Searching for coincidences

The RAVEN framework is a data-analysis pipeline used to identify GW events that coincide with external observatories. RAVEN ingests candidate gravitational-wave triggers, extracts physical parameters (time, sky location, significance), and cross-references them with event notices from partners in the electromagnetic domain. By comparing the timing and localization of these external alerts against gravitational-wave candidates, RAVEN assigns coincidence scores, flags statistically significant matches, and delivers rapid follow-up summaries. This enables coordinated multi-messenger observations and accelerates the discovery of events like binary mergers or supernovae.

Untargeted search

In this search RAVEN checks if there is any spatio-temporal coincidence between a confident external messenger (GBR, MeV or TeV, neutrino, FRB, X-ray transient) and any GW candidate with a given \(FAR<FAR_{max}\). The quantity \(FAR_{max}\) identifies the depth of the search. The joint FAR in this regime is computed as:

\[ F A R_c=F A R_{g w} \frac{R_{e x t} \Delta t}{I_{\Omega}} \]

We need to know what is the typical rate of discovery of the external class of transients. The overlap integral is defined as:

\[ I_{\Omega}\left(x_{g w}, x_{e x t}\right)=\int \frac{p\left(\Omega \mid x_{g w}, \mathcal{H}_{g w}^s\right) p\left(\Omega \mid x_{e x t}, \mathcal{H}_{e x t}^s\right)}{p\left(\Omega \mid \mathcal{H}^s\right)} d \Omega \]

Targeted search

In this case the external observatory performs a search triggered by the GW candidate, down to a depth defined again by \(\rm{FAR}_{GW}^{max}\)

\[ F A R_c=\frac{Z}{I_{\Omega}}\left(1+\ln \left(\frac{Z_{\max }}{Z}\right)\right) \]

where the test statistic Z is defined as:

\[ Z=F A R_{g w} F A R_{e x t} \Delta t \]

Note

In the case of a confident GW detection, the valid equation is the one of the untargeted search, swapping the GW and ext indexes.

Searching a GW event on GraceDB

from ligo.raven import gracedb_events, search

from gracedb_sdk import Client
gracedb = Client('https://gracedb.ligo.org/api/')

from astropy.time import Time
utc_time = '2025-10-17 12:41:04'
gps_from_utc = Time(utc_time, format='iso', scale='utc').gps

gpstime = gps_from_utc
tl, th = -1e4, 1e4
group = 'CBC'     # 'CBC', 'Burst', or 'Test'
pipelines = []    # 'Fermi', 'Swift', 'INTEGRAL', 'AGILE', 'SNEWS', or 'IceCube'
ext_searches = []     # 'GRB', 'SubGRB', 'SubGRBTargeted', 'HEN', or 'MDC'
se_searches = []  # 'AllSky', 'BBH', 'IMBH', or 'MDC'
results = search.query('Superevent', gpstime, tl, th, gracedb=gracedb,
                       group=group, pipelines=pipelines,
                       ext_searches=ext_searches, se_searches=se_searches)

for n in results:
    print(n['superevent_id'], n['far'])

The search on External events can be done only using LVK credentials

gpstime = gps_from_utc
tl, th = -1e5, 1e5
group = 'CBC'     # 'CBC', 'Burst', or 'Test'
pipelines = ['SVOM']    # 'Fermi', 'Swift', 'SVOM', 'SNEWS', or 'IceCube'
ext_searches = ['GRB']     # 'GRB', 'SubGRB', 'SubGRBTargeted', 'HEN', or 'MDC'
se_searches = []  # 'AllSky', 'BBH', 'IMBH', or 'MDC'
results = search.query('External', gpstime, tl, th, gracedb=gracedb,
                       pipelines=pipelines,
                       ext_searches=ext_searches, se_searches=se_searches)

for n in results:
    print(n['graceid'], n['far'])

Joint FAR calculation

We test here the calculation of joint FAR according to which search we are considering

