# Presentation: 394450

## The IMF of EMP stars and the probe into the star-formation process of the Milky Way

- Yutaka Komiya
- (Tohoku Univ.)
- Takuma Suda, Asao Habe, Masayuki Fujimoto (Hokkaido Univ.)

- First stars III Santa Fe

**Notes:**
I’m Yutaka Komiya. from Tohoku University. 

Today, I'd like to talk to you about “The initial mass function of extremely metal-poor stars and the probe into the star-formation process of the Milky Way”

## EMP (Extremely Metal-Poor) star, CEMP (Carbon-enhanced EMP) star

- EMP star is a nearby probe into early universe.
- Stars of [Fe/H]≦-2.5
- ~1000 EMP stars are observed in the Galactic halo.
_*Only low mass stars still alive.*_
- 20~25% of EMP stars show _carbon enhancement _(CEMP).

**Notes:**
I talk about EMP star. 
In this talk, 
I call stars of metallicity [Fe/H] = -2.5 or less EMP stars (and distinguish them from Pop2 stars and zero metal pop3 stars. )
As you know, EMP star is a nearby probe into early universe. 
However, we can observe only low mass EMP star still alive. 

Large fraction of EMP stars show enhancement of the surface carbon abundance. 
I focus on these CEMP stars. 

## Contents

**We give constraint on **_**the IMF of EMP stars**__** **_**from **_**observation of CEMP stars**_**. **

**We investigate metallicity distribution of EMP stars taking into account the **_**formation history of our Galaxy**_**.**

**Notes:**
In the first half, 
We estimate the IMF of EMP stars from the observation peculiarities of CEMP stars relying upon the theoretical knowledge of the evolution process of an EMP star. 

In the latter half, 
We investigate the formation history of EMP stars in comparison with the observed Metallicity Distribution Function taking into account the merging history and chemical evolution of Galaxy.

## Binary ― Probe into missing more massive EMP stars ―

- Observation peculiarities of surface abundance of CEMP stars.
- Theoretical knowledge of the evolution process of EMP star.
- Relation between observed abundance and mass of primary.
- Estimation of IMF.

- Estimate of the IMF

- CEMP star is formed in a binary system.

- How to estimate the IMF from observation of CEMP star.

- Evolution of a primary star  affects abundances of a secondary star.

- _Observed feature _of a CEMP star
-  _Mass _of a primary star.

**Notes:**
At first, 
I show you how to estimate the IMF from observations of CEMP stars. 

The key is a binary. 
In the binary system, 
 heavy elements synthesized in evolved primary star
 can be transferred to secondary star through stellar wind or RLO. 
So, surface abundance pattern of low mass secondary star possibly effected by evolution of primary. 

We think all CEMP stars are made in a binary system   with intermediate mass primary star. 

When we know the relation 
between observed feature of CEMP stars & mass of primary star 
 we can estimate the IMF. 

## Subclasses of CEMP starCEMP-s & CEMP-nos

- _CEMP-s (~70%)_s-process element rich [Ba/Fe]~2N rich ([C/N]~1)
- _CEMP-nos (~30%) _only C rich[Ba/Fe]~-1[C/N]=-1~2

- □:[C/Fe], ■:[N/Fe]

- [Ba/Fe]

**Notes:**
Observationally, we can divide CEMP stars into two subclasses. 

About 70% of CEMP stars show large s-process element enhancement. 
We call them CEMP-s. 

Another subclass is CEMP no-s, 
 CEMP stars with normal s-process elements abundances. 

## Many intermediate mass stars(especially 4~6M☉ ) 

- IMF with peak at larger mass

- (Komiya et al.2007)

- _Theory_
-   MPrimary = _0.8~3__M__☉_
-   Separation = 1~100AU
-   MPrimary = _4~6__M__☉__ _
-   Separation = 3~100AU

- CEMP-s

- CEMP-nos

- _Observation_
- 10~25% of EMP star
- 1/3~1/4 of CEMP star

**Notes:**
Theoretical studies of evolution of EMP stars and mass transfer show that, 

CEMP stars are formed in a binary with intermediate mass primary stars and this separation range 1 to 100 Mo. 
And when mass of the primary star is 4Mo or above, secondary star become CEMP-nos. 
See detail in this paper. 

