Limiting Magnitudes

Here I am calculating the limiting magnitude in each band in Roman Telescope for a potential Ultra Deep Field Survey.

Limiting magnitude

I found this link useful in describing magnitude systems.

The AB magnitude limit of a potential UDF is \(m_{AB} \sim 30\), which corresponds to \(f_{\nu} = 3.631 \times 10^{-9} \rm{Jy}\). Therefore, the limiting magnitude of each

\(m_{i} = -2.5 \log_{10} \dfrac{3.631 \times 10^{-9} \rm{Jy}}{Q_i}\),

where \(Q_i\) is the zero point of each filter.

This site has a summary of WFIRST filters and their zero points.

Therefore, here is the limiting magnitude in each of these bands, assuming the AB magnitude limit is \(m_{AB} \sim 30\).

Filter	\(ZP_{\nu}\) (Jy)	Limiting Magnitude
R062	3022.34	29.80
Z087	2298.31	29.50
Y106	1962.64	29.33
J129	1479.84	29.03
Prism	1388.79	28.96
Grism	1207.17	28.80
W146	1174.09	28.77
H158	1090.69	28.69
F184	863.33	28.44

As a function of redshift

Converting this to an absolute magnitude, as a function of distance, we can see the magnitude we will be able to detect in each filter.

\(M = m- 5 \log_{10}(D_L(z)/(\sqrt{1+z} 10 {\rm pc}))\). Here I have an extra factor of (1+z) to account for the fact that the object has been redshifted, which I didn’t include in this post.. I’m really not sure this is correct… Does this assume the spectrum of the object is flat?

Here is the plot I get for magnitude limits in each filter:

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