Temporal FAR

Imagine to have an EXT event and you only know its trigger time and FAR

se_far = 1e-6 # Hz
# this corresponds to
print("1 event every", format(1 / se_far / 3600 / 24, ".2f"), "days")
# indeed T = 1 / se_far = 1 / (1e-6) seconds = 1e6 seconds ~ 11.57 days
tl, th = -1, 10

Note

The default temporal windows used by RAVEN are these:

Event Type	Time window (s)		Notice Type Considered (see full list)
	CBC	Burst
GRB (Fermi, Swift, INTEGRAL, AGILE)	[-1,5]	[-60,600]	FERMI_GBM_ALERT FERMI_GBM_FIN_POS FERMI_GBM_FLT_POS FERMI_GBM_GND_POS SWIFT_BAT_GRB_ALERT SWIFT_BAT_GRB_LC INTEGRAL_WAKEUP INTEGRAL_REFINED INTEGRAL_OFFLINE AGILE_MCAL_ALERT
SubGRB (Fermi)	[-1,11]	[-1,11]	FERMI_GBM_SUBTHRESH
SubGRBTargeted (Fermi)	[-1,11]	[-1,11]	via Kafka alert
SubGRBTargeted (Swift)	[-10,20]	[-10,20]	via Kafka alert
Low-energy Neutrinos (SNEWS)	[-10,10]	[-10,10]	SNEWS

https://emfollow.docs.ligo.org/userguide/analysis/searches.html#coincident-with-external-trigger-search

The generic command to compute joint FAR is

far_joint = search.coinc_far(se_far, tl, th,
                joint_far_method = 'untargeted', # 'targeted' or 'untargeted'
                ext_rate = 1 / 24 / 3600, # once per day, it is used only if joint_far_method is 'untargeted'
                far_ext = 1e-5, # it is used only if joint_far_method is 'untargeted'
                far_gw_thresh = 1e-4, far_ext_thresh = 1e-4, # by default far_gw_thresh is 2/day and far_ext_thresh depends on the ext instrument, only used if joint_far_method is 'targeted'
                ext_search = None, # "GRB", "SubGRB", "SubGRBTargeted", "MDC", or "HEN" --> if you don't specify joint_far_method, you must specify ext_search
                # {'GRB', 'SubGRB', 'HEN'} --> uses untargeted
                # {'SubGRBTargeted'} --> uses targeted
                ext_pipeline=None # --> if you don't specify far_ext_thresh, you must specify ext_pipeline. Now it supports 'Fermi', 'Swift'
                )

Note

The following rates are used in the untargeted search:

the combined rate of independent GRB discovery by Swift, Fermi, and SVOM (avoiding double counts)

• Fermi: 236/yr

• Swift: 65/yr

• SVOM ECLAIRs: ~25/yr

grb_gcn_rate = 325. / (365. * 24. * 60. * 60.)

Rate of subthreshold GRBs (rate of above threshold plus rate of subthreshold)

subgrb_gcn_rate = 65. / (365. * 24. * 60. * 60.)

Combined rate of all GOLD IceCube notice from Table 1 of https://arxiv.org/pdf/2304.01174

hen_gcn_rate = 13.91 / (365. * 24. * 60. * 60.)

Joint FAR from untargeted search

far_joint = search.coinc_far(se_far, tl, th,
                joint_far_method = 'untargeted', # 'targeted' or 'untargeted'
                ext_rate = 1 / 24 / 3600, # once per day, it is used only if joint_far_method is 'untargeted'
                ext_search = None, # "GRB", "SubGRB", "SubGRBTargeted", "MDC", or "HEN" --> if you don't specify joint_far_method, you must specify ext_search
                # {'GRB', 'SubGRB', 'HEN'} --> uses untargeted
                # {'SubGRBTargeted'} --> uses targeted
                ext_pipeline=None # --> if you don't specify far_ext_thresh, you must specify ext_pipeline
                )

(th - tl) * 1 / 24 / 3600 * se_far
print(f"This coincidence happens every {format(1 / far_joint['temporal_coinc_far'] / 365 /3600 / 24, '.2f')} yrs")