Observationally, fractions of these stars are very large in comparison with more metal rich stars. 

So, fraction of intermediate mass star in EMP star is very large. 
However, 
If the IMF of EMP stars is similar to IMF of more metal rich stars, such large faction is impossible. 

It means that 
IMF of EMP stars is peaks at larger mass. 

## Assumptions

- _IMF_
- Lognormal form
- _Binary fraction_   : 50%
- _Mass ratio_
- uniform distribution      n(q)=const. (q=m2/m1)
- _Period_

- Duquennoy & Mayer (1991)

**Notes:**
I estimate the typical mass of the IMF quantitatively under following assumptions. 

We assume the form of function as lognormal form & search parameter Mmd. 

For mass ratio distribution, We assumed uniform mass ratio distribution for simplicity. 

For binary period, 
we adopted the distribution derived by DM91. 

## Constraints on the IMF

- Search typical mass (Mmd) consistent with observations.
- (σ=0.33)

- CEMP-s ⇒
-  Mmd =0.6~2 or 6~13 M☉.

- CEMP-s & CEMP-nos ⇒ IMF with _M__md __~10 M__☉__ _.

- Predicted fCEMP-S

- Predicted fCEMP-noS/fCEMP-S.

- 1
- 0.8
- 0.6
- 0.4
- 0.2
- 0

- Observed fCEMP-S.

-        0.5         1         2            5        10      20   (M☉ )

- _Results_

- ObservedfCEMP-noS/fCEMP-S.

- fCEMP-S = fraction of CEMP-s stars among EMP stars

- Mmd

**Notes:**
// To estimate typical mass of EMP star, 
I search parameter, Mmd, of lognormal IMF consistent with observation.(dispersion Δ assumed to 0.33)

This graph shows 
    fractions of CEMP-s and CEMP-nos stars among EMP stars
    as a function of the medium mass. 

   Thick solid line shows fraction of CEMP-s stars in EMP stars. 
   Thick dotted line shows fraction of CEMP-nos.
Observed fraction of CEMP-s star is in this range between 2 dashed lines. 
To meet constraint of CEMP-s stars, medium mass in these 2 range is needed. 

   Thin solid line shows the number ratio of CEMP-s and CEMP-nos. 
Observed number ratio is between 1/3(one third) to 1. 
So, to meet both constraint, IMF with Mmd similar to 10 Mo is needed. 

So, as a result, 
typical mass of EMP star is 10Mo. 

## IMF of EMP star

- EMP survivors

- Supernova
- Metal ejection

- White dwarf.
- Companion star become CEMP.

- IMF of primary star

- IMF of secondary companion

- Only 1/10 stars still alive.
- Most of them is secondary companion.
- They affected by primary star.

- 0.1                   1                    10                  100   (M☉ )

**Notes:**
This is the derived IMF of EMP stars. 

Red line is mass distribution of primary stars.  
Green line shows mass distribution of secondary companion stars. 

We can see
Observed EMP stars are tenth low mass survivor of them. 
 and almost all EMP survivors are secondary companion of binary system. 
So, many EMP stars possibly affected by primary stars. 

## Contents

**We estimate **_**typical mass of EMP stars**__** **_**from **_**observation of CEMP stars**_**. **

**We investigate MDF & formation history of EMP stars taking into account the **_**merging history of our Galaxy**_**.**

- (MDF: Metallicity Distribution Function)

**Notes:**
In the previous half, 
I have shown that IMF of EMP star is top heavy from observation of CEMP stars.

In the following, 
I investigate the formation history of EMP stars & metallicity distribution function. 

