Fast Radio Bursts

Fast Radio Bursts, aka FRB's, are ultra short electromagnetic pulses which last no longer than a few milliseconds. FRB's are detectable only with very sensitive telescopes. Through the properties of the signals, redshift, astrophysicists can tell that FRB's are generated at least thousands of light years away from Earth. The enormous distance over which they have travelled means that they got distorted by electromagnetic interaction with the intergalactic medium they pass through. This way these signals are dispersed over time and frequencies.
FRB bursts show up in a spectrogram as a sloping curve. After computer aided de-dispersion of the spectrum, we finally get a vertical profile.

Recently there has been an increase of FRB discoveries.
Physicists think that FRB's are originated during extreme high energy events very far away in the universe.
Currently FRB's are the only way to study the intergalactic medium.


Disclaimer: The primary purpose of these documents is to study the Python 3.7.4 environment. This means e.g. trying out many aspects of this higher level language, and using different modules and tools. Keywords are Jupyter Notebook, Jupyter Lab, data manipulation, visualization, content production and control, document generation, ...

Acknowlegdements

• The FRB properties data source for the equatorial and galactic coordinates : http://www.frbcat.org/
  

• The paper of astronomer Dr. Emily Petroff can be found here:
  http://adsabs.harvard.edu/abs/2016PASA...33...45P

  • Title: FRBCAT: The Fast Radio Burst Catalogue
  • Authors: Petroff, E.; Barr, E. D.; Jameson, A.; Keane, E. F.; Bailes, M.; Kramer, M.; Morello, V.; Tabbara, D.; van Straten, W.
    
  • Affiliation: AA (ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands; Swinburne University of Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia; CSIRO Astronomy & Space Science, Australia Telescope National Facility...
    
  • Publication: Publications of the Astronomical Society of Australia, Volume 33, id.e045 7 pp.

• The paper of Dr. Cordes and Chatterjee: Fast Radio Bursts: An Extragalactic Enigma
  https://arxiv.org/abs/1906.05878

FRB's "classification" by dispersion, energy and distance of source

Comparing FRB and Pulsar props

Pulsar and FRB signals are comparable in some properties. Notice the milliseconds pulse timelength of FRB and pulsar signals.
There are also some notable differences:

• The radiation energy density at the source is about ten billion times larger than the energy density from Galactic pulsars.
• The pulsation period: atomic clockwise repeating pulsars vs. the transient burst of FRB's.
• The redshift of a FRB pulse implicates a fenomenal distance between source and reception.

Pulsar spectrogram generated from wave file

The spectrogram below belongs to the 35 Hz Pulsar named PSR B0531+21, which is also called the Crab Pulsar.

c:\users\kurt\appdata\local\programs\python\python37\lib\site-packages\matplotlib\axes\_axes.py:7739: RuntimeWarning: divide by zero encountered in log10
  Z = 10. * np.log10(spec)

The spectrogram below belongs to a 1.4 Hz pulsar.

Plotting the source location of FRB with galactic coordinates

Info how to plot galactic coordinates using matplotlib and astropy

The data source for properties like the equatorial and galactic coordinates of the FRB's: http://www.frbcat.org/
SkyCoord: https://docs.astropy.org/en/stable/coordinates/skycoord.html
Search of Fast Radio Burst at the frequency 111 MHz : https://www.frb.su/pustaya-stranica

Plotting FRB observations by galactic coordinates in Aitoff projection

this plot shows that "confirmed" FRB's are observed coming from all directions of the universe.

	frb_name	rmp_dm	rmp_width	rmp_snr
0	FRB190523	760.8±0.6	0.42	11.5
1	FRB190222.J2052+69	460.6±0.1	2.97	0.0
2	FRB190209.J0937+77	424.6±0.6	3.70	0.0
3	FRB190116.J1249+27	444±0.6	4.00	0.0
4	FRB181228	354.2±0.9	1.24	12.0

Plotting the timeline of confirmed FRB events

The usage of accurate instruments and antenna's with better sensitivity, led to a rapid acceleration in the discovery of FRB's. The plot doesn't show observed FRB's which are not yet confirmed.

