS

Fit

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Guess profile

Gaussian Envelope

In order to get the best estimation of numax, we use three components for the fit : the granulation (that is a more or less a power law), the noise level (that is a constant) and the envelope (that is a Gaussian). We can add a fourth component : the activity component (more or less also a power law). But with this last component the fit is not better, even otherwise ! Maybe due to the few points in this part of the spectrum.

(Activity component ?)

Granulation component

Smoothed PDS

Raw PDS

Fit

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Guess profile

Gaussian Envelope

ν𝑚𝑎𝑥 = 33.99 ± 0.02µ𝐻𝑧

Noise level

The envelope component give us numax with a great precision.

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Δν guess: from envelope fit

To finish, the last step consists in re compute the autocorrelation around numax determine by the fit in order to define deltanu as well as possible. (In this example, the result of deltanu before and after the numax guess beacause is a quite good “star”, with a good curve light.

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1456 CoRoT targets brighter than mag. 13.

Luminosity class III

Spectral type : G-M

Seismic indices obtained for 775 targets (~53 %)

ν𝑚𝑎𝑥 𝑒𝑛𝑣

Δν𝐴𝐶𝐹

Scaling relation : (Mosser et al. 2010)

Δν = 0.280 ∗ ν𝑚𝑎𝑥

0.747

I show you an example for a set of data from CoRoT Apogee. We obtained seismics indices for around eight hundred stars out of one thousand five hundred .

Scaling relations are becoming essential tools for deduce information of stars

Easy access to stellar radii, masses and gravity for a large set of star

By the SPACEINN Project, a Stellar Seismic Indices data base is being established

Providing seismic data for scientific community


Seismic masses and radii are precise to 20 and 10% respectively but efforts are to be made to investigate possible biases, that ask for: Calibrate the scaling relations

Comparing seismic masses and radii with independent measurements, by interferometry and/or astrometry for example

Refine scaling relations :

Theoretical work to understand (and reduce) the dispersion of scaling relations

Study the influence of some parameters


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I feel good !

● CoRoT :

• Red Giants ~ 10,000

• Main Sequence + Sub-Giants ~ 100

● Kepler :


• Main Sequence + Sub-Giants ~ 1,000

● OGLE (Optical Gravitationnal Lensing Experiment) :



● 2 missions projects which will provide seismics indices :

• PLATO : its objective is to characterize exoplanets and their host stars in the solar neighborhood

• SINDICS (Seismic INDICes Survey) : propose the 1st seismic all sky survey of our galactic environment.


Scaling relations give us precise determination of M, R

but...


We saw that scaling relations are good tools to derive model independent determinations of stellar parameters. But Are the masses and radii derived from the seimis indices accurate ?

Typical accuracy : 15 methods of analysis have been applied by 6 teams on simulated power spectrum (Verner et al. 2011)

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ν𝑚𝑎𝑥 ∼ 5%

Δν ∼ 1%

Δ𝑇𝑒𝑓𝑓 ∼ 100K

Δ𝑀

𝑀∼ 20%

Δ𝑅

𝑅∼ 8%

R and M are rather insensitive to uncertainties on ΔTeff

The precision on νmax the limiting factor

± 5% ± 1%

Verner et al. Compared fifteen methods of analysis used by six teams on simulated power spectrum and they showed that the typical accuracy of the stellar seismic indices is quite good. Around 1 % for Δν and 5 % for νmax. Under the assumption that the effective temperature is determined with a precision of 100k, one deduce that the accuracy of the mass is about 20 % and 8 % for the radius. So, the precision on νmax is the limiting factor.

There are some uncertainties related to the definitions of the seismic parameters

Can scaling relations be considered as exact relations ? (e.g. Belkacem SF2A 2012)

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Miglio (2012)

We have some uncertainties related to the definitions of the seismic parameters. In this graph is plotted the difference between the interferometry and seismic radius versus the interferometry radius. And we can see that there is a significant deviation over 15%. The second plot shows the observed νmax versus predicted νmax for main sequence stars observed from the ground. A departure from the scaling relation but only for large νmax. It seems quite good for main sequence stars. So, can we say that scaling relations are exact ?

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Theoretical work

Belkacem et al. (2013)

In fact, Belkacem et al showed that numax is not directly proportional to nuc as we can see in the first plot, but we need to introduce to the Mach number. So, numax is equal at a constant to nuc

ν𝑚𝑎𝑥 ∝ 𝑀𝑎3 ν𝑐

ν𝑚𝑎𝑥 ∝ ν𝑐 ?

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White et al. (2011)

Effect of metallicity negligible

White et al studied the influence of some paramters like the effective temperature and the metalicity

They showed that the relation between deltanu and the mean density is strongly depending of the temperature.

Morever, the effect of metalicity remains negligeable

Study the influence of: Teff and metallicity

± 3%

Additional dependence on the effective temperature

Calibrate the scaling relations :

Comparing seismic masses and radii with independent measurements (interferometry and astrometry)

Uncertainties strongly depends on the star mass and evolutionary state

Refine scaling relations :

Theoretical work to understand (and reduce) the dispersion of scaling relations

Study of convection influence


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