And I show that 
 ♦MDF for derived IMF is consistent with observation 
 ♦ and MDF for [Fe/H]<-4 affected by galaxy formation process. 

## Metallicity Distribution Function (MDF)

- Derived top-heavy IMF is consistent with observation (for [Fe/H] > -4).

- One zone model.No infall/outflow.Instantaneous recycling. Fe yield: 0.07M☉

- -6              -5              -4               -3              -2

- Number100001000
- 100101

- [Fe/H]

- IMF of Galctic spheroid

- Theoretical MDF for IMF with Mmd =10 M☉.

- ObservationHK survey, HES survey(Beers et al.2005)

- _Assumptions_

- _Results_

**Notes:**
We derived theoretical MDF under these assumptions, simple one zone model with no infall and no outflow and instantaneous recycling. 
& 1 SN eject 0.07Mo of iron. 

This figure shows MDF. 
(Horizontal line shows metallicity &)
 vertical line shows number expected to be observed in HES survey. 

Red histogram shows the observed distribution. 
Blue line shows theoretical MDF for the derived top heavy IMF. 
Green line shows MDF for IMF of observed Galactic spheroid. 

Our theoretical estimation yield reasonable fit with observation, 
 except for lowest metallicity range. 
It support top heavy IMF we derived. 

For the lowest metallicity range, 
 we can point out cut-off of the distribution and hyper metal poor stars. 

Then, we try to explain such distribution. 

## Hierarchical galaxy formation

- The cut-off is originate from structure formation process

- -∞    -4     [Fe/H]

- First star

- Stars formed after first supernova.

- 1st mini-halo ~ 106-7 M☉

-  SN

- [Fe/H]~-4

- After 1st SN explosion,

- Pop.3 stars still alive ⇒HMP star. (Suda et al.2004)

- MDF cut-off at [Fe/H]~-4

- 2nd star [Fe/H]~-4

- merge

**Notes:**
I propose one scenario that  the cut-off is originate from structure formation process. 
It is thought that Galaxy is formed hierarchically. 
(That is, small halo collapse at first and, they merge and accrete the IGM, become Galaxy at last. )

In the starndard ΛCDM cosmology, 
The typical mass of host halo of first star forming cloud is 10^6Mo. (several million solar masses).
One SN eject 0.07Mo of iron. 
After 1st SN explosion, metallicity of cloud become
 mass of ejected iron over mass of gas cloud, 10^-4 Zo on average, in such small cloud. 
So, after only 1 SN, metallicity become [Fe/H]=-4. 

And, we expect to see the cut–off at [Fe/H]~-4. 
If some first stars still alive, they possibly become HMP star by surface pollution.

## Effect of structure formation

- Merging history: Press-Schechter approach
- (Somerville & Kollat1999)

- Model predict  cut-off at [Fe/H]~-4.

- SFE: 10-10/yr

- Z=0

- -∞              -5              -4               -3       -2.5[Fe/H]

- number
- 100001000
- 1001010.1

- Observed MDF

- Theoretical MDF with merger tree.

- Number of stars with Z = 0 is inconsistent.

- _Results_

- _Assumptions_

**Notes:**
To test this scenario, I estimate the MDF again. 
In this time, I take account with evolution of halo-mass. 
This figure shows the result. 
I realized merging history following the Press-Schechter approach. 

Blue line shows theoretical MDF with merger tree. 
Green line shows MDF for previous one zone model. 
We can see cut-off around [Fe/H]=-4 similar to observation. 
So, this cut-off can be understood as the effect of structure formation. 

However, this model predict large number of Pop.III stars, tens times as many as observation. 
It suggest that formation process of these stars are different from EMP stars. 

## First star

- _M__md __=100 M__☉_ for Z=0.

- _Pair-Instability supernovae_
- (Fe yield: 10M☉)
- ⇒iron overproduction

- First star : supermassive not PISN.

