Online Femtolensing Calculator


Figure 1. Femtolensing of a gamma-ray burst by a distant intermediate low-mass object.

This program calculates the femtolensing [1] signature of a point mass lens. Femtolensing is analogous to diffraction of laser light by a single slit, but the laser is replaced by an astrophysical object that emits gamma-rays and the slit is replaced by the curved space-time in the neighbourhood of a low-mass object, i.e., a gravitational lens. See Figure 1. For more information about the mathematical model, see [2]. For a discussion about observations, see [2,3] and references therein. Inputs should be specified below.

1. Lens Parameters

ML: kg.Mass.
zL: .Distance (redshift).

2. Source Parameters

rs: .Separation of source and lens, see [2].
σs: .Angular radius of source, see [2].

2.1 GRB Power-Law Spectrum (Optional)

These parameters are used to combine the femtolensing magnification function with a (connected) power-law model of a GRB spectrum, F0,


The parameters should be specified below. A2 and A3 are solved for automatically. Leave fields blank to exclude connected power-laws.

A1: .Flux in low-energy limit.
p1: .Exponent 1.
E1: keV.Energy threshold 1.
p2: .Exponent 2.
E2: keV.Energy threshold 2.
p3: .Exponent 3.

2.2 Non-Uniform Source (Optional)

This table is used to specify the energy/frequency dependent width of the source. The first column should contain the photon energy in keV and the second column should contain the width of the source. The two columns should be separated by tabs and/or spaces. The upper limit size of the table is 2 Mb. Be aware that some browsers limit the number of characters that can be written in a text field.

Energy (keV)          σs (see [2])

3. Plot Parameters

Minimas: .The number of diffraction minimas to plot (fractions allowed).
Steps: .The number of data points in-between two minimas.
X-label: .Label string in Grace format.
Y-label: .Label string in Grace format.
X-min: .
X-max: .
Y-min: .
Y-max: .

4. Calculate

The time needed to compute the femtolensing spectra depends on the requested resolution and energy range. Typically, the result should appear within 30 seconds to 1 minute depending on the load on my Linux box. If an error message appear the computation has been aborted.


[1] A. Gould, ApJ 386, L5-L7 (1992).
[2] K.Z. Stanek, B. Paczynski and J. Goodman, ApJ 413, L7-L10 (1993).
[3] G.F. Marani, R.J. Nemiroff, J.P. Norris, K. Hurley and J.T. Bonnell, ApJ 512, L13-L16 (1999).

This program uses cgic and was developed by F. Sandin.

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