2018年IOAA数据分析第1题-产星星系中的尘埃与年轻恒星

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(D1) Dust and Young Stars in Star-forming Galaxies             [75 points]

As a by-product of the star-forming process in a galaxy, interstellar dust can significantly absorb stellar light in ultraviolet (UV) and optical bands, and then re-emit in far-infrared (FIR), which corresponds to a wavelength range of 10-300 µm. 

1.1. In the UV spectrum of a galaxy, the major contribution is from the light of the young stellar population generated in recent star-formation processes, thus the UV luminosity can act as a reliable tracer of the starformation rate (SFR) of a galaxy. Since the observed UV luminosity is strongly affected by dust attenuation, extragalactic astronomers define an index called the UV continuum slope (β) to quantify the shape of the UV continuum:

𝑓λ=𝑄⋅𝜆β

where 𝑓V is the monochromatic flux of the galaxy at a given wavelength 𝜆 (in the unit of  W m-3) and 𝑄 is a scaling constant. 

(D1.1.1) (6 points) AB magnitude is a specific magnitude system. The AB magnitude is defined as:

$$\mathrm{m}_{\mathrm{AB}}=-2.5 \log \frac{f_{v}}{3631 \mathrm{Jy}}$$

The AB magnitude of a typical galaxy is roughly constant in the UV band. What is the UV continuum slope of this kind of galaxy? (Hint:  𝑓λ∆𝜈=𝑓𝜆∆𝜆 )

(D1.1.2) (12 points) Table 1 presents the observed IR photometry results for a 𝑧=6.60 galaxy called CR7. Plot the AB magnitude of CR7 versus the logarithm of the rest-frame wavelength on graph paper and labelled as Figure 1.

Table 1. (Observed Frame) IR Photometry of CR7 at z=6.60
Band Y J H K
Central Wavelength (μm) 1.05 1.25 1.65 2.15
AB Magnitude 24.71±0.11 24.63±0.13 25.08±0.14 25.15±0.15

(D1.1.3) (5 points) Calculate CR7’s UV slope, plot the best-fit UV continuum on Figure 1 and make a comparison with the results you obtained in (D1.1.1). Is it dustier than the typical galaxy in (D1.1.1)? Please answer with [YES] or [NO]. (Hint: Express mABas a function of 𝜆 and 𝑚1600 , where 𝑚1600 is the AB magnitude at 𝜆0=160 nm (1600 Å))

1.2. Under the assumption that dust grains in the galaxy absorb the energy of UV photons and re-emit it by blackbody radiation, the relation between the UV continuum slope (β), UV brightness (at 1600 Å) and FIR brightness could be established:

$$ \operatorname{IRX} \equiv \log \left(\frac{F_{F I R}}{F_{1600}}\right)=S(\beta) $$

where 𝐹FIR is the observed far-infrared flux and 𝐹1600 is the observed flux at rest-frame wavelength 160 nm ( 1600 Å) (The “flux” 𝐹λ is defined as 𝐹λ =𝜆⋅𝑓λ). Table 2 presents 20 measurements of 𝛽, 𝐹FIR and 𝐹1600 in nearby galaxies (Meurer et al. 1999).

Table 2. UV slope, flux and FIR flux of 20 nearby galaxies
Galaxy Name UV Slope

β

log(F1600/10-3Wm-2) log(FFIR/10-3Wm-2)
NGC 4861 -2.46 -9.89 -9.97
Mrk153 -2.41 -10.37 -10.92
Tol 1924-416 -2.12 -10.05 -10.17
UGC 9560 -2.02 -10.38 -10.41
NGC 3991 -1.91 -10.14 -9.80
Mrk 357 -1.80 -10.58 -10.37
Mrk 36 -1.72 -10.68 -10.94
NGC 4670 -1.65 -10.02 -9.85
NGC 3125 -1.49 -10.19 -9.64
UGC 3838 -1.41 -10.81 -10.55
NGC 7250 -1.33 -10.23 -9.77
NGC 7714 -1.23 -10.16 -9.32
NGC 3049 -1.14 -10.69 -9.84
NGC 3310 -1.05 -9.84 -8.83
NGC 2782 -0.90 -10.50 -9.33
NGC 1614 -0.76 -10.91 -8.84
NGC 6052 -0.72 -10.62 -9.48
NGC 3504 -0.56 -10.41 -8.96
NGC 4194 -0.26 -10.62 -8.99
NGC 3256 0.16 -10.32 -8.44


(D1.2.1) (14 points) Based on the data given in Table 2, plot the IRX−𝛽 diagram on graph paper and labelled as Figure 2 and find a linear fit to the data. Write down your best-fit equation (i.e. IRX=𝑎⋅𝛽+𝑏) by the side of your diagram.

(D1.2.2) (6 points) Quantify the dispersion (in ‘units’ of dex,  where 𝐟𝐨𝐫 𝐞𝐱𝐚𝐦𝐩𝐥𝐞,𝐥𝐨𝐠(𝟏𝟎𝟗)− 𝐥𝐨𝐠(𝟏𝟎𝟒)=𝟓 𝐝𝐞𝐱) between the observed IRXobs and predicted IRXpred using the following equation:

$$ \sigma=\sqrt{\frac{\sum\left(\Delta \operatorname{lRX} _{i}\right)^{2}}{N-1}}(\text { unit: dex }) \text { where } \Delta \operatorname{IRX} _{i}=\operatorname{IRX}_{\text {i,obs }}-\operatorname{IRX}_{\text {i,pred }} $$

1.3. Under the previous assumption of the energy transfer process, the ratio of 𝐹FIR to 𝐹1600 can be expressed as:

$$ \frac{F_{F I R}}{F_{1600}} \approx 10^{0.4 A_{1600}}-1 $$

Where 𝐹1600 is the unattenuated flux and 𝐴λ is the dust absorption (in magnitudes) as a function of wavelength λ

(D1.3.1) (6 points) Express 𝐴1600 as a function of IRX.

(D1.3.2) (12 points) Based on Table 2 data and the function of 𝐴1600(𝐼𝑅𝑋) you derived above, plot the AE/CC−𝛽 diagram on graph paper and label it as Figure 3 and find a linear fit to the data. Write down your best-fit equation (i.e.𝐴1600=𝑎'⋅𝛽+𝑏') by the side of your diagram.

(D1.3.3) (2 points) If your linear model in (D1.3.2) is correct, what is the expected UV continuum slope 𝛽0 of a dust-free galaxy?

1.4. After establishing the local relation between UV continuum slope and IRX, we could probably test this empirical law in the high-redshift universe. In 2016, researchers obtained an Atacama Large Millimeter / submillimeter Array (ALMA) observation of CR7, and the FIR continuum corresponded to a 3𝜎 upper limit of an FIR flux of 1.5×10-19 Wm-2.

(D1.4.1) (6 points) Calculate the IRX of CR7. Is it an upper limit or lower limit? Hint: here 𝐹1600 should be written in the form of: 𝐹1600=𝜆0⋅𝑓1600 where 𝜆0=160 nm (1600 Å) and 𝑓1600 is the observed flux in the rest-frame

(D 1.4.2) (6 points) Is the current observation long enough to show any deviation of CR7 from the IRX−𝛽 relationship you just derived in the local universe? Please answer with [YES] or [NO] on the summary answer sheet, give the IRX difference and show the working used to calculate it on the answer sheet.