**Notes:**
It is thought that first star is super-massive star. 

So, we assumed typical mass of zero metal star is 100 Mo. 
This figure shows the result. 
For this case, 
Predicted number of zero metal Pop.III stars are comparable to observed number of HMP stars. 

Then, we assumed that all first stars make Pair Instability Super-Novae. 
 & eject large mass of heavy element. 
So, in this case, all galactic gas become more metal rich quickly, and form few EMP stars. 

These results suggest that first stars are possibly super-massive star
 but most of them don’t make PISN. 

## Summary 

- Summary

- From binary stars, we can investigate the formation of EMP stars.
- EMP star can be a probe to history of galaxy and first star.
- _IMF of EMP star ([Fe/H]≦-2.5) is top heavy_.
- Top heavy IMF is consistent with observed MDF.
- EMP stars are affected by_** formation process of our Galaxy**_.

**Notes:**
I showed that binary stars are useful to investigate the formation of EMP stars. 
 & EMP star can be probe to history of galaxy and first star. 

Main result is this. 
IMF of EMP star,
 not only Pop3 star, but also EMP star with metallicity up to -2.5, is top heavy. 

Top heavy IMF is consistent with observed MDF of EMP stars. 
EMP stars are affected by formation process of our Galaxy.

Thank you very much for kind attention.

## Thank you!

## Evolutionary characteristics of intermediate mass EMP stars

- There is dredge up mechanism peculiar to EMP star.

- 0.8   1.2  1.5

- 3

- 7      (M☉)

- [Fe/H]

- -2.5

- -4

- Z=0

- Third Dredge Up

- He-FDDM
- (He-flash driven deep mixing)

** ****Dredge up of C, N and s-process elements.**

- He-FDDM (≦3 M☉)⇒_C, N and __s-process __element_enhancement.⇒CEMP-s
- Third dredge up _only Carbon _enhancement(in EMP stars)⇒CEMP-nos.

- Hot bottom burningC⇒N

** ****Dredge up of C. **

- (Suda et al.2004)

**Notes:**
Sub-classification of EMP star is explained by 2 carbon dredge-up mechanisms. 

This Fig shows general picture of evolution of surface abundance of intermediate mass EMP star
// on the diagram of initial stellar mass and pristine metallicity ([Fe/H]). 

One is He-FDDM. 
It’s dredge up mechanism peculiar to stars of [Fe/H]<-2.5. 
In the stars of mass with 3Mo or less, He-shell flash contact with Hydrogen rich layer and hydrogen burning cause deep mixing. 
This mechanism enhance surface abundance of C, N and s-process elements, 
 and make companion CEMP-s. 

The other mechanism is TDU. 
The stars with 4Mo and over undergo only TDU.
It dredge up carbon to surface but s-process elements are not synthesized in EMP star. 
//And, stars with mass larger than 6 Mo, hot bottom burning convert carbon to nitrogen. 
And, they make companion CEMP-nos. 

## Binary parameters of CEMP star

- Binary parameters of CEMP star

- _Result_
- CEMP-s:
- Mass of Primary Star = 0.8~3M☉
- Orbit ratius = 1~100AU
- CEMP-nos:
- Mass of Primary Star = 4~6M☉ Orbit radius = 3~100AU

- _Assumptions_
- Bondi-accretion of stellar wind
- Secondary star    mass = 0.8 M☉     envelope mass = 0.2 M☉
- Wind
-     velocity = 30km/s
-     carbon abundance [C/H]=0
-     spherical symmetry
- Circular orbit

- Transferred carbon is too little

- Roche lobe overflow happened before dredge-up Carbon in primary.

- Upper mass limit to TP-AGB evolution with C+O core

- Conditions of binary parameters under which secondary star become CEMP star.

