理論モデルを用いた銀河の分子輝線疑似観測
井上 茂樹
吉田 直紀
矢島 秀伸

（筑波大学 / 国立天文台）（東京大学）（筑波大学）

ALMA (Atacama Large Millimeter/submillimeter Array)• Major strength• Gas physics• Line-spectrum study for each species• CO, HCO, NH3, H2O, OIII, CII etc...

• 2D-spectral study• Dynamical analysis

Difficulties in studying molecular gas (H2)

• It is important but difficult to observe and predict H2 in galaxies.
• Observation:• It is (almost) hopeless to directly observe H2 since it little emits
electromagnetic waves.

• CO is used as a proxy of H2.
• The conversion factor 𝛼𝛼𝐶𝐶𝐶𝐶 is, however, determined empirically.

• Assumed constant or (at best) metallicity-dependent• Theory:• The main channel of H2 formation is via dust as catalyst.
• Molecules can be dissociated by UV radiation• The formation requires the self-shielding effects.

• Namely, various physics is involved with H2 formation/dissociation.
• UV radiation, dust properties, metallicity, gas pressure etc...

But, still we want to know molecules...

Illustris-TNG simulation
PAHNGS-ALMA survey• How should we interpret the molecular observations?

➡ mock observations for molecules by utilizing simulations.

• We aim to lay the foundation of future observations.

Post-processing model for molecules
A simulated galaxy
Inoue & Yoshida (2019)

Post-processing model for molecules
A simulated galaxy
Inoue & Yoshida (2019)

cell size ~10-100 pc

Post-processing model for molecules• Directory from simulation,• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Exclude diffuse gas• 𝑛𝑛𝐻𝐻 < 0.1 cm-3(SF criterion in simulation)

Post-processing model for molecules• Directory from simulation,

warm gascold gas• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Consider a two-phase ISM model• cold/warm neutral media in a cell
Wolfire et al. (1995)

Post-processing model for molecules• Directory from simulation,

warm gascold gas• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Consider a two-phase ISM model• cold/warm neutral media in a cell
Wolfire et al. (1995)~100 times

Post-processing model for molecules• Directory from simulation,

warm gascold gas• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Consider a two-phase ISM model• cold/warm neutral media in a cell
• Density contrast: ϕ ≡𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐= 100𝜌𝜌𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤• Pres.-equilibrium (e.g. Wolfire et al. 1995)• Cold-mass fraction: 𝑓𝑓𝑚𝑚 ≡𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐~0.8 − 1𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Cold-volume fraction: 𝑓𝑓𝑉𝑉 ≡𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑓𝑓𝑚𝑚=𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
1−𝑓𝑓𝑚𝑚 𝜙𝜙+𝑓𝑓𝑚𝑚• Springel & Hernquist (2003)

Post-processing model for molecules• Directory from simulation,

warm gascold gas• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• The cold gas has• 𝜌𝜌𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 , 𝑀𝑀𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Jeans length 𝜆𝜆𝐽𝐽 ≡𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝐺𝐺𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

Post-processing model for molecules• Directory from simulation,

warm gas• 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• The cold gas has• 𝜌𝜌𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 , 𝑀𝑀𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 , 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

cold gas• Jeans length 𝜆𝜆𝐽𝐽 ≡• Typical cloud size

cloud𝜆𝜆𝐽𝐽• 𝑅𝑅𝑐𝑐𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 = 𝜆𝜆𝐽𝐽 /2.
• Σ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝜆𝜆𝐽𝐽

𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝐺𝐺𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Dust abundance: 𝐷𝐷𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐷𝐷𝑀𝑀𝑀𝑀 𝑍𝑍𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑀𝑀𝑀𝑀• Radiation field: 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ~ 0• “well-shielded approximation”

Post-processing model for molecules

warm gas• Input these parameters into an chemo-RT code
• DESPOTIC (Krumholz 2014)• which returns molecular emissions andabundances for a cloud.

cold gas• Cumulate the cloud emissions and obtainthe total value of the cell.
• The number of clouds in a cellcloud• 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐• Implying the optically-thin approx.

𝜆𝜆𝐽𝐽• Cumulate the gas cells within every single galaxy.