Index(['frb_name', 'utc', 'telescope', 'rop_gl', 'rop_gb', 'rop_gain',
       'rop_mw_dm_limit', 'rmp_dm', 'Error', 'rmp_width', 'rmp_dm_index',
       'rmp_spectral_index', 'rmp_redshift_host'],
      dtype='object')
0   2019-05-23 06:05:55
1   2019-02-22 18:46:01
2   2019-02-09 08:20:20
3   2019-01-16 13:07:33
4   2018-12-28 13:48:50
Name: datetime, dtype: datetime64[ns]

<Figure size 1152x1080 with 0 Axes>

Plotting with pandas

Milky way dm limit vs excess Dispersion Measure, by galactic latitude

This plot reveals that the southern hemisphere - negative latitudes - has scored more observations. The reason: they have currently the most sensitive radio antenna's. The recently brought into service observatory in Australia can more efficiently detect these weak signals.

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 90 entries, 0 to 89
Data columns (total 15 columns):
Unnamed: 0            90 non-null int64
frb_name              90 non-null object
utc                   90 non-null object
telescope             90 non-null object
rop_gl                90 non-null float64
rop_gb                90 non-null float64
rop_gain              64 non-null float64
rop_mw_dm_limit       90 non-null float64
rmp_dm                90 non-null float64
Error                 90 non-null float64
rmp_width             88 non-null float64
rmp_dm_index          11 non-null float64
rmp_spectral_index    2 non-null float64
rmp_redshift_host     2 non-null float64
DMexcess              90 non-null float64
dtypes: float64(11), int64(1), object(3)
memory usage: 10.7+ KB

<Figure size 432x288 with 0 Axes>

df.rop_gb.min()= -66.6

bandwidth vs flux by ? with seaborn

Scatterplot centre frequency vs observed bandwidth, hue= telescope

scatter plot measured width vs dispersion measure.

Current working dir : 
C:\Users\Kurt\Documents\Notebooks\seaborn
                    rmp_width  rmp_snr       DM  Error
frb_name                                              
FRB190523                0.42     11.5   760.80   0.60
FRB190222.J2052+69       2.97      0.0   460.60   0.10
FRB190209.J0937+77       3.70      0.0   424.60   0.60
FRB190116.J1249+27       4.00      0.0   444.00   0.60
FRB181228                1.24     12.0   354.20   0.90
FRB181128.J0456+63       2.43      0.0   450.20   0.30
FRB181119.J12+65         6.30      0.0   364.20   1.00
FRB181030.J1054+73       0.59      0.0   103.50   0.70
FRB181017.J1705+68      13.40      0.0  1281.90   0.40
FRB181017                0.32     66.0   239.97   0.03
<class 'pandas.core.frame.DataFrame'>
Index: 90 entries, FRB190523 to FRB010125
Data columns (total 4 columns):
rmp_width    90 non-null float64
rmp_snr      90 non-null float64
DM           90 non-null float64
Error        90 non-null float64
dtypes: float64(4)
memory usage: 3.5+ KB
                    rmp_width  rmp_snr       DM  Error
frb_name                                              
FRB190523                0.42     11.5   760.80   0.60
FRB190222.J2052+69       2.97      0.0   460.60   0.10
FRB190209.J0937+77       3.70      0.0   424.60   0.60
FRB190116.J1249+27       4.00      0.0   444.00   0.60
FRB181228                1.24     12.0   354.20   0.90
...                       ...      ...      ...    ...
FRB090625                1.92     30.0   899.55   0.01
FRB010724                5.00     23.0   375.00   0.00
FRB010621                7.00     16.3   745.00  10.00
FRB010312               24.30     11.0  1187.00  14.00
FRB010125                9.40     17.0   790.00   3.00

[90 rows x 4 columns]

joint plot FRB_W_SN_DM_Error_OK.csv

Visualisation method Seaborn

Flux vs Dispersion Measure by obs. bandwidth

The Seaborn plotting package produces slick, high quality production plots. The drawback of this recent package is that less objects can be controlled in detail.

observed bandwidth vs dispersion measure by flux

Instrument width vs dispersion measure by bandwidth

width vs DM excess log/log

DM excess is the observed DM minus the expected milky way DM.

