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Transmission Spectroscopy

Astro 497, Week 9, Friday

TableOfContents()

Project Outline Feedback

  • Analyze/plot data for one object at a time

  • Allow user to select which object to analyze

  • Most transiting planets won't have mass measurements

question(md"""Is transmission spectroscopy limited by the thickness of a planet's atmosphere? 

Since it gets more dense closer to the center of the planet, are we only able to resolve what makes up the outer edges of said planet's atmosphere?""")
Question

Is transmission spectroscopy limited by the thickness of a planet's atmosphere?

Since it gets more dense closer to the center of the planet, are we only able to resolve what makes up the outer edges of said planet's atmosphere?

–- Kreidberg, chapter from Handbook of Exoplanets

question(md"""While analyzing atmosphere composition, how to distinguish between the spectrum footprint produced by the planet and that produced by the observed background star?""")
Question

While analyzing atmosphere composition, how to distinguish between the spectrum footprint produced by the planet and that produced by the observed background star?

LocalResource("../_assets/week2/circular_diagram.png", :width=>"80%")

Example Transmission Spectrum of WASP-43b

  • Main figure is transmission spectrum from Hubble WFC3

  • Inset figure is emission spectrum is Spitzer/IRAC 3.6 & 4.5μm

–- Kreidberg et al. 2015 & chapter from Handbook of Exoplanets

question(md"""Are the different filters used in a large variety of ways? Or or they just used based on certain properties of the planets that are being detected?""")
Question

Are the different filters used in a large variety of ways? Or or they just used based on certain properties of the planets that are being detected?

Ground-based transmision spectroscopy

XO-2b

–- Sing et al. 2011

What sets the scale for transmission spectroscopy signal?

Atmospheric Scale Height

$$H = \frac{k_B T}{\mu_m g}$$

  • Temperature: $T$

  • Mean molecular mass: $\mu_m$

  • Gravitational acceleration: $g$

  • Boltzmann constant: $k_B$

Assumes an isothermal atmosphere in hydrostatic equilbirum.

$$\rho(z) = \rho_0 \exp(-z/H)$$

Standard Transit depth

$$\delta \simeq \frac{\pi R_p^2}{\pi R_\star^2}$$

  • Radius of Planet: $R_p$ (where optically think at all wavelengths observed)

  • Radius of Star: $R_\star$

Increase in transit depth

$$\Delta\delta(\lambda) = \frac{\pi (R_p + N_H(\lambda) H)^2}{\pi R_\star^2} - \frac{\pi R_p^2}{\pi R_\star^2} \simeq 2 N_H \delta \left(\frac{H}{R_p}\right)$$

  • Number of scale heights of additional absorption: $N_H(\lambda)\simeq 2$ for cloud-free atmospheres at low resolution

  • Measurement wavelength: $\lambda$

Representative values

Planet$\delta$$T$$g$$\mu_m$$\Delta\delta$
(K)(m/s)(amu)
Hot-Jupiter$\simeq 10^{-2}$$\simeq 1300$$\simeq 25$$\simeq 2$$\simeq 10^{-4}$
Earth$\simeq 10^{-4}$2731028$\simeq 10^{-6}$
question(md"""Is a planet's transmission spectrum dependent on its temperature and mean molecular mass?  

Is this a confounding factor when determining its atmospheric composition?""")
Question

Is a planet's transmission spectrum dependent on its temperature and mean molecular mass?

Is this a confounding factor when determining its atmospheric composition?

Gallery of Transmission Spectroscopy measurements

–- Archive fo Exoplanet Transmission Spectra & Wakeford (2020)

question(md"""What information can we get about planets using transmission spectroscopy?""")
Question

What information can we get about planets using transmission spectroscopy?

Things to look for

  • Sodium absorption ~0.6μm (HAT-P-1)

  • Rayleigh scattering (HD 189733b)

  • Lack of rayleigh scattering → clouds (GJ 436b, GJ 1214b)

  • Water Absorption ~1.4μm (WASP-127b, WASP-39b, WASP-107b, WASP-52b, HAT-P26b)

  • Lack of features (TRAPPIST)

question(md"If we are able to gather the light that has run into a planet's atmosphere, is there enough data to detect what the atmosphere of exoplanets consist of?")
Question

If we are able to gather the light that has run into a planet's atmosphere, is there enough data to detect what the atmosphere of exoplanets consist of?

How to prioritize planets for detailed atmospheric characterization?

Transmission spectroscopy metric

$$\begin{eqnarray} \mathrm{TSM} & = & (\mathrm{Scale\; factor}) \times \left(\frac{R_p}{R_\oplus}\right)^3 \left(\frac{M_\oplus}{M_p}\right) \left(\frac{R_\odot}{R_\star}\right)^2 \left(\frac{T_{eq}}{K}\right) \times 10^{-m_J/5} \\ & \propto & R_p \frac{H}{R_\star} \left(\mathrm{stellar\; flux}\right) \end{eqnarray}$$

  • Proportional to SNR for transmission spectroscopy measurement

  • Starts with scale height model → assumes isothermal atmosphere with no clouds or hazes

  • Adds assumption of equilibrium temperature: $T_{eq} \equiv T_{\star,eff} \sqrt{\frac{R_\star}{a}} \left(2^{-1/4}\right)$

    • assumes zero albedo, full day-night heat redsitribution

  • Original TSM uses Apparent aagnitude in J band: $m_J$ → roughly corresponding to JWST's Near IR Imager and Slitless Spectrograph (NIRISS)

    • Variations on TSM use apparent magnitude in other bands.

–- Kempton et al. (2018)

–- Almenara et al. 2022

question(md"""Are there any drawbacks to transmission spectroscopy?""")
Question

Are there any drawbacks to transmission spectroscopy?

Reading Questions

Setup & Helper Code

ChooseDisplayMode()
      
using PlutoUI, PlutoTeachingTools
question(str; invite="Question") = Markdown.MD(Markdown.Admonition("tip", invite, [str]))
question (generic function with 1 method)

Built with Julia 1.8.2 and

PlutoTeachingTools 0.2.3
PlutoUI 0.7.44

To run this tutorial locally, download this file and open it with Pluto.jl.

To run this tutorial locally, download this file and open it with Pluto.jl.

To run this tutorial locally, download this file and open it with Pluto.jl.

To run this tutorial locally, download this file and open it with Pluto.jl.