- Initial mass of primary star (M☉ )

- Orbit separation (AU)

**Notes:**
Next, 
we estimate the change of surface Carbon abundance of secondary star through binary mass transfer. 
And we investigate the condition of binary parameters under which secondary star become CEMP star.

This Fig. Shows Evolution of binary system
  on the diagram of the initial mass of primary star and the initial separation. 

If radius is very wide, mass of carbon transferred by stellar wind is too little to form CEMP star. 
I calculate the upper limit under these assumptions. 
Green lines denote the separations for which the envelope of secondary stars enriched with [Fe/H]=-3, -2, -1, respectively. 
If radius is very small, Roche lobe overflow happened before dredge-up Carbon. 
Red line denote orbital separation below which primary fills RL before He-FDDM or the TDU starts. 

Now, we know
the binary parameters under which the secondary star can evolve to CEMP stars through mass transfer. 
Binary with mass of primary =(equal to)0.8~3.5Mo, and separation =1~100 become –CEMP-s 
And, mass of primary =3.5~6Mo, and separation =3~100 become –CEMP-nos . 
Now, We can discuss about statistical feature theoretically. 

## Estimation under other assumptions 

- 0.2         0.5       1        2            5       10      20

- 10.8
- 0.60.4
- 0.20

- Mmd(M)

- Estimation under other assumptions

- Mass of a secondary star is independent from mass of a primary.

-  _M__md __~3 M__☉__ _

**Notes:**
This graph shows fractions  when we assume the mass of a secondary star is independent from mass of a primary. 

For this case, estimated typical mass of EMP star is 3Mo. 

## He flash driven deep mixing

- 0.8~3.5M☉
- He shell flash recur and growth.
- Mixing of hydrogen leads to splitting of the He flash convective zone to trigger deep mixing.

- H mixing

- He flash convective zone

- _Result_
- Dredge up of carbon.
- Nitrogen & s-process element synthesized by H mixing.

- 12C(p,γ)13N(e+,ν)13C(α,n)16O

- H

- Dredge up

- S-process

- Mass

- Surface conzective zone

- time

- Suda et al. (2004)

**Notes:**
In the stars of mass with 3Mo or less, He-shell flash contact with Hydrogen rich layer and
 burning of mixed hydrogen leads to splitting of the He flash convective zone to trigger deep mixing. 

Additionally, mixed H react with C to form N & eject n, and s-process works. 

## Constraint on IMF

- IMF of EMP stars on the parameter diagram of Mmd and Δ.

- _CEMP-s & CEMP-nos_
- _⇒__ __Pink area _

- Mmd = 5~30 M☉

- Blue line: contour of total mass of EMP stars.

- 0.1                  1                    10                  100  (M☉)

- Mmd

- 0.8
- 0.6
- 0.40.2

- Δ

- Contour of fCEMP-S

- Contour of fCEMP-noS

- _CEMP-s_
- _⇒__ __Yellow area _

**Notes:**
This figure is similar estimation of IMF 
  but also dispersion is treated as free parameter in this figure. 
Horizontal axis is M medium & Vertical axis is dispersion, sigma.

Solid lines are contour of fraction of CEMP-s , 10%,25%, 30%
dotted lines are contour of number ratio between CEMP-s & CEMP-nos

We can explain the observed proportion of CEMP-s if IMF parameter is in this Yellow parameter region. 
& we can explain also the observed number ratio if IMF parameter is in this Pink parameter region. 

And these dashed vertical lines is contour of total mass of EMP stars formed in high z under the parameters. 
Total mass thought to be less than nine powers of ten. 

So, as a result, we estimate Mmd is 5-30Mo. 

## Merger tree

-  z

- mini-halo mass(M☉)

-                 0.1                     0.2             0.5    1    ( Age from Big Bang (Gyr))

- (sampling 1/1000 branches)

**Notes:**
This figure shows one realization of merger tree. 
Mass of each branches as functions of redshift or time. 

## Extended Press-Schechter theory

- (~1/z)

- (Bond et al.1991, Lacey&Cole 1993)

- Halo number density with mass M at redshift z is

- Probability distribution of trajectories inside halo with mass M at z = z+dz that are also in halo with mass M2 at z=z.

