Thoughts on Wide-Field Slitless Spectroscopy from Space

 Slit-less Survey Spectroscopy from Space

This reflects some rambling thoughts that HWR has harboured over the last years on the question of what's the ultimate all-sky spectroscopic survey. Given that there is much (MEGAMAPPER, MSE, ..) pondering about the ground-based options, this is about space (inspired by the Gaia, JWST and Euclid slitless data).

To cut long story short. One dream-option could be:

• let's presume a 6.5m (warm?) telescope could be designed [credit to Roger Angel here] with a near diffraction limited  0.25 (or 1) sqdeg FOV in a TESS-like or L2 orbit ; 
• and if one could then implement slitless spectroscopy with a resolution R (say R=1000, or 2000?), and a bandpass filter that picks out NR (say NR=1000, or 2000?) resolution elements
• the actual wavelength requires a great deal of thought, but let's take here 0.8mum-1.6mum
• Notes:
• a 1sqdeg FOV would require about 20 Gpixels (same as imaging at the same resolution and FOV); so, thinking about undersampling, or 0.25sqdeg may make this idea less pie-in-the-sky
• note that the number of pixels needed is the same as for direct imaging; it's just imaging with every source being a short streak 
• How long is the slitless spectral streak in the focal plane?  for NR resolution elements, the streak is NR * FWHM(PSF)  = 47" at NR=1000; lambda=1.5mum, D=6.5m
• then obvious science include (see section below the S/N estimates for more/growing detail). Brief quip:  that MSE, SpecTel, Roman, etc.. just much better.
• stellar physics
• Galactic history, structure and dynamics
• redshift surveys
• AGN finding
• good angular resolution
• spectral "follow-up" on LISA GW sources
• to cover a good portion of the sky "in a reasonable period" (few years?), exposure times per pointing 1000s-ish?

Why would that be a dream? 

The S/N estimates written out below illustrate the power that arise from combining:

• slitless (you get everything)
• observations from space (low background)
• a large and diffraction limited telescope
• compact sources (the last two boost the source/background contrast)

• 

Survey speed (to a given depth) for faint, compact sources scales with telescope size as D^4.

[This can do (more) in one year than Roman (slitless) in 50 years]

In addition, the probability of source confusion (at given R, and NR) goes down as D^-2.

Here are some plots that show an initial S/N estimate exercise. Given that the background tends to kill you in slitless spectroscopy, compact sources (PSF) are great.

Anyone who wants to play with S/N matters, go to the collab notebook here

This shows at R=1000, 1.5mum the continuum S/N (per resolution element) in a 1000 second exposure for sources of different spatial extent, as a function of their size (source diameter)

This shows the S/N (per resolution element) for a continuum point source, as a function of telescope diameter. For reference, Euclid~1m, Roman~2.4m

This is an analogous plot, but for a (spectrally) unresolved emission line on top of negligible source continuum. The envisioned line-flux sensitivity for ground-based "stage 5" redshift experiments (0.5e-16) is indicated (see https://arxiv.org/pdf/2209.03585.pdf )

This is a first attempt at mapping the S/N to some physical input, such as a star-forming region/galaxy as a function of of their size and SFR. Yes, spatial extendedness is a killer.

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Reminder 1: what is the physical resolution as a function of redshift

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Just as background, here's the sky values from Rigby+2023

Science Cases with such a Survey:

This deserves simulations and asking what range of lambda,R,NR, etc.. is optimal, and which acceptable

Spectra of Stars:

• 2-5 abundances of cool stars
• are there any zero-metallicity stars in the Milky Way?
• chemical identification of streams (as small-scale DM probes)
• find the fastest stars (in the bulge): BH dynamics
• spectra of every O stars within 5 Mpc
• free-floating (semi-young) planets and stuff

Spectra of AGNs:

• AGN as LSS probes to z=7(?)
• earliest AGN (z~12) ==> BH growth; seed BHs

Spectra of Galaxies 

What can we expect for emission line spectroscopy of galaxies?

Let's take the Yung, Somerville+2022 SC-SAM simulations, and the Kennicutt

conversion of SFR --> Halpha; and request a 7 sigma Halpha detection, given line flux and disk-size of the galaxy. Consider a total area of 10.000 sqdeg on the sky. Quite staggering galaxy numbers ....

• ?? <what are the most interesting things>
• host galaxy diagnostics of BH GW events with LISA

Cosmology:

• probes of inflationary signatures (by stage 5+ spectroscopy)

• kinematic lensing on steroids
• 
  

(inadvertent) Spectra of Transients

• way too many gravitational lenses with spectra
• serendipidous (single epoch) SN spectra to faint levels
• GRB hosts
• tidal disruption events in AGN
• <you name it>

Low-mass objects

• there are ATMO2020 models from Phillips+2020 and newer (JWST-oriented) models Legget&Tremblin 2024
  
  
  

from Theissen, Burgasser et al 2023.  LTY dwarf spectral library

How many more stars (for stellar streams) does one get going below the MS turn-off
(from Bellazini+ https://arxiv.org/abs/1203.3024) 

going from absmag 2 (in I) to 3 is 20x more stars

Notes on crowding:

I downloaded Gaia data in Baade's window, and did number counts, which resulted in an estimate of how many stars there are per spectral streak area (code at getBaadesWindow.ipynb) in 

/Users/rix/Science/Projects/SlitlessSpectroscopySpace/SpectraSims

The plots looks like this, and implies that the crowding is unproblematic to 21st magnitude

Next steps would be to 

a) get deeper data

b) calculate the Poisson probability of being uncontaminated and add it to that plot.

More science application ideas

The universe through a looking-glass

Strong (>30) lensing magnification (size and flux) happens, by is rare. When it happens, it opens up a new regime of spatial resolution.

Takahashi et al 2011 have calculated statistics. The plot below shows magnification averaged over 3kpc

For compact sources there should be much more magnification.

Extreme magnification probabilities have been discussed in Diego (2019)

So, there is a 1 in a million chance to get magnification of more than a 1000. A linear magnification of 20 leads to a physical resolution (6.5m at 0.75mum) of 9 pc at z=5.