Joint FAR from targeted search (confident EXT detection & any GW candidate)

far_joint = search.coinc_far(se_far, tl, th,
                joint_far_method = 'targeted', # 'targeted' or 'untargeted'
                far_ext = 1e-5, # it is used only if joint_far_method is 'untargeted'
                far_gw_thresh = 1e-4, far_ext_thresh = 1e-4, # by default far_gw_thresh is 2/day and far_ext_thresh depends on the ext instrument, only used if joint_far_method is 'targeted'
                ext_search = 'SubGRBTargeted', # "GRB", "SubGRB", "SubGRBTargeted", "MDC", or "HEN" --> if you don't specify joint_far_method, you must specify ext_search
                # {'GRB', 'SubGRB', 'HEN'} --> uses untargeted
                # {'SubGRBTargeted'} --> uses targeted
                ext_pipeline=None # --> if you don't specify far_ext_thresh, you must specify ext_pipeline
                )

Joint FAR from targeted search, but we are in the special case of a confident GW detection & any EXT candidate

gw_rate = 1 / 3 / 24 / 3600  # one GW event every 3 days
# But if there is strong evidence from GW data that it is either a BNS or NSBH merger,
# the rate can should be much lower, since we detect just a handful of these SO FAR
ext_far = 1e-5 # Hz

far_joint = search.coinc_far(ext_far, tl, th,
                joint_far_method = 'untargeted', # 'targeted' or 'untargeted'
                ext_rate = gw_rate, # once per day, it is used only if joint_far_method is 'untargeted'
                )

(th - tl) * 1 / 24 / 3600 * se_far
print(f"This coincidence happens every {format(1 / far_joint['temporal_coinc_far'] / 365 /3600 / 24, '.2f')} yrs")

Joint FAR from untargeted search, but we are in the special case of both GW and EXT are higly significant

grb_rate = 325. / (365. * 24. * 60. * 60.)  # Hz
gw_rate = 1 / 3 / 24 / 3600  # one GW event every 3 days
far_joint =  gw_rate * grb_rate * (th - tl)
print(f"This coincidence happens every {format(1 / far_joint / 365 /3600 / 24, '.2f')} yrs")

Note

Remember that after computing joint FAR, RAVEN applies a trials factor \(N(N+1)\), where \(N\) is the number of independent searches. Currently \(N = 6\) for CBC and \(N = 2\) for Burst. Since search pipelines are not really independent, this trials factor is a conservative choice.

Once the trials factor is applied, RAVEN sends a public alert if FAR < 1 / month for CBC and FAR < 1 / yr for Burst.

How to give empirically “weight” to each \(\mathcal{H}^{XY}\) hypothesis

To decide which FAR one should consider for a given couple of GW + EXT event, a possible proposal is to give a relative weight to each hypothesis, according to the properties of the events.

\[\begin{split} p_{astro}^{GRB} \sim \begin{cases} 1 & \text{if } \text{search = GRB} \\ 0 & \text{if } \text{search = SubGRBTargeted} \end{cases} \end{split}\]

Note

This is a rude approximation because we know that we could detect high significant GRB with Swift-BAT targeted search, for instance if we were slewing or the GRB is outside the FOV and not visible to other telescopes

The weights could look like:

\[ \mathcal{H}^{SS} \sim p_{astro}^{GW} \times p_{astro}^{EXT} \]

\[ \mathcal{H}^{SN} \sim p_{astro}^{GW} \times (1-p_{astro}^{EXT}) \]

\[ \mathcal{H}^{NS} \sim (1-p_{astro}^{GW}) \times p_{astro}^{EXT} \]

\[ \mathcal{H}^{NN} \sim (1-p_{astro}^{GW}) \times (1-p_{astro}^{EXT}) \]

Warning

Remember that FAR cannot be summed to have a final joint FAR. But you can still decide which \(\mathcal{H}^{XY}\) is more appropriate according to observational evidences and decide accordingly how to compute your FAR