radiative transfer in spiral galaxies

Radiative Transfer in Spiral Galaxies

Nick KylafisUniversity of Crete

andFoundation for Research and

Technology - Hellas

Introduction If spiral galaxies were simple objects, e.g.,

consisting only of stars, then radiative transfer would not be necessary.



We would simply add up all the emitted light along a line of sight and that would be the surface brightness at that point.



We would simply add up all the emitted light along a line of sight and that would be the surface brightness at that point.

However, the presence of dust (that absorbs and scatters radiation) in spiral galaxies, makes radiative transfer absolutely necessary.

A question: Can we get by with simple models ( “sandwich”-

type) where the radiative transfer can be done more or less analytically?



The answer is emphatically NO!




The reason is that spiral galaxies are complex systems (bulge, spiral structure, clumpiness).




The reason is that spiral galaxies are complex systems (bulge, spiral structure, clumpiness).

To zeroth order, galactic disks are described by exponential distributions of stars and dust in R and z, which are far from constant functions.

“It is more important to be stimulating than right” (M. Rees) In my opinion, two papers were extremely

stimulating in the study of spiral galaxies:

Disney, Davies, & Phillips 1989, MNRAS Valentijn 1990, Nature

“It is more important to be stimulating than right” (M. Rees) In my opinion, two papers were extremely

stimulating in the study of spiral galaxies:

Disney, Davies, & Phillips 1989, MNRAS Valentijn 1990, Nature

The conference in Cardiff in 1994 rendered the subject of the opacity of spiral galaxies as an important problem for people to work on.

At the time, it was not clear at all whether spiral disks are transparent or opaque.

Better late than never An earlier paper on radiative transfer in spiral

disks (Kylafis & Bahcall 1987) went largely unnoticed.

In my opinion for the following reasons:




The authors had not worked on this subject before. (This was actually a minus and a plus.)





They also stopped working on the subject afterwards. (The work was not presented at any conference.)





They also stopped working on the subject afterwards. (The work was not presented at any conference.)

People thought that it was not necessary to do detailed radiative transfer calculations.

It was the conference in Cardiff in 1994 that convinced me that I should return to the subject of the opacity in spiral galaxies.

Having experience with radiative transfer calculations and a 1.2 m telescope at home (Skinakas Observatory), we were able to start a systematic study of the opacity of spiral galaxies.

Radiation transfer methods Two methods have been used extensively to do

radiative transfer in spiral galaxies:

Method 1: Scattered intensities

Method 2: Monte Carlo

Method of scattered intensities (van de Hulst & de Jong, 1969, Physica)

...... '2

2'10210 IIIIIII

The observed intensity along a line of sight can be written as

where is the n-times scattered intensity.nI


...... '2

2'10210 IIIIIII


where is the n-times scattered intensity.

The series converges, but the calculation of the terms with n>1 is very computer intensive.

nI


...... '2

2'10210 IIIIIII


where is the n-times scattered intensity.

The series converges, but the calculation of the terms with n>1 is very computer intensive.

Therefore an approximation is needed.

nI

Approximation We made the reasonable assumption that

2,0

1

1

nI

III

n

n


Back in the 80’s, it was close to impossible to verify this approximation.

2,0

1

1

nI

III

n

n


Back in the 80’s, it was close to impossible to verify this approximation.

Baes & Dejonghe (2001) have verified that it is a good approximation at the ~1% level. Not bad for astrophysics!

2,0

1

1

nI

III

n

n

Monte Carlo method(Cashwell & Everett 1959, book) The Monte Carlo method is simple and elegant,

but only in the last decade it became possible to use it for radiative transfer problems in spiral galaxies.

Monte Carlo method(Cashwell & Everett 1959, book) The Monte Carlo method is simple and elegant, but only

in the last decade it became possible to use it for radiative transfer problems in spiral galaxies.

An incomplete list of papers:

Bianchi et al. 1996, ApJ De Jong 1996, A&A Wood & Jones 1997, AJ Baes & Dejonghe 2001, MNRAS Baes et al. 2003, MNRAS Pierini et al. 2004, ApJ Bianchi 2007, A&A

Monte Carlo method All physical processes that are quantified, can be

simulated by the Monte Carlo method.



In essence, the Monte Carlo method does exactly what Nature does!




A photon in Nature propagates and it does not know whether it will be absorbed or scattered, but something does happen.




A photon in Nature propagates and it does not know whether it will be absorbed or scattered, but something does happen.

Similarly, in a Monte Carlo code the decision about what will happen is made with the use of a properly selected random number.