Measured DM vs Milky way DM limit plot by galactic_electron_model

Multiple linear regression

https://seaborn.pydata.org/examples/multiple_regression.html

It is necessary to check the recent CHIME and Parkes data, after some corrections

Dit argeloos plotten leidde tot een te grote c.i. vd Parkes data, die alle andere data verborg.
Na selectie van de Non-Parkes data, kwam CHIME/FRB er uit met het meest consistente patroon.

Plot excess DM vs MW limit grouped by telescope

A plot where observations are grouped by telescope. CHIME/FRB and ASKAP are producing the most consisting results. These have had recent machinery innovations, or can be set up to detect faint signals over a large area.

Relation excess DM vs Flux by instrument width

   Unnamed: 0            frb_name                  utc  telescope    rop_gl  \
0           0           FRB190523  2019/05/23 06:05:55     DSA-10  117.0300   
1           1  FRB190222.J2052+69  2019/02/22 18:46:01  CHIME/FRB  104.9000   
2           2  FRB190209.J0937+77  2019/02/09 08:20:20  CHIME/FRB  134.2000   
3           3  FRB190116.J1249+27  2019/01/16 13:07:33  CHIME/FRB  210.5000   
4           4           FRB181228  2018/12/28 13:48:50     UTMOST  253.3915   

    rop_gb  rop_gain  rop_mw_dm_limit  rmp_dm  Error  rmp_width  rmp_dm_index  \
0  44.0000       NaN             37.0   760.8    0.6       0.42           NaN   
1  15.9000       NaN             87.0   460.6    0.1       2.97           NaN   
2  34.8000       NaN             46.0   424.6    0.6       3.70           NaN   
3  89.5000       NaN             20.0   444.0    0.6       4.00           NaN   
4 -26.0633       1.7             58.0   354.2    0.9       1.24           NaN   

   rmp_spectral_index  rmp_redshift_host  DMexcess  
0                 NaN               0.66     723.8  
1                 NaN                NaN     373.6  
2                 NaN                NaN     378.6  
3                 NaN                NaN     424.0  
4                 NaN                NaN     296.2  

Is there a relation between DM excess vs MW limit?

    Unnamed: 0            frb_name                      utc  telescope  \
0            0           FRB190523  2019/05/23 06:05:55.815     DSA-10   
1            1  FRB190222.J2052+69  2019/02/22 18:46:01.367  CHIME/FRB   
2            2  FRB190209.J0937+77  2019/02/09 08:20:20.977  CHIME/FRB   
3            3  FRB190116.J1249+27  2019/01/16 13:07:33.833  CHIME/FRB   
4            4           FRB181228  2018/12/28 13:48:50.100     UTMOST   
..         ...                 ...                      ...        ...   
70          70           FRB150215  2015/02/15 20:41:41.714     parkes   
71          71           FRB141113  2014/11/13 07:42:55.220    arecibo   
72          72           FRB140514  2014/05/14 17:14:11.060     parkes   
73          73           FRB131104  2013/11/04 18:04:11.200     parkes   
74          74           FRB130729  2013/07/29 09:01:51.190     parkes   

      rop_gl    rop_gb  rop_gain  rop_mw_dm_limit  rmp_dm  Error  rmp_width  \
0   117.0300  44.00000       NaN             37.0   760.8    0.6       0.42   
1   104.9000  15.90000       NaN             87.0   460.6    0.1       2.97   
2   134.2000  34.80000       NaN             46.0   424.6    0.6       3.70   
3   210.5000  89.50000       NaN             20.0   444.0    0.6       4.00   
4   253.3915 -26.06330     1.700             58.0   354.2    0.9       1.24   
..       ...       ...       ...              ...     ...    ...        ...   
70   24.6628   5.28092     0.581            427.2  1105.6    0.8       2.88   
71  191.9000   0.36000     8.200            188.0   400.3    2.0        NaN   
72   50.8413 -54.61200     0.735             34.9   562.7    0.6       2.80   
73  260.5500 -21.92530     0.690             71.1   779.0    1.0       2.08   
74  324.7880  54.74460     0.581             31.0   861.0    2.0      15.61   

