# acl EroCalibTemplate:read,write,revert MembersGroup:read SeniorMembersGroup:read EroIkiCalGroup:read,write,revert
== PSR 0656+14 timing analysis ==
G. Lamer with contributions by J. Kurpas, A. Schwope, I. Traulsen (AIP), and V. Doroshenko (IAAT)
The pulsar PSR 0656+14 was observed on 14/15-Oct-2019 for 115 ksec.
The cameras of all telescopes TM1-TM7 observed with the filter wheel in "FILTER" position.
However, it turned out that the data of TM1 are somehow corrupt for an electronics issue and
are only of limited use for this analysis.
A simultaneous observation of PSR 0656+14 was carried out with XMM-Newton. The combination of pulsar signal with XMM-observation shall serve as external reference source to support calibration of eROSITA timings.
The pulsations of PSR 0656+14 have a period of P=0.385 sec and have beeen observed
at radio frequencies, in X-rays, and Gamma-rays. The reference period used by us is based on Ray et al. (2011) and accessible
[[https://www.slac.stanford.edu/~kerrm/fermi_pulsar_timing/|here]]
At the time of the simultaneous eROSITA/XMM-Newton observation the expected period of the pulsar is 0.38493417645(3) sec, where the number in parentheses indicates the uncertainty in the last digit.
=== Barycentric correction: ===
In order to analyse the pulsations of PSR 0656+14 a barycentric correction of the event times needs
to be applied. Until the eSASS task with this functionality is implemented, a workaround using
the [[ https://heasarc.gsfc.nasa.gov/lheasoft/ftools/headas/barycen.html|HEASOFT ''barycen'']] task can be used. We have converted the orbit file ''omnia_orbit_october_2019.log'', provided by NPOL, into a FITS file with the format required by ''barycen''.
October 2019 orbit file: [[attachment:orbit_october_2019_scc.fits|orbit_october_2019_scc.fits]]
Also the headers of the event files to be corrected need to be modified:
keyword RADECSYS="ICRS"
keyword TIMEREF="LOCAL"
keyword TIMESYS="TT"
Since ''barycen'' only recognizes the extension name "GTI", the name of the GTI extension needs to
changed to "GTI" before calling ''barycen'' and then changed back to its original name.
The ''barycen'' task was called with the following command line:
barycen infile=src_events_tm2.fits \<
>
outfile=src_events_tm2_bary_icrs.fits \<
>
orbfile=orbit_october_2019_scc.fits \<
>
ra=104.9507468 \<
>
dec=14.23963084 \<
>
orbext="ORBIT" \<
>
orbform="COMPONENTS" \<
>
orbcol="X,Y,Z,VX,VY,VZ" \<
>
startcol="START" \<
>
stopcol="STOP" \<
>
refframe="ICRS" \<
>
orbinterp="WEIGHTED" \<
>
timecol="TIME" \<
>
chatter=3 \<
>
clobber=yes \<
>
debug=yes<
>
Example bash script: [[attachment:run_barycen.sh|run_barycen.sh]]
Before and after barycentric correction a chi^2 period search was applied to the data and a Gaussian was
fitted to the chi^2 peak near the published pulse period.
The XMM-Newton data were reduced and barycenter corrected using the XMMSAS package and the pulse period was determined,
details will be described elsewhere.
Update 20.02.2020 by VictorDoroshenko: An alternative python script for correction was prepared by VictorDoroshenko [[attachment:barycor.py.zip]].
This was actually inspired by barycen code, although is not a direct port of that and uses other libs/ephemerides, i.e. more or less independent.
Using this correction the timing analysis was carried out. The main issue that there appears to be an offset of ~7s between corrected times as per barycen and
python script (see i.e. [[attachment:diff_barycen_py.png]] for TM5 events). This is likely caused by heasarc barycen as the first 45 entries are corrected to meaningless values (on my machine at least). The 46th value from file corrected by barycen corresponds to first value from the raw event file, so an offset of ~7s is introduced. If we account for this shift,
the difference between the two scripts becomes less than 2e-3s. For periodicity search Z-statistics on unbinded events was used but here results are broadly comparable with that reported before.
=== Results: ===
eROSITA periods before and after barycentric correction
(see [[https://wiki.mpe.mpg.de/eRosita/timing#Figures_periods|Figures periods ]] below)
|| Camera || P before correction [s] || P after bary correction [s] ||
||TM1 || 0.38489567005 || 0.384933872 ||
||TM2 || 0.38489572213 || 0.384933945 ||
||TM3 || 0.38489567927 || 0.384933908 ||
||TM4 || 0.38489568964 || 0.384933919 ||
||TM5 || 0.38489572062 || 0.384933948 ||
||TM6 || 0.38489568900 || 0.384933918 ||
||TM7 || 0.38489571696 || 0.384933942 ||
||eRO(TM2-7)|| 0.38489570294 || 0.384933930 ||
||SD(TM2-7) || || 1.63234E-08 ||
||XMM || - || 0.38493427 ||
||Ref*|| - || 0.384934176454 ||
||XMM-Ref || || 9.9888E-08 ||
||eRO-Ref || || -2.57740E-07 ||
||eRO-XMM || || -3.57628E-07 ||
* Based on Fermi LAT data (Ray et al. 2011), corrected for spin down to 14-Oct-2019
Assuming the standard deviation of the TM2-TM7 period measurements as error estimate, the discrepancy
between the eROSITA measuments versus the reference by XMM-Newton or Fermi is clearly significant.