Some model results Here I will show some results obtained with the

method of scattered intensities.



Results obtained with the Monte Carlo method will be presented mainly by other participants.




The fresh, off-the-oven results of Simone Bianchi demonstrate that the two methods agree extremely well.




The fresh, off-the-oven results of Simone Bianchi demonstrate that the two methods agree extremely well.

Relief !!!

Model for late-type spiral galaxies Old stars: Disk with exponential distribution in

z and R +

a de Vaucouleurs spheroid.


z and R +


Dust: Disk with exponential distribution in z and R (with different length-scales).


z and R +


Dust: Disk with exponential distribution in z and R (with different length-scales).

Young stars: Disk with exponential distribution in z and R (also with different length-scales).

It has been shown that: The effects of spiral structure are negligible

(Misiriotis et al. 2000, A&A).



Similarly for the effects of clumpiness (Misiriotis & Bianchi 2002, A&A). Watch for Bianchi’s talk though.



Similarly for the effects of clumpiness (Misiriotis & Bianchi 2002, A&A). Watch for Bianchi’s talk though.

3-D radiative transfer calculations have been performed to produce model images that best fit the observations (Xilouris et al. 1997, 1998, 1999, A&A).

Example: NGC 891

From the optical and NIR images, we have inferred with our model the total amount of dust (warm and cold) and its spatial distribution.

Model fits

Qualitatively, the fits are good.

Quantitatively, how well does the model fit the observations?

Main results from the study of 10 edge-on late-type spiral galaxies:

,21

stars

dust

z

z

Central, face-on optical depth in the V band < 1.

Thus, IF all the dust has been accounted for, late-type spiral galaxies are transparent.

identical to the galactic one.

Similar conclusions have been reached by Alton et al. 1998, A&A, and Davies et al. 1999, MNRAS.

,4.1stars

dust

R

R400

dust

gas

M

M

A

Can the IR spectrum be computed? YES. This is because:


The energy absorbed at every point in the galaxy has been calculated.



Then, we make an assumption about the IR dust emissivity (e.g., what is thought appropriate for our Galaxy).



Then, we make an assumption about the IR dust emissivity (e.g., what is thought appropriate for our Galaxy).

We equate the two to determine the temperature of the dust at every point in the galaxy.

And then we integrate over all the points in the galaxy to compute the IR spectrum.

And then we integrate over all the points in the galaxy to compute the IR spectrum.

This was done by Popescu et al. 2000, A&A, under the assumption that the FIR emissivity of the dust is the same as the one thought appropriate for our Galaxy.

Unaccounted FIR flux In order to account for the observed FIR flux,

Popescu et al. assumed that there is dust near the plane of the galaxy associated with the young stars.

Such dust could go undetected in the optical modeling of the galaxies.

Success of the model

The model of Popescu et al. explains not only the FIR spectrum of NGC 891, but also the observed images at two FIR wavelengths (Popescu et al. 2004, A&A).

An alternative possibility Since the FIR emissivity of the dust is more or

less guessed,


less guessed,

could one explain the FIR spectrum of, say NGC 891, under the assumption that the FIR emissivity is larger (say 3 times more) than what we think it is?


less guessed,

could one explain the FIR spectrum of, say NGC 891, under the assumption that the FIR emissivity is larger (say 3 times more) than what we think it is?

The answer is probably yes (Alton et al. 2004, A&A, Dasyra et al. 2005, A&A), at least for the galaxy NGC 891.

Can one distinguish between the two possibilities?

Dust may go undetected at optical wavelengths. But, as the wavelength increases, at some point it will reveal itself.

Can one distinguish between the two possibilities?

Dust may go undetected at optical wavelengths. But, as the wavelength increases, at some point it will reveal itself.

It is a good idea then to look in the K band (Dasyra et al. 2005, A&A), though a final answer

for all spiral galaxies has not been given yet, in my opinion.

Comparison of the three compressed images gives

Can the model be used for a statistical study?

YES.

Misiriotis et al. (2004) modeled 62 bright IRAS galaxies and found the following:

Comparison with Kennicutt (1998)

Conclusions

The relation between SFR and IR emission in spiral galaxies seems to be well understood essentially from “first principles”.

Conclusions


The dust mass in a spiral galaxy can be determined with one observation at 850 microns.

Conclusions



The SFR in a spiral galaxy can be determined with one observation at 100 microns.

Conclusions



The SFR in a spiral galaxy can be determined with one observation at 100 microns.

THANKS

radiative transfer in spiral galaxies

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