- (δ(M,x):xを中心とした質量Mの領域の平均密度からのずれ)

## Surface pollution to HMP

- Heavy element on HMP stars are possibly accreted from ISM.

- Vvir: virial verosityrvir: virial radiusM: halo massm: mass of star

- I assumed Bondi accretion of ISM to star with virial velocity.

**Notes:**
Under these assumptions, 
 Mass accretion rate is anti proportional to halo mass. 
So, in the small halo in early universe, effect of surface pollution is important. 

## Effect of surface pollution

- Zero metal star typically become [Fe/H] = -7~-6.
- However, real pollution rate is strongly depend on SFR and relative velocity to ISM.

**Notes:**
We investigate accretion rate and metallicity of polluted stars. 
In this model, predicted metallicity of polluted Pop.3 stars are [Fe/H] -6 or less for main sequence stars and -8 for giants. 
However, accretion rate is strongly depend on relative velocity to ISM, 
 and it can not be same to virial velocity. 
Additionally, star formation efficiency in early universe is not revealed and it affect metallicity of polluted Pop2 star, too. 
So, we cannnot reject the possibility that HMP stars are the polluted Pop3. stars. 

## Period-[C/H] relation

- Period & [C/H]

- [C/H]

- Period

- Giant

- Dwarf

- 0.3M☉

- Primary massThick :1.5M☉ Thin:3M☉
- Jeans theoremconstant separation

- ■:giant●:Sub giant▲:Dwarf

**Notes:**
If carbon on the CEMP stars are derived by stellar wind, we can see correlation between orbital separation and accreted mass. 
Carbon abundance is a function of accreted mass. 

This figure shows predicted carbon abundance as function of orbit period, 
 and observed distribution of [C/H] and period of CEMP stars. 
We can see observed values are consistent with observed correlation. 

Notice that orbit if binary stars experienced RLO shrink and become to have short period. 

## Orbit distribution

- 軌道半径(AU)

- 個数

- CEMP star推定値

- CEMP star観測値

**Notes:**
Red histogram shows orbit distribution of CEMP stars. 
2 green vertical lines shows upper & lower limit of separation to be CEMP star. 
And green curve shows orbit distribution of observed binary systems. 

## Third dredge up

- 1.5~6M☉No hydrogen mixing No s-process in EMP stars.
- >5M☉
- Third dredge up + hot bottom burning
- C is converted to N (CS22949-037, CS29528-041, CS30302-023)
- N/C~10

- _Result _
- Enhance only C
- N enhance for >5M☉

**Notes:**
Third dredge up work in stars of 1.5Mo to 6Mo. 

## Pop.I, Pop.II

- Third dredge up

- 超金属欠乏星でもThird dredge upは起きるが、s-processは伴わないと考える。

- He shell flash

- 水素層

- S-process

- Assuming H mixing13C pocket

**S-process**** ****element**
- Assuming extra mixing  ⇒ convective overshooting
- radiative 13C(,n)16O  burning

- _Result_
- C, s-process element

- Iben (1983)Straniero et al. (1995)

## TDU: S-process

- Abundance pattern of s-process elements changes across [Fe/H]~-2.5
- _Different mechanism for S-process_

- Theoretical estimate(Busso et al.1999)

## Estimation under other assumptions 

-  n(q)∝q-1

- Estimation under other assumptions

-  n(q)∝q1

##  Mass of each stars are independent.

-  Mass of each stars are independent.

## Forming age of Milky Way

- MDM~106M☉Mgas~105M☉

- [Fe/H]=-4~-2.5

-  mstar~10M☉

- (Super)massive stars in mini-halo.

- Population III

- Population II Mgas~1011M☉

- EMP star formation