    rmp_dm_index  rmp_spectral_index  rmp_redshift_host  DMexcess  
0            NaN                 NaN               0.66     723.8  
1            NaN                 NaN                NaN     373.6  
2            NaN                 NaN                NaN     378.6  
3            NaN                 NaN                NaN     424.0  
4            NaN                 NaN                NaN     296.2  
..           ...                 ...                ...       ...  
70         2.001                 NaN                NaN     678.4  
71           NaN                 NaN                NaN     212.3  
72         2.000                 NaN                NaN     527.8  
73           NaN                 NaN                NaN     707.9  
74           NaN                 NaN                NaN     830.0  

[75 rows x 15 columns]

DM excess vs Flux joint plot

Plotting DM excess vs. the reciproke Flux² resulted in 1 outlier: FRB 141113.
It seems to me that this signal is so weak and dispersed, that it's Flux value and calculation needs a check.

The reporting scientists speak about assumptions and verification... ´We report on candidate FRB 141113, which is likely astrophysical and extragalactic, having DM sime 400 pc cm³, which is over the Galactic maximum along this line of sight by ~100–200 pc cm³. We consider implications for the FRB population and show via simulations that if FRB 141113 is real and extragalactic, the slope α of the distribution of integral source counts as a function of flux density (N(>S) ∝ S −α ) is 1.4 ± 0.5 (95% confidence range). However, this conclusion is dependent on assumptions that require verification. ´
https://iopscience.iop.org/article/10.3847/1538-4357/aaee65/meta

Dedispersed frequency vs time plot for the candidate FRB 141113. The pulse was detected with S/N = 8.4, pulse width 2 ms, and DM = 400 pc cm³ (well above the Galactic contribution).

     frb_name                  utc telescope  rop_gl  rop_gb  rop_gain  \
71  FRB141113  2014/11/13 07:42:55   arecibo   191.9    0.36       8.2   

    rop_mw_dm_limit  rmp_dm  Error  rmp_width  rmp_dm_index  \
71            188.0   400.3    2.0        NaN           NaN   

    rmp_spectral_index  rmp_redshift_host  DMexcess  
71                 NaN                NaN     212.3  

<Figure size 648x648 with 0 Axes>

calculate the DM excess from "DM" en "rop_mw_dm_limit"

calculate the 1 / Flux ² & create a new column df[flux_1_kwad]

	frb_name	telescope	rop_raj	rop_decj	rop_gl	rop_gb	rop_sampling_time	rop_bandwidth	rop_centre_frequency	rop_bits_per_sample	...	rmp_width	rmp_snr	rmp_flux	rmp_dm_index	rmp_scattering_index	rmp_scattering	rmp_scattering_model	rmp_scattering_timescale	rmp_spectral_index	rmp_dispersion_smearing
71	FRB141113	arecibo	06:13:00.1	18:47:11.2	191.9	0.36	0.0655	322.6	1375.0	4.0	...	2.0	8.4	0.039	NaN	NaN	NaN	NaN	NaN	NaN	NaN

1 rows × 24 columns

Versions

Software	Version
Python	3.7.4 64bit [MSC v.1916 64 bit (AMD64)]
IPython	7.5.0
OS	Windows 10 10.0.18362 SP0
jupyterlab	1.1.4
seaborn	0.9.0
numpy	1.17.3
scipy	1.2.1
matplotlib	3.1.1
pandas	0.25.1
astropy	3.2.2
nbconvert	5.6.1
Sun Nov 10 21:47:20 2019 Romance (standaardtijd)