Applying to Illustris-TNG (z=0, TNG100-1)

e.g. Springel et al (2018)

Applying to Illustris-TNG (z=0, TNG100-1)• Comparing with xCOLD GASS survey (Saintonge et al. 2017)
Density contrast: 𝜙𝜙 = 100

Radiation field: 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ~0Saintonge et al. (2017)

Completeness limit
This work

The CO-Universe
Stellar mass

CO(1-0) lightat redshift z=0

The top 10 CO-brightest galaxies
4All gasCO(1-0)light5

The top 10 CO-brightest galaxies
6All gasCO(1-0)
light

7

8

910

Applying to Illustris-TNG (z=0, TNG100-1)
Total gasCO(1-0)H2

𝜶𝜶𝐂𝐂𝐂𝐂In the Milky Way inner disc
• 𝛼𝛼𝐶𝐶𝐶𝐶 = 4.3 M/(K km/s pc2)
In local main-sequence galaxies• 𝛼𝛼𝐶𝐶𝐶𝐶 = 3.6 M/(K km/s pc2)

Dependence on radiation fields• Is the “well-shielded” approximation correct?
Density contrast: 𝜙𝜙 = 100
𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡
Radiation field: 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐼𝐼𝑀𝑀𝑀𝑀
Saintonge et al. (2017)

𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀

Radiation in massive galaxies needs to be well shielded.

Completeness limit
This workDependence on radiation fields• Is the “well-shielded” approximation correct?
Density contrast: 𝜙𝜙 = 1000𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡
Radiation field: 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐼𝐼𝑀𝑀𝑀𝑀
Saintonge et al. (2017)

𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀

Radiation in massive galaxies needs to be well shielded.

Completeness limitThis work

Dependence on cloud size
𝜆𝜆𝐽𝐽𝑅𝑅𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0.1 ×
2𝜆𝜆𝐽𝐽
𝑅𝑅𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =2Saintonge et al. (2017)

Cloud sizes need to be approximately as large as Jeans length.

𝜆𝜆𝐽𝐽
𝑅𝑅𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 10 ×2Density contrast: 𝜙𝜙 = 100
Radiation field: 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ~0

Kinematic analysis

Can dynamically unstable galaxies really exist?

𝜎𝜎𝜎𝜎Toomre instability criterion: 𝑄𝑄 ≡<1𝜋𝜋𝐺𝐺Σ

• Discs with 𝑄𝑄 < 1 are considered to be dynamically unstable.

Tadaki et al. (2018)• Due to their self-gravity

AzTEC-1

Qgas
Genzel et al. (2011)
Qgas

How do you measure velocity dispersions?

• Difference in measurement (definition) of velocity dispersion.
• In theory: mass-weighted• In observation: flux-weighted

𝐹𝐹𝜈𝜈• 𝐹𝐹𝜈𝜈 : flux density of line emission

e.g. in the case of Hαline,
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝐿𝐿𝐻𝐻𝛼𝛼 ∝ 𝑆𝑆𝑆𝑆𝑆𝑆 ∝∝ 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝜌𝜌𝑚𝑚𝑚𝑚𝑚𝑚 ,𝜏𝜏𝑆𝑆𝑆𝑆where𝜈𝜈Mock CO(1-0) observations for dynamical analysis• Simulations from Inoue & Yoshida (2019)
z=1.5
Ms=1.7×1011 M

z=1.0Ms=1.8×1011 M

Gas density

CO(1-0) luminosity

Mock CO(1-0) observations for dynamical analysis• Simulations from Inoue & Yoshida (2019)

z=1.0
Ms=1.8×1011 M

LCO(1-0)-weighted

Velocity dispersion [km/s]

z=1.5
Ms=1.7×1011 M

Mass-weighted

Mock CO(1-0) observations for dynamical analysis• Replacing only 𝜎𝜎 in 𝑄𝑄.

𝜎𝜎𝜅𝜅
𝑄𝑄 ≡𝜋𝜋𝐺𝐺Σ

Mass-weighted

LCO(1-0)-weighted

Tadaki et al. (2018)

Qgas

AzTEC-1

Summary• I am developing a new model for molecular line emissions.
• Designed to be independent from resolutions of simulations.
• In good agreement with the observations at z=0.
• Needs to assume all gas clouds to be well shielded.

• Kinematic analysis based on line spectra can be biased• depending on which line you are looking at.
• Observed VD can be biased because it is flux-weighted.
• The low values of Q<1 in high-z discs may be attributed to this bias.