The relative discrepancy of the eROSITA measurement vs. the Fermi reference is
(P_ero-P_fermi)/P_fermi = -6.4025E-7
The following sources of errors need to be considered:
* SRG clock drift: no calibration data are currently available for October 2019. However, the clock drift is estimated to be of the order 10 ms/day corresponding to a relative drift of 1.15741e-07. This is not sufficient to account for the observed discrepancy.
* Inaccuracy of the orbit file, the observed discrepancy would correspond to a velocity difference of ~200 m/s
* Other inaccuracies in the barycentric correction (''barycen'' task, wrong assumptions on time/reference frames etc.), suggestions or comparisons with other codes are welcome.
----------------------------------------
(begin insert Doroshenko)
=== Results with alternative correction: ===
For events between 0.3-2 keV within 40 arcsec from source position barycentric correction using the attached python script and orbit file was performed. After that,
a search with Z-statistics was conducted. Two harmonics were sufficient to describe the signal. The period search was done for individual modules
as well as for concatenated event list. The results are reported below and compared with barycen results presented above in [[attachment:periods_comparison_vd_vs_lamer.pdf]].
In general, there is a good agreement between two independent attempts to reduce eRosita data at least in context of observed period of the source.
|| Camera || P before correction [s] || P after bary correction [s] ||
||TM1 || 0.3848959710380255 || 0.3849341592690358 ||
||TM2 || 0.38489571065513584 || 0.38493393442207546 ||
||TM3 || 0.38489566656028723 || 0.38493391900328405 ||
||TM4 || 0.38489573178127434 || 0.3849339257237277 ||
||TM5 || 0.3848956642017522 || 0.3849339579434112 ||
||TM6 || 0.3848956385909294 || 0.384933886442975 ||
||TM7 || 0.38489571824733776 || 0.384933980446571 ||
||eRO(TM2-7)|| 0.38489570294 || 0.38493393(2) ||
||eRO-Ref || || -2.43687138e-07 ||
||eRO-XMM || || -3.37233138e-07 ||
(end insert Doroshenko)
----------------------------------------
=== Time lags ===
We calculated folded pulse profiles with start time T0_scc=6.243790548902941D8
and P=0.38493392969366 (see [[https://wiki.mpe.mpg.de/eRosita/timing#Figures_pulse_profiles|Figures pulse profiles ]] below)
When comparing the folded pulse profiles the following offsets in event times were detected
(assuming that the phase shifts are caused by the known +- 1sec time jumps):
|| Camera || Time offset [s] 14-Oct-2019 || Time offset [s] 15-Nov-2019 ||
|| TM1 || 0.0 || 1.0 ||
|| TM2 || 1.0 || 1.0 ||
|| TM3 || 0.0 || 0.0 ||
|| TM4 || 0.0 || 1.0 ||
|| TM5 || 1.0 || 0.0 ||
|| TM6 || 1.0 || 0.0 ||
|| TM7 || 1.0 || 1.0 ||
The offsets on 15-Nov were determined using positional offsets measured in the eFEDS scans.
This indicates that time jumps have occurred in cameras TM1,TM4,TM5, and TM6 between 14-Oct and 15-Nov.
----------------------------------------
=== Figures periods ===
Chi^2 vs. period for barycenter corrected eROSITA data:
{{attachment:periods_tm1_barycorr2.png|TM1|width=600}}
{{attachment:periods_tm2_barycorr2.png|TM2|width=600}}
{{attachment:periods_tm3_barycorr2.png|TM3|width=600}}
{{attachment:periods_tm4_barycorr2.png|TM4|width=600}}
{{attachment:periods_tm5_barycorr2.png|TM5|width=600}}
{{attachment:periods_tm6_barycorr2.png|TM6|width=600}}
{{attachment:periods_tm7_barycorr2.png|TM7|width=600}}
----------------------------------------
=== Figures pulse profiles ===
Folded pulse profiles with barycenter corrected data TM1-TM7:
{{attachment:phase_plot_alltm.png|no correction|width=600}}
Folded pulse profiles with additional correction TIME=TIME-1s for cameras TM1,TM3,TM4:
{{attachment:phase_plot_alltm_corr_jumps.png|no correction|width=600}}