AdvancedIOAA 2018 | Beijing, China | Data Analysis D1 | 75 pt

2018 D1 | Dust and young stars: the IRX–β relation

Skills:Linearise Least squares Statistics Photometry

As a by-product of star formation, interstellar dust absorbs ultraviolet (UV) and optical starlight and re-emits it in the far infrared (FIR, 10–300 μm).

1.1 The UV light of a galaxy comes mainly from young stars, so UV luminosity traces the star formation rate. Because dust strongly attenuates the UV, astronomers define the UV continuum slope $\beta$ :

f_\lambda = Q\cdot\lambda^\beta,

where $f_\lambda$ is the monochromatic flux (W m⁻³) and $Q$ a constant.

(D1.1.1) The AB magnitude is $m_{\rm AB} = -2.5\log\dfrac{f_\nu}{3631\ {\rm Jy}}$ . A typical galaxy has a roughly constant AB magnitude across the UV. What is its UV slope? (Hint: $f_\nu\Delta\nu = f_\lambda\Delta\lambda$ .) (6)

(D1.1.2) Table 1 gives infrared photometry of the $z = 6.60$ galaxy CR7. Plot its AB magnitude against the logarithm of the rest-frame wavelength. (12)

(D1.1.3) Calculate CR7's UV slope, plot the best-fit UV continuum, and compare with (D1.1.1). Is CR7 dustier than the typical galaxy [YES/NO]? (Hint: write $m_{\rm AB}$ in terms of $\lambda$ and $m_{1600}$ , the AB magnitude at $\lambda_0 = 1600$ Å.) (5)

1.2 If dust absorbs UV photons and re-emits the energy as blackbody radiation, the UV slope relates to the ratio of FIR to UV flux:

\mathrm{IRX} \equiv \log\frac{F_{\rm FIR}}{F_{1600}} = S(\beta),

where $F_{1600}$ is the observed flux at rest-frame 1600 Å, defined as $F_\lambda = \lambda f_\lambda$ . Table 2 gives $\beta$ , $F_{1600}$ and $F_{\rm FIR}$ for 20 nearby galaxies (Meurer et al. 1999).

(D1.2.1) Plot the IRX–β diagram and find a linear fit $\mathrm{IRX} = a\beta + b$ . (14)

(D1.2.2) Quantify the dispersion (in dex) between observed and predicted IRX:

\sigma = \sqrt{\frac{\sum(\Delta{\rm IRX}_i)^2}{N-1}}, \qquad \Delta{\rm IRX}_i = {\rm IRX}_{i,\rm obs} - {\rm IRX}_{i,\rm pred}.

(6)

1.3 Under the same energy balance assumption,

\frac{F_{\rm FIR}}{F_{1600}} \approx 10^{0.4A_{1600}} - 1,

where $A_\lambda$ is the dust absorption in magnitudes.

(D1.3.1) Express $A_{1600}$ as a function of IRX. (6)

(D1.3.2) Plot $A_{1600}$ against $\beta$ and find a linear fit $A_{1600} = a'\beta + b'$ . (12)

(D1.3.3) If this model is correct, what is the UV slope $\beta_0$ of a dust-free galaxy? (2)

1.4 In 2016, ALMA observed CR7. The FIR continuum was not detected, with a $3\sigma$ upper limit on the FIR flux of $1.5\times10^{-19}$ W m⁻².

(D1.4.1) Calculate the IRX of CR7. Is it an upper or a lower limit? (Hint: write $F_{1600} = \lambda_0 f_{1600}$ , with $f_{1600}$ the observed flux at rest-frame 1600 Å.) (6)

(D1.4.2) Is the observation deep enough to show any deviation of CR7 from the local IRX–β relation [YES/NO]? Give the IRX difference. (6)

Table 1 | Observed-frame photometry of CR7 (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

Table 2 | UV slope, UV flux and FIR flux of 20 nearby galaxies

Galaxy	β	log(F₁₆₀₀ / 10⁻³ W m⁻²)	log(F_FIR / 10⁻³ W m⁻²)
NGC 4861	−2.46	−9.89	−9.97
Mrk 153	−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

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